PHYSICAL CHEMISTRY EWELL A TEXT-BOOK OF PHYSICAL CHEMISTRY THEORY AND PRACTICE BY ARTHUR W. EWELL, Ph. D. i \ ASSISTANT PROFESSOR OF PHYSICS, WORCESTER POLYTECHNIC INSTITUTE WITH ONE HUNDRED AND TWO ILLUSTRATIONS AND SIXTY-THREE TABLES k-***- F THE UNIVERSITY OF PHILADELPHIA P. BLAKISTON'S SON & CO. 1012 WALNUT STREET 1909 GENERAL c COPYRIGHT, 1909, BY P. BLAKISTON'S SON & Co. Printed by The Maple Press York, Pa. PREFACE. This book is intended to serve as a laboratory manual, as a text-book to accompany recitations or lectures and as a conven- ient book of reference. The author has felt the need of such a book in a general course in Physical Chemistry which he has conducted for several years, but has failed to find any single book of this scope. This book has been prepared in the belief that others have felt a similar want. It is designed for students in American colleges and tech- nical schools who have completed the equivalent of the prescribed Freshman and Sophomore class-room and laboratory courses, in mathematics, physics, and chemistry. A knowledge of the calculus is assumed in many of the theoretical discus- sions. The value and necessity of the calculus have been so emphasized during recent years that most students of this grade have studied it. The paragraphing has, however, been arranged in such a manner that students unfamiliar with the calculus can omit the portions in which it is employed assume the results of the omitted discussions or derivations. The laboratory exercises are chosen with the aim of giving the student a 'clear understanding of the principles involved in the subjects usually included under the title of Physical Chem- istry, and also in certain other subjects in advanced physics, which, though not usually included under this title, are of par- ticular importance to chemists. Effort has been made to have the experiments more than mere manipulation. Close arid careful thinking is required in working up many of the experiments, the results of practi- cally all of which are compared with the results required by the theory immediately preceding. Each experiment is followed by^questions designed to stimulate thought upon the principles id applications of the experiment. All but a very few of the 187211 VI PREFACE. exercises described have been performed by the author's laboratory class for several years. The few exceptions have been tested by the author under laboratory conditions. It is probable that the majority of students will have had already a few of the more distinctly physical experiments. Much of the general information regarding units, etc., in the Introduction and in the first part of several chapters is also probably familiar to some, but is included for completeness and for reference. Physical Chemistry apparatus which is understood with difficulty or the description of which is instructive, is described under the appropriate topic in the body of the book. All other apparatus, methods, etc., are described in the Intro- duction. The Introduction also contains references to all the apparatus considered elsewhere, together with mathematical data, discussion of errors, etc., so that the book constitutes a complete manual for all ordinary work in Physical Chemistry. Experiments requiring expensive chemicals are avoided and apparatus which is not readily procurable is not employed. Any apparatus which cannot readily be purchased can be constructed easily from the accompanying directions. Sug- gestions are given with each experiment for suitable materials, etc., and in almost every one there is a choice of several sub- stances, so that there may be some variation in each experi- ment as performed by different students. Theory and experiment are logically arranged together. It is usually impossible or undesirable to have all the students in such a course pursuing the same exercise, and therefore many of the students will necessarily be working in advance of the text if the laboratory work and the recitations are parallel. Each experiment, however, is immediately preceded by its theory. The student may have to defer a complete grasp of the experiment until he has reached the corresponding point in the text. A large number of problems covering every topic are distrib- uted throughout the book. If these are carefully considered and the attempts at solution are written out and handed in to PREFACE. Vll the instructor, it will contribute an important factor toward the attainment of the goal of such a course the ability to discover problems in Physical Chemistry, to meet such problems with the best mental and mechanical methods, and to find pleasure in the struggle. Mathematical tables and tables constantly employed throughout the book are placed at the end. With these tables are references, arranged by topics, to all tables in the Introduction and main portion of the book, so that the most recent determinations of any quantity employed in Physical Chemistry may be found by reference to the final section of the book. The figures are schematic rather than detailed, in order to bring out more clearly what is essential. Therefore different scales are often used for different portions (e.g., subsidiary electrical connections are often on a much smaller scale than the main apparatus) . The author has attempted to describe the most important facts of Physical Chemistry and to derive and develop as fully as possible the fundamental principles. Details regard- ing minor extensions or exceptions will be found in the numer- ous references in the foot-notes. The writer wishes to acknowledge his indebtedness to the following standard works: Nernst, Theoretical Chemistry; Van't Hoff's Lectures; Jiiptner's Physikalische Chemie; Reychler-Kuhn, Physikalisch-Chemische Theorieen; Walker's Introduction to Physical Chemistry, and Findlay's Practical Physical Chemistry. Dr. A. Wilmer Duff kindly examined certain portions of the manuscript and the undersigned is indebted to him for many valuable suggestions and criticisms. ARTHUR W. EWELL. WORCESTER, September, 1909. CONTENTS. PAGE INTRODUCTION i CHAPTER I. GASES, VAPORS AND LIQUIDS 79 CHAPTER II. THERMODYNAMICS ... . . . . .* . . 123 CHAPTER III. SOLUTIONS T> . . .-*.'... 150 CHAPTER IV. THERMOCHEMISTRY 181 CHAPTER V. LIGHT '. . . ... . .... . . 198 CHAPTER VI. CHEMICAL KINETICS . . .' . . 225 CHAPTER VII. CHEMICAL STATICS 250 CHAPTER VIII. ELECTROLYTIC CONDUCTION 279 CHAPTER IX. POTENTIAL DIFFERENCES 313 CHAPTER X. GASEOUS IONS, RADIOACTIVITY 339 TABLES 347 ix HE " DIVERSITY OF PHYSICAL CHEMISTRY. INTRODUCTION. i. Symbols. Table I gives the symbols of all the quantities which frequently appear in this book. Customary usage has been followed as far as possible without confusing duplication in the use of symbols. Quantities which appear under one topic only are not listed in this table and are usually rep- resented by the symbols used by the original investigators. TABLE I. Symbols. temp. coef. ist constant of , van der Waal's Eq. B = radiant energy b =2d const, of van. d. Waal's Eq. C \ = f constant c j \ concentration D =Coef. of diffusion , = / distance I sign of differential f difference of potential E = < electromotive force [ coefficient of elasticity ' Naperian base small quantity electric charge water equivalent F = fluidity G = additive property g = acceleration of gravity H = kinetic energy of mole- cules h = height / = internal energy i = electric current / = mechanical equivalent */ = ionic conductivity iissociation constant k = I M m N n P a q f molecular elevation j (molecular lowering =&') I velocity constant [ specific conductivity = latent heat per gram mo le- cule = latent heat per gram = molecular weight = mass (grams) = no. atoms in molecule = /number \ transport number f number \ normal > = pressure = quantity, heat per gram molecule = quantity of heat per gram f gas constant for gram molecule = < (gas constant for one gram = R') resistance = specific heat per gram molecule = specific heat per gram f titration = | time I surface tension INTRODUCTION. , = / temperature \ in Chap. VI, =time u \ = velocity v \ = volume W =work, energy w = number of gram mole- cules X = / f orce ' 1 unknown quantity f unknown quantity \ change in concentration y = fraction Z = coefficient of solubility f temp, coef . de- ft (alpha) = ( gree of dissocia- [ tion 2d power con- stant in thermal (beta) = equations (gamma) = ratio of specific heats J (delta) = prefix, signifying that the quan- tity is small e (epsilon) = dielectric constant r? (eta) =coef. of viscosity 6 (theta) = absolute temper- ature f wave length "j equivalent con- A (lambda) = \ ductivity reduced pres- sure , N f refractive index '' (mu)= i reduced volume f x f reduced temperature v < nu) * I valency p (rho) = density fspecific resist- a (si S ma > = \ radfatlon con- [ stant (phi) = angle 2. NOTATION OF VERY LARGE AND VERY SMALL NUMBERS. Partly to save space and partly to indicate at once the magnitude of very large or very small numbers, the following notation is often used. The digits are written down and a decimal point placed after the first, and its position in the scale indicated by multiplying by some power of 10. Thus 42140000 is written 4.214X107 and .00000588 is written 5-88Xio~ 6 . This also enables us to abbreviate the multi- plication and division of such numbers. Thus, 421 40000 X .00000588 is the same as 4.214X5.88X10 and 42140000-=- .00000588 is the same as (4.124-1-5.88) Xio 13 . UNITS. 3. Fundamental Units. Unless otherwise specified, the unit of length throughout this book is the centimeter, the unit of mass is the gram, and the unit of time is the second. UNITS. 3 In measuring the wave length of ether waves the following units are often employed : ^(=0.00 1 mm. micron =/*// = .000001 mm. Angstrom unit = .0000001 mm. In specifying the concentration of solutions and also in problems concerning gases, the gram-molecule is the unit of mass; that is, in place of one gram, the unit is a number of grams numerically equal to the molecular weight. For example, the unit for sodium chloride is 58.5 grams, for oxygen the unit is 32 grams. Sometimes the gram-atom is a convenient unit of mass. A gram atom of oxygen would be 1 6 grams, of chlorine 35 grams, etc. If the valency of the dissolved substance is greater than one, the gram equivalent is usually chosen as the unit; that is, a number of grams equal to the molecular or atomic weight divided by the valency. A normal solution contains one gram equivalent of the dissolved substance in one litre of the solu- tion. A litre of such a solution contains, therefore,, 58.5 grams of sodium chloride, or 63.4 grams of ferrous chloride, or 54.18 grams of ferric chloride or 31.8 grams of copper, etc. The concentration of a solution in terms of that of a normal solution is designated by a fraction preceding the letter n. Thus .02n NaCl signifies a one-fiftieth normal solution of salt, etc. The density of a body is the mass divided by the volume, or, if the density is constant, the mass per unit volume. 4. A body of gas or vapor is said to be under standard conditions if its temperature is o and if its pressure is equal to that of a column of o mercury, 76 cm. high. The stand- ard force of gravity for estimating this pressure is that at sea level, and 45 latitude (980.6, 41). Equations for calcu- lating the volume or density under standard conditions are given in 103. 4 INTRODUCTION. MECHANICAL UNITS. 5. (Velocity) = i cm. per sec. (Acceleration) =i cm. per sec. per sec. (Force) =(dyne) = force required to give a mass of one gram an acceleration of i cm. per sec. per sec. (Pressure) = force -=- area. The absolute unit of pressure is one dyne per square centimeter. A more customary unit is the weight of one cubic centimeter of mercury per square centimeter (reduced to o, sea level, and 45 latitude) =13.59X980.6 or 13326 dynes per sq. cm. Energy and Work. The absolute unit is the erg=the work done by one dyne acting through a distance of i cm. This unit is very small and a more practical unit is the joule = io 7 ergs. Activity, Power, or Rate of Doing Work. The watt is one joule per second. 1000 joules per second is called a kilowatt. One horse power is 746 watts. HEAT UNITS. 6. Temperature. The centigrade unit of temperature is one- hundredth of the increase of pressure of a perfect gas, between ice-water and steam at 76 cm. pressure, the volume being constant (101, 149). The Fahrenheit unit of temperature is 5 / 9 of the centigrade unit and the temperature of ice and water is called 3 2 instead of zero as in the centigrade scale. 7. The unit of heat energy is the calorie and is the amount of heat absorbed by one gram of water in warming one degree centigrade. The most common range is 15 to 16 and this calorie is equal to 4.i87Xio 7 ergs =4. 187 joules. The large calorie is the amount of heat required to raise the temperature of one kilogram of water one degree. Table II illustrates how the amount of heat required to raise the temperature of a gram of water one degree varies with the temperature. The unit of heat energy commonly employed in engineering work in England and America is the British Thermal Unit -which rs usually abbreviated to B.T.U. i-B.T.U. =453.6X5/9, ELECTRICAL UNITS. 5 or 252 calories. Heat values, calorific powers, or heats of combustion are often expressed in calories per gram, or B.T.U. per pound. Evidently the unit of mass cancels out, and, therefore, one calorie per gram is 9/5 of one B.T.U. per pound.' For example, 1000 calories =3. 97 B.T.U.'s. A heat value of 1000 calories per gram is equal to 1800 B.T.U.'s per pound. TABLE II. Specific Heat of Water. 5 is the true specific heat at temperature t, in terms of the o 1 calorie. (s) is the similar mean specific heat between o and t. To change to the 15 16 calorie, multiply by 1.0075. t > (*) o i .0000 i .0000 5 0.9967 0.9983 10 0.9942 0.9967 15 0.9925 0.9956 20 o .9916 0.9947 25 0.9914 0.9941 3 0-99*5 0.9936 35 o .9922 0.9934 40 o 9933 0-9933 45 o .9946 0-9933 5 o .9962 -9935 55 0.9929 0.9938 60 -9995 0.9942 65 .0010 0.9946 70 .0025 0.9952 75 .0039 0.9958 80 .0047 0.9963 85 0053 o .9968 90 .0052 o-9973 95 1.0045 0.9976 IOO 1.0033 0.9979 ELECTRICAL UNITS. 8. Absolute Electromagnetic Units. A Unit Magnetic Pole is a pole which, placed one centimeter from a similar pole, is repelled with a force of one dyne. The magnetic force Sit a point is measured by the force (in dynes) upon a unit positive pole. 6 INTRODUCTION. The absolute unit of current is the current which, flowing through a wire one centimeter long, bent into a circular arc of one centimeter radius, produces unit magnetic force at the center. The unit of charge or quantity of electricity is the amount transported by unit current in one second. The difference of potential, or, the electromotive force between two bodies or two points, is measured, in absolute units, by the work, in ergs, required to carry a unit positive charge of electricity from one to the other. A conductor has unit resistance, if unit difference of potential at the terminals produces unit current. 9. Absolute Electrostatic Units. We may also define a unit charge of electricity analogously to the above definition of unit pole. A body has unit charge if, placed one centimeter from a similarly charged body, it is repelled with a force of one dyne. The electromagnetic unit of charge is 3 Xio 10 (velocity of light) greater than the electrostatic unit. The electric force between two bodies having charges e^ and e 2 is given by the expression Where d is the distance in centimeters between the charges, e is a constant called the dielectric constant (Table XLIII), and F is expressed in dynes. The difference of potential or electromotive force between two bodies or two points is one electrostatic unit, if one erg of work is required to convey an electrostatic unit of' electricity from one to the other. The capacity of a body is the charge required to change its potential by unity, or the ratio of the charge to the potential. If both charge and potential are expressed in electrostatic units, the capacity of a condenser consisting of parallel plates whose area is A, separated by d centimeters of a dielectric whose constant is e, is ~ As C = j (2) 47T d ELECTRICAL UNITS. 7 The Electrical Energy, in ergs, of a body having a charge e and a potential E is W = \Ee (3) 10. Practical Units. The above units give either incon- veniently large or inconveniently small numbers for the electrical quantities commonly used, and, therefore, multiples or submultiples are used as practical units. The practical unit of current is the ampere, which is one- tenth of the electromagnetic unit. The practical unit of electric charge or quantity is the charge carried by one ampere in one second, and is called a coulomb. The coulomb is evi- dently, also, one-tenth of the corresponding electromagnetic unit. The practical unit of difference of potential or electromotive force is the volt. The potential difference between two bodies or two points is one volt if one practical unit of work, the joule, is required to carry one coulomb from one point to the other. Since one joule is io 7 absolute units (ergs) and one coulomb is io~ x , the volt is io 7 -j-io- 1 =io 8 electromagnetic units of potential. The quantity of electricity carried by a current of i amperes, flowing for T seconds, is i T coulombs, and if the difference of potential of the two points between which it flows is E, the work done between these points is E i t W = E i T joules = -calories (4) 4- 187 The rate at which work is done is W -r . joules _ . -^=E i - = E i watts (c) T sec or the product of amperes by volts gives the electric power in watts. The practical unit of resistance is the ohm and is equal to the resistance of a conductor which carries one ampere when the difference of potential of the ends is one volt. Since 8 INTRODUCTION. the resistance is equal to the difference of potential divided by the current, one ohm is equal to io 8 -Mo~ I= =io 9 electro- magnetic units. The resistance of a column of mercury 106.3 cm - l n an d one square millimeter cross section, at o, is one ohm. The resistance of a conductor may be expressed in terms of the length /, the cross section, A, and a constant, z '. The base of natural logarithms, 2.7 i8---, is usually designated by e. We shall denote the common loga- rithm by log, and the natural logarithm by In. Therefore, z =log y, z' =lrry. Evidently log 10 = i, In 2.718 =i. Natural logarithms are obtained as the result of mathe- matical operations, such as integration. Common logarithms are usually employed in calculations and are given in Table XLVIII. 14. Exponential Equations. If the exponent is a fraction or a variable, the equation may be simplified by taking the logarithm of each side. Examples: (i). y=a z , \ogy=z log a (2). r = (i.y). 3 , logr = .3 log 1.7 =.06912, r = 1.17 15. Conversion of Natural Logarithms to Common and 10 INTRODUCTION. vice -versa. If we equate the two values of y given in 13, io z = 2.7i8 2 ' :.z =z r log 2.718 =.4343 s'. Or, logy = -4343 m :V ( 8 ) Reciprocally, z' = 2.3032, or, ln;y = 2.303 logy (9) Illustrations, (i) What is the natural logarithm of 141 .5 ? We find in common logarithm tables that log 141. 5 =2. 15076 .'. In 141.5=2.303X2.15076=4.953 (2) hry = 1.217. Find y. log y = -4343 Xi.aiy =.5285. We find in a table of common logarithms that 3.377 has this logarithm, and is therefore the value of y. ERRORS. 16. Inaccuracy may arise from several different causes: (1) errors of observation, due to the inherent limitations of the observer's powers of observing, judging and adjusting; (2) instrumental errors, arising from imperfections in the work of the instrument -maker in constructing and subdividing the scale used by the observer; (3) mistakes, such as the mistaking of an 8 for a 3 on a scale ; (4) systematic errors due to faultiness in the general method employed. The first may be decreased by making a number of independent observations and taking the mean, the second by using a more accurate instrument, the third by care and repetition, the fourth by seeking a better method. We shall consider the estimation of errors of the first type. If we have a large number of observations of the same quantity we may reasonably consider the result reliable within the average deviation from the mean, for it is shown in treatises upon probabilities that there is an even chance of the observational error being greater or less than .84 average deviation \/number of observations. (10) ERRORS. II If, for example, we are measuring the pressure of a gas, and the readings of the manometer height for six independent ad- justments are 31.33, 31.37, 3 I -4<>, 31.31, 31.32, and 31.38 cm., the mean is 30.35, the sum of the deviations (irrespective of sign) is .20 and the average deviation is .03. We therefore consider that the manometer height is 31.35 and that this result is reliable to .03 cm., or, /z =31.35 .03. We will call .03 the possible error. We may similarly estimate the error of a result involving both observation and calculation if we have several independent determinations of this result. Usually, however, we introduce, the mean observations into a formula and obtain one result, and we will now consider the calculation of the possible error of such a result. 17. If the final result is a sum or difference, the possible error of the result should be taken as the sum of the possible errors of the two terms, for one may be too great and the other too small. Illustration. If the weight of an exhausted bulb is 28.4325 .0003 gr. and the weight filled with a vapor is 29. 1007 .0003 gr., the weight of the vapor is .6682 .0006 gr. Al- though the possible error of each weighing is but .001%, the error in the weight of the vapor is . i % . 1 8. We cannot find the possible error of a product or quotient directly, from the possible errors of the factors. The percentage, or proportional, error of each factor must be determined and the percentage or proportional error of the result is their sum. Let the volume of the above bulb =982.3 .ic.c. The density is .6682^.0006 . 6682 (i+ .001) 982.3=b-i 982.3 (i .0001) = .00068024 (iifc.ooiqp.oooi) (Equation 13) = . ooo68o . oooooi The main purpose of an estimation of the possible error is to determine what significant figure (note 22) should be retained and therefore the order (power of ten) of the error is all that is 12 INTRODUCTION. usually required. In the above illustration, .0001 is negligible compared with .001. .001 X.ooo68o24 is .00000068 which we call .000001. The 2 and 4 in the preliminary calculation are therefore uncertain. If the second term of the parenthesis of the next to the last equation had been appreciable, the two proportional errors should have been added since the signs are uncertain. Instead of the proportional errors, the percentage errors might have been used. ~' I = .ooo68o . i%= .oooo68o .000001 982.3+. 01% 19. The possible error of a power or root must also be deter- mined from the percentage or proportional error. If e is the error in a quantity A , (/? \ > liH-j-J (Equation u), where r- is the proportional error. Therefore, the proportional error of the square of a quantity is twice that of the quantity itself, of the square root, is half that of the original quantity. Illustration. Suppose the above bulb is a sphere and we wish to determine its radius r 4 3X981-3 (i. =6 . I6669 ( I . 00003) = 4^ 6 . 1667+ .0002 20. Calculation of Possible Error of Complicated Expressions. If the final result is given by a complicated expression in which one or more of the observed quantities appear in several factors, the errors may neutralize each other to some extent; and the previous directions may overestimate the error. In such cases the best and simplest process is to take the loga- rithm of the expression, for this will separate the factors, and then differentiate. Since the differential of the logarithm of a function is equal to the differential of the function divided by the function, the differentials of the logarithms of the ERRORS. 13 factors will equal their proportional errors, if we let the differentials of the different quantities represent their possible errors. Illustration. Derive a formula for the proportional error of the molecular ref ractivity (223). M /* 2 -i ~~ log <7 = log Af + log (/JL 2 i) -log p log Differentiating dG _d M 2/j.dfi dp 2judju G M JJL 2 I p fJL + 2 fa /Ltd u. dp M, the molecular weight, is taken from Table L, and is as- sumed accurate, or, dM =o. Since dp, the error in p, may be plus or minus, the sign (minus) is chosen, which would give the greatest possible error. The signs cannot, however, be disregarded in combining the second and fourth terms, since dfi will have the same sign in both. Application. Benzol. 1 20 (Yellow (D) light). M=y8, ^=.8701^.003, /*= i .5014+ .0003 =26.437 dG_6Xi . 5X .0003 .003 G == (1.25) (4.25) " .87 = . 0005 + . 003 = . 003 5 = . 004 If the proportional error in G is .004, the actual error in G is .1 and the last two significant figures have no meaning; we should therefore write (7 = 26. 4+ . i 1 The organic compound, C6H 6 , will be called benzol, throughout this book rather than benzene, on account of possible confusion with benzine. 14 INTRODUCTION. Limits to Calculations. 21. By the above methods the possible error in any calcula- tion from experimental quantities may be deduced. The magnitude of the possible error in any calculation indicates how far it is useful and desirable to carry the calculation. A calculation should be carried as far as, but not farther than, the first doubtful figure. This rule must be applied not only to the calculation of the final result, but also to each intermediate step. When a calculation is carried too far, useless and very unscientific labor is expended, and when it is not carried far enough very absurd results are often obtained. In addition and subtraction a place of decimals that is doubtful in any one of the quantities is doubtful in the result. In multiplication and division (performed in the ordinary way) decimal places that have not been determined are usually filled up by zeros. Any figure in the result that would be altered by changing one of these zeros to 5 is doubtful. Abbreviated Calculations. 22. Abbreviated Multiplication. In the long multiplication and the long division of numbers obtained by experimental observations, many meaningless figures are retained. For example, suppose we wish to determine the area of a plate which measures 21.64 cm. by 17.49 cm. Long multiplica- tion gives 378.4836. The last three figures are absolutely uncertain and their calculation represents wasted time. This may be avoided by the use of logarithms and also by the approximate method of multiplication illustrated below. The first figure of the inverted multiplier (i) is placed beneath the last figure of the multiplicand (4). Each figure in the multiplier is multiplied into the figures of the multipli- 947I cand, above, and to the left, carrying from the first 2164 number above and to the right. The first number of I5 J 5 each product is placed in the first column. For ex- IQ ample, 7 times 6 is 42, but three should be carried from 37 8 5 7X4 (nearer 3 than 2). Therefore 5 is placed in the first ERRORS. 15 column. 7X1, plus 4 carried, is n. 7X2,+! carried, is 15, etc. The pointing off may be done by inspection, if the factors are expressed in units and powers of 10 (2). If the above numbers had been 216.4 an d .01749, their product would have been 2. 1 64X10* XL 749 Xio- 2 =3.785. If the number of significant figures 1 in the two factors is not the same, add a cipher to the less and replace all that are still in excess in the greater by zeros. For example, 2i7ooX .00867281 should be written 2.i7oXio 4 X8.673 Xio~ 3 , if the ciphers in the first represent undetermined figures. 23. Abbreviated Division. If we knew that the area of the plate was 378.5 cm. and that one of the sides was 21.64 and sought the length of the other side by long division, we should obtain 17.4861 .... cm. The abbreviated division illus- trated below obviates the calculation of the meaningless figures. The first division and the first subtraction are similar to long division. One figure of the divisor is struck off for the next division, leaving 216. In multiplying by the quotient, 7, we carry from the figure struck 2/03784(1749 off; that is, 7 X6 is 42, but 3 is carried from 2164 7X4 giving 45, etc. The divisor for the next I02 dividend is, similarly, 21, which goes into 105 4 times. In multiplying out, we carry as 86 before. 4X1 =4. and 2 is carried from 4X6, J 9 etc. The final dividend, .19, is divided by the final divisor, 2. The quotient may be pointed off by inspection, if the numbers are expressed as suggested in 2. Approximation Formulae. 24. Products, quotients, or powers, of expressions of the form (ie) are given by simple formulae, if e is so small that its square and higher powers may be neglected. If the operations indicated in the examples below are carried out for several 1 The significant figures are the figures which are definitely known, counting from the right, irrespective of the decimal point. 407.2 and .004072 have each four significant figures. If it is known that the next figure is o, each has five significant figures. 1 6 INTRODUCTION. terms, it will be found -that the approximate expressions are correct within these limits. (n) ; \/ (ie) =i --- 2 i e ^ H ' ' (\ i !-*)! 2 (ie 2 ) = ie I e 2 ' (12) d3) - Therefore, the geometric mean of two nearly identical numbers is equal to the arithmetic mean, within the above limits. Illustrations. (i) If t is small, xl i H -- = iH -- -; 80 i+~ i -- oi4= - 986: APPARATUS. The more common apparatus of physical chemistry is described in the following pages. Apparatus which is only used in one or two experiments is described under the respect- ive experiments, but a reference to such descriptions will be found in this Introduction. APPARATUS. 17 25. The Use of a Vernier. The vernier is a contrivance for reading to fractions of the unit in which a scale is graduated. It is a second scale parallel to the main scale of the instrument and so divided that n of its units equal n i of the units of the scale. If 5 is the length of a scale unit and v that of a vernier unit, nv=(n i) s .'. s v = s + n Or the unit of the vernier is less than that of the scale by one-wth of a scale unit. If we did not have a vernier there would be something in the nature of an index to indicate what division of the scale should be read in making a certain measurement, and fractions I I LL J L FIG. i. FIG. 2. would be estimated by eye. The zero of the vernier is taken as an index, the whole number of scale divisions being the number just below the zero of the vernier, while the fraction of a scale division is determined with the vernier. If the with division of the vernier coincides with the scale division, the zero of the vernier must be m wths of a scale unit from the scale division just below it. The reading of the scale of Fig. i, would be 5.235, for the coincidence is evidently between the third and fourth vernier divisions. The most common verniers with linear scales are those reading to tenths, twen- tieths or twenty-fifths, and with circular scales, the usual vernier reads to thirtieths. 26. Vernier Caliper. The ^vernier caliper consists of a straight graduated bar and two jaws at right angles to it, one of which is fixed, while the other is movable. The position of the movable jaw can be accurately determined by means of r8 INTRODUCTION. the scale and a vernier which should read zero when the jaws are in contact. (If this be not the case, allowance must be made for the zero reading.) 27. Micrometer Microscope. The micrometer microscope is a microscope with cross hairs at the focus. In one type of instrument these cross hairs are movable by a micrometer screw. In the other and more common type the whole micro- scope is moved by a micrometer screw (Fig. 3 ) . The best instru- ments have both adjustments. The rotations of the screw are T FIG. 3. read on a fixed linear scale, the fraction of a rotation is read by a circular scale attached to the screw, and thus the amount of movement is ascertained if the pitch of the screw is known . The pitch is best determined by measuring a definite length on a reliable scale, placed in the field of view. 28. Comparator. The comparator consists essentially of a pair of microscopes movable along a horizontal bar to which they are at right angles. The length to be measured is placed under the microscopes. The eye-piece of each microscope is first focused clearly on the cross hairs and then the whole microscope is focused without parallax on the point to be observed, and the position is adjusted until the image of the point coincides with the intersection of the cross hairs. The object is then removed and a good scale put in its place, and a reading of the scale gives the required length, this reading being facilitated by the use of the micrometer screws. APPARATUS. 19 29. Cathetometer. The cathetometer is a vertical pillar, supported on a tripod and leveling screws, and capable of rotation about its axis ; the pillar is graduated and a horizontal telescope with cross hairs is borne by a carriage that travels on the pillar and can be clamped at any desired position. A slow-motion screw serves for accurate adjustment of the posi- tion of the telescope. Adjustments. (i) The intersection of the cross hairs must be in the optical axis of the telescope. To secure this, focus the intersection of the cross hairs on some mark, rotate the telescope about its own axis, and see whether the cross hairs remain on the mark. If not, the adjusting screws of the cross hairs must be changed until this is attained. (2) The level must be properly adjusted. Level the telescope until the bubble comes to the center of the scale. Turn the level end for end. If the bubble does not come to the same position, the level must be adjusted until it will stand this test. (3) The scale must be vertical. If there are separate levels for the shaft, this is readily attained. If there is but one level for telescope and shaft, this and the next adjustment must be made simultaneously. (4) The telescope must be perpendicular to the scale. The top of the scale, T, may be regarded as having two degrees of freedom first, parallel to the line of two leveling screws of the base, A and B; second, in a line through the third leveling screw, C, perpendicular to AB. If A and B be screwed equal amounts in opposite directions, T will move parallel to AB. If C only be turned, T will move perpendicular to AB. First, make the telescope horizontal and parallel to AB. Turn the shaft through 180. It is evident that if the tele- scope makes an angle (/> with the normal to the scale, turning the scale through 180 will cause the telescope to make an angle 2< with its former direction. Hence, with the leveling screw of the telescope, correct half the error in the level, and, by turning A and B equally in opposite directions, correct the remainder. Turn the telescope to the first position and 20 INTRODUCTION. repeat the above adjustments, then to the second, and repeat as many times as is necessary. Then turn the telescope normal to AB and adjust by C. When the adjustment is complete, turning the shaft through 360 will not alter the position of the bubble. Adjustments (i) and (2) are not usually required. The eye-piece of the telescope is focused until the cross hairs are seen clearly, and the focus of the objective is changed until the object is seen very distinctly and without parallax, i.e., with no relative motion with respect to the cross hairs when the eye is moved about. THE BALANCE. 30. Precautions in Use of Balance. 1. Note the maximum load that may be placed on the balance and take care not to exceed it. 2. Always stop the swinging of the beam by means of the arrestment, before in any way altering the load on the pans. 3. Do not stop the swinging of the balance with a jerk. It is best to stop it when the pointer is vertical. 4. To set the beam in vibration, do not touch it with the hand, but raise and lower the arrestment. 5. Place the large weights in the center of the pan. 6. Make final weighings with the case closed. 7. Do not place anything in contact with a pan that is liable to injure it. 8. Avoid, if possible, weighing a hot body. 9. Never handle the weights with the fingers, as this may change some of the weights appreciably. Always use the pincers. Instead of using milligram weights, it is customary to use a rider of .01 g., which can be placed on the beam at various distances from the center. The beam is for this purpose graduated into 10 divisions, which may be still further sub- divided. Thus the .010 g. rider placed at the division of 4 of the beam is equivalent to .004 g. placed on the pan. THE BALANCE. 21 3 1 . Weighing by Oscillations. The zero-point of the balance is the position on the scale behind the pointer at which, the pans being empty, the pointer would ultimately come to rest; it must not be confused with the zero of the scale. As much time would be wasted in always waiting for the pointer to come to rest, the zero of the balance is best obtained from the swings of the pointer. For this purpose, readings of the successive "turning-points" are made as follows three successive "turning points" on the right and the two inter- mediate ones on the left, or vice versa; e.g., Turning points. L. R. + 2.1 + 2.0 Mean, 1.13 +2.05 -1-13 Zero point = + 0.92-1-2= +0.46 By taking an odd number of successive turning-points on one side and the intermediate even number on the other side and then averaging each set, we eliminate the effect of the gradual decrease of amplitude of the swing. The resting-point of the balance with any loads on the pans is the point at which the pointer would ultimately come to rest, and is found in the same way as the zero-point. If the resting-point should happen to be the same as the zero-point, the weight of the body on one pan is immediately found by the weights on the other pan and the position of the rider. Usually, however, this will not be so. It will then be neces- sary to find the nearest resting-point to the right of the zero, and then, after altering the rider one place, to find the nearest resting-point on the other side of the zero. By interpolation, the change of the position of the rider necessary to make the resting-point coincide with the zero-point is deduced. For example, the zero is +0.46 (Fig. 4); with the rider at 4 the resting-point is +0.51; with the rider at 5 the resting- 22 INTRODUCTION. point is H-o.io. By changing the rider from 4 to 5, o.ooi g. was added. To bring the resting-point to the zero we should have added .05 -f-(o.5i o.io) of .001 g., or .0001 g. approx- imately. Hence the weight of the body is the weight on the pan plus 0.0041 g. FIG. 4. 3 2 ' The Arms of the Balance May be Unequal. If this be so, the weight obtained above will not be the true weight. To eliminate this error the body must be changed to the other pan and another weighing made. If / be the length of the left arm and r that of the right and if u be the counterbalancing weight when the body is in the left pan and v when it is in the right, while w is the true weight of the body, then lw = ru, lv = rw, .-. w = \/uv = (u + v). (Eq.-i4.) (15) 33. The buoyancy of the air on the weights and on the body must be allowed for in accurate work. To the apparent weight of the body must be added a correction equal to the weight of the air displaced by the body and from the apparent weight must be subtracted the weight of the air displaced by the weights. Let m = apparent mass of body ; p = density of body ; d= density of air. The density of ordinary brass weights is 8.4. Since m P is the approximate volume, the correction to be added for buoyancy on the body is ^-d, P and the correction to be subtracted for the buoyancy on the weights is m THE BALANCE. or, the total correction is md ( - P (16) The density of dry air at o and 76 cm. pressure is .001293. The density at any other pressure and temperature can be calculated by Equation 53. Unless extreme accuracy is re- quired, the density under ordinary working conditions may be assumed as .001 2 . Table IV gives the values of this correction in milligrams, or, IOOOX .0012 for different values of p. An approximate value of p, the density of a body, may be obtained from the uncorrected weight and volume. For example, the uncorrected weight of a body was 6.2341 gr. and the approximate density was 2.5, the approximate volume was therefore 2.5 and the correction was 6.2X-34=2.i milligrams. Therefore the weight reduced to vacuum was 6.2362 grams. TABLE IV. Reduction of Weighings to Vacuum. (The density of air is assumed as .0012 and that of the weights as 8.4.) Density of Body 5 .6 34. Correction of a Set of Weights. Weights by good makers are usually so accurate that errors in them may for most purposes be neglected. But when less perfect weights are erection Density of Correction illigrams) Body (milligrams) 2 .26 2 -5 34 .86 3- .26 57 3-5 . 20 36 4- .16 .19 5- .10 .06 6. .06 .86 8. .01 7i 10 . .02 .61 1 5- .06 52 20. .08 46 24 INTRODUCTION. to be used or when weighings are to be made with the highest possible degree of accuracy, the errors in the weights must be carefully ascertained. We shall suppose that a 100 g. box of weights is to be tested and that a reliable 100 g. weight is supplied as a stand- ard and that an accurate 10 mg. rider is supplied for making the weighings. The weights of the box will be denoted by ioc/, 50', 20', 20", 10', and so on, and the sum 5' + 2' + 2" + i' by 10". To find the six unknown quantities, 100', 50', 20', 20", ic/, 10", we 'must make six weighings and obtain six relations between these quantities. Such a set of weighings are indicated in the following table. Each should be performed by the method of double-weighing just described, ic/ = 10" -fa 20' =io' + io"+6 100' = 50' + 20' + 20" + 10' +c IOO =IOC/+/ To solve these equations, substitute the value of 10' given by the first in the second; then substitute the value of 20' given by the second in the third, and so on to the last, when the value of 10" in terms of the standard 100 and a, 6, c, d, e, f will be obtained. The calculation of the other quan- tities will then present no difficulty. To standardize the box completely the same process must be applied to 10',$', 2' 2" ', i', i" and sirnilarly to the smaller weights. DENSITY OF LIQUIDS. 35. Pyknometer. A simple, accurate method of finding the density of a liquid is to weigh a suitable vessel, (a) empty, (6) filled with water at a known temperature, and (c) filled with the liquid. The first two weighings, together with the density of water (Table LI), give the volume of the vessel and the first and last weighings give the mass of the liquid. The quotient of the mass divided by the volume is the density. DENSITY OF LIQUIDS. 25 The most convenient form of vessel is the Ostwald pyknometer (Fig. 5). The vessel is properly filled when the liquid fills it completely from the mark B to the tip of the capillary A . An Ostwald pkynometer is very convenient as a weighing pipette. It is partly filled with the liquid and weighed. The desired amount of liquid is expelled from A by blowing at B, and the exact amount of liquid expelled is determined by reweighing. FIG. 5. 36. Mohr-Westphal Specific Gravity Balance. This is a convenient form of hydrostatic balance for finding the density of a liquid by determining the buoyancy of the liquid on a float hung from an arm of the balance and immersed in the liquid. Instead of weights, riders are used, the arm of the balance from which the float hangs being graduated into ten divisions. The float is made of such a size that when hanging in air from the graduated arm of the balance (which is less massive than the other arm) it will just produce equilib- rium. Four riders of different mass are employed, each one being ten times as heavy as the next smaller. The largest rider is of such a size that if the float hanging from the balance be immersed in water at 15 C., the addition of the rider to the hook at the end of the beam will restore equilibrium. Hence it counterbalances the buoyancy of the water on the float Thus it is evident that if the water be replaced by a liquid of unknown density at the same temperature (so that the volume of the float is the same) and if the largest rider under the cir- 26 INTRODUCTION. cumstances produces equilibrium when placed at the sixth division, then, for equal volumes, this liquid can weigh only six-tenths as much as 'water, or its density is 0.6. A second rider, one-tenth as heavy as the first, would evidently enable us to carry the process one decimal place farther, etc. For liquids of a density exceed- ing unity, another rider equal to the largest must be hung from the ends of the beam, FIG. 6. an d s tiH a third may be necessary for liquids of density above 2. From the above it will be seen that (i) the balance must be adjusted by the leveling screw on the base until the end of the beam is opposite the stud in the framework when the float is suspended in the air; (2) the beaker must always be filled to the same level, that level being such that when the liquid is water at 15 C. the balance is in equilibrium with the largest rider hanging above the float, and (3) the liquid tested should be at 15. If, however, the expansion of the glass sinker is calculated from the coefficient of cubical expansion (Table LV) , it will be found that the error in using the balance at any temperature between 10 and 20 is within the errors of observation. The density of a liquid may be approximately determined with a carefully graduated hydrometer of variable immersion. For measurement of viscosity, see experiment XI, and for measurement of surface tension see experiment X. MEASUREMENT OF PRESSURE. 37. The open-tube manometer consists of a U-tube containing mercury, or, some lighter liquid, such as castor oil, if the change of pressure is small. One side is connected to the vessel in which it is desired to determine the pressure and the other side is open to the air (see Fig. 57). The pressure in the vessel is the corrected barometric pressure plus or minus the difference in level in the two arms, reduced to mercury at zero degrees. If, for example, the mercury in the arm BAROMETER. 2J next the vessel is 12.05 cm - below the level in the open arm, and the temperature is 20 and the corrected barometer height is 74.11 cm., the pressure in the vessel is 74.11 +12.05 (i 20 X- 000181) =86.07 cm - [-000181 is the coefficient of cubical expansion of mercury (Table LIII).] 38. An open-tube manometer is obviously limited to moderate pressures. For higher pressures a closed-tube manometer must be used. This is similar to an open manometer except that a closed tube is attached to what would be the open arm. The pressure in the vessel attached to the other end is equal to the corrected difference of level plus the pressure of the inclosed air. The latter is calculated from the volume of the inclosed air and the initial volume and pressure (Equation 38'). BAROMETER. 39. Cistern Barometer. The cistern is raised or lowered by means of the screw at the bottom until the mercury in the cistern just meets an ivory stud near the side of the cistern. The zero of the scale is the tip of this stud. A collar, to which is attached a vernier, is so placed that the top of the meniscus of the mercury column is tangent to the plane of the two lower edges. The height of the barometer should be reduced to zero by the formula h = h (i .000162 t) (17) where h is the observed height, h the height at o and t the temperature centigrade. For, the expansion of the mercury will increase the height in the ratio (i .000181 t), and the expansion of the brass scale will reduce the apparent height in the ratio (i .000019 0- 40. Syphon Barometer. By means of two scales, graduated in opposite directions from a common zero, the position of the mercury is read in both arms. The length of the mercury column is the sum of the two readings. The scale is usually etched directly on the glass, and since the glass expands much less than brass, the correction is a little greater. The correc- tion formula is h = h (i - .000173) (18) 28 INTRODUCTION. Since the mercury may adhere to glass to some extent, barometer tubes should be tapped before reading. Table V gives the barometric correction for different pressures and tem- peratures. The correction for intermediate pressures must be found by interpolation or direct calculation by the above equations. 41. If the pressure is not expressed in absolute measure (5), the height, reduced to o, should further be reduced to the height under the standard value of gravity, 980.6. If h is the corrected height where the acceleration of gravity is g, the final corrected height is (19) TABLE V. Reduction of Barometer Readings to o. (The corrections below are in mm. and are to be substracted. The uncorrected height is in cm.) Temp. Brass Scale Glass Scale 7 2 73 74 75 76 77 78 74 75 76 77 78 i5 r -75 1.77 1.81 1-83 i 86 1.88 1.91 1.92 1.94 1.97 2.IO 2.OO 2.02 16 1.87 1.89 i-93 1.96 1.98 2.01 2.03 2.05 2.07 2.132.16 J 7 1.98 2.10 2.OI 2.13 2.0_5 2.17 2.08 2.20 2.10 2.13 2.l6 i 2.17 2.30 2.43 2. 2O 2.2 3 2. 3 6 2.49 2.62 2.76 2.26 2-39 2 2 9 2-43 18 2.23 2.26 2.29 2-33 2.46 2-59 !Q 2.22 2.25 2.29 2.32 2 -35 2.38 2.41 2-53 2. 5 6 2.69 2.8 3 20 2 -33 2 -37 2.41 2.44 2.56 2.47 2-5 1 2-54 '2.56 2.66 2.79 21 2.45 2.48 2 -53 2.60 2.72 2,3 2.67 2.79 2.68 2.81 2.72 22 2-57 2.60 2.65 2.6 9 2.81 2.93 2.76 2.85 2.89 2.92 2.96 2 3 2.6812.72 2-77 2.89 2.84 2.97 3-09 2 88 2.92 3-5 3-17 2.94 2.98 3.02 3- 11 3-J5 3.06 3- 10 2 4 2.80 2.84 3.01 3- J 3 3.06 3- J 9 3-23 336 2 5 2.92 2.96 3-01 3.05 3-!9 3-23 3.28 3-32 HYGROMETRY. 29 If the value of g is not known at a place in latitude (j> and d meters above the sea level, it may be calculated by Broch's formula. = 980.6 (i .0026 cos 2 . 000000196 d) (20) HYGROMETRY. Three methods may be used for studying the hygrometric state of the atmosphere. The first method (A) determines the dew point, the second (B) determines, indirectly, the actual vapor pressure, and the third (C) determines the relative humidity. 42. (A) Regnault's Hygrometer. A thin silvered glass test- tube is half filled with ether. The test-tube is tightly closed by a cork through which passes a sensitive thermometer which gives the temperature of the ether. Two glass tubes also pass through the cork, one extending to the bottom, the other ending below the cork. An aspirator gently draws air from the shorter tube. The ether is evaporated by the air bubbles and the entire vessel cools. The silvered surface and the thermometer are watched through a telescope and the tem- perature is read the moment moisture appears on the metal. The air current is stopped and the temperature of disappearance of the moisture is observed. This is repeated several times and the mean is taken as the dew point. (114). The detection of moisture is facilitated by observing at the same time a similar piece of silvered glass which covers a part of the test-tube, but which is insulated from it. The temperature of the air should also be carefully determined, preferably with a thermometer in a similar apparatus where there is no evaporation. 43. (B) Wet and Dry Bulb Hygrometer. Two thermometers are mounted a few inches apart. About the bulb of one is wrapped muslin cloth to which is attached a muslin wick dipping in water. The other is bare. The temperatures of both are read when they have become steady. The tempera- ture of the first thermometer will be lower than that of the bare thermometer, on account of the evaporation of the water. From the difference of temperature of the two thermometers INTRODUCTION. and the temperature of the bare thermometer, the actual vapor pressure may be determined with the aid of empirical tables (see Table VI). The accuracy will be much increased' if the "wet" thermometer is in motion, e.g., attached to a pendulum. TABLE VI. Wet and Dry Bulb Hygrometer. (Actual vapor pressures (mm.) for different temperatures of dry thermometer and various differences of temperature between the two thermometers. The first vertical column gives the temperature of the dry-bulb thermometer. The first horizontal line gives the difference between the two thermometers. Since the difference is zero if the air is satu- rated, the second vertical column gives the saturated vapor pressure for the corresponding temperatures in the first column.) tC. O I 2 3 4 5 6 7 8 9 10 I I o 4-6 3-7 2.9 2.1 J-3 i 4-9 4.0 3-2 2.4 1.6 0.8 2 5-3 4.4 3-4 2-7 1.9 I.O 3 5-7 4-7 3-7 2.8 2.2 i-3 4 6.1 5- 1 4.1 3-2 2.4 1.6 0.8 5 6-5 5-5 4-5 3-5 2.6 1.8 I.O 6 7.0 5-9 4.9 3-9 2-9 2.0 i.i 7 7-5 6.4 5-3 4-3 3-3 2-3 1.4 0.4 8 8.0 6.9 5-8 4-7 3-7 2.7 i-7 0.8 9 8.6 7-4 6-3 5-2 4.1 3- 1 2.1 i.i 0.2 10 9.2 8.0 6.8 5-7 4-6 3-5 2-5 -5 o-5 1 1 9.8 8.6 7-4 6.2 5- 1 4.0 2-9 1.9 09 12 IO -S 9.2 8.0 6.8 5-6 4-5 3-4 2-3 !-3 J 3 I 1.2 9.8 8.6 7-3 6.2 5-o 3-9 2.8 I -7 14 II.9 10.6 9.2 8.0 6.7 56 4-4 3-3 2.2 i.i 15 12.7 n-3 9-9 8.6 7-4 6.1 5- 3-8 2-7 1.6 -5 16 I 3-S 12. I 10.7 9-3 8.0 6.8 5-5 4-3 3-2 2.1 I.O !? 14.4 I 3 .0 n-5 10. 1 8.7 7-4 6.2 4.9 3-7 2.6 i-5 0.4 18 i'5-4 13-8 12.3 10.9 9-5 8.1 6.8 5-5 4-3 3-i 2.O 0.9 19 16.4 14-7 13.2 11.7 10.3 8.9 7-5 6.2 4-9 3-7 2-5 1.4 20 17.4 I S-7 14.1 12.6 i i.i 9-7 8-3 6.9 5-6 4-3 3- 1 1.9 2 I 18-5 16.8 *5- x I3-S 12.0 10.5 9.0 7.6 6-3 5-o 37 2-5 22 19.7 17.9 1-6.2 14-5 I2. 9 11.4 9-9 8.4 7.0 5-7 4.4 3- 1 2 3 20.9 19.0 J 7-3 15.6 13-9 12.3 10.8 9-2 7-8 6.4 5- 1 3-8 2 4 22.2 20.3 18.4 16.6 14.9 J3-3 11.7 IO.I 8-7 7-2 5-8 4-5 25 2 3 .6 21.6 19.7 17.8 16.0 J 4-3 12.7 I I.I 9-5 8.0 6.6 5-2 26 25.0 22.9 21. 19.0 17.2 15-4 *3-7 12. I IO -5 8.9 7-4 6.0 27 26.5 24.9 22-3 20.3 18.4 16.6 14.8 I3- 1 11.4 9-8 8-3 6.8 28 28.1 2 5-9 23-7 21.7 19.7 ! 7 .6 16.0 14.2 12.5 10.8 9-2 7-7 2 9 29.8 27-5 25-3 23.1 2 I.I 19.1 17.2 15-3 13.6 n.9 IO.2 8.6 3 3 1.6 29.2 26.9 24.6 22-5 20.5 18.5 16.6 14.7 13.0 I 1.2 9.6 MEASUREMENT OF TEMPERATURE. 31 Illustration. The temperature of the wet thermometer was 21.4 when the dry thermometer read 26. Finding 26 'in the first column, and then going along the horizontal line we find 1 6. i, approximately, for the pressure corresponding to the difference of 4.6. The saturated vapor pressure for 26 is given in the second column (25). The relative humidity is therefore 16.1 = .642 and the dew point is the temperature in the first column corresponding to 16.1 in the second column, or 18.7. 44. (C) Chemical Hygrometer. Fill three ordinary balance drying vessels with pumice. Saturate two with strong sul- phuric acid and the third with distilled water. Weigh very carefully the two which have the acid and then connect them to an aspirator with the water vessel between them. After a gentle stream of air has passed through for a considerable time, disconnect and weigh the sulphuric acid vessels. The ratio of the gains in weight will obviously be the relative humidity. Observe also the temperature of the air. If the actual aqueous vapor pressure is determined, the relative humidity is the ratio of this actual vapor pressure to the saturated vapor pressure corresponding to the actual temperature (Table LVII) . The dew point is the temperature at which the actual vapor pressure is the saturated vapor pressure. If the dew point is determined, the actual vapor pressure is the saturated vapor pressure corresponding to the dew point (Table LVII) . If the relative humidity is determined the actual vapor pressure is the saturated vapor pressure for the observed temperature multiplied by the relative humidity. MEASUREMENT OF TEMPERATURE. Calibration of Mercury Thermometer. 45. Testing Zero Point. A calorimeter consisting of a small copper vessel inside of a larger is suitable for holding the ice. Both vessels should be washed in ordinary tap water. 32 INTRODUCTION. The space between the two vessels should be filled with cracked ice, and the inner vessel filled with cracked ice and then distilled water poured in until the vessel is filled to the brim. The thermometer, having been washed clean, is inserted in the inner vessel, just enough of the stem being exposed to admit of the zero being observed. When the reading has fallen to i the reading should be observed every minute until it is stationary for five minutes. This stationary temperature, read to .1 of the smallest division, is the true zero point. 46. Testing Boiling Point. The form of boiler used for this test consists of a vessel for boiling water surmounted by a tube up which the steam passes, this tube being enclosed in another down which the steam passes to an exit tube and a pressure gauge, Half fill the lower part of the vessel with water. Push the thermometer to be tested through a cork in. the top until the boiling point is only a degree or two above the cork, but take care that the bulb of the thermometer does not reach down to the water. Apply heat, adjusting it care- fully as boiling begins, so that the pressure inside, as indicated by the pressure gauge, shall not materially exceed atmospheric oressure. Some excess is, of course necessary, if there is to be a free flow of steam. What excess is permissible may be deduced from the consideration that a rise of pressure of i cm. (of mercury column) corresponds to a rise of boiling point of .373. If water is used in the pressure gauge, a pressure of i cm. of water column would correspond to only .03 rise of steam temperature. Correction Table. Let /' Dreading in steam and let / =true boiling temperature as given in Table VII for the observed barometric height. If t is the observed reading in ice water, the true value of each degree is The true temperature corresponding to a reading /" is therefore (t"-Qr MEASUREMENT OF TEMPERATURE. 33 A table of corrections will be found very convenient. For every five degrees, for instance, the true temperature is calcu- lated and the nominal temperature is subtracted. The differences are the corrections which must be added. TABLE VII. Boiling Temperature of Water, t, at Barometer Pressure, p (mm.). P- t. P: t. P- t. 740 I ! 99.26 750 99-63 760 100.00 41 .29 51 .67 61 .04 42 33 52 .70 62 .07 43 37 53 74 63 .1 1 44 4i 54 .78 64 J 5 45 44 55 -82 65 .18 46 .48 56 .85 66 .22 47 52 57 -89 67 .26 48 56 58 -93 68 29 49 59 59 -96 69 33 750 99.63 760 100.00 770 100.36 47. The Beckmann Thermometer. The Beckmann ther- mometer is used for determining changes in temperature. The bulb is large and the stem is small so that a small change of temperature is shown by a large change in reading. The amount of mercury may be varied, and the temperature corresponding to a particular reading will vary with the amount of mercury in the bulb and stem. There is a reservoir at the end of the stem into which surplus mercury may be driven by warming the bulb. A gentle jar will detach the mercury in this reservoir when sufficient has been expelled. If one desires to study high temperature changes, the bulb is warmed until the thread of mercury extends to the reservoir, when the mercury in the reservoir is joined to it. The bulb is then allowed to cool until sufficient mercury has been drawn over, when the thread is detached from the mercury in the reservoir by a gentle jar. Several trials are often necessary before the proper amount of mercury is secured. In an improved type of Beckmann thermometer, two reservoirs are provided, and the first has a scale which tells 34 INTRODUCTION. the amount of mercury required in that reservoir for different ranges of temperature. A thermometer should be gently tapped before a final read- ing, since the mercury may adhere slightly to the glass. ELECTRICAL THERMOMETERS. 48. The most accurate thermometer for work below 1000 is the platinum resistance thermometer which is described under Experiment XXV 1 . A bolometer is a platinum resistance thermometer with a very thin blackened platinum strip in place of the coil. It is used for measuring the intensity of the radiations which fall upon it. 49. The thermocouple is a simpler instrument. For temperatures below about 300 a couple composed of copper and constantin 2 wire is excellent. The two wires are soldered together with hard solder, and the junction is placed where the temperature is to be determined. The other end of the constantin wire is soldered to a copper wire and this junction is preferably kept in ice-water. The electromotive force developed is preferably measured by a potentiometer method (73). It is often simpler and -more expeditious to connect the thermocouple directly to a galvanometer through a key and high resistance (see Fig. 57). The galvanometer with resistance is calibrated by applying a small known electro- motive force (77), and finding the value in volts of one divi- sion on the scale. For higher temperatures, a couple composed of platinum, and platinum alloyed with 10% of rhodium is excellent. 3 The calibration curve of a thermocouple that is, a curve giving the temperature corresponding to different electro- motive forces should be constructed by finding the electro- motive force when one junction is in ice-water and the other 1 See also Bui. Bu. Standards, 1907, 4, p. 641 ; 1909, p. 467. 2 "Constantin" wire (60% Cu., 40% Ni) is sold by the Driver-Harris Co., of Newark, N. J., under the trade name of "Advance" wire. 3 Excellent platinum thermocouples are obtainable from Hereaus, of Hanau, Germany, or his American agent, Charles Engelhardt, Hudson Terminal Building, New York City. ELECTRICAL THERMOMETERS. 35 junction is in steam, and also when the junction is at some other definitely known temperature. The boiling point of sulphur 444.7 (76 cm.) is often convenient. Table XLII gives the melting points of the more common metals. The electromotive force of a copper-constantin thermocouple is about 40 micro-volts per degree difference in temperature of the junctions, and that of a platinum, platinum-rhodium thermocouple is about 10 micro- volts. Radiation Thermometers. Optical pyrometers are described in 212-214, and in Experiment XXV. 50. Beckmann Apparatus for Determining the Freezing Point of a Solution. The apparatus is somewhat delicate and should be handled with great care, particularly the Beckmann thermometer. Adjust the thermometer until it reads about i at the melting point of the pure solvent. A stirrer and the Beckmann thermometer are in a special test-tube which stands in a larger test-tube, which in turn stands in a cooling bath (see Fig. 7). The solution should, if possible, be undercooled by placing the test- tube with the solution in the outer bath, which should be several degrees below the expected freezing point. The test-tube the outside hav- ing been wiped dry is quickly transferred to the larger test-tube, and both solution and outer liquid are stirred. If the solution has been undercooled, the temperature will rise, when freezing begins, and the highest steady temperature attained should be recorded. Measurement of Boiling Point of a Solution. 51. Beckmann Apparatus. There are two common forms of boiling point apparatus. In both the solution (about 20 c.c.) is contained in a special boiling tube, with glass beads, garnets or platinum tetrahedra at the bottom. The solution entirely covers the bulb of a Beckmann thermometer. The latter should not touch the glass beads, etc. In one form of INTRODUCTION. apparatus, this boiling tube is heated from beneath by a special small flame and is well protected by gauze beneath, and around the sides by two glass cylinders covered by a mica cap. In another form the boiling tube is surrounded by a vapor jacket. With the latter, both boiling tube and jacket are provided with spiral air condensers for condensing the vapor. The first type (Fig. 8) uses a small internal water condenser, to which water is supplied from a reservoir at a small elevation. The Beckmann thermometer should be so adjusted that it reads about i in the vapor of the boiling solvent. For directions for adjustment see 47. If a vapor jacket is used, it should contain about 40 c.c. of solvent, which will probably have to be replenished from time to time. Use a small flame or flames, and even when the inner liquid boils, the boiling should be so gentle that only one drop in about 10 sec. falls from the con- denser. Gently tap the thermometer before reading. 52. Landesberger- Walker Apparatus. In this method for de- termining the boiling point, the pure solvent is boiled rather than the solution. The vapor from the pure solvent in the boiling vessel (Fig. 8a) is largely condensed in the solution contained in B. What is not condensed escapes through a small hole, (a), and condenses and collects in the outer vessel, C, or is condensed in the attached condenser. The latent heat of the vapor raises the temperature of the solution in B to its boiling point. When this state is attained the tempera- ture as read on the tenth degree thermometer T becomes approximately constant. B is first filled with enough of the pure solvent to cover the bulb of the thermometer, and its boiling point is carefully determined to hundredths of a degree by estimating tenths of the thermometer divisions. Repeat FIG. BOILING POINT APPARATUS. 37 twice. The excess of the solvent which has condensed in B and also what is in C is then poured into the boiling vessel, and a very carefully weighed amount of the solute is placed in B. The boiling point is redetermined by passing vapor into the solution in B until the temperature becomes constant. FIG. 8a. Immediately after constancy is obtained, the delivery tube and thermometer are removed from the solution and its volume is carefully read from the graduations on the outside of the vessel. Reassemble the apparatus, start again the flow of vapor, and redetermine the boiling point and the volume. If possible, repeat a second time. If the solvent is inflammable, the flame must be removed or put out before the vessel B is opened. If garnets, glass beads, or fresh tile are placed in the boiling vessel, the boiling will be more regular. 38 INTRODUCTION. CALORIMETERS. 53. Fig. 9 represents Berthelot's calorimeter which, with modifications for special purposes, is suitable for most heat experiments. The inner calorimeter consists of a highly polished vessel of thin metal (or glass, if the liquid attacks metals) with a cardboard cover, through which pass the FIG. 9. thermometer and the stirrer, and which supports any other necessary bodies. It rests on a cardboard cross formed by cutting half through two pieces of cardboard and fitting them together at the cuts. This cross sets in an outer, highly polished vessel which, in turn, is surrounded by a large water jacket. The intermediate vessel is closed by a second card- board cover. If the temperature changes are small, an outer CALORIMETERS. 39 wooden casing serves almost as satisfactorily as the water jacket. It is very essential that the radiation correction (59) be determined with great care. 54. The water equivalent of a simple calorimeter is equal to the sum of the water equivalents (mass X specific heat) of the inner calorimeter vessel, stirrer, thermometer bulb, etc. The specific heats of the more common substances are given in Tables LI 1 1 LV. The specific heat of glass and mercury may be taken as .47 per cubic centimeter. Combustion Calorimeters. 55. Constant Volume Calorimeter (Hempel Bomb Calor- imeter). A pellet of the substance to be consumed is formed in a press, a cotton cord being imbedded with a loose end. After being pared down to about i gr. and brushed, it is carefully weighed. . It is then suspended in a Hempel combustion bomb, and the thread is wrapped around a platinum wire connecting the platinum supports of the basket. The terminals attached to these supports are later connected (through a key) with sufficient Edison or storage cells to just bring the wire to a brilliant incandescence (as ascertained by a preliminary trial) . The bomb is charged with oxygen under at least fifteen atmospheres pressure either from a charged cylinder or pro- duced by a retort. Bomb and pressure gauge should be immersed in water while the oxygen is being supplied. Ascer- tain that the bomb valve is open and that all connections are screwed tight. Open the cylinder valve (if a cylinder is used) until the pressure becomes high, and then close. Lift the bomb-out of the water, loosen one of the connections, and allow the mixture of air and oxygen to escape; then tighten, replace in water, open the cylinder valve again until the pressure be- comes high ; close both the cylinder valve and that of the bomb, and, finally, disconnect and dry the bomb. (If the oxygen is produced in a retort, partly fill the latter with a five-to-one mixture of potassium chlorate and manganese dioxide, connect to the bomb and pressure gauge, and heat the upper par of the retort slowly with a Bunsen burner.) 4O INTRODUCTION. Attach the electric terminals, place the bomb in the special vessel containing about a litre of water, adjust the Beck- mann thermometer to read about i (see 47), stir the water continually, and read its temperature every half-minute for five minutes, estimating to tenths of the smallest division. Close the electric switch; after a few seconds open it and read the temperature of the continually stirred water for ten minutes. Let q be the heat value of the substance and m the mass of the specimen, m w the mass of the water, e the water equiva- lent of the bomb, ^ the initial temperature, and t 2 the final temperature (corrected for radiation, see 59). Then (cal . pergr .) The best method in practice to determine e is to repeat the determination, using salicylic acid as fuel, and assuming its heat value to be 5300 calories per gram. 1 56. Constant Pressure Calorimeter (Rosenhain's Calor- imeter 2 ) . Instead of burning the substance in a fixed volume of highly compressed oxygen, the oxygen is supplied continu- ously at only slightly above atmospheric pressure. The substance is pulverized, and a sample is compressed, in a special screw press, into a pellet weighing about one gram. This is placed on a porcelain dish which rests on the bottom of the inside chamber. The ignition wire should be about 3 cm. of No. 30 platinum wire and the external terminals should be connected to storage battery terminals through a key and a resistance such that the wire will glow brightly. A tank is charged with oxygen from a cylinder or generated from "oxone" and water. The action of the different valves having been studied, the apparatus should be assembled, the upper side valve (Fig. 10) being closed and the ball 1 Jaeger and Steinwehr have shown that the most accurate method of deter- mining e is to use a heating coil on the outside of the calorimeter. Ann. der Phys. 1906, 21, p. 23. 2 This excellent calorimeter which is very satisfactory for students' laboratory use, is made by the Cambridge Scientific Instrument Co., Cambridge, England. CALORIMETERS. LJ valve, lowered. Connect with the oxygen supply through a wash-bottle, turn on a very gentle stream of oxygen, and pour into the outer vessel 1500 c.c. of water at the room temperature. The water should just cover the combustion chamber. If a Beckmann thermometer (see 47) is used, adjust to read between o and i in this water. The bulb should be supported on a level with the center of the combustion chamber. Read the tempera- ture every half-minute for five minutes, then increase the oxygen current, and care- fully read the temperature and the time, close the key and ignite the pellet with the hot platinum wire, and immediately remove the wire. During such operations it is best to hold the inner vessel steady by grasping the oxygen inlet tube. Keep the water pressure in the gasometer constant and as combustion proceeds, increase the flow of oxygen. Read the thermometer every FIG. 10. minute. When combustion has ceased, move the hot wire about to ignite any unconsumed particles. Keep the wire hot as short a time as possible and remove it immediately from any com- bustion, otherwise it is liable to be melted. Finally, turn off the oxygen supply, open the upper valve, and raise the ball valve, allowing the water to fill the inner chamber. Then force out the water by closing both valves and turning on the oxygen. Record the highest tempera- ture and the time, and the temperature every half minute for five minutes. For the radiation correction, see 59 and for the formulas, see the preceding section. To determine e, assemble the apparatus, including the Beckmann thermometer, and pour in 1000 c.c. of water. Determine very carefully the temperature with a 0.1 ther- mometer and then add 500 c.c. of water at about 50, the temperature of which has also been very carefully determined. INTRODUCTION. Determine also very carefully the final steady temperature. From these data calculate e. Add to anthracite coal one-third its weight of cane sugar. (Heat of combustion of sugar =3900 calories per gram.) 57. Heat Value of a Gas (Junker's Calorimeter). A measured volume (v liters) of gas under an observed pressure, p, is burned in the calorimeter, and the rise of temperature, from tj to t a of a mass of m gr. of water, is determined. The flow of water and gas is so regulated that the burned gas leaves the calorimeter, at ap- proximately the temperature of the entering gas, and there should be a difference of at least 6 in the temperature of the in- and out- flowing water. Also, the flow of water must be sufficient to furnish a constant small overflow at the supply reservoir (Fig. n). The burner should be lighted outside of the calorimeter. When the temperatures indi- cated on the various thermome- ters have become constant, note the gasometer reading, and imme- diately collect in graduates the heated overflowing water, and also the water condensed by the combustion of the gas. Let the mass of the latter be m' gr., and its temperature t'. Note the temperatures of the inflowing and outflowing water every 15 sec. until two or three liters have passed through. Then immediately note the gasometer reading, and remove the graduates. Assuming that condensation of the gas occurs at 100, the heat liberated is m' (537 +100 ') If q represents the heat value of the gas in gram-calories per liter, and v the volume reduced to o, 760 mm., mfe-f,) m' (637-0 v FIG. ii. RADIATION CORRECTION. 43 58. Heat Value of a Liquid. To determine the heat value of a liquid fuel, the burner (57) is replaced by a suitable lamp which is attached to one arm of a balance. The rate at which the liquid is consumed is determined from the weights in the pan on the other side at different times. It is best to make the weight in the pan slightly deficient and note the exact time when the balance pointer passes zero as the liquid is consumed. Practically complete combustion is obtained with a " Primus" burner, supplied from a reservoir where the liquid is under considerable pressure. With very volatile liquids, the opening of the burner must be large and the pre- heating tubes must be in the cooler part of the flame. TO T t T 2 T 3 FIG.' 12. RADIATION CORRECTION. 59. Fig. 12 represents, on an exaggerated scale, typical observations during a calorimeter experiment. The calor- imeter and contents are cooled initially below the temperature 44 INTRODUCTION. of the room. The temperature is read at regular intervals before the heating commences, during heating, and during the subsequent cooling. The initial rate of rise of temperature r,-r is determined. At time 7\ heating begins and continues till time T 2 . The final temperature gradient T 3 -T is then determined by regular observations of the temperature after the maximum is reached. During the time TT^ the calorimeter was gaining heat from the room as well as from the source in the calorimeter. By Newton's law of cooling, the rate of change of temperature is proportional to the difference of temperature. If t' is the average difference of temperature between the calorimeter and the room during this time, the average rate of warming from the room is and the resulting gain of temperature is If the curve B C is approximately a straight line, this is equal to Similarly, the loss of temperature during the time T 2 T is t" t 2 t where t" is the mean excess above the room temperature. Therefore, the corrected rise of temperature is t' and t" can easily be estimated from such a plot of the temperature readings. If B C D is approximately a straight line, then the above expression reduces to RADIATION CORRECTION. 45 If we agree to call a rise of temperature positive, this expression becomes (23) Or, the corrected rise of temperature is the apparent rise in temperature ; less the average rate of rise of temperature due to radiation, multiplied by the time of heating. An analogous expression will give the correction if there is an absorption rather than an emission of heat in the calorimeter. These approximate equations are particularly useful when the temperature of the room is indefinite. Measurements in Light. 60. Monochromatic Light. The simplest and most useful monochromatic light is the sodium flame. Sodium may be introduced into a bunsen flame by surrounding the tube of the burner with a tightly fitting cylinder of asbestos which has been saturated with a strong solution of common salt and formed into cylindrical shape by wrapping around the burner while still damp. As the top of the cylinder is exhausted, it is torn off and the rest of the tube is pushed up into the lower part of the flame. A piece of hard glass tubing held in the flame will also give a good sodium light. Elements giving red, green, blue and violet light will be found in Table LXII. Salts of these elements (e.g., KNO 3 , SrCl 2 , CaCl 2 , LiCl) may be introduced into the outer edge of a bunsen flame, either in a thin platinum spoon, on copper gauze, or by a piece of wood charcoal which has absorbed a solution. If a very intense light is not required, a vacuum tube is a very satisfactory source (215 and Table LXII I). Intense light of one general color may be obtained by filtering sun light or the light from an arc light through colored glass or gelatine. The solutions given in Table VIII give much purer mono-chromatic light. INTRODUCTION. TABLE VIII. Light Filters (Landolf). Color Thickness of Layer (mm.) Aqueous Solution of Grams per 100 C.C. Average Wave Length (Angstrom Units) Red 20 20 Crystal violet 560 Potassium chromate .005 10. 6560 Green 20 20 Copper chloride Potassium chromate 60. 10. 533 Blue 20 20 Crystal violet Copper sulphate I5 : s The Spectrometer. 61. Spectrometer Adjustment. A spectrometer consists of a framework supporting a telescope and a collimator, which are movable about a vertical axis, and a platform movable about the same axis. The collimator is a tube containing an adjusta- ble slit at one end and a lens at the other end. The purpose of the collimator is to render light coming from the slit parallel. Hence, the slit of the collimator should be in the principal focus of the lens. The telescope is for the purpose of viewing the light that comes from the collimator, either directly or after the light has been refracted, reflected, or diffracted. Hence, since the light that comes from the collimator is supposed to be parallel- that is, as if it comes from a very distant source it follows that if the telescope is to receive the light and form a distinct image of the slit, the telescope must be focused as for a very distant object (theoretically an infinitely distant one). The first adjustment is to focus the telescope. First focus the eye-piece of the telescope on the cross hairs and then focus the whole telescope on the most distant object visible. The telescope will now be in focus for parallel rays. Turn the telescope to view the image of the slit formed by the collimator and adjust the slit until its image is seen most distinctly. T Mann, "Manual of Advanced Optics," p. 185. SPECTROMETER. 47 62. Measurements of the Angle of a Prism. Fix both tele- scope and collimator and, rotating the platform upon which the prism is mounted, find the positions of the prism and platform in which the light is reflected from the two faces inclosing the angle. The supplement of the angle between these two positions is the angle of the prism. 63. Minimum Deviation. The position of minimum deviation (Fig. 13) is such that the image of the slit seen in the telescope moves in the same direction (that of increasing deviation) no matter which way the platform carrying the prism is turned. There are, of course, two positions in which the deviation can be obtained, one with the refracting edge pointing to the right of the observer, and the other with it pointing to the left. The deviation in each case is the angle between the corresponding position of the telescope and its position when looking directly into the collimator, the prism being removed. But it is not necessary to remove the prism, for it is easily seen that the minimum deviation must also be equal to half of the angle between the two positions of the telescope when observing the minimum deviation. From A, the angle of the prism and D, the angle of the minimum deviation, the index of refraction may be calculated by the formula . A+D sin sn - 2 (24) Descriptions of the two principal types of refractometer are given in 220, 221. The most common types of polarimeter are described in 230-233. 48 INTRODUCTION. Wave Length of Light by Diffraction Grating. 64. A diffraction grating consists of a great many lines ruled parallel and equidistant on a plane (or concave) surface. If the surface be that of glass, the grating is a transmission grat- ing; if of metal, a reflection grating. If a transmission grating be placed perpendicular to homogeneous parallel light from a colli- mator (see 61) and with the lines parallel to the slit, a series of spectra will be formed on either side of the beam of light which is transmitted without deviation (Fig. 13 a). If n = the number or order of a particular spectrum counting from the center, = the deviation or angle that the rays forming the spectrum make with the original direction of the light, a = the grating space or average distance between the centers of adjacent lines, and X =the wave-length of the light X = -a sin d (25) The slit of the collimator is made accurately vertical. The grating is mounted on the platform of a spectrometer so that the lines are vertical and so that the plane of the lines includes the axis of rotation of the instrument and is perpendicular to the axis of the collimator. The lines are parallel to the slit when the spectrum of some homogenous light (e.g., from a sodium flame) is as distinct as possible. When the plane of the grating is perpendicular to the incident light, the deviation (on opposite sides) of the two spectra of the same order should be equal. This adjustment is also secured when that part of the beam which is reflected back to the collimator appears co-axial with its object-glass. For a final measurement of the deviation of any. portion of a spectrum the mean of at least three observations on each side should be taken. is half the mean angle between the positions on the two sides. Analogous directions apply to a reflection grating. ELECTRICAL MEASUREMENTS. 49 If the grating space be not too small it may be obtained by measurements with a micrometer microscope . (27.) Secure the best possible illumination of the lines. Set the cross hair of the microscope on a line and read the position of the divided head (circular scale) . Watching the lines through the microscope, turn the screw, always in the same direction, until, for example, the tenth line is under the cross hair, and read the circular scale. Then turn the screw until the tenth line from this is under the cross hair, read the scale, and so on. Take ten such groups in different parts of the grating. From the mean find the average grating space. When the grating space is very small, the wave-length of some well-known spectrum (e.g., sodium) is assumed (Table LXIII) and the grating space is derived by reversing the process of finding the wave-length. Electrical Measurements. 65. Resistance. The resistance of a conductor is determined by comparison with another conductor whose resistance is known. Standard resistances can be bought of several makers with a guaranteed accuracy of .02%, as certified by one of the National Laboratories. A resistance-box consists of a number of known resistance coils joined so that each one bridges the gap between two of a series of brass blocks, placed in line on the cover of the box in which the coils are suspended. For each gap a plug or connector is also provided, and when the plug is inserted into the gap the resistance at the gap is "cut out" or practically reduced to zero. The coils are wound so as to be free from self-induction. Before beginning work, it is advisable to clean the plugs with fine emery-cloth so that they may make good contacts, and thereafter care should be taken not to soil them with the fingers. If any of the plugs are in loosely, there will be ap- preciable resistance at the contact. Hence, every plug should be screwed in firmly, but not violently. When any one plug has been withdrawn, the others should be tested before 50 INTRODUCTION. proceeding, for the removal of one may loosen the contact of the others. This precaution is especially important in making a final determination. 66. Wheatstone's Bridge. The unknown resistance is usually compared with a known resistance by means of the arrangement of conductors known as Wheatstone's bridge, the elementary principles, construction, and manipulation of which is undoubtedly familiar to the student. I, - h B 12 FIG 14, The simplest type of bridge is the slide wire bridge, illustrated in Fig. 14. The known resistance R is adjusted until the slide, B, is as near as possible to the center of the uniform, high resistance wire A C, when the galvanometer deflection is a minimum. If / x and 1 2 are the lengths of the two portions of the wire, when the deflection of the galvanometer is a minimum, X= l fR (26) The length of the slide wire can be greatly increased by winding it in a groove on a drum. The contact revolves around the drum and is advanced by a screw whose pitch is equal to the distance between the turns of the wire. The length of the common slide wire is 100 cm. .'. / 2 = ioo / x Table IX gives the value of 100 for various values of Z x . WHEATSTONE'S BRIDGE. TABLE IX. Meter Slide Wire Bridge (Obach). [Value of - l r for various values of / x .l 100 /r /I o.o O.I O. 2 -3 0.4 o-5 0.6 0.7 0.8 0.9 30 0.4286 4306 4327 4347 4368 4389 4409 443 445 1 4472 31 4493 45 J 4 4535 4556 4577 4599 4620 4641 4663 4684 32 4706 4728 4749 477 1 4793 4815 4837 4859 4881 4903 33 49 2 5 4948 497 4993 5!5 5038 5060 5083 5106 5*29 34 5 J 5 2 5175 5198 5221 5244 5267 529 1 53*4 5337 5361 35 5385 5408 5432 5456 548o 554 5528 5552 5576 5601 36 5625 5650 5674 5699 5723 5748 5773 5798 5823 5848 37 5873 5898 5924 5949 5974 6000 6026 6051 6077 6103 38 6129 6i55 6181 6208 6234 6260 6287 63 !3 6340 6367 39 6393 6420 6447 6475 6502 6529 6556 6584 6611 6639 40 0.6667 6695 6722 6750 6779 6807 6835 6863 6892 6921 4i 6949 6978 7007 7036 7065 7094 7123 7153 7182 7212 42 7241 7271 730i 733i 736i 739 1 7422 7452 7483 7513 43 7544 7575 7606 7 6 37 7668 7699 773 1 7762 7794 7825 44 7857 7889 7921 7953 7986 8018 8051 8083 8116 8149 45 8182 8215 8248 8282 8315 8349 8382 8416 8450 8484 46 8519 8553 8587 8622 8657 8692 8727 8762 8797 8832 47 8868 8904 8939 8975 9011 9048 9084 9121 9*57 9194 48 9231 9268 9305 9342 9380 9418 9455 9493 953 1 957 49 9608 9646 9685 9724 97 6 3 9802 9841 9881" 9920 9960 50 I.OOO .004 .008 .012 1.016 .020 .024 1.028 I -33 i 037 5i 1.041 045 .049 053 1.058 .062 .066 1.070 I -7S 1.079 52 1.083 .088 .092 .096 I.IOI .105 .no .114 1.119 1.123 53 1.128 .132 *37 .141 1.146 !5i 155 .160 1.165 1.169 54 1.174 .179 183 .188 1-193 .198 .203 .208 1.212 1.217 55 1.222 .227 .232 2 37 1.242 .247 252 257 I V 262 1.268 56 !- 2 73 -278 .283 .288 1.294 299 304 39 I-3I5 1.320 57 1.326 331 336 342 J-347 353 358 364 J -37 J-375 58 1.381 387 392 .398 1.404 .410 415 .421 1.427 1-433 59 r -439 445 451 457 1.463 .469 475 .481 1.488 1.494 60 1.500 .506 5 r 3 5i9 !-5 2 5 532 538 545 i-55i I-558 61 1.564 57 1 577 584 I -59 I 597 .604 .611 1.618 1.625 62 1.632 639 .646 -653 i. 660 .667 .674 .681 1.688 1.695 63 *-1 Q 3 .710 .717 725 !-732 .740 747 755 1.762 1.770 64 1.778 .786 793 .801 1.809 .817 .825 833 1.841 1.849 65 1-857 .865 874 .882 1.890 .899 .907 i-9i5 1.924 1-933 66 1.941 95 959 .967 1.976 985 994 2.003 2.012 2.021 67 2 030 2.040 2.049 2.058 2.067 2.077 2.086 2.096 2.IO6 2.II5 68 2.125 2-135 2-145 2-155 2.165 2-175 2.18.5 2-195 ! 2.2O5 2.215 69 2.226 2.236 2.247 2.257 2.268 2.279 2.289 2.300 2.3II 2.322 5.2 INTRODUCTION. 67. The Box Type of Bridge or Post Office Bridge will usually be found more accurate and convenient. The two lengths of resistance wire / x and 1 2 are replaced by groups of resistances (Pand Q, Fig. 15) each containing a i-ohm, a zo-ohm, a zoo-ohm and a icoo-ohm coil. One coil is used in each group or " arm " and the choice is such that the known resistance, R, is as great as possible. The galvanometer must be so sensitive that, FIG. 15. whatever P and Q, a change of one ohm in the known resistance, R, is detected by the galvanometer. Since the known resistance usually has no coil smaller than one ohm, the error from uncertainty in smaller units is less, the greater the known resistance. If, for example, the sum of all the coils in R is 11,000 and X is less than 100, P had better be 1000 and Q 10. If, however, X is between 1 00,000 and i ,000,000, P should be i o and Q 1000. When the approximate value of X has been determined, suitable values are given P and Q, and R is adjusted until a change of one ohm changes the direction of WHEATS-TONE'S BRIDGE. 53 the deflection of the galvanometer. P and Q are called the ratio coils. The coils of a box bridge may have appreciable capacity, and with alternating currents this reduces but does not usually annul its advantages over the slide wire bridge. 68. A modification known as the Callendar and Griffith's bridge is very satisfactory for such resistances as platinum FIG. i 6. thermometers (48, Exp. XXV). It is schematically illus- trated in Fig. 1 6. The two ratio arms P and Q are single equal coils. The known arm A D and the unknown arm E C are joined by a slide wire D E. The galvanometer is connected to an exactly similar parallel wire and the two are joined by a sliding cross-piece, y, of the same material as the wires. R is adjusted until a position of y is found for which the galvan- ometer shows no deflection. Since P =Q, the resistance R plus that of D y is then equal to the resistance X plus that of E y, or X = R + 2 F y (27) 54 INTRODUCTION. where F y stands for the resistance of a length of the slide wire equal to the distance of y from the center. The two parallel wires and cross-piece of the same material eliminate all disturbance from thermoelectric effects. 69. Measurement of Electrolytic Resistance. A steady current from a battery and a galvanometer cannot satisfac- FIG. 17. torily be used in measuring the resistance of an electrolyte, for a steady current produces in a short time polarization at the electrodes. This polarization leads to too high an estimate of the resistance of the electrolyte, for when no current flows through the galvanometer, the three other arms of the bridge are balancing the potential difference necessary to overcome vfi*ur\wi i i RESISTANCE OF ELECTROLYTES. 55 the true resistance of the electrolyte plus the potential differ- ence required for overcoming the polarization potential dif- ference at the electrodes. This difficulty is obviated by using the rapidly alternating current from the secondary of an induc- tion coil instead of a steady current from a battery (Fig. 17). The time that the current continues in one direction is so short that no appreciable accumulation can form at the electrodes to produce an opposing difference of potential. An ordinary galvanometer would not be affected by an alternating current, but a telephone receiver is substituted, which is a very delicate detector of an alternating current by the sound emitted from the diaphragm set in vibration by the alternate strengthening and weakening of the magnet about which the alternating current flows. The best type of induction coil is one with a very light interrupter so that the number of the alternations is very high. 1 The telephone receiver should be as sensitive as possible. It is impossible to obtain a balance for which there is no sound, for even though there were a balance for a steady current, there would not in general be a balance for varying currents such as are used in this experiment, owing to the inductive electromotive forces of capacity and self-induction in the resistance coils. If a bridge box is used and there is uncertainty as to whether a small resistance should be added or cut out, the ear is often assisted by adding and cutting out a larger resistance about which there is no doubt. On com- paring the change of tone on a variation of this latter resistance with the variation of tone with the uncertain resistance, one can often decide whether the small resistance should be added or not. 70. Conductivity Vessels. Figs. 18 and 19 represent two satisfactory forms of conductivity vessels. The Arrhenius cell (Fig. 1 8) is excellent for all electrolytic work, except for liquids of high conductivity. The distance between the 1 Gebriider Ruhstrat, of Gottingen, Germany, manufacture a very satisfactory induction coil. The interrupter is surrounded by a padded box so that no sound escapes. It is operated by one dry cell. INTRODUCTION. electrodes of the other type (Fig. 19) can be varied and it is therefore better adapted than the other to such liquids. 71. The platinum electrodes must be platinized; that is, covered with platinum black. Dissolve some platinum scraps in hot aqua regia. When cool, dilute, and add a very little lead acetate. The exact composition is not essential. The cells should be filled with this solution and a direct current at about 5 volts should be sent through the cell for about 5 minutes. The cur- [UU FIG. 18. FIG. 19. rent should then be reversed for about 5 minutes, which should be followed by about 5 minutes with the current in the original direction, and these reversals should be continued until the electrodes are covered with a black, velvety deposit. The cell should be carefully washed out with distilled water, and then filled with dilute sodium hydroxide solution and a weak current sent through in each direction RESISTANCE OF ELECTROLYTES. 57 for a few minutes, to remove all traces- of chlorine. After several more washings with distilled water, the cell is ready for calibration. 72. Cell Constant. If R = resistance of a solution, k = specific conductivity, /= distance between electrodes, and A = equivalent area of electrodes (Eq. 7). TABLE X. Specific Conductivity of .02 Normal Potassium Chloride Solution. (1.492 gr. KC1 per liter of solution.)! Temp. Sp. Cond. 10 I.996X 10-3 18 2.399X10-3 25 2.768X10-3 C is a constant for the cell and is determined by finding, with great care, the resistance, R, of a solution of known specific conductivity, k. Then C = kR (29) A .02 n solution of potassium chloride is very suitable for calibrating most cells (Table X). The cell should be in a thermostat (81) in which the temperature has become constant, for the conductivity changes greatly with change of temperature. Measurement of Electromotive Force. 73. Compensation or Potentiometer Method. An unknown electromotive force is usually measured by comparison with a known. The best method of comparison is the compensation or potentiometer method, illustrated in Fig.. 20. One or more 1 Findlay, "Practical Physical Chemistry," p. 160. INTRODUCTION. cells (top Fig. 20) whose e. m. f., E, is known or constant, are connected to a high resistance, ABC. The cell of unknown e. m. f., is connected through a galvanometer and key to two points, A and B, such that, on closing the key, the galvan- (a) FIG. 20. ometer is not deflected. When such is the case, the potentials at B and D must be the same, hence the fall of potential from A to B (=i r) must equal that from A to D (=X). E=i R' where R' is the resistance of the entire circuit. .X r = -^r. (30) If the resistance of the battery and connecting wires is neg- ligible compared with A C, we may let R=R' and f R (31) If an accuracy of half of one per cent, is sufficient (which suffices for all the experiments in Chapter IX) and E consists of Daniell cells, this approximate formula may be used. The electromotive force, E, is 1.105 volts (339) multiplied by the number of cells. If a higher accuracy is required, the value of r is found, both for the unknown cell X and for a Weston or Clark POTENTIAL MEASUREMENTS. 59 cell (336-338). If the total resistance R r is constant and r is the resistance A B for the cell of unknown e. m. f., X, and r' is the corresponding resistance for the Weston or Clark cell of e. m. f. E'. . X=^E' (32) Notice that the like poles of E and X adjoin. Do not seek necessarily a minimum deflection of the galvanometer, since such may be due to a break or high resistance in the connec- tions. Vary r until a change of one ohm changes the direction of the galvanometer deflections. The resistance A C may consist of a single, high-resistance box, if it is provided with traveling plugs, by which connection may be made at inter- mediate points, such as B. If two resistance boxes are avail- able so that A B and B C may each be a separate box, the resistance R may be kept constant, a plug being inserted in one box whenever the corresponding one is withdrawn from the other. Resistance boxes made up particularly for such potential work are called potentiometers. They are more accurate and convenient than simple boxes, but are also more complicated and expensive. 74. Capillary Electrometer. A capillary electrometer may be used in place of a galvanometer. The theory of this instru- ment is given in 320. Two convenient forms are illustrated in Figs. 21 and 22. Mercury and dilute sulphuric acid (i :6 by volume) meet in a capillary tube. If the two liquids are given slightly different potentials, the meniscus moves. If the potential of the mercury is higher, or positive, the mercury rises in the capillary and vice versa. The type of Fig. 22 is convenient because the nearly horizontal capillary requires a considerable movement of the meniscus for a small change of level, and the position of the meniscus can therefore be read directly on a scale. The other type (Fig. 21) is more easily adjusted, but the motion of the meniscus is much less and should be followed with a micro- scope. The sensitiveness of both is about .001 volt. The 6o INTRODUCTION. great difficulty with capillary electrometers is to keep them chemically clean. If a tube becomes foul, it is better to dis- card it, since they may be imported from any German dealer at very low prices. Fig. 20 (a) illustrates how the capillary electrometer may be used in place of a galvanometer. The electrometer requires a key consisting of a strip of spring metal which ordinarily makes contact with a point above. The spring is connected with one electrode of the electrometer and the FIG. 21. FIG. 22. upper contact is connected with the other electrode, so that the electrometer is normally short-circuited. Beneath the spring is a lower contact. The two points between which the potential is to be determined (Band Din Fig. 20) are connected, one to this lower contact and the other to the upper contact (which is also connected to one electrode of the electrometer) . Therefore, when the spring is depressed, the short circuit is broken and the electrometer is connected into the circuit (replacing the galvanometer and its key in Fig. 20) . 75. Single Potential Differences, Calomel Electrode. The difference of potential between a metal and a solution cannot be directly determined on account of the additional difference ELECTRODE POTENTIALS. 6l of potential introduced with the metal by which connection is made to the solution. We therefore require a metal and solu- tion whose difference of potential is known or assumed. The most common standard single difference of potential is that of the normal or tenth-normal calomel electrode. This consists of mercury in contact with mercurous chloride crystals and normal or tenth-normal potassium chloride solution. The mercury is usually at the bottom of a small glass bottle and on top of the mercury is the mercurous chloride. The FIG. 23. remainder of the bottle is filled with the potassium chloride solution. Through a rubber stopper pass a glass tube contain- ing a platinum wire connecting with the mercury and another glass tube which is filled with the solution and which serves as a syphon to connect the potassium chloride solution with the solution to be tested. If the solution is not neutral toward potassium chloride, they should be connected through a third solution which is neutral toward both (see Fig. 23). Both vessels are provided with a third tube, with which, by blowing in or sucking out air, the liquid may be forced into the syphons. The electromotive force of the complex cell whose electrodes are the electrode being tested (A, Fig. 23) and the mercury 62 INTRODUCTION. of the calomel electrode is determined by connecting it to the compensation apparatus, as the cell X is connected in Fig. 20. The potential difference of the normal calomel electrode at temperature / is usually taken as (318) E = . 560 [i+. 0006 (*-i8)] (33) and that of the tenth-normal electrode as = .613 [i +.00008 (*-i8)] (34) the mercury in both cases being at the higher potential. 76. Signs. After the potential difference has been deter- mined, great care is required in determining whether the above potentials should be added or subtracted. Remember that the positive pole of the complex cell is the pole adjacent to the positive pole of the battery at the top of Fig. 20, and that the mercury is positive toward its solution by the above values. For example, suppose the positive pole of the battery of the compensation apparatus is the one marked + and the galvanometer or capillary electrometer shows a balance when the resistance between A and B =652 ohms and that between B and C is 4867 ohms. We will suppose further that the battery consists of two Daniell cells = 2. 21 volts. Hence X =-- 2.21 =.262 volts 5499 If X consists of a normal calomel electrode and a metal electrode with intervening solutions (Fig. 23), at 18, and the mercury is next A, and V is the potential of the metal above its solution .262 =.56 V /. V = . 298 volts If the same value had been obtained with the unknown elec- trode next A , we should have had .262=F-.56 /. ^ = .822 volts for, the positive mercury electrode is adjacent to the negative side of E and its potential must be overcome by V, the poten- tial difference of the unknown electrode. MEASUREMENT OF CURRENT. 63 77. Small Known E. M. F. A small e. m. f. whose value is accurately known is often required for calibration. Fig. 24 represents a convenient arrangement for obtaining such an e. m. f. A high resistance R (e.g., 11,000 ohms) is connected to a Daniell cell. The lead wires to which it is desired to FIG. 24. apply the small e. m. f. are connected to two points between which the resistance is r . If the resistance of this circuit is very high compared with r, the e. m. f. is (35) If R = 1 1000 and r = 10, E = .0010045 Measurement of Current. 78. Currents above . i ampere are most conveniently measured by a good ammeter, such as a Weston or Hoyt (Whitney Elec. Inst. Co.) instrument. Smaller currents are best measured by finding the fall of potential, with a galvanometer calibrated as a voltmeter (49), when the current passes through a known resistance. If the current is alternating, an electrostatic voltmeter, or an idiostatically connected, Dolezalek electrometer must be used. If a direct current is very small, it may be sent directly through a galvanometer which has been calibrated by observing the deflection by a current from a small known e. m. f. (77) and measuring the resistance of the circuit. A current may be obtained in absolute measure 6 4 INTRODUCTION. with a tangent galvanometer, but the magnetic disturbances in most laboratories render the instrument so impractical that it will not be described. Measurement of Quantity of Electricity. 79. Copper Voltameter. Figs. 25 and 25 (a) give two side views of a convenient type of copper voltameter. The anode plates A are clamped against a brass plate B. The B : FIG. 25. cathode plate is considerably narrowed above the solution and passes through a wide and long slot, and is clamped to the brass strip D which is mounted on the paraffined wood block E. The block E is attached by screws to the brasses B and D. Connection is made to the anode plates at the binding point L and to the cathode at M. The ends of the brass B rest on COPPER VOLTAMETER. 65 the rim of a battery jar containing the solution. A solution containing 100 gr. of crystallized copper sulphate, 50 gr. of sulphuric acid and 50 gr.-of alcohol, dissolved in a litre of distilled water, will prove satisfactory. Anode and cathode plates are carefully cleaned with sand- paper. The cathode is then washed with distilled water and rinsed with alcohol, dried, and weighed to tenths of milli- grams by the method of oscillations (31). The cleaned I B0 ! 01 FIG. 250. plate must be handled with filter-paper. Copper will not deposit where touched by the fingers. Mount cathode and anode plates, being careful that the cathode plate does not touch the brass B. If it is desired to know the current as well as the total quantity, note the exact time to seconds at which the current commences to flow and the exact time 5 66 INTRODUCTION. when the current ceases. The cathode should be removed as soon as the current ceases, washed with distilled water followed by alcohol, dried and weighed to tenths of milligrams. If m is the gain in weight in T seconds, the quantity of electricity in coulombs which has traversed the voltameter is m , AX (3 6 ) .0003292 and the average current is _ e Any preliminary adjustments should be made with an'auxiliary cathode in place of the one which has been carefully cleaned and weighed. The negative wire can easily be ascertained by attaching the other wire to the anode plates and dipping the supposed negative wire in the solution. If it is immediately covered by a heavy dark brown deposit, it is the negative wire and should be connected to the cathode. The current in amperes should not exceed one-fiftieth of the area in cm 2 of both sides of the cathode (i.e., a current density of .02). If an accuracy higher than 1/5% is required, a silver voltameter should be employed. This voltameter will not be described here, as such accuracy is rarely attainable in electro- chemical experiments. x Measurement of Dielectric Constant. 80. The following method (De Sauty's) may be used with high-resistance liquids, such as benzol, kerosene, etc. The con- nections, Fig. 26, resemble those of a Wheatstone bridge. /?! and R 2 are two variable resistances. C x is a fixed con- denser, for example, a Leyden jar of high insulation. C 2 is a variable condenser, illustrated in detail in Fig. 27.* Two circular brass plates A, A', about ten centimeters in diameter, 1 Complete directions for the silver voltameter are given by Guthe in Bui. Bu. of Standards, 1905, I, p. 349. 2 Such variable condensers are supplied by Max Kohl, Chemnitz, Germany. DIELECTRIC CONSTANT. 6 7 are mounted on brass supports B, B. One of these is fixed in the collar D', and the other can move horizontally through the collar D, and the distance apart of the plates can be measured by means of a scale on B and a vernier (25) on D. D and D f are mounted on hard-rubber pillars, P and P f . A FIG. 26. glass vessel surrounds the plates A and A' with the liquid under investigation. The terminals of the secondary of a high-frequency induc- tion coil are connected to the points L and M (Fig. 26) and a very sensitive telephone is connected to N and P. The plates A and A' are separated by a few millimeters of air. One of the resistances is made several thousand ohms, and the other is 68 INTRODUCTION. adjusted until the sound in the telephone is a minimum. When such is the case C~ (37) For, if no current flows through the telephone, Af and P must be at the same potential. Therefore, the fall of potential in each con- denser must be the same, or e^ _ e 2 C z C 2 where e^ and e 2 are the charges on the plates. But e t , must have flowed through R It and e 2 through R 2 e 2 Rt C 2 Now surround the plates A and A ' with the liquid and deter- mine similarly the ratio of the new capacity to C l . The die- B' FIG. 27. lectric constant is, by definition, the ratio of the capacity with the liquid to that with air, the area and distance apart of the plates being the same. 1 A less accurate method, which may be used as a check, 1 A guard-ring condenser must be used for more accurate work. For partially conducting liquids, see Nernst, Zeit. phys. Chem., 1894, 14, p. 622; Drude, Zeit. phys. Chem., 1897, 2 3> P- 26 7- THERMOSTATS. 69 consists in keeping the resistances the same for the liquid as they were for minimum sound with air, and adjusting the distance apart of the plates, A and A', until the sound is a minimum. The dielectric constant of the liquid is approxi- mately the distance apart of the plates in the liquid, divided by the distance apart in air. Since the capacity of two parallel plates is given approximately by the formula where A is the area of either plate, d is the distance between the plates and is the dielectric constant, if d=C 2 Miscellaneous Apparatus. 81. Thermostats. Many of the experiments in Chapters VI, VII, VIII, and IX, require a constant temperature. The simplest means of maintaining apparatus at an approxi- mately constant temperature is to place it in a bath of water which is protected from loss or gain of heat by wrappings of asbestos, felt, etc. The water should constantly be stirred and hot or cold water added from time to time, as required. It is much more satisfactory to maintain the temperatures constant by an automatic supply of heat or cold. Fig. 28 represents a toluene thermo-regulator, which is very satis- factory for temperatures above room temperature. A bulb E, about 15 cm. long and about 3 cm. in diameter, is nearly filled with toluene, and is placed in the bath whose tempera- ture is to be kept constant. The rest of the bulb E, the vertical tube F, and a small part of the larger tube C are filled with mercury. The amount of mercury is so chosen that the inner tube at C is just open when the bulb E is at the desired temperature. The gas enters at A and goes to the burner at D. The by-pass B, is controlled by a screw pinch-cock which allows slightly less gas to pass than is required to maintain the desired tern- 7 o INTRODUCTION. perature. Toluene is a very expansive liquid and slight fluctuations in the temperature of the bath cause the inner tube at C to be opened or closed. The bulb E may be filled by removing the tube A, closing the upper part of C by a cork, connecting B to an exhaust FIG. 28. FIG. 29. pump or aspirator, and connecting D to a supply of toluene through a glass tube with a glass stop-cock which is attached to D by a short length of rubber tubing. (Toluene attacks rubber.) The cock at D is closed, and that at B is opened and the bulb is exhausted. Then B is closed and D opened and the toluene rushes over to occupy the partially exhausted THERMOSTATS. 71 bulb. It may be necessary to repeat the operation several times and to place E in warm water. When sufficient toluene has entered, pour in the approxi- mate amount of mercury required and re-exhaust. The final adjustment of the mercury had better be done with a fine pipette. A small adjustment may be made by raising and lowering A . Air bubbles must be carefully excluded. FIG. 30. Fig. 29 represents a less sensitive but very convenient gas regulator. The gas enters at A and passes to the tube D and the burner, both through a by-pass at B and also through the bottom of the inner tube at C, if the bulb E, which is in the bath, is below the desired temperature. A fits into the vertical tube by a ground-glass joint. The by-pass B consists of a small hole in A and a corresponding slight groove in the conical ground-glass neck into which A fits. By slightly turning A, the opening of the by-pass may be regulated. The amount of mercury for different temperatures is adjusted by the piston in the side tube F. Still another type of regulator is illustrated in Fig. 30. INTRODUCTION. FIG. 31. The reservoir and cock at L serve to regulate the amount of liquid in the bulb E and tube F. The final adjustment for a particular temperature is made by raising or lowering A. A 10% solution of calcium chloride is a _ A satisfactory, liquid for E and F. The /Y" bottom of F contains mercury. If it is desired to maintain the bath at a temperature below that of the room, a Foote regulator may be used. Cold water enters by the tube A, Fig. 31, and flows out through the tube D to the bath, unless the temperature in the bath is too low, in which case the mercury at C falls and the water leaves by the tube B to the waste. C represents the mercury column of any one of the regu- lators described above. Unless the temperature is high or the bath is large a bunsen burner is not as suitable for thermostats as is a small luminous burner provided with a mica or glass chimney. 82. Stirrers. A good stirrer is a wheel, with spokes similar to propeller blades, mounted hori- zontally, near the bottom of the bath, with the blades so turned as to raise the water as they are revolved by a small motor outside. A light fan similar to the stirrer but with larger blades, mounted on the top of the vertical axis of the stirrer, will usually rotate by the hot air rising from the ther- mostat and run the stirrer. The Witt stirrer illustrated in Fig. 32 is very useful for tubes or bottles. The liquid enters at the bottom and is centrifugally thrown out at the sides. 83. Gas Burette. Gases are conveniently collected in a Hempel gas burette (Fig. 33). The gas is col- lected in the vertical graduated tube afnd the reservoir is adjusted until the liquid is at the same level in both. The FIG. 32. MISCELLANEOUS APPARATUS. 73 pressure of the gas in the graduated tube is the barometric pressure less the vapor pressure of the liquid. 84. Gas Condensing Vessel. Fig. 34 represents a useful vessel for condensing such liquids as nitrogen peroxide. The gas enters at B and is condensed in the bulb A which is sur- rounded by a freezing mixture. The neck C has a ground- glass stopper. When sufficient gas has been condensed, B is closed, D is connected to the apparatus where the gas is to be used, and A is warmed. FIG. 33. FIG. 34. 85. Gas Seal. It is sometimes necessary to stir a liquid in a bottle without any gas escaping. The gas seal illustrated in Fig. 35 will be found quite satisfactory. The bottle must have a long, wide, uniform neck such as is usually the case with Bunsen gas washing bottles. The stirrer is mounted on a tube A about 4 mm. in diameter. This is surrounded by a very slightly larger tube B which is firmly held by an expanded, single-hole, rubber stopper, C. A short piece of similar glass tubing, D, is fastened to A by rubber tubing, E. The 74 INTRODUCTION. lower edge of D and the upper edge of B are the bearing sur- faces and are as smooth as possible, and are lubricated with vaseline. An outer tube, F, has a diameter intermediate be- tween the internal diameter of the neck of the bottle and the external diameter of B. The upper portion of F is contracted and at- tached to A by rubber tubing G. The space above C is filled with mercury. 86. Drying Tubes. It is often necessary to fill a vessel with dry air. The apparatus of Ames and Bliss, 1 Fig. 36, will be found very convenient for this purpose. By means of the three-way cock, A, (i) a steady current of air is drawn through the sulphuric acid and calcium chloride vessels and the tubes are filled with dry air, (2) the vessel is connected to the aspirator and exhausted, (3) the vessel is connected to the drying vessels and is allowed to fill slowly with dry air. The operation should be repeated several times. B is a plug of glass wool to exclude dust. 87. Purifying Mercury. Mechan- ical impurities may be removed from mercury by filtering through fine holes in glazed paper, the final portion on the filter being dis- carded. Amalgams etc., are best removed by distilling. The still illustrated in Fig. 37 runs continuously with little attention. A is the bulb of a boiling flask and is about 10 cm. in diameter. It is sealed to a glass tube C about 2 cm. in diameter. The distance from the end of the tube to 1 "Manual of Experiments in Physics," p. 484. FIG. 35. MISCELLANEOUS APPARATUS. 75 the top of A should be about 10 cm. greater than the normal barometric light. The bottom of the reservoir B is about i cm. below the end of C, and 2 cm. below the side tube D. The height of this reservoir is about 15 cm. The length of the inner tube from the top of the bend near the bottom to the side tube H must exceed the barometric height. The upper end of L is about i cm. below the top of A . After the still has been set up, F must be filled with pure mercury and E with the mercury to be distilled. The side FIG. 36. connection, H, is connected to a Geryk or other vacuum pump and the inner tube is exhausted until the mercury rises within a few centimeters of the barometric height in L and C. The reservoir E is adjusted until the bulb A is about one-third filled with mercury. The cock in H is then closed, and A is heated gently by the ring burner. The mercury will continuously distill over into the inner tube L and overflow into the reservoir F. Calibrating Measuring Vessels. 88. The true volume of bulbs, flasks, graduates, pipettes, etc., is found by weighing them clean and dry, and then full of distilled water at a definite temperature. All the precautions 7 6 INTRODUCTION. in weighing mentioned in 30-33 should be observed. The volume of the water is found from Table LI. 1 89. Burettes may be calibrated by the arrangement (due to Ostwald) shown in Fig. 38. A carefully calibrated pipette s with such a side connection as is shown in the figure is connected to the bottom of the burette, care being taken to exclude all air bubbles. The burette is filled with water at the temperature for which the pipette was cali- J^H^ !L brated. The pinch-cock, or B oB glass stop-cock, at S is opened JJJ^ME /^"PH and the pipette is allowed IT E- FIG. 37. FIG. 38. to fill until the water stands at the zero division of the burette. Cock C is then opened until the water has run out of A to the lower mark D. B is now opened and A is filled to the upper 1 For more extensive tables of water volumes and general directions for calibrating, see Bui. Bur. of Stand., 1908, 4, p. 553. MISCELLANEOUS APPARATUS. 77 mark E. The reading on the burette is equal to the corrected capacity of the pipette. A is emptied to D, B is again opened, and A is filled to E and the reading for twice the capacity of the pipette is determined, etc. The results of such a calibration should be preserved in a chart or a table of corrections. Carbon-dioxide-free Water and Alkali. 90. Liquids which must be preserved from contact with the carbon dioxide of the atmosphere are conveniently kept in a reservoir bottle and burette such as is shown in Fig. 39 (Ostwald). A and A' are soda- lime tubes. The burette is filled by opening B and sucking the liquid up by D. Vessels and liquids may be freed from carbon dioxide by drawing through them a current of air from which the carbon dioxide has been removed by passage through soda-lime tubes. Filling and Emptying Bulbs, etc. 91. To fill a bulb with a liquid, warm with the hand or by playing a flame about some distance be- neath. Remove from the source of heat and plunge the end of the stem into the liquid. As the air in the bulb cools liquid will be drawn in. Never allow the flame for an FIG. 39. instant to remain stationary be- neath the bulb, and until the bulb contains considerable warm liquid do not allow the flame to touch the bulb, and then only where there is liquid. Successively warm the bulb ;8 INTRODUCTION. and allow it to cool a little until the bulb is filled. When nearly full it may be best to gently boil the liquid in the bulb. When the bulb is almost full the liquid can be made to expand to fill the entire stem. Then allow it to cool completely while it draws over liquid from the beaker. To expel liquid, warm gently with the bulb so turned that the stem is filled with the liquid; then, invert so that the stem is highest, and allow to partially cool. Repeat until all the liquid is expelled. 92. Cleaning Glass Apparatus. Glass apparatus can usually be satisfactorily cleaned with hot chromic acid followed by repeated washings with distilled water and a final rinsing with alcohol. Grease is best removed with caustic potash or soda, followed by repeated rinsings with water. Steam is excellent for a final purification of conductivity vessels. 93. Cock Lubricant. An excellent lubricant for glass stop- cocks which must be air-tight is composed of equal parts of pure rubber gum, vaseline and paraffine. The two latter are melted together and the rubber is cut in small pieces and dissolved in the heated liquid. 94. Universal Wax. This very use- FlG ' 4 * ful soft wax consists of one part by weight of Venetian turpentine and four parts of beeswax, which are thoroughly mixed and worked together. The ap- pearance is improved if best English red vermilion is added before mixing. 1 95. Clip Connectors. The spring-clip connectors illustrated in Fig. 40 are very convenient and satisfactory for all electrical connections. 2 1 Ames, and Bliss, p. 496. 2 Made by Fahnestock Elec. Co., Brooklyn, N. Y. CHAPTER I. GASES, VAPORS AND LIQUIDS. 1 96. Gases. Following the custom of physicists and chemists since the time of the Greek philosophers, we shall assume that matter is composed of discrete, indivisible particles, called molecules. The simplest form of matter is the gaseous state, for less matter is present, and therefore the particles, or mole- cules of matter, being further apart, are more independent and obey simpler laws. The variables which determine the state of a gas are mass, m, temperature, t, pressure, p, and volume, v. These variables are not independent and we shall determine the relations between them. 97. Boyle's Law. Let m and / be constant. Robert Boyle, 2 in 1 66 2, discovered as a result of careful measurements that under these conditions the volume of a gas varies in- versely as the pressure, or, expressed in mathematical language, . . pv = constant (3 8) or, if /?j and v l are the pressure and corresponding volume for one state and p 2 and v a are the respective quantities in a dif- ferent state P 1 v l = p 2 v 2 (38') If p is the density of the gas (4) m =_ 1 General references for Chapter I: Meyer, "Kinetic Theory of Gases," translated by Baynes; Boynton, "Kinetic Theory"; Poynting and Thomson, "Properties of Matter," "Heat"; Winkelmann, 1905, Volumes I, II, and III; "Stoichiometry," Young. 2 "A Defence of the Doctrine Touching the Spring and Weight of the Air." London, 1662. Also in "The Laws of Gases," Barus. 79 80 GASES, VAPORS AND LIQUIDS. Therefore, other expressions for Boyle's law are: = constant (39) P, P. (39') 98. The Kinetic Theory of Gases. We shall show that Boyle's law is a direct consequence of a simple theory respecting the nature and motion of the molecules of a gas. The molecules of a pure gas are assumed to be of uniform mass and shape. They are also assumed to be in constant FIG. 41. motion, and when they collide with each other or the walls of the vessel, the coefficient of restitution is assumed to be unity, or no energy is lost by the impact. These three assumptions are in accord with all experience. Consider a body of gas enclosed in a rectangular box, the lengths of whose edges are a, 5, and c (Fig. 41) . Let m =mass THE KINETIC THEORY OF GASES. 8 1 of a single molecule of the gas. Let u = instantaneous velocity of the molecule, and let u a , u b , u c be the components of this velocity in the directions of the three edges of the box. If this molecule was the only molecule of gas, it would strike the side whose area is be with a momentum mu a and, rebounding with an equal opposite velocity, would give this side a total momentum 2 mu a . Before it again strikes this wall it must travel to the opposite wall and back, or a distance 2 a. There- fore, the number of times which it strikes the area be in one second is 2d and the total momentum per second; that is, the force, on this wall is a and the pressure, or force per unit area, is m u abc Impacts upon other molecules and the other faces will not affect the component velocity u a , since the elasticity is perfect. If there are N molecules, the total pressure on the face be is p = ^ c (u a * + u a " +u a *" +u a "" + - -) where the dashes refer to the different individual molecules. If u a 2 is the average value of u a 2 the parenthesis is equal to N u a 2 . p=-^^=*=(>^ (40) for abc is the volume of gas, and therefore __ abc is the number of molecules per cubic centimeter =n. The number per cubic centimeter multiplied by the mass of each 6 82 GASES, VAPORS AND LIQUIDS. molecule is the total mass per cubic centimeter, or the density p. The average value of the square of the total velocity is given by the equation w 2 = u a 2 -f u b 2 + u c 2 = 3 u a 2 For there are an enormous number of molecules with no preference for any particular direction of motion. /. p = L mnu 2 o (41) Therefore if u 2 is constant, is also constant. We shall see later that u 2 depends upon the temperature, and, therefore, if the temperature is constant, so also is and pv. Therefore, Boyle's law is a necessary consequence of the kinetic theory of gases. EXPERIMENT I. Boyle's Law. 1 A 50 c.c. burette and a similar ungraduated glass tube are mounted on adjustable slides on each side of a vertical scale (meter stick) and are connected by rubber pressure tubing. Mercury is poured in until both glass tubes, when at the same level, are about half full. The burette has a one-hole rubber stopper. A calcium chloride drying tube is inserted in the stopper and the burette is filled with dry air by lowering the other tube. Since it is very essential that the air should be dry, the burette should be filled and emptied several times. The last time it is filled, the top of the mercury column should be left in the middle of the burette. The drying tube should now be replaced by a tight fitting, square end, metal rod which is inserted until it is flush with the bottom of the stopper. Observe the levels of the two mercury columns for at least a dozen carefully measured air volumes between the least possible volume and the greatest. The reading of the scale corresponding to the mercury meniscus may be found with the help of a square. A 1 The apparatus used in this experiment is similar to that devised by Duff and described in his "Elementary Experimental Mechanics." (Macmillan.) VOLUMENOMETER. (a) piece of mirror glass behind each tube obviates error from parallax. Read the barometer and the temperature. For each observation, calculate and tabulate the volume and the pressure. The latter evidently equals the barometric pressure, plus or minus the difference of level of the two columns. Plot the results in a diagram in which volumes are abscissae and pres- sures ordinates. QUESTIONS. 1 . Why must the air be dry ? 2. How much air did the bu- rette contain? (Find from the curve the volume at 76 cm. Calculate the density from Table LII and Equation 49.) 3. Calculate the volume and density if the pressure was (a) i cm. of mercury, (6) 200 cm., (c) 10 dynes per sq. cm. 4. (a) What is the constant of equation 38 ? (b) Of equation 39 ? 99. Volumenometer. An interesting practical applica- tion of Boyle's law is the volumenometer which is an instrument for measuring the volume of bodies by finding the volume of the air which they displace. Replace the rod in the stopper of the burette in Fig. 42 by a glass tube which is connected by pressure tubing to a gas washing bottle (Fig. 420). Let P = pressure when the tightly closed by (c) J rft I J J>, " A i \j ? / / ! r C j ^ 1 r i \ \ 1 / FIG. 42. bottle is a rubber stopper and the mercury is at a definite division A . Lower the mercury to a point B near the bottom of the burette, and let =new pressure. Let the volume of the bottle and connections, to A , = V and to B = V +v. Then, by Boyle's law, i (42) 84 GASES, VAPORS AND LIQUIDS. Since P, p, and v are known, V may be calculated. Fill the bottle about half full with a carefully weighed amount of an assigned salt, sugar, cement, or similar body. Let the pressure, when the mercury is at A, =P' ' ; and let p f be the pressure when the mercury is at B. The unknown volume, x, of the substance can be calculated from the equation P'(V-x) =p'(V-x+v) (42') EXPERIMENT II. Volumenometer. Clamp the burette used in the previous experiment and connect a 150 c.c. gas washing bottle to a glass tube inserted in the rubber stopper (Fig. 42). Use heavy pressure tubing and make all joints tight with rubber grease (93). Close the bottle with a tight stopper, marking how far it goes into the bottle. Set the mercury at a division A near the top of the burette and read the position of each mercury column. Lower the mercury to a division B near the bottom of the burette and again read the mercury levels. Repeat at least six times, returning each time to the same points A and B. Weigh carefully about 75 c.c. of the assigned substance and pour it into the bottle. Make six more observations of the mercury levels when the mercury in the burette is successively at the same two divisions A and B. Observe the barometer and the tem- perature. From the mean positions of the mercury, calculate P, p, P', and p', and, finally, x, the volume of the substance, and its density. If time permit, determine the density also with a pyknometer (36). Weighings should be made of (i) bottle empty; (2) bottle filled with a liquid of known density (Table LIV) which is inert toward the body; and (3) containing a known mass of the body, the rest of the bottle being filled with the liquid. An equation for the density can easily be worked out. QUESTIONS. 1. What would be the most suitable values of v and x for a given value of V? (Estimate accuracy-, 20.) 2. Would this method be suitable for finding the density of a liquid? Explain. 3. How else might V be determined? 4. Calculate the weight, in kilograms, of one cubic metre of the substance used. 100. Dalton's Law. In 1802 Dalton 1 announced the law that the pressure exerted by a mixture of gases is equal to the sum of the separate pressures which each gas would exert 1 Mem. Manch. Lit. & Phil. Soc., 1802, p. 535. GAY LUSSAC'S LAW. 85 if it alone occupied the space. This law follows immediately from the kinetic theory. For, if there are different molecules of masses, m l} m 2 , etc., the mean squares of whose velocities are u^, u 2 2 , etc., the total pressure on the walls of the vessel is III 222 jf I I f* ' \T"O/ v5 O where p lt p 2 , etc., are the pressures which each gas alone would exert. An illustration of Dalton's law is given in Experiment VII. 101. Gay Lussac's Law. 1 This law states that the propor- tional change of volume of a gas, for a given change of tempera- ture under constant pressure, is the same for all gases and numerically equal to the proportional change of pressure for the same change of temperature when the volume is kept constant. In analytical language, if v I and v are the volumes of a certain mass of gas at the temperatures / T and t , the pressure being constant, VIVQ . , . J ? ~a(*i *J (44) and a v is a constant which is the same for all gases. Also, if p T and p are the corresponding values of the pressure when the volume is kept constant, Pl ~ Po =a p (t I -t ) (45) and a v = a p = a If the centigrade scale was used and t=o, Gay Lussac found that i "273 1 Ann. de Chemie et de Physique, 1802, xliii, p. 137. Also reprinted (in original French) in Mach, "Principien der Warmelehre." Charles discovered this law several years before Gay Lussac, but did not publish it. 86 GASES, VAPORS AND LIQUIDS. 102. Absolute Temperature and Absolute Zero. Evidently if t I = 273, pi =o, v t =o, and therefore this temperature was called the absolute zero and temperatures measured from this point were called absolute temperatures. We shall designate the absolute temperature by ft ft (v = const.). (48) o- w Since v = i r ^ = ^' (/> = const.) (49) 103. General Gas Equation. We shall now derive an equa- tion connecting the laws of Boyle and Gay Lussac. Suppose we have m grams of gas at o occupying a volume v under a pressure p . Let us increase the temperature to t at constant pressure, thereby increasing the volume to v f . 273 Now change the pressure from p to p while the temperature is kept constant. By Boyle's law the new volume v will be determined by the equation V p = vp = p v or pv = R' where ABSOLUTE TEMPERATURE. 87 R' is evidently a constant for a given mass of a particular gas, for p is any arbitrarily chosen pressure and v is the volume of this gas under that pressure at o. p is usually taken as the pressure exerted by a column of mercury (density = 13.59) 76 cm. high, where the acceleration of gravity is 980.6 dynes, or p= 76 X 13.59 X 980.6 =1013200 dynes per sq. cm. (52) Dividing Equation 50 by m JL^P-Lor^^m* ( 53 ) p 273^ P e If, for example, we consider i gram of oxygen v= - (Table LII) =699.8 c.c. .001429 600.8 X 1013200 /. R' = - *^ =2-597X io 6 / O If we have m grams of oxygen pv= 2.597Xio 6 w# (54) or ^- = 2.597Xio 6 # Similar equations may be derived for other gases. 104. Absolute Temperature and Kinetic Energy of Mole- cules. Comparing this equation with Equation 41, we see that the mean square of the velocity of the molecules is propor- tional to the absolute temperature. Since the mass of the molecule is constant, m/ 2 times the mean square of the veloc- ity, or the mean kinetic energy of the molecule must also be proportional to the absolute temperature. Moreover, Clausius 1 demonstrated that in any mixture of gases, the col- lisions between the different molecules of a mixture, reduce to a common value the mean kinetic energy of each kind of molecule. The reader is referred to the references for the i Phil. Mag. 1857 (4), xiv, p. 108. Also Maxwell, Phil. Mag., 1860 (4), 19, p. 25, Boynton, Kinetic Theory, p. 39. 88 GASES, VAPORS AND LIQUIDS. proof of this proposition. Since the different gases of the mixture have the same temperature, equality of temperature must mean also equality of the mean kinetic energy, J win* PROBLEMS I. 1. A lo-litre cylinder contains 10 gr. of air at 10. What is (a) the density of the air? (b) the density when the volume has been increased to i 5 litres ? (c) the pressure in each case ? 2. A 4o-litre tank is filled with a mass of oxygen which occupies 10 litres at 80 cm. pressure, nitrogen which occupies 50 litres at 40 cm. pressure, and hydrogen which has a volume of 20 litres at 100 cm. pressure. What pressure must the tank sustain? 3. Calculate the mean square of the velocity and the square root of the mean square of the velocity of the molecules of (a) hydrogen, (6) carbon dioxide at o (Equation 41 and Table LII). 4. What is the density of hydrogen at (a) 20, 76 cm. pressure? (Equation 49 and Table LII.) (b) at 20 and 80 cm. pressure? (Equation 53.) 5. A loo-c.e. glass bulb contains i gram of oxygen at 30; what is the pressure of the gas? What would be the pressure at 200? 6. Calculate the gas constant R for one gram of (a) hydrogen, (b) air. 7. What is the mass of air in a room 7 m. x 5 m. x 6 m. at 20 and 70 cm. pressure? 8. A mass of gas collected over mercury at 25 occupies a volume of 40 c.c. when the mercury is 10.5 cm. above the general level out- side. The barometer reads 74 cm. What is the volume under standard conditions (76 cm. and o) ? 9. If the gas were nitrogen, what would be the mass? EXPERIMENT III. Coefficient of Increase of Pressure of Air. The burette of the apparatus used in the previous experiments is clamped in the lower half of the slide. A bulb of about 100 c.c. capacity with a capillary stem about one mm. internal diameter (Fig. 426) is filled with dry air by exhausting and allowing air to re-enter through a drying tube (86). The bulb should be ex- hausted and filled several times and then connected by pressure tubing to a bent capillary tube, the other end of which is inserted in the rubber stopper of the burette. The end of the capillary should be flush with the bottom of the stopper. Surround the bulb by a bath of ice and water. The mercury in the burette should be brought to a definite mark within one mm. of the stopper, so that the amount of air outside of the bulb may be a minimum. Observe the levels of the two mercury columns. Readjust the mercury columns, and reobserve the mercury levels, and repeat at least five times. Surround the bulb by water at about 10, adjust the mercury in the burette to the former mark, and again observe the mercury levels. Thus find the difference of level of the mercury columns for every 10 until the water boils, at which temperature at least five AVOGADRO'S LAW. 89 independent observations should be made. Observe the barometer, the temperature of the room, and the temperature of the mercury in the manometer. Calculate the pressure for each temperature from the difference of level of the mercury columns and the barometer height. Both should be reduced to o (41). Plot the pressures against the temperatures as abscissae. The points should lie on a straight line. Calculate the coefficient of apparent increase of pressure from the pressures for o and the highest temperature, t (approximately 100), since at these temperatures the observations could be repeated and are therefore more accurate. The apparent increase of pressure is the observed increase, neglecting the ex- pansion of the bulb. If po and pt are the observed pressures, the coefficient of apparent increase of pressure is If /? is the coefficient of cubical expansion of the material of the bulb vt=v (i+ftt) Where vt and v are the volumes at t and o. If the bulb at t had kept its original volume at o, the pressure pt would have been increased to and therefore the true coefficient of increase of pressure is pot o,PtP* pot ^ p t = ' + /? (55) for the second term is so very small, that for a moderate change in temperature, we may neglect the difference between pt and p . The value of ft may be found in Table LV. QUESTIONS. 1. A litre vessel is filled with air at 20 and 80 cm. pressure. What will be the pressure of the air at (a) ioo? (6) 500? 2. Why must (a) the air be dry? (6) a capillary connect the bulb and the manometer? 3. What would be the percentage error if the expansion of the bulb was neglected? 105. Avogadro's Law. In 1811 Avogadro 1 announced the law that there are the same number of molecules in two different bodies of gas, if they occupy equal volumes at the 1 Jour, de Phys., 1811, Ixxiii, p. 58. go GASES, VAPORS AND LIQUIDS. same pressure and temperature. This law of Avogadro follows at once from the kinetic theory, for, if we distinguish the different quantities for the two gases by subscripts m If we divide one equation by the other n 2 since they are at the same pressure. (98). since the temperatures are equal (104), Furthermore, 106. Molecular Weights. This suggests a method for comparing the masses of the molecules of different gases. Since one cubic centimeter of each gas under like pressure and temperature contains the same number of molecules, the masses of each kind of molecule must be in the proportion of the masses of one cubic centimeter, that is, the densities. Oxygen is the most convenient standard gas and the mass of its molecule is given the number 32. If p is the density of oxygen and p is the density of any other gas at the same pressure and temperature, the molecular weight of this gas is If both gases are under standard conditions (4) M = 3 2 .001429 (56) (560 107. The Molecular Gas Equation. If instead of using the same unit, the gram, for measuring the masses of different gases, we take as the unit of mass a number of grams numerically equal to the molecular weight of the gas, the gas is said to be measured in gram-molecules. Since the masses of equal MOLECULAR GAS EQUATION. 9 1 volumes, at the same temperature and pressure, are propor- tional to the molecular weights, the volume of a gram-molecule is the same for all gases. If we denote by w the mass of a gas expressed not in grams, but in gram-molecules, Equation 50 becomes pv = Rw6 (57) where R is a new constant. Since equal volumes of all gases at the same pressure and temperature must have the same value of w, they must also have a common value of R. Since m R' M W = M> R = -^T (58) and since we have already found that R' for one gram of oxygen is 2.597 Xio 6 , R must be 8.31 Xio 7 (ergs, 108, note). .'. pv= 8.31 Xio^wd (59) R is also 8.31 joules = 1.985 calories (5-7). (59') If p is expressed in centimeters of mercury, rather than dynes per square centimeter pv= 6235 wO (60) The volume of one gram-molecule under standard conditions is 32 X699.8 =22.40 litres. EXPERIMENT IV. Density and Molecular Weight of Vapor by Dumas' Method. A glass bulb of determined volume is weighed empty and when filled with vapor at an observed temperature and pressure. From these observations is deduced the density under standard conditions. Let m = original weight of bulb, m v = weight of bulb filled with vapor, m w = weight of bulb filled with water at t, t' = temperature of bulb when sealed, p = barometric pressure, p w = density of water at t (Table LI), /? = coefficient of cubical expansion of glass, pa = density of air at the temperature of the balance, p' a = density of the air at *' (Table LII and Equation 53) p' = density of vapor (and possibly some air) at t 1 . The volume of the bulb at t' is V= * pw Q2 GASES, VAPORS AND LIQUIDS. The mass of the vapor, corrected for air buoyancy, is (33, the correction for buoyancy on the weights is negligible) m v nt + Vp .*.*'- -r- A bulb which has been cleansed with chromic acid and distilled water and dried with alcohol, is weighed to milligrams and about one-tenth filled with the liquid whose vapor density is to be deter- mined; for example, chloroform. For directions for filling with liquid and emptying, see 91. The bulb is suspended in a large bath filled with a liquid which boils at a higher temperature than the assigned liquid, and is heated until all the liquid in the bulb has evaporated. The neck is then sealed with a small flame and the temperature of the bath noted. When cool, the bulb is reweighed. The bulb is filled with water by scratching the top of the neck with a file and breaking off under water. Then weigh, with the broken tip. If a bubble of air remains when the water enters, hold the bulb so that the water is at the same level inside and out, close the neck, remove, dry and weigh. Let the weight be m-w Then completely fill the bulb with water (91), dry and weigh. The weight will now be m w - Volume of air = Pw The volume of the air at t' is 273 If p is the true density at t', p' V=p' a v+p (V-v) Calculate the density under standard conditions ( 4) . Calculate the molecular weight and compare it with that represented by the formula. QUESTIONS. 1. What corrections have been neglected? 2. Why must the liquid entirely evaporate? 3. Why is it only necessary to consider the buoyancy of air on .the vapor? 4. What objection would there be to sealing the bulb at a tem- perature considerably above that at which all the liquid evaporates? 5. Calculate the weight of one cubic meter of this vapor at 20 and 76 cm. pressure. DENSITY OF A VAPOR. 93 EXPERIMENT V. Density and Molecular Weight of a Vapor. Victor Meyer's Method. A mass m of liquid is vaporized and displaces a mass of air which occupies a volume if at temperature t and pressure p. The volume v under standard conditions is deduced (4), and the density is found from m and v. The liquid assigned I is carefully weighed in a small glass-stoppered bottle and introduced into a long tube, sealed at one end and closed by a rubber stopper at the other end (Fig. 43). This tube is surrounded by an outer tube containing a boiling liquid 1 of much higher boiling point. The air displaced passes through a side tube and is collected in a gas burette (83). The inner tube should have asbestos or glass wool at the bottom to break the fall of the small glass bottle. Be careful not to lose the small bottles or mix up their stoppers. Numbers should be etched on stoppers and bottles. Support the smaller tube inside the outer, the bottoms being separated by several cms. Pro- tect the glass tubes where clamped by rubber tubing or asbestos paper. Pour the high boiling liquid into the outer tube to a depth of 4 to 6 cm. The outer tube must be well protected from the flame by asbestos, gauze, or a sand- bath, and it must be protected from drafts by asbestos wrappings. When no further adjustment of the reservoir of the gas burette is necessary, we know that the pressure and therefore the temperature have become constant. The filled and carefully stoppered and weighed glass vial is placed upon the flexible glass detent at the side of the inner tube and the rubber stopper is replaced. The reservoir is adjusted until the water in it and the burette are at the same level ; and if the pressure still remains constant, the burette is carefully read and the bottle is released from the detent. As soon as the bottle reaches the heated bottom of the tube, the liquid will escape from the bottle as vapor, and the reservoir must be lowered to maintain the same level as that of the burette. FIG. 43. When the pressure has again become constant, the burette is care- fully read. The temperature of the water and the barometric height should be ascertained. The difference of the burette readings is v', and p is the barometric pressure less the water vapor pressure (Table LVII). Without disturbing the apparatus, two or more other bottles should be similarly vaporized and the equivalent volumes of air determined. 1 If the outer boiling tube contains water; chloroform, benzol, ether, or acetone are suitable vaporizable liquids. If a less volatile liquid than these is used, the water in the outer vessel may be replaced by aniline (boiling point = 183) or a bromonaphthalene (279). 94 GASES, VAPORS AND LIQUIDS. Calculate the mean density of the vapor at o and 76 cm. and the molecular weight (Equation 56). Compare with that represented by the chemical formula. For the determination of molecular weight by this method at high temperatures, see Nernst, Zeit. f. Electrochemie, 1903, p. 622. QUESTIONS. 1. Why is the actual temperature of the vapor unnecessary? 2. Should the air displaced by the vial be regarded? Explain. 3. Calculate the weight in grams of one cubic meter of this vapor at (a) o and 76 cm.; (6) 20 and 78 cm. EFFUSION. 108. A gas escapes through a very small opening with an average velocity u. The kinetic energy of a mass m of the escaping gas is therefore 1/2 mu 2 and this must be equal to the work done by the remaining gas or pv. 1 But the volume is equal to the mass divided by the density /, p = J m u 2 4 7 ,!. <"> Therefore, if we allow two different gases to escape through the same opening under the same difference of pressure, the velocities of efflux will be inversely proportional to the square roots of the densities. If we observe the times 7\ and T 2 required for the same amount of gas to escape, these times will be inversely proportional to the velocities and therefore directly proportional to the square roots of the densities. P* ' (6j'\ ' ' T~ T7 ( ) @2 -L 2 PROBLEMS II. 1. The weight of a certain volume of air is 5 grams. What would be the weight of a similar volume (like pressure and temperature) of (a) carbon dioxide ? (b) hydrogen ? 2. What is the pressure of a gram-molecule of gas which occupies i litre at o? 1 Work, by definition, is the product of force X times distance, d, but if the force consists of a pressure, p, applied to an area A , X = pA and W= pAd = pv (62) COMPARISON OF DENSITIES OF GASES. 95 3. Ten grams of ammonia gas occupy a litre vessel; what is the pressure at (a) o? (6) ioo? 4. The density of a vapor is .00497 at 20 an d 7 cm - Calculate its molecular weight. 5. What is the volume of 100 grams of nitrogen at 30 and 80 cm. pressure ? 6. What is the density of hydrogen at 100 and TOO cm. pressure? 7. With what velocity will oxygen escape through a small aperture at 25 when the pressure on one side is 70 cm. and that on the other side is 74 cm. ? In what time would i litre escape if the aperture is .1 mm. in diameter? EXPERIMENT VI. Comparison of Densities of Gases by Bunsen Effusion Apparatus. This apparatus consists of a glass tube which is closed by a three way cock and which is filled with the assigned gas and depressed in a deep mercury reservoir (see Fig. 44). A float rests on the mercury inside the tube, and this float usually has a black knob at the top and two black lines near the bottom. One position of the cock connects with a minute aperture in a thin platinum plate. 1 The apparatus should stand in a mercury tray so that in case of accident no mercury may be lost. The side opening of the three-way cock is on the marked side. With the interior of the glass tube connected with the air, lower until one of the lower marks on the outside of the tube is on a level with the mercury. Close the cock and lower further until one of the higher marks is on a level with the mercury. Connect the interior of the tube with the fine aperture and observe with a telescope the number of seconds between the passage of the lower part of the black knob of the float and the lower of the two lines near its bottom. Repeat several times, and also repeat with the tube initially depressed to a different mark. Make similar observations with several other gases. To fill the tube, raise it full of mercury. Connect the side tube to the source of gas, and opening the cock a small amount, allow the tube to fill as the mercury descends. Fill several times to remove any residual gas. From the mean times, calculate the relative densities of the different gases. From the known density of one gas (e.g., air which under standard conditions has a density of .001293) calculate the densities of the others. From the latter, determine the molecular weights (Equation 56) and compare with the accepted values. QUESTIONS. 1. Did you find the velocity of efflux at different mean pressures? 2. Should, the densities be reduced to standard conditions (4)? Explain. 3. Why must the aperture be small? In a thin plate? 1 The aperture is liable to become clogged, in which case it is simpler to insert a new plate than to clean the old one. A hole is pricked with a fine needle in thin sheet platinum, and then hammfered down until only an excessively small hole remains in a flat plate. The plate is trimmed to the proper size and mounted with universal wax (94). FIG. 44. 96 GASES, VAPORS AND LIQUIDS. Deviations from Boyle's Law. 109. The announcement of Boyle's law was soon followed by the discovery of exceptions. The most careful and exhaustive study of these exceptions was made by Amagat 1 whose original papers must be consulted for details, since only the briefest possible resume is possible here. He carried his observations up to the enormous pressure of three thousand atmospheres, and Witkowski, Wroblewski, Olszewski, and Kamerlingh-Onnes have extended the study of common gases to extremely low temperatures. Table XI illustrates the deviations of three typical gases. Hydrogen shows comparatively little deviation, while the values of pv for carbon dioxide are far from constant. Air, nitrogen, and oxygen show greater deviations than hydrogen. If the product pv is taken as unity at one atmosphere and the pressure is varied at different constant temperatures, the value of this product is a minimum at some particular pressure for each temperature. The higher the temperature, the lower the pressure at which this minimum occurs . For air ; this minimum is at 79 atmospheres at 16, 95 atmospheres at o and 123 atmospheres at 78.5. Kamerlingh-Onnes 2 found no per- ceptible minimum with hydrogen until very low tempera- tures were reached. At 139.9 the minimum was at less than 25 atmospheres, at 195 it was at about 45 atmospheres, and at 213 it was at 51 atmospheres. The pressure of this minimum for an easily condensed gas, such as carbon dioxide, increases as the temperature is raised till a certain temperature is reached beyond which it behaves as do more permanent* gases. At o the minimum is at about 4 atmospheres, at 50 at about 130, at 100 at about 200, at 200 at about 250, but at 250 it is approximately 225 atmospheres. 1 Ann. Chem. et Phys., 1880, 19, p. 345; 1893, 29, p. 40; 29, p. 37. 2 Leyden Communications, 1902, 78; 1907, 97, p. 99. 3 Gases which closely follow Boyle's and Gay Lussac's laws under ordinary conditions and which remain gases to very low temperatures are often called permanent. VAN DER WAALS' EQUATION. 97 TABLE XI. Deviations from Boyle's Law. 1 Values of pv at o. Pressure (Atmospheres) i 5 100 200 500 1000 2000 3000 Air i .068 .072 I.OIO 1.340 I.QQQ 3.226 4.323 Hydrogen i 1.032 1.069 1.138 1.356 !-7 2 5 2. 3 89 Carbon dioxide. . . i .105 .202 .385 .890 1.66 no. Van der Waals' Equation. Many modifications of Boyle's law have been proposed for the purpose of meeting these exceptions. The equation which on the whole is most satisfactory was invented by Van der Waals 2 and is (63) b is a constant which represents the limiting volume of the gas. Obviously, this cannot be zero, as is assumed in Boyle's law. a is another constant, proportional to the attraction between the molecules of the gas. Such an attraction would evidently increase the effective pressure. It would also be proportional to the square of the density, or inversely pro- portional to the square of the volume, for the closer the mole- cules are together, the greater the number of both attracting and attracted molecules. Deviations from Gay Lussac's Law. in. Amagat 3 also made a classical investigation upon this subject. If the coefficient of increase of volume, is measured under different constant pressures, and each pressure is greater than the preceding, the value of this coefficient generally increases to a maximum and then decreases. It varies little with the temperature. 1 Amagat, /. c. 2 " Kontinuitat," 1872 (Leipsic, 1881). 3 Ann. Chem. et Phys., 1893, 29, p. 68. 7 GASES, VAPORS AND LIQUIDS. Table XII gives typical values for typical gases. It will be noticed that hydrogen is also peculiar in this respect. The coefficient of increase of pressure (constant volume) ex- hibits similar deviations as Table XIII illustrates. TABLE XII. Coefficient of Expansion under Constant Pressure (ay). 1 o-ioo. Pressure (Atmospheres) i IOO 200 * 500 IOOO Air 00367 004.4.4 OO4. tJ tJ OO^ ^ I 00214 Hydrogen 00366 OO33 2 .00278 .00218 Carbon dioxide .00371 .0414 .OIII .00349 .00206 TABLE XIII. Coefficient of Increase of Pressure at Constant Volume o-ioo c Pressure' (Atmospheres) i 50 IOO 200 500 Air 00366 00371 ' 00462 .00^2 .00617 Hydrogen .00367 00373 .00383 .00379 Carbon dioxide .00369 .00386 00373 Comparing Tables XII and XIII, we notice that a v is, at ordinary pressures, greater than ap, except in the case of hydrogen, where the reverse is true. Now, using the notation of the calculus _dp_ _ dv pdt ' vdt Differentiating Van der Waals' equation (63) we find R R (64) ap pv --- which is the case with most gases at moderate pressures. At high pressures, however, all gases behave like hydrogen. The explanation of these deviations is the .fact that when a gas is cooled and sufficiently compressed it changes to a liquid, and the influence of this transition is felt at pressures and temperatures considerably removed from actual liquefaction. Isothermals. 112. Fig. 45 is constructed from Andrews' and Amagat's observations upon carbon dioxide. 1 The line marked 2i.5, for example, shows the different pressures and corresponding volumes of one gram of carbon dioxide when the temperature is maintained constant at this value. Such a curve is called an isothermal. At low pressures (portion A B of curve) the gas approxi- mately obeys Boyle's law, as is evident from the shape of the curve. When the pressure reaches about 60 atmospheres, the volume may be decreased without an accompanying increase of pressure until the volume becomes about i c.c. (BC). Upon further decrease of volume, the pressure increases enormously (CD). It was observed that at B, liquid commenced to appear, and as the volume was decreased, the amount of liquid increased, until at C all the carbon dioxide had become liquid. A gas which may thus be liquefied (states A B} is called a vapor, and a vapor in the presence of its liquid (states BC) is called a saturated vapor. Evi- dently, the pressure of a saturated vapor is constant if the temperature is constant. Between C and D we are reducing the volume of the liquid and, since liquids are very incompressible, the pressure greatly increases. 1 /. c. and "The Laws of Gases." Barus. 100 GASES, VAPORS AND LIQUIDS. 113. Application of Van der Waals' Equation. Let us apply Van der Waals' equation (63) to one gram of carbon dioxide at 21. 5 = 294. 5, absolute, taking one atmosphere 100 -80 60 40 4567 89 10 FIG. 45. as our unit of pressure, and the cubic centimeter as our unit of volume, since these are the units of Fig. 45. By Equa- tion 51 and Table LIT R' 273 X- 001965 = 1.86 PRESSURE OF SATURATED VAPOR. IOI For one gram of carbon dioxide a = i857, 6 = .9 71 (Table LVI, compiled from the excellent tables in Winkelmann, 1906, 3, P- 857). A few values of p for different values of v will be given. If v = 2o c.c., = 24.2; v = io, p=42] v = j, = 52.7; v = 5, p=6i; v=3, =66; ^ = 1.5, = 50; v = i, = 17000. These points are represented by crosses and connected by a curve. The agreement with the experimental results represented by the curve A BCD for the same temperature is not exact, but remarkably close considering the nature of the curve. The values of the pressure for large volumes show approximate agreement with Boyle's law. Between 8 c.c. and 1.5 c.c. the pressure is approximately constant, and if the volume is further reduced the pressure becomes enormous. Prof. James Thomson x made the suggestion that a continu- ous curve such as is given by Van der Waals' equation repre- sents the actual physical states better than the discontinuous curve, with the horizontal portion, which is obtained experi- mentally and which really represents the mean states of a mixture of liquid and vapor. The portions BE and CF can with care be traced experimentally for a short distance. The portion EF represents unrealizable states, since a decrease of pressure is accompanied by a decrease of volume. EXPERIMENT VII. Pressure of Saturated Vapor. Dalton's Law. The same apparatus is employed as was used in Experiments I, II, and III, except that the pressure tubing is disconnected from the burette and is connected to the small separating funnel shown in Fig. 46. The funnel must have a tight stop-cock. It may be neces- sary to regrind it with a little fine emery and water. It should be lubricated with rubber grease (93). The funnel is surrounded by an open glass vessel (see figure) containing water and a stirrer and thermometer, and is placed directly in front of, and as close as possible to, the sliding mirror glass behind the burette, so that the level of the mercury can be read as in the previous experiments. 1 Proc. Royal Soc. 1871, .p. 130. 102 GASES, VAPORS AND LIQUIDS. (A) The first part of the experiment, although not more im- portant, is given precedence because it requires that the burette be perfectly clean and dry, in which condition it is supposed to be at the beginning of the experiment. When the temperature has become constant, introduce sufficient air so that when the stop-cock is tightly closed and the mercury is at a definite point, the mercury in the other arm is about 20 cm. lower. Make several careful independent measurements of the difference of level. The water- bath must be stirred constantly and the temperature kept constant. If there is no leak, pour a little of the assigned volatile liquid into the top of the funnel, lower the other mercury tube as far as possible, and open the cock sufficiently to allow a very small amount of liquid to enter the tube, and close tightly. Adjust the mercury until the level of the liquid above the mercury is at the former point, and read the difference of level of the two mercury columns and the temperature. There must be some liquid above the mercury so that the vapor may certainly be saturated. If there is much, its height must be reduced to mercury (see Table LIV) and added to that of the mercury. Make several care- ful independent determinations of this difference of level. The temperature must be kept constant. Since the volume of the air is the same as before the vapor was admitted, the change in level must equal the pressure of the saturated vapor, if Dalton's law is true (100). (B) Remove all the air from the tube by opening the stop-cock and elevating the mercury to the cock. Close the cock and lower the mercury to allow any air left in mercury or tube to come out. Again elevate the mercury until any air which has collected is forced to the top and allowed to escape through the cock which is then closed. Lower the mercury and if there is no leak, admit a little liquid through the stop-cock. The temperature of the water-bath must be the same as in (A). Find the difference of level of the two columns for at least four different volumes of the vapor. Since the pressure of a saturated vapor is independent of the volume, these differences should be equal. Read the barometer and calculate the actual mean pressure exerted by the vapor. It should agree with that determined in (A), thus establishing Dalton's law. Repeat all the observations of (B) at four other temperatures. Tabulate your results and also plot them in a curve with temperatures as abscissae and pressures as ordinates. Another method of measuring the vapor pressure is given in Experiment IX. FIG. 46. HYGROMETRY. 103 QUESTIONS. 1. What was (a) the pressure exerted by the air in (A)? (6) the total final pressure ? 2. Why must (A) be performed before (B) ? 3. What difficulty would be experienced at low temperatures (114)? 4. What advantages has (A) over () ? What disadvantages? 5. The tube of the funnel will generally be much smaller than the other sliding tube. Does either method eliminate error from capillarity? 114. Hygrometry. The horizontal lines of Fig. 45 which represent the coexistence of liquid and vapor are limited by the dotted line* LMN '. If the pressure, volume, and tempera- ture of the substance correspond to points on the left of this dotted line, the substance is in the liquid state; if the points are on the right of this line, it is in the vapor state. The state of the water vapor in the atmosphere would be represented by the latter points in a similar diagram for water. If a portion of the air and water vapor are cooled, the pressure will remain equal to that in the rest of the atmosphere and the different states will be represented by points on a line similar to x y. The temperature corresponding to the point y where the vapor becomes saturated and moisture appears is called the dew point. The dew point can be approximately determined by gradually adding cold water or ice to water in a brightly polished metal vessel, stirring constantly and noting the temperature of the water when dew first appears outside the vessel. The vessel should then be allowed to warm up while constantly stirred and the temperature of disappearance of the dew observed. The mean of the two temperatures is the approximate dew point. More refined methods are described in 42-44. The pressure of the water vapor in the air is evidently the saturated vapor pressure for the temperature of the dew point. The relative humidity of the air is the ratio of the actual vapor pressure to the saturated vapor pressure for that temperature. 115. Critical State, Liquefaction of Gases. Notice that the horizontal lines of coexisting liquid and vapor (Fig. 45) grow IO4 GASES, VAPORS AND LIQUIDS. shorter as the temperature rises and disappear for isothermals above 30.9. Above this temperature liquid and vapor do riot coexist, and therefore it is called the critical temperature. The corresponding pressure is called the critical pressure. The critical volume is the volume occupied by one gram (or one gram-molecule) of the gas at this temperature and pressure. The characteristic of the liquid state is the so-called free surface; that is, a boundary other than the walls of the con- taining vessel. If the vessel is closed, the space above this free surface will contain the saturated vapor. We see, there- fore, that a gas above the critical temperature cannot be liquefied. It may be compressed to a smaller volume than the liquefied gas occupies; for example, in the state represented by the point P in Fig. 45, the carbon dioxide has a smaller volume than much of the area inclosed by the dotted line or even than parts of the area at the left of this line but no free surface will appear. To liquefy a gas, its temperature must be lowered below the critical temperature, and the volume must be decreased by increased pressure until its state is repre- sented by a point at the left of the right-hand branch of the dotted line. The methods of securing the necessary cooling are described in 138-141. Van der Waals' Generalized Equation. 116. Corresponding States. If we multiply out Equation 63 and divide by p we have +-^-|= -; (6s) which is a cubical equation, and, therefore, for a given value of p there are either three real values of v; v lt v 2t v 3 ; or, one real value and two imaginary values. The curve in Fig. 45 plotted from the numbers in 113 shows these three real roots for certain pressures; for example, 60 atmospheres. Since the three real roots are evidently limited to the area included within the dotted line LMN, the higher the pressure the more CORRESPONDING STATES. 105 nearly equal they must be, until, at the critical point, they become identical, or v l = v 2 = v 3 = v c where the subscript indicates the critical state. Equation 65 must be equivalent to (l) 7;.) 3 = y3 7 y yi -4- ? y 2 y qj 3 = Q \^ "c/ o c ' O c c Equating coefficients, 3^=6+^1 PC 2_ a 3= ^ Hence, dividing the third equation by the second, v c = 3 b (66) Substituting in the second equation Finally, substituting in the first equation '^=i- R ^ and, conversely, &=y (68) a=3P c v c ' (68') IO6 GASES, VAPORS AND LIQUIDS. If we chose as our units of pressure, volume, and tempera- ture the respective values for the critical state, and if we designate these so-called reduced values of the pressure, volume, and temperature by X, p, and v, respectively, ;=-|-,/-f ,v = f. (69) PC v c u c Substituting these values of p, v, 0, a, b, and R in Van rler Waals' equation, we have, upon reducing i) = 8 V (70) which is Van der Waals' reduced equation. Notice that it involves no constants peculiar to a par- ticular substance. In other words, this one equation states the relation between the reduced pressure, volume and temperature for all bodies in any state except solid. 117. The state of any single substance is completely defined by the three quantities, pressure, volume, and temperature, and if for two substances the reduced values of these factors are equal, the substances are said to be in corre- sponding states. In the case of liquids and saturated vapors the condi- tions are somewhat simpler, since the volume of the former is practically constant and the pressure of the latter is inde- pendent of the volume. As an example of the application of this generalized equa- tion, we will consider the two very dissimilar substances, sulphur dioxide and ethyl ether. For sulphur dioxide, ^ = 78.9 atmospheres, ^ = 428.4. At 412.9 absolute the pressure of the saturated vapor of SO 2 is 60 atmospheres. , 60 412.9 .-.^=-=.76; v = - ^ = .96 78.9 428.4 For ether, ^=36.9; ^ = 463. If p is the actual pressure in atmospheres of ether in the corresponding state to that of CORRESPONDING STATES. 107 the SO 2 , P = . 76X36. 9 =28.4. Sajobschewski found that sat- urated ether vapor had this pressure at 445.8 absolute. The reduced temperature is, The agreement is not, however, usually as close as this. If the experimental values of p, v, and are substituted in Equations 69 and the values of X, //, and v are in turn substi- tuted in Equation 70, a true equation is not obtained unless a variable factor is substituted for the number 8. This factor is usually different for the gas and vapor states for the same A and v (there are usually, of course, three values of /* for one value of A and v) , but the mean of these two factors is usually approximately 8. Moreover, for given values of A and v, the values of p are approximately the same for all liquids, particularly if they have similar constitutions, and /* is also approximately the same for their vapors. This is illustrated in Table XIV. PROBLEMS III. 1. 10 grams of air are contained in a steel cylinder of 2 litres capacity, (a) What is the pressure at 20? (b) To what volume must it be compressed to increase the pressure at this temperature to 1000 atmospheres? 2. A certain mass of hydrogen occupies i c.c. at 2000 atmospheres pressure. What would be its volume at one atmosphere? 3. Ten grams of air are heated from 20 to 100 under a constant pressure of 100 atmospheres. What is the proportional increase of volume ? 4. A steel vessel of one litre capacity contains air under a pressure of 200 atmospheres at 30. Calculate the pressure upon heating to 50. 5. Calculate the pressure for typical volumes on the 100 isother- mal for one gram of ether (a) by means of Van der Waals' equation ; the constants a and b of Table LVI and R' calculated by Equation 51. (6) by Van der Waals' reduced equation, using the values of the critical pressure, critical temperature and critical volume ( = re- ciprocal of critical density), given in Table LVI. 6. Ten grams of ammonia gas are contained in a litre reservoir. Calculate the pressure at 100 by Van der Waals' equation, taking a and b from Table LVI, and calculating R' by Equation 51. p Q , the reciprocal of v , may be calculated from the molecular weight and Equation 56. 'For further illustrations see Winkelmann, 1906, 3, pp. 936-944. io8 GASES, VAPORS AND LIQUIDS. 7. The dew point was 10 when the temperature was 22. What was (a) the pressure of aqueous vapor? (6) the relative humidity? (c) the amount of water vapor in one cubic metre of air? TABLE XIV.' Corresponding States under the Reduced Pressure, A = .08846. V H liquid H vapor Propyl acetate 7 <\4 2QQ4 2Q 7 Methyl acetate . .7 ZOA .4006 3O. 3 Methyl alcohol 7734 3949 34-2 Ethyl alcohol 7 704. 4.O4 7 32 I Propyl alcohol 7736 .4028 3I-I Acetic acid .7624 .4106 *5-5 Ethyl ether 737 1 .4044 28.2 Benzol 7282 4O C 3 28 2 Carbon tetrachloride .... 725 1 .4072 27.4 Stannic chloride 7357 .402 I 28.1 EXPERIMENT VIII. Critical State, Isometric and Isothermal Lines of Vapor. The vapor to be studied is contained in thick-walled tubes of about 3 mm. internal diameter, and 4 cm. long, with a capillary stem on one end, through which they are filled, and which is after- ward sealed. Each contains the same amount of ether or other substance 2 which should occupy about one-fifth of the tube. The tubes also contain different amounts of mercury to vary the volume occupied by liquid and vapor. The least volume should be about one and a half times the volume of liquid, and the greatest volume should be about four times the volume of the liquid. At least four such tubes should be used for any one liquid. The tubes are heated successively in an asbestos-lined metal box with mica sides (Fig. 47). The junction of a copper-constantin thermocouple (49) is secured against the tube by a wrapping of thin mica. The wires pass through a hole with asbestos insulation and are connected to a galvanometer through a proper resistance. 1 From Juptner, I, p. 49. 2 Ether, ethyl alcohol, benzol, and chloroform are suitable liquids. CRITICAL STATE. 109 The deflection of the galvanometer at disappearance and reappear- ance of the meniscus is carefully observed and also where the dis- appearance occurs, whether at top (all liquid), bottom (all vapor), or intermediate (critical point.) When near the required tem- perature, the heating or cooling should be very gradual. Estimate carefully the volume occupied by liquid and vapor in each tube, FIG. 47. which is, of course, the volume occupied by the homogeneous sub- stance above the observed temperature. Calibrate the galvan- ometer as described in ^49 and calculate for each tube the tem- perature corresponding to the mean of the galvanometer deflections at disappearance and reappearance of the meniscus. Before plotting, study carefully the isothermal diagrams of Fig- 45- 110 GASES, VAPORS AND LIQUIDS. On the volume axis, lay off the estimated volumes of the sub- stance in the different tubes and at each point erect a perpendicular (equal volume, or isometric line), and on the perpendicular note the observed average temperature corresponding to this volume, and whether the homogeneous substance was vapor or liquid. Mark on the pressure axis the critical pressure as given in Table LVI. Locate the point on the critical temperature isothermal corresponding to this pressure and the observed critical volume. Draw a curve through this point similar to the typical critical tem- perature isothermal of Fig. 45. This will be the approximate critical temperature isothermal. Draw a short horizontal line from each vertical line towards in- creasing volume, if a vertical for change to all liquid, and vice versa for vapor verticals. Raise or lower these short lines until they are in the order of the temperatures and until their junctions with the vertical lines lie on a smooth curve tangent to the critical tem- perature isothermal at the critical -volume and pressure (critical point). Draw this curve (curve LMN in Fig. 45) as a dotted line and prolong each horizontal line to meet it. Complete the steep portions (liquid) and the hyperbolic portions (vapor), and write against each isothermal its temperature. Since the exact pres- sures were not measured, the positions of the isothermals will be only approximate, but the form of the curves should be quite exact. 1 . Estimate the critical density. 2. What would be the influence upon the observed temperature of air in the tube? 3. Why is a thermocouple preferable to a mercury thermometer? Latent Heat of Liquids. 118. A change of state, for example, from vapor to liquid or vice versa, involves a change in the potential energy of the molecules and possibly also external work, and is, therefore, always accompanied by an absorption or emission of heat energy. This heat energy per gram of substance is called the latent heat. Although the latent heats of fusion and vaporization are accurately determined with great difficulty, approximate experimental methods are described in all laboratory manuals of physics. The latent heats of the more common liquids are given in Table LVI. A liquid continues to give off vapor from the surface, or 11 evaporate," as long as the pressure of the vapor above the liquid is less than the saturated vapor pressure, independent of the total atmospheric pressure above the liquid. After the pressure of the vapor reaches the saturated vapor pressure PRESSURE OF SATURATED WATER VAPOR. Ill for that temperature, the total quantity of vapor in the atmos- >here above the liquid remains constant, since for any vapor liven off from the surface an equal quantity is condensed. 119. Boiling. If heat is now applied to the liquid, the miperature will not rise if the pressure above the liquid imains constant, for the heat absorbed becomes the latent icat of the increase of vapor. If the total pressure above the liquid is equal to, or slightly less than the saturated vapor pressure, portions of the liquid below the surface can change to vapor, and this is called boiling. If, therefore, the pressure above a boiling liquid is observed, this pressure is numerically equal to the saturated vapor pressure for the temperature of the liquid. This kinetic method of determining saturated vapor pressure (in contrast to the statical method of Experi- ment VII) was invented by Regnault. EXPERIMENT IX. Pressure of Saturated Water Vapor by Regnault's Method. In Regnault's apparatus the total pressure above the surface of the liquid can be kept very constant. As the liquid is heated, the vapor is condensed in a Liebig condenser (see Fig. 48), and as the pressure of vapor distributed through several conducting vessels is the vapor pressure cor- responding to the vessel at lowest temperature, the pressure exerted by the vapor cannot exceed the maximum pressure corre- sponding to the tempera- ture of the tap-water and is therefore very small. As the temperature of the boiler changes, the temperature of the air in the boiler varies, but a large air reservoir, sur- rounded by water, is con- nected between the con- denser and the manometer and air-pump or aspirator, which makes the volume of the air in the boiler small FIG. 48. compared with the total volume of air in the system, and thus the increase of pressure due to the heating of the air in the boiler is also small. The boiler should be about two-thirds full of water; fill with water the small tube running down into the boiler (which tube is closed at the bottom), and insert in this tube, through a cork, an accurate 112 GASES, VAPORS AND LIQUIDS. thermometer. Draw out any water which may be in the air reservoir by means of a stopper in the bottom. Fill the surrounding vessel with water. Exhaust the air from the system to the highest vacuum obtainable, by means of a Geryk pump or aspirator. Close the cock through which connection is made to the aspirator or pump, and let the system stand a few minutes to see if there is any leakage. If not, start a gentle stream of water through the condenser, and place a Bunsen flame under the boiler. (Rubber stoppers will hold tighter if moistened before insertion.) Read the barometer (see 40, 41). When the temperature as registered by the thermometer in the boiler becomes very steady, we know that the water is boiling. Read the temperature and record at once the two extremities of the mercury column of the manometer. Let in a little air by slightly opening the cock near he air-pump or aspirator. At first increase the pressure by steps of about i 5 mm. Gradually increase the steps, and when near atmospheric pressure make the changes of pressure about 1 2 cm. The reason for the difference is that it is better to have the steps represent about equal changes of temperature, for instance, about 5. Calculate the corrected pressure from the barometer reading and the difference of level of the mercury columns. By 119 this pressure is equal to the saturated vapor pressure for this temperature. Tabulate your results and also plot them, making temperatures abscissae and pressures ordinates. QUESTIONS. 1. State precisely what you have observed in this experiment and what relation it bears to saturated vapor pressure. 2 . What condition determines whether a liquid will boil or evaporate at a given temperature? 3. What was the actual pressure of water vapor above the boiling liquid? (Table LVII.) 4. What determines (a) the lowest temperature, (b) the highest temperature for which this experiment is applicable? 1 20. Mean Vapor Density. Mathias' Rule. 1 This rule states that the mean of the densities of coexistant liquid and vapor states is a linear function 2 of the temperature. If p l = density of liquid, p v = density of vapor, Cl O+ c , .,'. ;"'". . (71) 1 Jour, de Phys., 1892, 3; 1893, IX - 2 One quantity is said to be a linear function of another when their relation can be expressed by an equation which involves only first powers and constant terms or factors. For example, y is a linear function of x if y = ax + b where a and b are constants. Such a relation would be represented by a straight line. Also, dy ~- = a = constant. doc MEAN VAPOR DENSITY. where c x and c 2 are constants. If we plot density against temperature, the density of the liquid will decrease if the temperature is raised, while that of the vapor must increase, until, at the critical temperature, the two densities become equal. The mean of the two densities must lie upon a straight line, inclined to the horizontal temperature axis. For this reason it is often known as the rule of the straight diameter (gerade Mittellinie) . The experiments of Batschinski 1 and others have shown that this mean line may be regarded as straight with little error in most cases. At the absolute zero we may reasonably suppose that the volume is a minimum, and this would require by Van der Waals' equation that v = b = (Equation 68) Although the absolute zero has never been attained, exter- polation from experimental results indicates that the volume Reduced Temperature FIG. 49. at the absolute zero is nearer one-fourth of the critical volume than one-third. Therefore, the density at absolute zero is between three and four times the critical density. For reduced temperatures below .7, the density of the vapor is negligible compared with that of the liquid. Therefore the 1 Zeit. phys. Chem., 41, p. 741. 114 GASES, VAPORS AND LIQUIDS. mean line which represents the average of the densities of vapor and liquid and which passes through the critical density at the critical temperature must, at the absolute zero, pass through a point for which the density is about twice the critical density. We can thus construct a diagram which will give an approximate representation for all substances, of the vari- ation in density of liquid and vapor as the temperature is changed. Such a diagram is shown in Fig. 49. 121. Since below the reduced temperature .7 the density of the vapor is negligible compared with that of the liquid, below this temperature the density of the liquid p t is repre- sented by a straight line and is therefore a linear function of the temperature. The change in potential energy during change of state is evidently dependent upon a/v 2 the term in Van der Waals' equation which expresses the equivalent pressure contributed by the attraction between the molecules. The internal work or potential energy accompanying evapor- ation is therefore v v I' = I -dv = a( \ =ap J v* \v t v v '/ v i if the temperature is so far from the critical temperature that the density of the vapor is negligible compared with that of the liquid. Under these circumstances, p t is, as we have just seen, a lineal function of the temperature, and therefore the internal work accompanying evaporation is also approxi- mately a linear function of the temperature. SURFACE TENSION. 122. This attraction between the molecules also manifests itself as surface forces and surface energy. Molecules near the surface are subject to an unbalanced internal force. The dots a, b, and c of Fig. 50 represent molecules and the circles represent the sphere within which lie all the other molecules which exert an appreciable attraction upon a, b, or c. The SURFACE TENSION. 115 shaded portion represents the molecules which exert an un- balanced attraction. This resultant inward force will evidently tend to make the surface as small as possible and an increase of surface requires work and increases the energy of the liquid. The energy per unit area is called the surface tension. Since work or energy is equal to force times distance, the surface tension is also equal to the tangential force across any line in the surface of one centimeter length. FIG. 50. 123. Eotvos' Equation. Since surface tension depends on the same physical quantities as evaporation, it will show the same variation with the temperature. Therefore the surface tension is a linear function (120, note) of the temperature or dT dt (73) when T is the surface tension and c' is a constant. The volume of a sphere containing one gram molecule of liquid is M where M is the molecular weight and p is the density. The area of the sphere which contains one gram molecule is therefore (73') Il6 GASES, VAPORS AND LIQUIDS. c should have the same value in every liquid, since there are the same number of molecules in a mass equal to the molecular weight. This equation was discovered by Eotvos. 1 While c is not absolutely constant, it is quite nearly so, and has the approximate value 2.1. By integrating 73 'between t l and t 2 (74) T I and T 2 and p t and p 2 are the values of the surface tension and density, respectively, at the two temperatures t-, and t a . This is one of the few methods available for determining the molecular weight of a liquid. 2 124. Measurement of Surface Tension. The simplest method of measuring the surface tension of a liquid is to measure the height to which a liquid will rise in a capillary tube. We shall suppose that the liquid wets the tube and that the liquid has been raised in the tube so that there is a film of liquid over the interior. Let r be the radius of the tube and h the height to which the liquid rises. 3 If T is the surface tension, the force upward due to the surface tension is 27irT and the downward force is the weight of the column of liquid, or nr 2 hpg where g is the acceleration of gravity. At equilibrium the two must be equal (7S) 1 Wied. Ann., 27, p. 448. 2 For the application of Eotvos' equation to solutions, see Zemplen, Ann. d. Phys., 1906, 20, p. 783; 1907, 22, p. 391; and for the application to fused salts, see Lorenz-Kaufler, Ber., 1908, 41, p. 3727. 3 If the liquid wets the tube, the surface in the tube is concave and the height h is the distance from the general outside level to the bottom of the meniscus, plus one-third the radius of the tube. For the volume of liquid above the meniscus is TI r $ r 7ir 2 r ?> nrz = = it r 2 3 3 If the liquid does not wet the tube approximately must be subtracted from the height of the meniscus. SURFACE TENSION. 117 TABLE XV. Surface Tension T (15), Temperature Coefficient of Surface Tension c', and Angle of Contact a. T c' a Ethyl ether iQ . I I 1 6 Ethyl alcohol 2 43> P- 2 59; Haber, " Thermodynamics of Gas Reactions." 2 Maxwell, Heat, p. 152. 3 Ames, Rapports Paris Congres, 1900, i, p. 178. I2 3 124 THERMODYNAMICS. 130. Specific Heat. The specific heat of a body, s, is the value of Q for one gram and for one degree rise of temperature. Therefore, if the mass of a body is m, the amount of heat required to change its temperature from / x to t 2 is Q = ws (/,-/,) (79) The specific heats of various solids and liquids are given in Tables XLIII, XLIV, and XLV. The molecular heat of a body, 5, is the heat required to give a mass numerically equal to the molecular weight, M, a rise of temperature of one degree, or S =Ms. Similarly, if A is the atomic weight of an element, its atomic heat is As. In 1819 Dulong and Petit 1 announced the law that all the solid elements have the same atomic heat. More careful later measurements have shown that the atomic heats are not identical, but that, with a few exceptions, the values at or- dinary temperatures lie between 5.8 and 6.9. The mean value is about 6.4. The principal exceptions are boron, carbon, and silicon, the atomic heats of which are low. At high temperatures these three elements have atomic heats within the above limits. 131. The Specific Heats of Gases. The thermal expansion of solids and liquids is so slight that W in Equation 78 is usually negligible. With gases, however, L is usually negligible since it is the work done in expanding the gas against the attraction between the molecules represented by the term a/v 2 of Van der Waals' equation (Eq. 63), but the coefficient of ex- pansion is large, and W may therefore be large. Since the external work W will depend on the conditions under which the gas changes its temperature, the specific heat is indefinite unless these conditions are specified. If the volume of the gas is kept constant, the external work, W, is zero. Denoting this specific heat by s v JQ=Jms v (t a -tJ = -I (80) 1 Ann. Chem. Phys., 1819, x, p. 395. SPECIFIC HEATS. 125 If the same amount of gas is heated through the same range of temperature, and is allowed to expand under constant pressure, p, from a volume Vj. to a volume v 2 JQ = Jms p (t a -t I )=W-I (81) Where s p is the specific heat under constant pressure. 132. Difference of Specific Heats. By Equations 62 and 57 Subtracting Equation 80 from Equation 81 W = Jm(t 2 -t l )(s p -s v }. Since (0 a -0.) =(* a -/i) S P -S v =^ = - 3 * Xl '=i. 9 S$ (107) (82) J 4> I5 7 X IO Or the difference between the molecular heat of any gas at constant pressure and that at constant volume is the molec- ular gas constant in calories or approximately 2 . 133. Ratio of Specific Heats. Dividing Equation 81 by Equation 80 we have s _ I+W H+W v = ^rr TT r (83) for L (Equation 78) is so small for gases, under ordinary conditions, that we will neglect it. H, which represents the increase in the kinetic energy of the molecules, may be resolved into two parts: H It which is equal. to the increase in the kinetic energy of translation of the molecules = 1/2 m ^_^) (104), and H 2) which represents the gain in other forms of kinetic energy, for example, rotation, vibration of the constituent atoms, etc. Since (Eq. 41), pv = 126 THERMODYNAMICS. If the gas is monatomic and if there is no increase in the speed of rotation of the molecules, H 2 =o and ^ = 1.67. The experimental values of f for the monatomic gases, mercury vapor, argon, and helium agree well with this number (see Table XVII). The more complex the gas, the greater is the opportunity for other forms of kinetic energy than the trans- lational, and, therefore, as the number of atoms increases, we should expect that H 2 would increase and y would therefore decrease. Table XVII shows clearly that such is the case. TABLE XVII. Specific Heats of Gases. 1 Temp. Sp Sp r= ^ Argon Helium Mercury 20 20 27 rO_~ -6 .1205 !- 2 5 0246 .66 .64 66 Hydrogen Nitrogen '/ 3.. 3 3 _ 0-200 3O-2OO 3.406 24.4. 396 4.0 s Oxygen Air 0-200 0-200 .217 .2^7 5 .40 .405 Chlorine Iodine Bromine Water . i9-343 2oo-377 85-228 iio-2 = 6.5 + .o5i ( + 273) The mean molecular specific heat between 273 and 273+* is equal to the above figures if the coefficient is halved. For example, the mean molecular specific heat of water vapor at constant pressure between 273 and 273+^ is 6.5 + . 0029 (2 + 273) 135. Adiabatic Changes. If we combine Equations 78, 80, and 62 we have JQ = Jms v (t 2 -tj+p (v 2 - v,) (85) In 97 we have considered the relation between the pressure and volume when the temperature is constant. We shall now consider the relations between all three quantities when no heat, Q, either enters or leaves the body. Such changes are called adiabatic, The simplest method is to consider first very small changes and later find the relation for finite changes by integration. .'. O=Jms v dt + pdv (86) We shall first find the relation between p and v and therefore we shall eliminate dt. Differentiating Equation 57, we have R-jfdB (86') . ^^ (pdv+vdp)+pdv = o K. dv + JMs v vdp = 1 LeChatelier, Zeit. phys. Chem., 1887, i, p. 456. 128 THERMODYNAMICS. But JMs v + R=JMs p (Equation 82) Hence, dividing by JM sppdv + s v vdp = o vdp _ _sp _ 136. Velocity of Sound. This equation is the basis of a method of determining y. The velocity of elastic waves in any medium is I <> where p is the density and E is the coefficient of elasticity or the ratio of stress to strain. If the stress dp is applied to a gas, the strain, or change in volume per unit volume, is Equation 87 shows that E is equal to yp if no heat leaves or enters the gas. Such is the case with the rapid vibrations of sound waves. Their velocity is therefore given by the formula (880 Since u, p, and p may easily be measured with high accuracy, this indirect method gives accurate values of y. Since p/p is proportional to 6 (Equation 53), the velocity at any tem- perature t is related to u , the velocity at o by the equation r ; ' (88 " } EXPERIMENT XII. Velocity of Sound by Kundt's Method. Ratio of Specific Heats. A glass tube, A G, about a metre long and about 3 cm. internal diameter is closed at one end by a tight-fitting piston, C, and at the other end by a cork through which passes a glass tube having at one end a loosely-fitting cardboard disk, D (Fig. 53). The glass tube should be about a metre long. A little dry lycopodium powder is sprinkled in the tube, the stopper at G is loosened, and a current EQUATIONS OF ADIABATIC. 1 29 of air, dried by passage through several drying tubes, is slowly forced through the hollow rod of the piston, C. The stopper at G is then replaced and the glass tube, F, is held at the center and stroked longitudinally with a damp cloth. The piston, C, is adjusted until the powder collects in the sharpest attainable ridges. These ridges will appear where the pressure changes are least; that is, at the loops. Measure carefully the distance between two extreme ridges and divide by the number of segments into which the tube is divided. This distance (between two loops) is a half-wave length, of the E ' 1 1 | C..^ F 1 1 | c | _n A C D G FIG. 53. waves in the tube. Disturb the powder and make a new adjust- ment of the piston, C, and a new measurement of the half -wave length. Make a third repetition of the adjustments and readings. Fill the tube with another dried gas, for example, carbon dioxide, illuminating gas, hydrogen, oxygen, or hydrogen sulphide, and determine the half -wave length. If n is the constant pitch of the note emitted by the glass tube and >i is the wave length in the gas (88'") -M-2 2 Since the velocity changes at the same rate with change of tem- perature in all gases (Eq. 88"), the velocity of sound or compressional waves at zero degrees in any other gas than air can be calculated from the ratio of the wave lengths at a common temperature, and the velocity in air at zero degrees (33,200 cm. per second). From the velocity of sound at zero degrees in the gases other than air, calculate the ratio of specific heats, f. Table LI I gives the densities of the more common gases and vapors at zero degrees and a pressure of 76 cm. of mercury = 1013200 dynes per square centi- meter. QUESTIONS. 1. Calculate (a) the velocity of compressional waves in glass, (b) the elasticity E. (Notice that each end of the glass rod must be a loop, and the center a node. The density of glass can be obtained from Table LV). 2. Why must the glass rod be set in longitudinal vibration? 3. Why does the powder collect at the loops? 137. Equations of Adiabatic. We shall show that the equa- tion for an adiabatic change is $=) r (89) I3O THERMODYNAMICS. Let us integrate Equation 87, between the limits pi and p 2 , v lt and v 2 or . _i /Mr 'Pi \V a J If we draw adiabatic curves in a pressure volume diagram, they will be steeper than the isothermal curves for which (38) h. = ^L for Y is always greater than unity. We shall next show that the relation between the pressure and the absolute temperature in an adiabatic change is 8 ^ /M 0, \PJ r (90) Substitute for pdv in Equation 86 its value from Equation 86'. .'. mMspdO = MR-j-j- dp (Equations 82 and 57) dd_ _ R dp_ _ sp-Sy dp_ _ y-i dp_ ~ Msp p ~ sp P ~ T P Integrating between the limits O lt and 2 , pi, and p? 2 f I p2 la ^ "~r ln ?r 2 I p2\ * : TZ-(K) Also, by Equation 89 0, \v LIQUEFACTION OF GASES. 131 Liquefaction of Gases. 138. Method of Claude. We saw in 115 that, in order to liquefy a gas, the temperature must be reduced below the critical temperature and a suitable pressure must be applied. The most successful apparatus for liquefying gases is that of Claude 1 where the gas is compressed and then cooled by adiabatic expansion. The essential features of the apparatus Liq. Air. 40 at.,- 140 FIG. 54 are represented in Fig. 54. The air, compressed to 40 atmos- pheres pressure by a compressor (not shown) , passes through the tube (actually a worm) A, and divides at B. A portion enters the cylinder through a suitable valve, and, expanding, forces out the piston, thereby doing work and cooling itself (Equation 78). This very cold air circulates through the liquefier L where it liquefies the portion of the compressed air which entered at B, and then, emerging along the outside 1 Comptes Renclus, 1900, II, p. 500; 1902, I, p. 1568; 1905, II, p. 762; p. 823; Journal de Physique, 1906, p. 5. 132 THERMODYNAMICS. of A ("regenerator"), cools the entering air and returns to the compressor. Its pressure after leaving D is not far from atmospheric and its temperature is below 140, but not as low as 190 at which temperature air liquefies under atmospheric pressure. The highly compressed air in the inner tubes of the liquefier is, of course, liquefied at a higher temperature (about 140). The motor D restores about one-fourth of the power consumed by the compressors. Nearly one litre of liquid air is obtained per horse-power hour. 139. Method of Linde. Previous to the development of the adiabatic method of liquefying gases, the most efficient method was that of Linde. In this method the gas was allowed to expand through a small opening from a pressure of about 200 atmospheres to about 20. The work done against the attraction between the molecules (a/v 2 term in Van der Waals' equation) cools the gas until, by a regenerative process similar to that of A and M of Fig. 54, the critical temperature is reached and the gas is liquefied. 140. Separation of Oxygen. The technical importance of liquid air arises from the possibility of separating the oxygen and nitrogen by fractional distillation. Under atmospheric pressure, nitrogen boils at 194 and oxygen at 180.5. Therefore, the vapor above liquid air is excessively rich in nitrogen while the remaining liquid is very rich in oxygen. The two gases may be almost completely separated by the apparatus sketched in Fig. 55. (Apparatus of Linde and Claude.) The compressed and cooled air enters at A and as it rises to B much of the oxygen and some of the nitrogen is condensed by the liquid oxygen outside the tubes, and falls to C. The remainder, which is almost pure nitrogen, is further condensed as it comes down through the tubes surrounded by liquid oxygen, and collects in D. E is a tower about three metres high, filled with glass marbles or similar bodies. The pressure in C forces the impure liquid oxygen up through the tube, F, which discharges into the middle of the column. As the liquid trickles down, the nitrogen gradually evaporates and rises, LIQUEFACTION OF HELIUM. 133 and the purified oxygen finally collects in H, whence it is drawn off by the tube, K. The liquefied impure nitrogen discharges at the top of the column. Since the vapors arising from the oxygen in H and E are at a higher temperature, practi- cally all the nitrogen will evap- orate and escape at N. 141. Liquefaction of Helium. On July 10, 1908, Kamerlingh- Onnes liquefied helium which had hitherto resisted liquefac- tion. He found the critical temperature about 5 degrees absolute, the boiling point about 4.3 absolute and the critical pressure between 2 and 3 at- mospheres. The density at the boiling point was .15. By boil- ing liquefied helium under re- duced pressure, he attained the extremely low temperature of 3 degrees absolute. 1 142. Clement and Desormes' Method of Measuring 7- (Gay Lussac's Modification) . 2 The gas is compressed into a vessel until the pressure has a value which we will designate by p t . The vessel is then opened for an instant, and the gas rushes out until the pressure inside falls to the atmospheric pressure, p . This expansion may be made so sudden that it is practi- cally adiabatic and the temperature of the gas will therefore fall. After the vessel has been closed for a few minutes, the 98% 0, Ar 1 Comm. Phys. Lab., Leyden, No. 108. 2 Jour, de Phys., 1819, Ixxxix, p. 333. 134 THERMODYNAMICS. gas will have warmed to the room temperature and the pres- sure, p 2 , will be above that of the atmosphere. Consider one gram of the gas. During the adiabatic expansion, its volume changed from v l to v 2 , according to Equation 89 or Since the initial and final temperatures are the same, and since the volume remains v 2 while the gas is warming, and the pressure is rising from p to p 2 , P 'r = (92) The successive operations will be evident from a study of Fig. 56- FIG. 56. Lummer and Pringsheim x improved the method by observ- ing, with a bolometer strip .0006 mm. thick, the fall in tem- 1 Wied. Ann., 1898, Ixiv, p. 555. RATIO OF SPECIFIC HEATS. 135 perature during the adiabatic expansion, and, knowing p L and p , they calculated f by Equation 90. PROBLEMS V. 1. A copper stirrer weighing 30 gr., turning in 200 c.c. of dilute solution requires 20 watts (5). Assuming that practically all the power is absorbed by the viscous resistance between the solution and the stirrer, calculate (a) the total amount of heat produced in one minute; (b) the rise of temperature, if there are no heat losses. 2. The specific heat of indium is .0569. What is the approximate atomic weight ? 3. How much heat is required to warm a body of air which occupies one cubic meter at o and 76 cm. from o to 100, (a) the volume being constant? (b) the pressure being constant? (c) Find the corresponding amounts of heat for hydrogen. 4. Calculate the mechanical equivalent of heat from the two specific heats of oxygen and the gas constant (Equation 82). 5. How much heat is required to warm, from o to 1000, 5 grams of (a) oxygen at constant volume? (b) hydrogen at constant pressure? (Table XVIII.) 6. How much heat is required to warm, from 950 to 1000, 100 grams of (a) oxygen at constant volume ; (b) hydrogen at constant pressure? (Table XVIII.) 7. The velocity of sound in ammonia gas at o is 415 meters per second. Calculate the ratio of specific heats (find the density by Equation -56). 8. A mass of nitrogen which occupies one litre at 100 and a pressure of 200 cm. of mercury, expands adiabatically to one and a quarter litres. Calculate (a) final pressure; (b) final temperature. EXPERIMENT XIII. Measurement of the Ratio of Specific Heats by Adiabatic Expansion. A large carboy is mounted in a wooden case and may be sur- rounded with cotton batting. The neck is closed with a rubber stopper through which passes a T-tube connected on one side with a compression pump (e.g. a bicycle pump), and on the other side with a manometer containing castor oil. 1 A large glass tube, which may be closed by a rubber stopper, also passes through this large stopper. A little sulphuric acid in the bottom of the carboy keeps the air dry. A very fine copper wire and a very fine constantin wire pass tightly through minute holes in the stopper and meet at the center of the carboy, in a minute drop of solder. The air in the carboy is compressed until the difference in pressure is about 40 cm. of oil ( fi p ). The tube connecting with the pump is closed, and, after waiting about 1 5 minutes to allow the air inside to regain its initial temperature (as shown by the pressure becoming constant), the ends of the oil column are carefully read. The carboy is now carefully surrounded with cotton batting, which may have been removed to facilitate cooling. The air inside is momentarily 1 The density of castor oil is about .97, but it should properly be determined (36). i 3 6 THERMODYNAMICS . allowed to return to atmospheric pressure by removing, for about one second, the rubber stopper from the glass tube. After waiting until the air inside has assumed the room temperature (shown by the pressure becoming constant), the final pressure p 2 is determined. The cotton wool had better be removed during this stage. Connect the wires to a calibrated galvanometer (49), apply the initial compression p lt and observe the reading of the galvanometer when it has become steady. Remove the stopper as before (for not over one second), replace the stopper, and observe the galvanometer reading. The proper reading to record is the fairly steady deflection which is attained immediately after the stopper is removed. There are liable to be rapid fluctuations which should be disregarded, and FIG. 57. of course the temperature does not long remain steady, owing to heating or cooling from the outside. Record as before the final pressure p 2 . Repeat several times, starting with the same initial pressure p I . Record the temperature of the room, t, and p , the height of the barometer (40, 41). Calculate y, the ratio of specific heat by Equation 92. Calculate the change of temperature from the galvanometer deflections and the constants ( 49). Compare the result with #i 6 , where 0, =273 + t and is calculated by Equation 90. Unless exceedingly fine wire is employed, the heat capacity of the wire is relatively so great that the thermocouple will not show the full change of temperature. THE SECOND LAW OF THERMODYNAMICS. 137 Draw a curve with volumes as abscissae, and pressures as ordinates, which will represent the changes in this experiment. (Let specific volumes, i.e., volumes of one gram, be abscissae. Calculate from Table LII and Equation 53 the specific volumes cor- responding to the room temperature and p , pi, and p 2 , and draw the corresponding isothermal. Draw the horizontal line corresponding to p . Draw a vertical through the point corresponding to p 2 on the above isothermal. The intersection of these two straight lines will evidently be p , v 2 . QUESTIONS. 1. Do you see any objection to an initial exhaustion of the gas in place of the compression? 2. What are the advantages and disadvantages of a large opening? Short time of opening? Castor oil manometer? 3. How would an aneroid manometer be preferable in this experi- ment to a liquid manometer? The Second Law of Thermodynamics. 143. The second law of thermodynamics is a statement of the conditions which govern the transformation of heat energy into mechanical energy. The first law states that, if such a transformation takes place, the two are equivalent, but does not state whether or not such a transformation is possible. The following is Clausius' 1 statement of the second law. "It is impossible for a self-acting engine, unaided by any external energy, to convey heat from one body to another at a higher temperature." Kelvin's statement of the law is, "It is impossible, by means of inanimate material energy, to derive mechanical effect from any portion of matter by cooling it below the tem- perature of the surrounding objects." 1 This law will be best understood by considering a concrete example of the transformation of heat energy into mechanical energy or vice versa. In order to measure the net energy changes, the working substance should be brought back to its original condition, or, as it is termed, the working substance must be carried through a cycle. 144. Carnot's Cycle. The simplest case to consider is Car not 's cycle. 1 1 "The Second Law of Thermodynamics," Magie. 138 THERMODYNAMICS. A given mass of gas expands in succession isothermally and adiabatically and is then isothermally and adiabatically compressed to its original state. Suppose we have in a cylinder with a movable piston a mass, m, of a permanent gas, such as oxygen, at a pressure p l , FIG. 58. and a volume v lt represented by the point A in the diagram, Fig. 58. Allow the gas to expand in a thermostat to a volume v 2 while 0! calories of heat are supplied to maintain the temperature constant at its initial value 0^. By the first law of thermodynamics, the work done by the gas is v 2 V 2 S* i=7Qi= I pdv = R'mO l 1 J (93) Now surround the cylinder by a non-conducting envelope and allow it to expand adiabatically to the volume v 3t at the temperature (absolute) O a . The work done, represented by 1 Sur la puissance motrice du feu. Paris, 1844. Reprinted in "The Second Law of Thermodynamics," Magie. 139 the area below B C, is equal to the loss of energy of the gas, since there is no transfer of heat. The non-conducting envelope is now removed and the cylin- der is placed in a thermostat at this temperature 2 . The gas is compressed until the volume is v 4 . In order to keep the temperature constant, the thermostat must have absorbed an amount of heat Q 2 , which is equivalent to the work done in compressing the gas, or J^ pdv = R'mln^ (94) VT, (The minus signs signify that the heat is emitted by, and the work is done upon the working substance.) The volume v 4 at which the compression was stopped was so chosen that if at this point (D) the cylinder is removed from the thermostat and is surrounded by a non-conducting envelope, a further adiabatic compression restores the gas to its original state, where the pressure, volume, and temperature were, respectively, p ly v lt and I . Dividing Equation 93 by Equation 94, and remembering that a negative logarithm is the logarithm of the reciprocal, But by Equation 91 ;<-.* (95) which may also be written, by the laws of proportion, t~T = Q*=&-^-.w. (96) 140 THERMODYNAMICS. For the net work done in the cycle, W =W l W 2 , is equal to J times the net heat absorbed (Q t Q 2 ) W^JQ-'- (97) 145. Isothermal Cycle. If 6 l =6 2 , W=o, or the total work performed in an isothermal cycle is zero. 146. Reverse Cycle. If we performed the operation in the reverse order A D C B A , we would evidently obtain the same relations between Q 2 , which would now be the heat absorbed by the gas during the expansion D C and Q x , which would be the heat emitted during the compression B A. In this case W would be the net work done upon the working substance. Notice that, in accord with the above statements of the second law, work is required to transfer heat from a low tem- perature to a high temperature (above reverse process) and that when heat is absorbed at a low temperature no work can be obtained from this heat, but on the contrary, work must be expended, if the working substance is to be returned to the initial state. 147. Reversible Processes. Before discussing Equations 95-97, we shall show that they are independent of the nature of the working substance or operations, provided all the steps are reversible. A process is reversible if at each instant the system is in equilibrium, so that a very small change in the conditions will change the direction of the process. For example, if the expansion A B (Fig. 58) is reversible, a very small increase in the external pressure will cause the gas to compress and thereby emit heat instead of absorbing heat. Similarly, a slight fall in the temperature of the thermostat would change an absorption of heat along A B to an emission with an accompanying reversal from expansion to con- traction. If Equations 95 and 97 do not hold for all working substances and reversible processes, we will choose a system or "engine" which absorbs the same amount of heat, Q x , at temperature I as the engine which we have just considered, but gives EFFICIENCY. 141 up a less amount of heat, Q 2 ', at temperature 2 . By the first law of thermodynamics, it must do a greater amount of work =/ (Qi QaO- Suppose, for example, that Q a ' = .9 Q 2 . Allow this engine to make ten cycles between O l and 2 . ioQi units of heat will be absorbed at temperature 6 T , ioQ 2 ' = 902 will be emitted at temperature 6 2 , and an amount of work/ (loQj 90 2 ) will be gained. Now run the original gas engine through ten cycles in the reverse direction. It will absorb ioQ 2 units of heat at the low temperature, emit loQj units at the high temperature and will require for the operation 10 J (Qi~ 82) units of work. The net result will therefore be a gain ofJQ 2 units of work, the equivalent of which has come from the cold body. This would be contrary to the second law of thermodynamics, and therefore the second type of engine does not exist. By a similar consideration of other imaginary engines we can show that Equations 95-97 apply to every reversible process by which heat energy is transformed into other forms of energy. 148. Efficiency. According to Equation 97, the work which is obtainable from a quantity of heat Q, under the rngst perfect conditions, is the fraction 9, of the energy of the heat. This fraction is called the efficiency of the engine. If a steam engine receives steam at a tempera- ture of 140 and exhausts into the air at a temperature of 105, the theoretical efficiency is .085. If high-pressure steam at 250 is used and the exhaust is into a condenser at tempera- ture 4d, the efficiency is raised to .40. 149. Kelvin's Absolute Scale of Temperature. Kelvin's absolute scale of temperature is based upon the converse of Equation 97. The temperature of a body is measured by the efficiency of a reversible engine working between this temperature and a standard temperature. The temperature interval between ice- water and steam at 76 cm. pressure is 142 THERMODYNAMICS. taken as 100. Equation 97 and the preceding derivation shows that this scale (which is called absolute because, as we have seen, the efficiency is independent of the working sub- stance) coincides with the absolute gas thermometer scale of a gas which obeys Boyle's and Gay Lussac's laws. No gas completely fulfills these conditions, but the deviations can be obtained experimentally and thus a table of corrections can be made by which any gas thermometer can be reduced to Kelvin's scale. The temperature of ice and water is 273.13 absolute. 1 150. Entropy. When a body receives a quantity of heat Q at the absolute temperature it is said to gain an amount of entropy numerically equal to the quotient of the two numbers. If we designate the gain in entropy by T? 9 f- (98) The actual amount of entropy in a body is as difficult to define (and relatively as unimportant) as the actual quantity of energy. We are only interested in the changes in these quantities. Equation 95 states that a reversible cycle produces no change in the entropy of the system composed of the working substance and the thermostats. 151. Irreversible Cycles. The reversible cycles thus far considered are unrealizable in practice. The pressure of the working substance must be greater than the external pressure in order to overcome inevitable friction, and therefore the work obtained is less than is represented by the area A B C D of Fig. 58. The temperature of the thermostat must be slightly above # r in order that the heat may flow into the gas, and for the same reason the temperature of the thermostat which receives the heat Q 2 must be somewhat below 2 . Moreover, some of the heat transferred will invariably escape to other bodies. 1 Buckingham has published an excellent summary of the deviations, and of the correction at different temperatures, in Bull. Bureau of Standards, 1907, P- 2 37- IRREVERSIBLE CYCLES. . ? or (99) (990 Expressed in words, the entropy of any irreversible system tends to increase. Since all actual systems are irreversible, we have the general laws, "The entropy of the universe tends to increase," "The energy of the universe is constant" (Clausius). If we are more directly interested in the heat energy than in the mechanical energy, a temperature-entropy diagram is often more convenient than a pressure-volume diagram. Fig. 59 gives the temperature-entropy diagram 9 FIG. 59. of the Carnot cycle of Fig. 58. Since the initial value of T) is unimportant, it is taken as zero. The ratio of the numeri- cal values of the areas, A B C D, in the two figures should equal the mechanical equivalent, for The actual cycles of heat engines are not likely to be made up of isothermal and adiabatic steps as is Carnot's cycle, but 144 THERMODYNAMICS. any cycle may be resolved into infinitesimal isothermal and adiabatic cycles, as is illustrated in Fig. 60 for a portion of a circular cycle. The long portions are common to two cycles and neutralize each other. The short portions may be made to differ infmitesimally from the original curve. FIG. 60. 152. Free Energy Equation. If the cycle itself is very small we may write Equation 97 as (100) or, for infinitesimal changes, we may use the notation of the differential calculus or = O-- = W-I (Eq. 78) (100') (101) 153. Total, Free and Latent Energy. Helmholtz called W, which is the reversible and therefore the maximum work, the decrease in free energy, and he gave the name of latent energy to JQ = WI, which is the excess of the mechanical APPLICATIONS OF THE SECOND LAW. 145 energy or free energy produced over the decrease in total internal energy I. We will consider a few examples. When a reaction occurs at constant volume, W, the work or change in free energy, is zero, and the decrease / of the total internal energy is measured by the latent energy, JQ, which is the heat emitted. Similarly, during a change of state, for example, the freezing of water, W may be negligible compared with the decrease of internal energy / or its equivalent JQ, the latent heat energy. In all such cases dWjdd must be large. When a gas expands isothermally, there is no change in the total internal energy / and the change in latent energy is equal to the change in free energy, or . (102) Finally, in certain cases, the free energy W is approximately equal to the decrease in total energy /. A stretched spring will do an amount of work approximately equal to the loss in internal energy. The Daniell cell ( 339) delivers an amount of electrical energy almost exactly equal to the decrease of chemical energy. +'" The reader is recommended to read the recent papers of Nernst in which he has attempted to find the relation between the change in free energy (Equilibrium conditions, 254) and the latent energy (heat absorbed). 1 It is impossible to do more than state that his mathematical and experimental investi- gations have resulted in a general formula which he has applied to many interesting problems, such as equilibria at high temperatures. Applications of the Second Law. 154. Effect of Pressure upon the Freezing Point of Water. Imagine a gram of water carried through the following cycle. It is allowed to freeze at o and 76 cm. pressure. The air is now removed so that the only pressure upon the ice is its own 1 These papers are summarized in his "Thermodynamics and Chemistry." 146 THERMODYNAMICS. vapor pressure of .46 cm. (Table LVII), and at the same time it is heated dt to the melting point. It is then melted at this constant temperature. Finally, the atmospheric pressure is re- stored and the temperature is lowered to zero, thus completing the cycle and bringing the water back to its initial state. The cycle is illustrated in Fig. 61. Notice that the isothermals are .46- FIG. 61. in the opposite order to what they are in the case of a gas, i.e., the higher the temperature, the lower the isothermal. The difference in the volumes of one gram of water and one gram of ice is .0907 c.c. ^ = 75.54 Xi3-6 XgSo = 9.52 X io 6 . Therefore 1^ = 9.52 X. 0907 Xio 6 . q, 1 the heat absorbed, is the latent heat of fusion, or 80 calories. Therefore, substitut- ing in Equation 100 AM Aft . 0907X9.5 2 Xio 6 = 4.187 Xio7X8o X J# = 0.007 At this temperature, therefore, ice and water are in equilibrium under the pressure of their common vapor. 155. Vaporization and Sublimation. Clapeyron's Equa- tion. W = p(v v -v w ) q represents the heat per gram ; Q, the heat per gram molecule. CLAUSIUS' EQUATION, TROUTON'S RULE. 147 where v v is the volume of the vapor and v w is that of the liquid. Hence (Equation loi) 1 Q = -j(v v -v w )^ (103) or, in the notation of the calculus Q = j-( v v v w)~Jfi (Clapeyron's equation) (104) This equation gives the relation between the latent heat of vaporization, Q (or _ c irL__ ___/ 885 IOO Water Isobutyl Alcohol 316 O Water 100 Isobutyl Alcohol FIG. 63. pressure, a mixture of two insoluble liquids boils at a tempera- ture be.low the boiling point of either of its components. 162. Partially Miscible Liquids. If aniline is gradually added to water at 22, solution takes place until the concen- tration (by volume) is 3.48%. Further addition of aniline forms a separate layer which dissolves sufficient water from the original layer to form a saturated solution of water (5.22%); The continued addition of aniline simply increases the amount of this second layer, thereby reducing the first layer until it disappears when the volume of water is but 5.22% of that SOLUTIONS. of the aniline. If more aniline is added, an unsaturated solution of water in aniline is formed. The vapors are only slightly soluble in the liquids and consequently the vapor pressure of two semi-miscible liquids is usually greater and the boiling point lower than that of either component. Since the concentration of neither layer changes while both are present, the vapor pressure remains constant. The heavy line of Fig. 63 represents the form of an isothermal vapor-pressure curve for two semi-miscible liquids (water and isobutyl alcohol) . The dotted line represents the typical boiling-point curve. TABLE XX. Solubility of Semi-miscible Liquids (22). * Liquid Volume of Liquid in 100 Volumes of Water Volume of Water in 100 Volumes of Liquid Chloroform Carbon bisulphide .... Ether 42 8.1? 15 .96 2 Q3 Benzol 08 22 Amyl alcohol 3 28 2 21 Aniline cv- 50 3 4.8 522 < Isobutyl alcohol II. 6. 163. Liquids Miscible in all Proportions. We shall see later that the partial pressure of a solvent is less in a solution than in the pure state. The vapor pressure of a solution of liquid (B) in liquid (A) is p A -f+p B and may be greater or less than p A . If the vapor of (B) is quite insoluble in (A) , p B more than compensates for the lowering /. Water and propyl alcohol are an example of a mixture where both vapors are quite insoluble. The heavy line of Fig. 64 illustrates the general form of iso- thermal vapor pressure curves and the dotted line the boiling- point curve for a particular pressure. A solution with- the concentration represented by the point (P) ( e -g-> 80% propyl alcohol) has a maximum vapor pressure and consequently a minimum boiling point. Konowalow 2 1 Walker, p. 53 (except isobutyl alcohol). 2 Wied. Ann., 1881, xiv, p. 48. LIQUIDS MISCIBLE IN ALL PROPORTIONS. has shown that the vapor of a mixture with a minimum or maximum boiling point has the same composition as that of the liquid. At a lower concentration of alcohol the vapor has relatively more alcohol than the liquid, since propyl alcohol vapor is quite insoluble in water. If the amount of alcohol exceeds 80% the vapor contains more of the relatively in- soluble water vapor. Therefore, whatever the composition, the mixed vapor or distillate" approximates to the composition of minimum 100 Water* Propyl Alcohol 80% o Water 100 Propyl Alcohol FIG. 64. boiling point, while the residue progressively changes to the pure water or alcohol, according as the original concentra- tion is below or above 80% of propyl alcohol. Noyes and Warfel J have shown that ethyl alcohol has a minimum boiling point at 96. 164. If each vapor is very soluble in the other liquid, p B is small and the addition of either component reduces the vapor pressure of the other. Formic acid and water is an example of such a mixture. The vapor pressure and boiling point curves are shown in Fig. 65. A 73% solution has a minimum vapor pressure and a maximum boiling point, and therefore by Konowalow's theorem vapor and liquid have the same composition. ^^fb 1 Am. Chem. Soc., 1901, xxiii, p. 463. '56 SOLUTIONS. If the concentration of acid is less, the vapor has less acid than the liquid, owing to the solubility of the vapor. If 76 76 <}:. " 100,.--'-" ior 75.2 100 Water Formic Acid 73% Water 100 Formic Acid FIG. 65. the acid is more concentrated, the vapor has less water than the liquid. Therefore, whatever the concentration, continued boiling will give a residue containing 73% of acid. 18.8 100 100 Water Methyl Alcohol O Water 100 Methyl Alcohol FIG. 66. nitric acid has a maximum boiling point at 120 and 20.2% hydrochloric acid has a maximum boiling point at 1 10. BOILING-POINT AND VAPOR-PRESSURE CURVES. 157 165. A third type of solution remains, where but one of the vapors is readily soluble in the other liquid. The solubility of water vapor in methyl alcohol is much greater than that of the alcohol vapor in water, and the vapor-pressure curve for 65.2 has the form of the heavy line of Fig. 66. The dotted line gives the corresponding boiling-point curve. The vapor is therefore always richer in alcohol, and continued boiling will give a residue of relatively pure water boiling at 100. By successively reboiling the distillate, practically all the water will be left behind in the residues (fractional distillation}. EXPERIMENT XV. Boiling-point and Vapor-pressure Curves of Liquid Mixtures. Determine the boiling points of as many different concentrations of water and the assigned liquid 1 as possible. Use the Beckmann boiling-point apparatus (51) and start with about 20 c.c. of the assigned liquid. When its boiling point has been determined, add i c.c. of distilled water from a burette and again determine the boiling point, and so continue. When the total amount exceeds 30 c.c., pour into a beaker and discard an accurately measured amount, so that, on pouring the remainder into the boiling vessel, the amount is again about 20 c.c. Continue until it is almost pure water. Plot your results with concentrations as abscissae and boiling temperatures as ordinates. Make a second diagram with concentrations as abscissae and vapor pressures as ordinates. For each observed boiling point there should be a curve which shows the general relation between the vapor pressure and the concentration, at this temperature, i.e., an isothermal. In general but three points on each curve are known, namely, the concentration at which the . vapor pressure equals the atmospheric pressure, the pressure at zero concentration or pure water (Table LVII) and, in certain cases, the pressure of the pure solute (Tables LIX and LX). Nevertheless, the curves can be drawn approximately, for the slope at each of these points will be opposite to that of the boiling-point curve, and where the boiling point is constant, the vapor pressure must be constant, and these isothermals must be in the order of the temperatures. It will be found convenient to draw a horizontal line at the observed atmospheric pressure, and to mark on this line, at the points corresponding to the concentrations studied, the temperature at which the vapor pressure had this value (boiling points). Also, against the pressure axis, on each side (pure solvent and pure solute), mark the pressure for each of these temperatures. Through these points draw a curve which is horizontal when the boiling-point curve is horizontal and which slopes upward where the boiling-point curve goes downward, 1 Water and a partially miscible liquid, such as amyl alcohol or isobutyl alcohol, gives a particularly interesting and simple solution. 158 SOLUTIONS. and vice versa. It will be instructive to return to this experiment after Chapter VII has been finished, and interpret the curves in the light of the phase rule. QUESTIONS. 1. Explain why the slope of the vapor pressure curve is opposite to that of the boiling-point curve. 2. If semi-miscible liquids have been used, estimate (a) saturated concentration of each component ; (b) volume of each layer in i oo c.c. of a 20% (by volume) solution of (a) water; (b} liquid. 1 66. Solution of Solids in Liquids. In one respect such solu- tions are much simpler than solutions of liquids or gases for the vapor of the solute is negligible. The curves of Fig. 67 illustrate the solubility of certain salts at different tempera- tures. The ordinates are the number of grams of salt dis- solved in 100 grams of water. The solubility of Glauber's salts, Na 2 SO 4 . 10 H 2 O, is particularly interesting. Below 34 the solubility increases with rising temperature, but above 34 it decreases. We shall see in Chapter VII that at these higher temperatures we are really considering a different salt, namely anhydrous sodium sulphate. 167. Additive Properties of Solutions. Additive properties are such as can be calculated for a solution or compound by adding the values of the particular property for the different VALSON'S LAW OF MODULI. 159 constitutents. If G is the magnitude of a certain additive property and y the per cent, of a certain constituent, ioo = [ioo- (y l + y a + - -)]G + yiGi + y 2 G 2 + - (107) where G refers to the solution, G to the solvent, and G It G 2 , to the solutes. i67a. Valson's Law of Moduli. Valson 1 pointed out that the density of a salt solution is an additive property and is equal to the sum of two numbers, one of which is contributed by the base and the other by the acid. If Z a is the number for the acid and Z b that for the base, the density is p=Z a + Z b A normal (4) solution of ammonia chloride has a low density, 1.0153, an d is used as a standard. The numbers for a normal solution of any other salt, Z a ' and Z b ', are deter- mined by the equation. p' =Z a ' +Z & ' =1.0153 +(Z a ' -Z a ) +(Z b f -Z b ) (108) Z a f Z a is called the modulus of the acid and Z b Z b is called the modulus of the base. Table XXI gives the more common moduli. TABLE XXI. Valson's Moduli (i8). NH 4 .0000 Cl .0000 K .0296 SO 4 .0160 Na -0235 NO 3 .0200 $Ba -0739 Br .0370 JCa .0282 I -0733 .0221 .0410 .0413 .1090 Ag .1069 The explanation of the frequent factor i / 2 is that such bases or acids are bivalent, and therefore the equivalent or normal 1 C. R., 1871, Ixxiii, p. 441; 1873, Ixxvii, p. 806. 2 Reychler-Kuhn, pp. 120, 121. l6o SOLUTIONS. concentration is one-half of that calculated from the atomic or molecular weight. Table XXII gives the density of dif- ferent concentrations of ammonium chloride. TABLE XXII. Density of Ammonium Chloride (18). Compiled from Different Sources. Concentration. Density. (gr. equiv. per litre.) .5 T.ooSo 1. 1.0153 2. 1.0299 3. 1.0438 4- 1.0577 Illustration. The density of a thrice-normal solution of sodium nitrate is ,0 = 1.0438+3 X. 023 5 +3 X- 0200 = 1.1 743 167!). Other Additive Properties. Groshaus 1 has shown that the molecular volume (molecular weight divided by den- sity) of a salt solution is an additive property; that is, is the sum of two terms, one of which is contributed by the acid and the other by the base. Von Bender 2 has calculated moduli by which the refrac- tive index of a solution can be calculated. It is, however, more logical to consider not the refractive index, but the molecular refractive power or refractivity which is defined by the expression of Lorentz-Lorenz.s p ft 2 + 2 where M/p is the molecular volume and /z is the refractive index (219). If A is the refractivity of a y per cent, solution, A that of the solvent, and A T that of the solute 100 A = (100 y) A , + y AI ( I0 9) With many salt solutions the last term can be resolved into two, one representing the refractivity of the acid and the 1 Wied. Ann., 1883, xx, p. 492. 2 Wied. Ann., 1890, xxxix, p. 89. 3 Wied. Ann., 1880, ix, p. 641; xi, p. 70. DENSITY OF SALT SOLUTIONS. l6l other that of the base, and these terms possess approximately constant values, whatever the particular combination. The refractivity of a solution will be determined in Experiment XXVII. The power which a salt solution possesses of absorbing light (218) may be resolved into two portions, one of which depends on the acid and the other on the salt. For example, all the different permanganates show the same characteristic absorption, the explanation being that the acid radical alone produces the absorption. Both the natural 1 and the magnetic 2 rotatory power (226, 228) are additive, so that if, for example, the acid radical is active, the rotation is independent of the particular inactive base associated with it, and vice versa. Such cases will be further studied in Chapter V. PROBLEMS VII. 1. The space above 100 c.c. of water (at 20) is filled with ammonia gas under a pressure of 200 cm. of mercury. Find (a) equivalent volume of gas in water ; (b) mass of gas in water. 2. A litre vessel is filled with carbon dioxide gas at 20 and 76 cm. pressure. How will the pressure be affected by the injection of 500 c.c. of ethyl alcohol? 3. What is (a) the vapor pressure of a mixture of water and carbon bisulphide at 30? (Tables LVII and LXI.) (6) At what temperature will the mixture boil under a pressure of 74 cm. of mercury ? 4. What is the effect of continued boiling upon (a) the residue (6) the distillate, of 70% ethyl alcohol? (c] 98% ethyl alcohol? 5. Estimate from Fig. 67 the maximum mass of (a) sodium chloride; (b) potassium chlorate; (c) sodium sulphate which will dissolve in one litre of water at 50. EXPERIMENT XVI. Density of Salt Solutions. Prepare carefully half-normal or normal solutions of several salts having a common base and also similar solutions with a different com- mon base, for example, i/aNaCl, i/2NaNO 3 , i/4Na 2 SO 4 , i/aNH 4 Cl, i /2NH 4 NO 3 , i /4(NH 4 ) 2 SO 4 . Determine the densities with great care, at 1 8, with a Mohr balance (see 36 for full instructions). For each acid, find the difference in density for the two bases. The difference should be constant. Prepare carefully similar solutions of two acids 1 Oudemann, Beibl., 1885, ix, p. 635. 2 Wiedermann, Magnetismus, Ladenberg's Handb., vii, 1889. 162 SOLUTIONS. and different bases and determine the densities ; (for example, i /2 Nad, i/ 2 NH 4 Cl, i/ 2 KCl, i/ 2 NaN0 3 , i/ 2 NH 4 NO 3 , i/ 2 KNO 3 . Determine the difference in density contributed by these two acids for each of the bases. This difference also should be constant. Taking normal ammonium chloride solution as a standard, calculate the density moduli. [If the above solutions have been used, the modulus of sodium will be twice the difference between the densities of ammonium chloride (half-normal) and sodium chloride (and there should be the same difference in density between each sodium salt and the corresponding ammonium salt). The modulus for the nitrate radical will be twice the difference between ammonium nitrate and ammonium chloride or any pair of chloride and nitrate salts with a common base.] QUESTIONS. 1. Assuming i.oi 53 as the density of a normal ammonium chloride solution, calculate (a) the density of a normal sodium chloride solution; (6) the density of a twice-normal solution of potassium sulphate. 2. What is the weight in kilos of a cubic meter of half-normal sodium sulphate solution? 3. What sources of error may there be in a determination of density by the Mohr balance? 4. How might the accuracy of the riders be tested? 5. How might the accuracy of graduation of the beam be tested? 6. What effect has capillarity? 1 68. Dissociation. Association. The preceding para- graphs and experiments suggest that when a salt is dissolved in water, it breaks up into two parts an acid portion and a base portion and that each of these portions has characteristic properties which are independent of the other portion. In this and in later chapters we will have much additional evi- dence that this is true and that it is not only true of most salts, but also of bases and acids. We shall see in Chapter VIII that the acid portion has a charge of negative electricity, and that hydrogen, in the case of acids, has a positive charge. Such also has the metal, or corresponding radical, in the case of bases and salts. The portions are called ions and the general theory is known as the dissociation theory of Arrhenius. A fuller discussion must be postponecl till later chapters. In certain cases the molecules, instead of dissociating, unite to form groups of two or more molecules. This phenomenon is called association. OSMOTIC PRESSURE. 163 169. Osmotic Pressure. In 1877 Pfeffer 1 found that when a sugar solution is separated from pure water by a wall which is permeable to water but not to sugar, the water penetrated into the solution until the level of the solution was consider- ably above that of the pure water, or if the solution rose into a closed tube, the water penetrated until the air was consider- ably compressed (see Fig. 69). When the final concentration was i% of cane-sugar, this pressure was equivalent to 50.5 cm. of mercury at 6.8, 53.1 cm. at 14.2, 54.8 cm. at 22, and 56.7 at 36. Solutions of different concentrations at a common tempera- ture gave the following pressures: i% gave 53.5 cm., 2% gave 101.6 cm., 4% gave 208.2 cm., and 6% gave 307.5 cm. This pressure is called the osmotic pressure of the solution. Pfeffer's experiments have been repeated by many ob- servers not only with cane-sugar, but with many other solutes, such as glucose, manite, dextrose, gum arabic, and many in- organic salts. 2 170. Pfeffer and his successors used as a semi-permeable wall a membrane of copper ferrocyanide which was deposited in the pores of a porous earthenware vessel. This membrane is permeable to water but is quite impermeable to the above solutes. De Vries 3 found that the walls of certain living vegetables cells were in the same sense semi-permeable. These cells contained a solution, and when surrounded by a similar solution outside, remained of constant size. If, however, the outside solution was weaker, water entered and the cell en- larged, and vice versa. He found that it was not necessary that the outside solution be identical with that inside. Out- side solutions of cane-sugar, glycerine, etc., produced no change in the size of the cell if the molecular concentration (4) was the same as that of the solution inside. Such solutions, 1 "Osmotische Untersuchungen," Leipsic, 1877, translated in "The Modern Theory of Solution," Jones. 2 See the numerous papers of Morse and his assistants in Am. Chem. Jo., 1909, xli, p. 276, and previous numbers; of Berkeley and Hartley, Proc. Roy. Soc., 1904, Ixxiii, p. 436; 1906, Ixxviii, p. 68, and a general review in Zeit. phys. Chem. 1908, Ixiv, p. i. 3 Zeit. phys. Chem., 1888, ii, p. 415; 1889, iii, p. 103. 164 SOLUTIONS. of equal osmotic pressure, he called iso tonic. De Vries found that solutes which showed dissociation, such as the inorganic salts, sodium chloride, potassium nitrate, etc., were isotonic at lower concentrations than non-dissociable solutes, such as cane-sugar. The osmotic pressure of a solution, which we have just de- scribed, appears to be an actual pressure exerted by the molecules of the solute. For, a non-volatile substance, such as cane-sugar, cannot leave the solution, and if there were such a pressure it would be exerted on the free surface of the solution, on the semi-permeable wall, and on the other walls of the vessel. Since the first wall is permeable to the solvent, it would experience no pressure from the latter, and the other walls are fixed, but the free surface is not. Owing to this pressure the volume of the solution increases until this pres- sure is counteracted by the sum of the pressure due to eleva- tion of the solution above the pure solvent outside, and the air pressure above the solution. 171. Van't Hoff J pointed out that this pressure was, within the limits of experimental errors, equal to the pressure which would be exerted by the dissolved substance if it occupied the same volume in a gaseous state. Since the molecular weight of cane-sugar is 342, a i% solution has a molecular concentration of i 34^2 gram molecules per litre. By Equation 60 the pressure of an equal concentration of gas at 14.2 is 6235 X 287.2 1000 p = - 34 .2 ' P = 52.4cm. while Pfeffer found experimentally 53.1 cm. pressure. More- over, Van't Hoff pointed out that the pressure was proportional to the absolute temperature and therefore obeys Gay Lussac's 1 Phil. Mag., 1888, xxvi, p. 81, also "The Modern Theory of Solution." THERMODYNAMIC STUDY OF OSMOTIC PRESSURE. 165 law. The ratio of 56.7 to 50.5 is 1.12 while the ratio of 273+36 to 273+6.8 is i. ii. Pfeffer's figures quoted in 169 show that the pressure is proportional to the concentra- tion, that is, the density. In other words, the osmotic pressure obeys Boyle's law. 172. Thermodynamic Study of Osmotic Pressure. Van't Hoff not only pointed out from Pfeffer's observations that 1% I V C A B D FIG. 68. osmotic pressure followed Boyle's and Gay Lussac's laws and iad the same gas constant, but he showed that such must be the case by considerations of an isothermal cycle, involving both gas pressure and osmotic pressure. 1 The solute is supposed to be such that, on reducing the pressure above the solution, the solute leaves the solution as a gas or vapor and obeys Henry's law (158). The solution is contained between semi-permeable walls, AE, BF, a piston M If and a free surface AB. The walls AE and BF are surrounded on the outside by the pure )lvent. The solute, when in a gaseous state, is contained between The following demonstration is due to Van't Hoff, Rayleigh, and Donnan (Van't Hoff, Lectures II, p. 23). 1 66 SOLUTIONS. the solid walls AG and BH, the piston M 2 and the free surface A B. The pressures p on M 2 and P on M x have such values that there is constant equilibrium. We will consider the following cycle of operations performed at constant temperature. 1. M 2 is at A B. M is in a position where the volume of the solution is V and the pressure which must be applied to this piston, to counteract the osmotic pressure, is P. Now raise M j to AB, while M 2 is allowed to rise, against a pressure p, such that the concen- tration of the solute in the solution and (consequently) the osmotic pressure P remains constant. The work done upon the solution is PV (the negative sign indicating work expended). The work done by the gaseous solution is pv = wRO (Eq. 57) where v is the final volume between A B and M 2 . 2. Allow the gas to expand from v to a very great volume v y__. The work done is (Eq. 62, 57) l/ ^x / I pdv = wRO I - v y 3. Lower piston M z until the volume between it and A B is the original volume V. The volume above -AJ3 is so great that the con- centration of solute and the osmotic pressure below AB are negli- gible and consequently no work is involved in lowering M x . 4. Lower M 2 to AB. The work done upon the gas is r r - I p'dv=-wRO I o *J dv --,ltfln-^ v + sV sV For the solute not only occupies the volume v above A B, but also the volume V of the solution. We have assumed that Henry's law is applicable and therefore a volume V of the liquid absorbs a volume sV of the gas above, where s is the coefficient of solubility (159). Hence the total equivalent volume is v +sV. The system has been returned to the initial state, and, since the temperature has been constant, the second law of thermodynamics requires that the total work must be zero (145) v v M +sV .', -PV + wRO -\-WRO\n --WROln-^-^^o v sV But sV = v and this is negligible compared with v^ .'.PV = wR6 = pv (no) If the solute, as a gas, occupies the volume V t the pressure p' is determined by Boyle's law. p'V = pv=PV .\ p' = P (no') VAN'T HOFF'S EQUATION AND COEFFICIENT. 167 Therefore, the osmotic pressure of a dissolved, vaporizable substance which obeys Henry's law is equal to the gaseous pressure which it would exhibit at the same temperature and occupying the same volume. All the deductions from this law apply to non-vaporizable solutes, and therefore it is concluded that the law itself applies to such solutes as well as to those which obey Henry's law. We have already seen that the experimental values for the osmotic pressure are in agreement. Equation 57 is therefore applicable to osmotic pressure. 173. Van't Hoff's Equation and Coefficient. We have seen that where there is dissociation of molecules into two or more ions, the osmotic pressure is greater than it is if there is no dissociation and that the converse is true of association. If the number of gram equivalents (w in Equation 57) is calculated for the normal molecular weight, the calculated pressure will be in error. Instead of estimating the actual molecular weight it is simpler to use the normal molecular weight and add a correction factor. This factor is called Van't Hoff's coefficient and is denoted by i. Therefore the equation for osmotic pressure is pv == iRwO (in) If a fraction a of the total number of solute molecules, N, is dissociated into n ions, the total number of particles is N(i a) +Nna. Since i represents the proportional increase in the number of particles . N (i a) + Nna N = i + (n i)a (112) An analogous equation may be worked out for association. 174. Diffusion. If the particles of a dissolved substance are more concentrated in one portion of the solvent, the osmo- tic pressure is greater, which causes them to spread out until the concentration is uniform. This process is called diffusion. Pick 1 proved theoretically and experimentally that the fol- 1 Pogg. Ann., 1855, xciv, p. 59. 1 68 SOLUTIONS. TABLE XXIII. Coefficients of Diffusion (18).' (The values below must be divided by 10?.) Concentration NaCl KC1 KI HC1 C 2 H 4 2 NaOH KOH OI J 35 169 169 269 108 166 220 05 132 , 163 163 261 104 1 60 2I 7 .1 129 161 161 258 IO2 158 215 5 125 156 159 253 99 i 52 213 i. 124 154 158 257 96 149 215 lowing expression gives the quantity of salt, dm, which passes through an area A in time dT, when the concentration changes an amount dc, in a distance dx, perpendicular to A . D is a constant called the coefficient of diffusion. If we interpret the equation in words, we see that this coefficient is the amount of salt which would traverse one square centi- meter in one second, if the change of concentration per centimeter is unity. It is customary to measure c in grams (of dissolved substance) per cubic centimeter. PROBLEMS VIII. 1. Calculate the approximate osmotic pressure of a solution of i 5 grams of cane-sugar in a litre of water at (a) 20 (6) 80. 2. What is the approximate osmotic pressure of a solution of 2 grams of potassium chloride in a litre of water at (a) 30? (b) 90, assuming that the dissociation is .93 in both cases? 3. If all the molecules of benzoic acid are associated into double molecules when 5 grams are dissolved in benzol to make a solution of 50 c.c., what is the osmotic pressure at 30? 4. 50 gr. of cane-sugar are dissolved in a litre of water. Isotonic solutions are prepared of (a) ethyl alcohol, (b) hydrochloric acid. Calculate the approximate number of grams of each required per litre. 5. An 11.3% solution of raffinose is isotonic with a solution of cane-sugar containing 19 gr. mol. per litre (de Vries). Calculate the molecular weight of raffinose. 6. Derive an expression for Van't Hoff's coefficient for a liquid, the fraction a' of whose molecules are associated to double molecules. 1 Oholm, Zeit. phys. Chem., 1904, 1, p. 309. STUDY OF OSMOTIC PRESSURE. 169 7. The concentration of acetic acid at the bottom of a tank whose cross section is i square meter is 50%. One meter higher in the tank the concentration is 10%. How many grams of acid will cross any intermediate section in one hour at 18, assuming that during this time the concentrations do not change appreciably ? EXPERIMENT XVII. Study of Osmotic Pressure. The object of this experiment is the formation of a semi-per- meable membrane which will show qualitatively the osmotic pressure of a sugar solution. Water ^ 'B \ C c / ^> B \ A \_ L / A ( c C ) 1 i ) 5uc an Solu liion Water A- Cement B-Paraffm CrRubber D=Glass. FIG. 69. The semi-permeable membrane is prepared by electrolytic deposi- tion of copper ferrocyanide in the pores of a porous cap. 1 If there 1 Method of Morse, Am. Chem. Jo., 1901, xxvi, p. 80. The most suitable porous cups are made by C. Desaga, Heidelberg, Germany, of "Pukalische Masse." Any unglazed and quite porous cups may, however, be used. 1 70 SOLUTIONS. are remains of a former membrane, surround the cup, inside and out, with dilute nitric acid for some minutes, after which the cup should be carefully washed with water. Mount a large glass tube in the top of the cup by means of a rubber collar, on top of which is poured a 5:1 cement of litharge and glycerine. Coat the upper outside portion with paraffin. (See Fig. 69.) To remove the air from the pores, surround the cup with a solution of potassium sulphate (5 gr. per litre) and send a current of 2 amperes from a platinum electrode outside the cell to a similar one inside, until a large amount of the solution has passed through. Wash the cell carefully. Pour inside a tenth-normal solution of potassium ferrocyanide, and outside a tenth-normal solution of copper sulphate. Send a current, initially of two amperes, from a cylindrical copper electrode outside the cell to a platinum electrode inside the cell, until the formation of the membrane practically stops the current. Be careful that no potas- sium ferrocyanide comes outside. It may be necessary to remove some of the solution owing to the electric endosmosis, i.e., passage of liquid in the direction of the current. Rinse thoroughly with water, fill with a definite strong solution of sugar, and insert through a rubber stopper a long capillary tube, being careful to exclude air bubbles. Note the pressure every ten minutes for an hour. If the solution overflows the capillary, a closed tube manometer may be attached. QUESTIONS. 1. Calculate what the pressure should be. (Eq. m.) 2. Why does not the total pressure immediately manifest itself? 3. Why is a small-bore tube preferable for measuring the pressure? 4. What influence has ionization? 175. Vapor Pressure of Solutions. Since the free surface of a solution contains some molecules of solute and therefore less molecules of solvent than the pure liquid, we would naturally expect that the vapor pressure would be less. We will prove that such is the case and determine the magnitude of the lowering of vapor pressure. We will show that if p is the vapor pressure of the pure solvent and p' is that of the solution = -TJ = (for infinitesimal lowering) (114) where n is the number of gram molecules of solute dissolved in N gram molecules of solvent. x We will imagine a very dilute solution contained in a tall tube, with a semi-permeable membrane at the bottom, which dips into a closed vessel containing the pure solvent (Fig. 70). 2 1 If the solvent has a different molecular weight in liquid and vapor, N is the number of equivalent gram molecules of vapor. 2 Demonstration of Arrhenius, Zeit. phys. Chem., iii, p. 115. VAPOR PRESSURE OF SOLUTIONS. 171 Let h be the equilibrium difference of level between the solution and the solvent. Such equilibrium must be attained, for continued movement of vapor or liquid would violate the conservation of energy. If p is the vapor pressure of the pure solvent, the vapor pressure at the level of the solution is pdp, where dp is the pressure due to a column of vapor of height, h. Since at equilibrium the So/Yen t FIG. 70. pressure must be the same at all points on the same level, pdp is the vapor pressure above the solution. The height h therefore measures both the lowering of the vapor pressure dp and the osmotic pressure P, and dp mass of vapor P mass of equal volume of solution Let v = volume of one gram molecule, M , of vapor. Let V = volume of solution containing one gram molecule of solute, pv = PV, since the product of pressure and volume for one gram molecule of any substance, in "either the vapor state or dissolved, is equal to RO (172). Therefore the volume v which contains M grams of vapor is P/p times the volume V of solution which contains one gram molecule of solute. The mass of V is M N In, if n gram mole- cules of solute are dissolved in N gram molecules of solvent. The volume v of vapor is therefore P/p NJn times the volume of an equal mass (M gr.) of solution. Hence, since the masses of equal volumes are in the inverse proportion of the volumes of equal masses, dp pn P " PN or dp _ n p ~ N (114) 172 SOLUTIONS. If the solution is moderately dilute, we may write p p' in place dp, where p' is the vapor pressure over the solution, Y *?--*. ;':"; ^ Expressed in words, the relative lowering of vapor pressure is proportional to the relative number of solute molecules. If the change of vapor pressure is large, we must integrate dp dn_ ~p " ~~N between the limits of p f and p; zero and n. 176. Illustration. 1 2.47 grams of ethyl benzoate dissolved in 100 gr. of benzol'gave a relative lowering of .0123. Cal- culate the molecular weight. Since the molecular weight of benzol is 78 N= j--ft;a3 : .0123 XL 28 = ^ = .0158 ..- .0158 Raoult made a great number of observations upon the vapor pressures of solutions and found close agreement with the above equation. 2 The average proportional lowering for a great number of solutions for which n/N = .oi, was .0105. Measurements of the vapor pressure are difficult and therefore 1 Walker, p. 179. 2 Zeit. phys. Chem., 1888, ii, p. 372, also translated in "The Modern Theory of Solution." ELEVATION OF THE BOILING POINT. it is customary to measure the change in boiling point or melting point, both of which depend upon the change in vapor pressure. 177. Elevation of the Boiling Point. BC in Fig. 71 repre- sents the vapor-pressure curve of the pure solvent, DE that of the solution. If the atmospheric pressure is ,'the solvent At' At FIG. 71. boils at the corresponding temperature t. The solution will boil when its vapor pressure is equal to p , which necessitates a temperature At higher. We can easily observe this eleva- tion of the boiling point. Clausius' equation (105) tells us that * -f- , / s 1 If m is the mass of the solvent and m is the mass of the solute, and if M is the molecular weight of the solvent and M that of the solute m _ At M mM m MQ 174 SOLUTIONS. Q/M is the latent heat of vaporization per gram =/. m I m M (115) 178. The molecular elevation, k, is denned as the elevation of the boiling point produced by dissolving one gram molecule of solute (w/M = i, 4) in 100 grams of solvent (w = ioo). (116) Table XXIV gives the experimental molecular elevations of the more common solvents at the normal boiling point. The theoretical values of k calculated from Equation 116 and Table LVI agree well with these numbers. For example, for benzol ((?, (-/ S fc== .oi98 (273 + 80.2)*^ 26 93 The fourth column, which gives the molecular elevation for 100 c.c. of solvent, is convenient in cases where the volume can be measured easier than the mass. TABLE XXIV. Molecular Elevations (Experimental). Solvent Boil. Temp. Mol. Elev. (100 gr.) Mol. Elev. (100 c.c.) Acetic acid 118 2 C 2 26 * j-o Acetone 56 I6. 7 22.2 Alcohol 7 8 II ^ i q.6 Benzol 80.2 26.7 32.8 Chloroform 61 3 6.6 2 J. Ether . . . -2 e 211 2 O "? Water r A a MOLECULAR WEIGHT. 175 From Equations 115 and 116, ,, 100 km which gives the molecular weight of a dissolved substance in terms of easily observed quantities and the constant of the solvent. EXPERIMENT XVIII. Determination of Molecular Weight of a Dissolved Substance from the Elevation of the Boiling Point. (Beckmann Apparatus.) Study carefully the directions for the boiling-point apparatus (51) and the Beckmann thermometer (47). Having several times determined the boiling point of the pure solvent, add the assigned 1 solute in successive quantities of from 0.2 to 0.6 grams, depending on its solubility and molecular weight, and for each addition determine the boiling point. Solid substances should be pressed into convenient pellets. Liquids should be introduced from a special pipette with a long bent neck, and of such a form that it can be hung in a balance, and the liquid expelled determined by weight (36). Calculate the molecular weight for each concen- tration, by Equation 117. Compare the result with that represented by the chemical formula. QUESTIONS. 1. Explain any abnormal molecular weights observed. 2. Why must the bulb of the thermometer be in the liquid rather than in the vapor? 3. Calculate the boiling point of a solution whose concentration is (a) i gram of the assigned solute in 200 gr. of the solvent (b) one gram molecule of the solute in too gram molecules of the solvent. 4. Calculate the molecular elevation of this solvent (Equation 116 and Table LVI). EXPERIMENT XIX. Determination of the Molecular Weight of a Dissolved Substance by Elevation of the Boiling Point. (Landesberger-Walker Method.) Before beginning the experiment, study carefully the directions for the use of this apparatus (52) and the Beckmann thermometer (47). Make several observations of the boiling point of the pure solvent and 1 Any one of the solvents in Table XXIV is suitable. The solute may be any non-volatile or slightly volatile substance of definite chemical composition. A substance which shows dissociation (e.g., an inorganic salt), or one showing association (e.g., benzoic acid in benzol) is particularly interesting. 176 SOLUTIONS. then observations with several concentrations of the assigned solute. 1 Solid solutes are preferably pressed into small pellets, and liquid solutes should be discharged from a weighing pipette (36). Calculate the molecular weight for each concentration by Equation 117, using the value of k for 100 c.c. (Table XXIV), and compare the results with that represented by the chemical formula QUESTIONS. 1. Explain any abnormal molecular weights obtained. 2. What advantages and what disadvantages has this method compared with the Beckmann method? 3. Calculate the boiling point of a solution containing (a) one gram of this solute in 100 grams of this solvent ; (b) one gram molecule of this solute in 100 gram molecules of this solvent. 4. Calculate the molecular elevation of this solvent (Equation 116 and Table LVI). 5. Reconcile this transfer of heat to the warmer solution with the second law of thermodynamics. 179. Lowering of the Freezing Point. We shall see later that when a solution begins to solidify, the solid pure solvent separates out and the vapor pressure above the solution is equal to that above the solid pure solvent at this temperature. If, therefore, AB (Fig. 71) represents the vapor-pressure curve of the solid solvent, the solution begins to freeze at the tempera- ture corresponding to the point D where the vapor-pressure curve of the solution meets that of the solid solvent. At', the lowering of the freezing point by the addition of the solute, can be expressed in terms of Ap', the lowering of vapor pressure of the solid solvent. Let m =mass of solvent, w=mass of solute, and M=mo- lecular weight of solute. The number of gram molecules of solute is j-=- and consequently one gram molecule of solute is contained in - grams of solvent. Let V= volume of this m mass of solvent. If this amount of solvent freezes out from the solution, the latent heat liberated is /' - and by 148 m At' the fraction -^- of this heat does the mechanical work neces- v 1 Ethyl alcohol and ether are the best solvents. The solute may be any substance of definite chemical composition which is readily soluble in either of these solvents and which is only slightly volatile. MOLECULAR LOWERINGS. I 77 sary to reduce the volume of the solution by an amount V against the osmotic pressure P. Therefore, TJf " *&'* JL ~r~o~ = and the latter, by 172, is equal to RO. Therefore, f _Rd 2 m '~~JV~mM TABLE XXV. Molecular Lowerings (Experimental). (118) Solvent Freezing Point Molecular Lowering (100 gr.) Water o 18 =; Benzol 5 A TO Nitrobenzol 7O 7 Acetic acid I 7 18 6 180. The molecular lowering k' is denned as the lowering of the freezing point produced by dissolving one gram mole- cule of solute in 100 grams of solvent (w = ioo) .0198^ ~^T which is an analogous expression to Equation 116. For ex- ample, for benzol _ .0198(273 + 5.4)* _ K - i 32.2 Table XXV gives the experimental values of the molecular lowering of the more common solvents. The figures agree well with the calculated values. 178 SOLUTIONS. From Equations 118 and 119 ,, look'm M= ^f^r (I20) With the help of this equation, the molecular weight of a dissolved substance can be determined from easily observed quantities and the constant of the solvent. The freezing-point is preferable to the boiling-point method because it is inde- pendent of the vapor pressure of the solute. 181. Molecular Weight in Solution. Equations 117 and 120 are the bases of the two best methods for determining the molecular weights of bodies in solution. It is only necessary to know the mass of solvent m , the mass m of the substance, the difference between either the boiling point or the freezing point and that of the pure solvent, and the constant of the solvent (Tables XXIV and XXV). If the molecular weight in solution is lower than the normal molecular weight, it shows that the molecules have partially or wholly dissociated. Solution of salts, acids, and bases show dissociation, and the dissociation, as measured by the decrease in molecular weight, increases if the solution is diluted (compare Table XXXVI) . An abnormally high molecular weight, on the other hand, shows that there is association of the molecules into groups of two or more. The above formulae are inapplicable if the molec- ular weight of the solvent is different in liquid and vapor, and Equation 117 cannot be used if the solvent is volatile (175 and note) . 182. Solid Solutions. Solids as well as liquids often form what may be very properly called solutions. For example, palladium dissolves hydrogen gas, and the various alloys, in particular steel, are mixtures which show many of the properties of ordinary solutions. A discussion of these solutions must, however, be postponed until after we have considered the phase rule. 1 183. Colloidal Solutions. A colloidal solution is one where there is (usually) great association (168) of the solute particles. 1 For detailed information respecting solid solution, see the Lectures of Van't Hoff, the pioneer in such investigations (Part I, i, 5; Part II, i, 3). COLLOIDAL SOLUTIONS. 179 A solution of gelatine in water is a reversible colloid solution; that is, if, by drying or cooling, it forms a solid jelly, heating or the addition of water will restore it to solution. Other colloidal solutions, such as that of ferric hydroxide, or finely divided metals will not go into solution if once coagulated. Such irreversible colloids appear to carry electric charges, and are coagulated by the addition of a highly ionized solute. The reader is referred to the references for fuller information. 1 PROBLEMS IX. 1 . Pfeffer found that a i % colloidal solution of dextrine gave an osmotic pressure of 16.6 cm. at 16. Calculate the molecular weight. 2. What is the relative lowering of vapor pressure produced by dissolving (a) i 5 grams of cane-sugar in a litre of water? (b) 2 grams of potassium chloride? (c) What is the actual vapor pressure of each solution at ioo? 3. Calculate the boiling point of both solutions of Problem 2. 4. Calculate the freezing point of both solutions of Problem 2. 5. Calculate for water (a) the molecular elevation; (b) the molecular lowering. 6. If i gr. of benzoic acid lowers the freezing point of 20 c.c. of water .24 ; of 20 c.c. of benzol .67, and of 20 c.c. of acetone i, calculate the molecular weight in each. Explain the differences. EXPERIMENT XX. Determination of the Molecular Weight of a Dissolved Substance by Lowering of the Melting Point. Study carefully the directions in 50 for the use of the Beck- mann apparatus and 47 for the adjustments of the Beckmann thermometer. Having made several careful determinations of the freezing point of the pure solvent, 2 add the assigned solute in successive amounts of from .2 to .6 grams, depending upon the molecular weight, and for each concentration make a careful determination of the freezing point. Solid solutes are preferably pressed into pellets and liquid solutes should be discharged from a weighing pipette (36). Calculate the molecular weight for each concentration by Equation 120 and compare the results with that represented by the chemical formula. 'Wood and Hardy, Pro. Roy. Soc., 1909, Ixxxi, B, 545, p. 38;' Burton Phil. Mag., 1906, xi, p. 425. 2 Any of the solvents of Table XXV are suitable, and the solute may be any readily soluble substance of definite chemical composition. Acetic acid requires special precautions on account of its hygroscopic nature. It is particularly interesting to use a solute which shows dissociation or association. i8o SOLUTIONS. QUESTIONS. 1. Explain why the freezing point does not remain constant during the freezing of a solution. 2. If the freezing point of acetic acid used as a solvent is higher than that of pure acetic acid, how could you determine the amount of water present ? 3. How could you determine which of two specimens of a liquid is the purer? 4. Calculate the coefficient of lowering for the solvent used. (Equation 119 and Table LVI.) 5. Explain any abnormal molecular weights. 6. Calculate the approximate freezing point of a solution of this solute in this solvent, the concentration being (a) one gram in 100 grams of solvent, (6) one gram molecule in 100 gram molecules of solvent. CHAPTER IV. THERMOCHEMISTRY. 1 184. Heat of Formation. If two bodies unite to form a chemical compound or a physical solution, the energy of the united bodies is generally different from the sum of the energies of the constituents. For example, at a moderate temperature, hydrogen and oxygen unite to form water. For each gram- molecule of water vapor formed, 58,700 calories of heat energy are given to surrounding bodies. Therefore, the energy of a gram molecule of water vapor must be about 58,700 calories less than that of a grammolecule of hydrogen plus that of half a grammolecule of oxygen. We can state the reacting substances, the final product,- and the energy change as H 2 + iO. = H 2 0+ 58700 or, in Thomsen's notation, (H 2 ,0) = 58700 This energy is generally in the form of heat energy, but it may take the form of electrical energy (321) or mechanical work (129). For example, Zn +H 2 SO 4 -ag = ZnSO 4 'ag + H 2 + 248000 2 248,000 calories do not represent the entire loss of energy, for some energy is consumed by the hydrogen gas in over- coming the outside atmosphere. This work is equal to P(v 2 ~v,)=pv 2 = RO (Eq.sy) (121) for the volume v t of the constituents is negligible compared with the volume v 2 of the gas. If the temperature is 27, 1 General references for Chapter IV: Thomsen, "Thermo Chemistry," trans- lated by Burke; Nernst, "Theoretical Chemistry," Book IV; Reychler- Kiihn, Part III, i. 2 The symbol aq signifies that the substance is in dilute solution. 181 182 THERMOCHEMISTRY. ^# = 1.985X300 = 595 (Eq. 59) and the total energy change is 248,600 calories. If the zinc is an element of a galvanic cell, no hydrogen is evolved and 248,600 calories or 1,040,000 joules of electrical energy are produced. 1 In general, I=W-Q (122) where Q is the heat emitted, W is the external work done and / is the decrease in internal energy (Equation 78). This decrease in the internal energy is called the heat of formation, or, better, the heat accompanying the formation of the new sub- stance or substances. 185. In many cases I can be measured without difficulty by causing the entire energy change to appear as heat, and measuring this heat in a suitable calorimeter ( 53-58). The result will evidently be different according as the union takes place at constant pressure or constant volume. For example, in the illustration of the formation of water, the number of molecules, and therefore the volume, is decreased one-third. If, therefore, the reaction proceeds at constant pressure, the external atmosphere does an amount of work i/^RO which it does not do when the reaction proceeds at constant volume, and therefore the heat produced is greater by this amount when the pressure rather than the volume is constant. Unless otherwise specified, we will understand that the heat of formation is measured at constant pressure or reduced to such a condition, and also that before a final estimate of the heat, the final products are brought to the initial temperature of the original bodies. 186. Heat of Solution. Physical examples of the energy change accompanying the union of two bodies are the so-called heats of solution and dilution. The heat of solution is the number of calories of heat emitted during the solution of one gram molecule of the substance in so great an amount of water that further addition of water causes no additional heat emission or absorption. The heat of solution of anhydrous calcium nitrate is 4000 calories; that is, when 164 gr. are 1 The heat of formation of hydrogen ions is negligible (201). HEAT OF DILUTION. 183 dissolved in a large amount of water, 4000 calories of heat energy are emitted. The heat of solution of hydrates is less than that of the anhydrous salts. For example, the hydrate of calcium nitrate, Ca(NO 3 ) 2 4H 2 O, has a heat of solution of 7600. (The negation sign means that the solution is ac- companied by an absorption of heat.) 187. Heat of Dilution. The heat of dilution of a solution is the amount of heat per gram molecule of dissolved substance which is emitted when the solution is greatly diluted. Beyond a certain dilution, further addition of water produces no ap- preciable affect. While a particular solvent and a particular dissolved substance have a definite heat of solution, they have no definite heat of dilution, since the latter will of course decrease as the dilution becomes greater. Table XXVII illustrates this fact. Practically the only substances without appreciable heats of solution or dilution are gases which closely obey Henry's law (158). The general existence of such heats is an argument of Kahlenberg and others that solution is akin to chemical combination rather than a purely physical phenomenon. The heat of formation of the more common compounds and their heats of solution in water are given in Table XXVI. To avoid long numbers, the values given are in large calories (7). To reduce to the common calorie, multiply the values given by 1000. TABLE XXVII. Heat of Dilution of Different Solutions of Nitric Acid. 1 (Heat of Solution = 71 50.) HN0 3 + H 2 3840 + 2H 2 O 2320 + 3H 2 O 1420 + 4H 2 O 790 + 6H 2 O 200 + 8H 2 O -40 f-iooH 2 O -30 1 84 THERMOCHEMISTRY. TABLE XXVI. Heats of Formation and Heats of Solution (18).* (The unit is the large calorie = 1000 common calories. The nega- tive sign signifies that heat is absorbed during the formation of the compound.) Compound Chemical Symbol Heat of Formation Heat of Solution Ozone O 3 34- i 2 Water vapor \ f 58.7 Water, liquid / Hydrogen dioxide H 2 O H 2 O 2 168.4 45 2 Hydrochloric acid HC1 22 . 20 . 3 Hydrobromic acid (gaseous bromine) Hydriodic acid HBr HI 12 . I 6. i 19.9 19 . 2 (solid iodine) Hydrogen sulphide .... H 2 S 2 . 7 4 .6 Sulphuric acid H 2 SO 4 IQT, . I 17.8 Ammonia Nitric acid NH 3 HNO 3 12 41 . 9 8. 4 7 . 2 Nitrous oxide N 2 O 18. Nitric oxide NO 21.6 Nitrogen peroxide /N 2 4 2.6 Nitrogen pentoxide Phosphoric acid \ NO 2 N 2 0< H,PO 4 7-7 J3- 1 T.O2 . Q 2 . 7 Carbon dioxide c6 2 07-6 6.0 (from amorphous carbon) Carbon monoxide CO 2Q . Methane CH 4 22-4 Carbon tetrachloride Carbon bisulphide Hydrocyanic acid CC1 4 CS 2 HCN 21.6 IQ- 27.6 Potassium hydroxide KOH IO3 . 2 13 .3 Potassium chloride Potassium chlorate KC1 KC1O 3 104.3 Q C . Q 3- 1 Potassium perchlorate . KC1O 4 I I T. . I 12 . I Potassium bromide KBr Q s;. i 5 J Potassium iodide KI 80. i 5. i Potassium sulphate Potassium nitrate Potassium sulphide K 2 S0 4 KN0 3 K 2 S 344-6 119.5 IOI . 2 6.4 -8.5 10 .0 Potassium carbonate Potassium permanganate . . . Sodium hydroxide Sodium chloride K 2 C0 3 KMnO 4 : NaOH NaCl 28l . I !95- ioi . 9 07 6 -6-5 10.4 10. 9 I . 2 Sodium bromide NaBr St. 8 . 2 1 Compiled from the excellent table in Juptner, vol. i, Chap. XXII. 2 Jahn, Zeit. anorg. Chem., 1908, Ix, 3, p. 292. HEATS OF FORMATION AND SOLUTION. TABLE XXVI. Continued. Compound Chemical Symbol Heat of Formation Heat of Solution Sodium sulphide . Na 2 S 87 .0 I C . Sodium hyposulphite Na 2 S 2 O 3 -5aq 26^.2 1 1 . 4 Sodium sulphite . Na 2 SO 3 268. 5 1 1 . i Sodium sulphate Na 2 SO 4 328.8 . 2 Sodium nitrate NaNO 3 I I I . ^ *G . Sodium carbonate Na 2 CO 3 272.6 c.6 Ammonium chloride NH 4 C1 7^.8 4 Ammonium sulphate . (NH 4 ) 2 SO 4 282 .2 2 .6 Ammonium nitrate . NH 4 NCK 88. 6.2 Calcium hydroxide Calcium oxide gS OH) * 215. 1 1. 1 . (Heat of Calcium chloride Calcium carbonate Magnesium hydroxide CaCl 2 CaCO 3 Mg(OH) 2 170. 270. 217.3 hydration = iS-5) 17.4 Magnesium sulphate MgSO 4 502 . 2O . 3 Aluminum hydroxide Manganese hydroxide A1(OH) 3 Mn(OH), 297. 163 . Ferrous hydroxide Ferrous chloride Fe(OH) 2 FeCl 2 136.7 82 I7.O Ferrous sulphate Ferric hydroxide Ferric chloride Cobalt hydroxide FeSO 4 'aq Fe(OH) 3 FeCl 3 Co(OH) 2 235-6 198. 96. i 131 .8 63.3 Cobalt chloride CoCl 2 76 <; 18.3 Nickel hydroxide Nickel chloride Ni(OH) 2 NiCl 2 / o 129.2 74. . ^ 6 IQ . 2 Zinc oxide . ZnO 85 8 Zinc chloride. ZnCl 2 07 . i s.6 Zinc sulphide ZnS 'aq "? o 6 Zinc sulphate ZnSO 4 220. 18. c Cadmium hydroxide Cd(OH) 2 i 34 . i Cadmium chloride CdCl 2 03 2 3 . Cupric oxide CuO 77 2 Cupric chloride CuCl 2 51.6 1 1 . I Cupric sulphate CuSO 4 182 . 6 15.8 Cupric nitrate . CufNOOa'aq 82.3 Cuprous oxide . Cu 2 O 40 . 8 Cuprous chloride . Cu 2 O 40 . 8 Cuprous chloride . Cu 2 Cl 2 6s. 7 Mercurous oxide Mercurous chloride Hg 2 Hg 2 Cl 2 22 .2 62 .6 Mercuric oxide Mercuric chloride ... HgO HgCl 2 20.7 C3 . 2 3 . 3 Potassium amalgam KHg 12 34 . Sodium amalgam . . NaHg 6 2 I . I Silver oxide Ag 2 O C . Q i86 THERMOCHEMISTRY. TABLE XXVI - Continued. Compound Chemical Symbol Heat of Formation Heat of Solution Silver chloride AgCl 20.4 Silver bromide Silver iodide Silver nitrate AgBr Agl AeNO, 22.7 13.8 28.7 5 -4 Stannous chloride Stannic chloride ...... SnCl, 3 SnCl 4 80.8 127.3 3 29 . 9 Lead oxide Lead chloride PbO PbCl 2 50-3 82.8 6.8 Lead sulphate PbSO 4 216.2 Lead nitrate Pb(NO 3 ) 2 105 . 5 7.6 188. The Principle of Stable Equilibrium. It is a funda- mental principle of mechanics that a body is in a stable equilibrium when its potential energy is a minimum. When such is the case, any disturbance increases the potential energy and thereby assists the return to the initial condition. Berthelot 2 in 1879 announced that an analogous principle was applicable to chemistry. We have seen that the tempera- ture is a measure of the kinetic energy of the molecules (104). An increase of temperature or an emission of heat would usually mean, therefore, a decrease of potential energy, and therefore it would be expected that most reactions would be of this type. 189. The Principle of Maximum Work. Berthelot's theo- rem states that every spontaneous chemical transformation proceeds in the manner which will be accompanied by the greatest emission of heat. Table XXVI illustrates the general applicability of this theorem, for the compounds are stable and, with a few exceptions, the heats of formation are positive. These exceptions, ozone, oxide of nitrogen, carbon bisulphide, etc., together with the majority of heats of solution, show that this theorem is not a natural law. 190. Le Chatelier's Principle. Le Chatelier greatly restricted 1 Reychler-Kiihn, p. 166. 2 Essai de Meechanique Chimique, Paris, 1878. LE CHATELIER'S PRINCIPLE. 187 Berthelot's theorem, but thereby obtained a rigorous law. The modified law states that any disturbance of a system in equilibrium is accompanied by forces which oppose the disturbance. In particular, if the temperature of an equilib- rium system is raised or lowered, the resulting modifications are accompanied by such heat absorption or emission as will reduce the change in temperature. For example, the formation of a compound, such as water, which has a positive heat of forma- tion, is checked by the heat liberated. At 1124, 99.9922% of the equivalents of hydrogen and oxygen form water, while but 98.23% of water is formed at I984 . 1 Such compounds which have less energy than their constituents are called exothermic. If, on the other hand, energy is absorbed, as is the case when NO 2 is formed from N 2 O 4 , the actual cooling reduces the amount formed. Fig. 85 illustrates how the amount of N0 2 in- creases with rise in temperature. Compounds such as this, which absorb energy in their formation, are called endothermic compounds. The higher the temperature, the greater the equilibrium amount of endothermic, and the less the amount of exothermic compounds. 191. Heats of formation are measured in a calorimeter imilar to that described in 53 unless gases are among the litial or final products, in which case a calorimeter of the >omb type (55) is used. Heats of solution and dilution re usually measured in a calorimeter of the first type. EXPERIMENT XXI. Heat of Solution. A calorimeter is set up as described in 53. A measured amount of water or other solvent is poured into the inner calorimeter. The substance to be dissolved 2 is carefully weighed and placed 1 Nernst, " Thermodynamics and Chemistry," p. 36. a Any of the common salts, acids or bases' are suitable. Sodium sulphate is a particularly interesting example of LeChatelier's principle. The heat of solution of the hydrate should be determined at about room temperature and that of the anhydrous salt in water, at about 40. If one of the organic acids suggested in Experiment XL is used, ths results of the two experiments can be Compared. 1 88 THERMOCHEMISTRY. in a thin-walled test-tube. The latter is supported in the solvent by the cardboard cover. When the solvent has been stirred for some time and the temperature as read by a sensitive thermo- meter is approximately constant, readings are made of the tem- perature every minute for five minutes and then the bottom of the test-tube is broken by a glass rod. The liquid is continually stirred and the temperature is read every minute until five minutes after a maximum, minimum, or approximately constant temperature is attained. The inner calorimeter, stirrer and test-tube are weighed and their water equivalents, together with that of the thermometer, are calculated (54). The temperature observations are plotted against the time and the radiation correction is calculated (59). Let m =mass of dissolved substance, M = molecular weight, m w = mass of water, e = water equivalent of calorimeter, etc., ti = initial corrected temperature, t 2 = final corrected temperature. The quantity of heat emitted is ,-/,) (123) and the heat of solution is Another method of determining the heat of solution is given in Experiment XL. QUESTIONS. 1. Why is it necessary that the final solution be quite dilute? (186, 187.) 2. Is this particular solution endothermic or exothermic? 3. Will the solubility be greater or less at a higher temperature? 4. Calculate the approximate heat developed by the solution of one kilo of the solute in 100 litres of the solvent. 192. Hess's Law. In 1840 Hess 1 announced the law that the emission or absorption of heat accompanying a chemical transformation is the same whether the transformation from the initial to the final state proceeds in one step or many. This is the most important law of thermochemistry. A large number of the results given in Table XXVI were not observed directly, but were calculated by this law. The following examples illustrate the applicability and utility of the law. 193. (A) Heat of formation of carbon monoxide. It is impossible to measure directly the heat emitted 1 Pogg. Ann., 1840, 1, 9,385, also Ostwald's Klassiker No. 9. HESS'S LAW. 189 when carbon and oxygen unite to form carbon monoxide. Under normal conditions carbon dioxide is formed C+O 2 =CO 2 +97600 When carbon monoxide is oxidized to the dioxide CO + O = CO 2 + 68600 By Hess's law, the heat emitted must be 97,600 if the reaction proceeded from C +O 2 to CO 2 by the two steps C+O=CO+Q; CO + O=CO 2 +68600 .'. Q, the heat of formation of carbon monoxide must be 29,000. 194. (B) If lime is treated with dilute hydrochloric acid, a solution of chloride of calcium is obtained and 46,000 calories are liberated per gram molecule CaO +2HC1' aq =CaCl 2 +H 2 O +aq +46000 The production of calcium chloride may also proceed by three steps, the formation of hydroxide from the oxide and water (not from the elements as in Table XXVI), the solution of the hydroxide, and finally the reaction between the hydroxide and the hydrochloric acid. CaO +H 2 O=Ca(OH) 2 + 21500 Heat of solution of Ca (OH) 2 = 3 ooo aq + 2HC]'aq=CaCl 2 +2H 2 O+aq + 28000 The total heat emitted is 46,000 calories, or the same value that was obtained by the single step. I 95- (Q The heat of solution of hydrochloric acid is 17,430 calories. The heat of dilution of a solution of the composi- tion HCl+3-2H 2 O is 3770 calories. By Hess's law the heat emitted when one gram molecule of hydrochloric acid is added to 3.2 molecules of water must equal 174303770 = 13660 calories, which agrees well with experimental results. I QO THERMOCHEMISTRY. (Remember that the heat of solution applies to the formation of a very dilute solution.) 196. Thermal Neutrality. In the same year Hess announced a second law. Two dilute salt solutions may be mixed with no change in energy (no emission or absorption of heat). This law only holds for salts which are highly dissociated, in dilute solution (168), and under these conditions we should expect no change in the energy, for the ions have an indepen- dent existence before and after mixing. PROBLEMS X. 1. Calculate the difference between the heat of formation at constant pressure and constant volume of carbon dioxide from carbon monoxide and oxygen for (a) one gram molecule of carbon dioxide; (6) 100 grams of carbon monoxide, both at 100. 2. (a) How much heat is developed during the solution of 50 grams of sodium hydroxide in 10 litres of water? (b) How much potassium chloride would have to be dissolved simultaneously to prevent any change of temperature? 3. The heat of solution of hydrochloric acid in 2.7 molecules of water is 12,100. Calculate the heat of dilution for this concentration (Table XXVI). 4. The heat of solution of potassium hydroxide hydrate, KOH'- 2H 2 O is practically zero. What is the heat of formation of this hydrate from water and the solid base? (Find in Table XXVI the heat of solution of the anhydrous salt.) 5. The formation of phosphoric acid from yellow phosphorus is accompanied by an emission of 2386 calories per gram atom of phosphorus, while only 2113 calories are emitted if red phosphorus is used. What is the heat of formation of the red modification from the yellow? 6. State which of the following compounds are (a) endothermic; (b) absolutely stable at ordinary temperatures; (c) stable at ex- ceedingly high temperatures. Ozone, hydrogen dioxide, nitrogen peroxide, carbon dioxide, methane, carbon bisulphide, sodium carbonate. 197. Variations of Heat Evolution with Temperature. If a compound is formed at ^ degrees, and raised to / 2 , or, if the constituents are heated from tj to t and then react, the final and initial products are the same, and therefore, by Hess's law, both procedures give the same evolution of heat. If S I is the molecular specific heat of the constituents, and 5 2 that of the compound, and if, following the uniform HEAT OF NEUTRALIZATION. 19 1 notation, Q l and Q 2 are the heat energies absorbed, or Q x and 02 are the evolutions of heat energy at the two temperatures, t 2 t 2 t 2 - 0i - j S 2 dt = - 1 S,dt - 2 , or, Q 2 = Q, - j (5, - 5 2 ) dt If the specific heats are constant If the equation is divided by M, the molecular weight, q 2 = q i - (s l - s 2 ) (t 2 - /,) [Table I] (126) 198. Applications. (A) Heat of vaporization. The specific heat of water is approximately unity, that of saturated water vapor, at constant pressure, is .48. The latent heat of vaporiza- tion (per gram) at 1 00 is 53 7 . What is the latent heatat 1 8 ? 537 = qi& (i -48) (100 18) ' ^18=580 199. (B) Heat of formation of one gram molecule of water vapor at 1000 l8 =68400 (liquid, Table XXVI) - 1 8 X 580 = 57900 (vapor) S H = 5 =7. 2 ; 5^0=10.1=5, (Table XVIII) Si = 7-2 + 3.6= 10.8 ' 0iooo=- 579- (10.8- 10.1)982 = -58700 Another method of solving such problems is given in 266. 200. Heat of Neutralization. If we mix an acid with an ilkaline solution, the concentrations of hydrogen and hydroxyl ions become greater than is possible for equilibrium (258) and consequently the majority of these ions unite to form water. In so doing they liberate a certain amount of heat energy. The amount of heat liberated per gram molecule of water formed is called the heat of neutralization. Evi- dently this quantity should be the same for all completely dis- sociated acids and bases, and all the common strong acids and alkalies give about 13,800 calories. If either base or acid is 192 THERMOCHEMISTRY. feebly ionized, the heat of neutralization may be greater or less than this value according as heat is emitted or absorbed, in the progressive ionization which must accompany the neutralization. 20 1. Heat of Ionization. Evidently the heat of neutraliza- tion, 13,800 calories, is the energy required to dissociate one gram molecule of water into its ions (for the dissociation to be permanent, this gram molecule of water must be mixed with a very great volume of undissociated water (258, 328). Table XXVI shows that 68,400 calories are required to form one gram molecule of liquid water from its elements. There- fore, 68400 13800 = 54600 calories is the heat of formation of one gram molecule of hydrogen and hydroxyl ions. ' It is known that very little energy is required to ionize gaseous hydrogen . dissolved in water. 1 Therefore, 54,600 calories is approximately the heat of formation of one equivalent of OH' ions (17 grams). (For meaning of symbols, see 287 ) TABLE XXVIII. Heats of Formation of Ions." (The unit is the large calorie = 1000 common calories.) Ion Symbol Ion Symbol Hydrogen TT . o Copper . . Cu" -i < 8 Potassium Sodium Lithium K- Na- Li- 61.9 57-5 62.0 Copper Mercury Silver Cu- ? g ' Ag' -16. -19.8 2 C. 7 Ammonium .... NH 4 ' 32. 8 Lead Pb" . c Hydroxylamine NH 4 O' -} 1 C Tin Sn" 3? Magnesium . Mg" TOO Chlorine Cl' 2 Q -7 Calcium Ca" IOQ Bromine Br' 28 2 Aluminum Manganese ..... Ferrous ion A1-" Mn- Fe" 121 50.2 22.2 lod'ne Sulphate Sulphite V SO/' SO 3 " I 3- 1 214.4 I ^ I ^ Ferric ion Fe"- o 7 Nitrous NO 2 ' 2 7 Cobalt Co" I 7 Nitric NO/ Nickel Zinc Ni" Zn" 16.- ? c. i Carbonate Hydroxyl .... CO/ HO' 161.1 ?A 6 Cadmium Cd" 18.4 * Jiiptner, i, p. i 2 Jiiptner, i, p. i 79- So. HEAT OF NEUTRALIZATION. 193 Other ionic heats of formation may now be calculated. For example, KOH'aq = 116500 calories (Table XXVI). The ionic heat of formation of K' ions must be 116500 54600 = 61900. KCl'aq = 104300 3100 = 101200. Hence the ionic heat of formation of chlorine ions, (Cl') is 10120061900 = 39300 calories. In this manner Table XXVIII has been constructed. EXPERIMENT XXII. Heat of Neutralization. A calorimeter is prepared as described in 53. Equivalent solutions (for example, twice-normal) of the assigned acid and base are also prepared. One solution is placed in the inner glass calorimeter vessel and the other is poured into a large test-tube which is held by the cardboard cover about a centimeter from the bottom of the inner calorimeter. A delicate thermometer and a glass stirrer are also placed in the inner calorimeter vessel. The outer solution is constantly stirred, and when sufficient time has elapsed for the temperature to become constant, the temperature is read to tenths of the smallest division (e.g. .01), every minute for five minutes, and then the bottom of the test-tube is broken with a glass rod. The liquid is stirred gently but steadily throughout the experiment and the temperature is read every minute until five minutes after the maximum temperature is attained. The temperatures are plotted against the times and the radiation correction is calculated as described in 59. The heat developed is calculated from the corrected change in temperature and the water equivalent of the calorimeter (54) and contents. The specific heats of the solutions may be taken as the same as that of the con- tained water, with little error. The ratio of the heat developed to the number of gram equivalents of salt formed is the molecular heat of neutralization. QUESTIONS. 1. Why should the result be independent of the kind of acid or base employed? 2. Calculate the rise in temperature upon mixing (a) a litre of the assigned base and a litre of the assigned acid; (6) a litre of a 10% solution of the base with a litre of a 10% solution of the acid; (c) a litre of one-half normal solution of the base with a litre of half-normal solution of the acid. 3. Write the ordinary chemical equation for the reaction and also the ionic equation. 202. Heat of Combustion. The heat emitted during the complete oxidization of a unit mass of substance is called the heat of combustion. The unit of mass in physical chemistry 194 THERMOCHEMISTRY. TABLE XXIX. Heat of Formation and Heat of Combustion of Organic Compounds.' (The unit is the large calorie = 1000 common calories). Compound Symbol Heat of Formation Heat of Combus- tion (Vapor) (Liquid) \ Solution Methane CH 4 C 2 H 6 C 3 H 8 C 2 H 4 C 2 H 2 CH 3 OH C 2 H S OH C S H I0 OH C 3 H 8 3 C 2 H 4 2 C l8 H 36 2 CeHe C IO H 8 C 6 H 6 C 7 H 6 2 C 7 H 6 3 C 6 H 7 N C 6 H,N0 2 C IO H I6 18.9 23-3 30-5 14.6 -58.1 53-3 59-8 80.9 112. 1 2 4 of? 11.3 22. 8f 3 6.8f 94- 2f 132.1! "8o'. 3 t' 213-5 372-3 528.4 34i.i 3 I S-7 170.6 325-7 793-9 397-2 209.4 2712. 784 1242. 736 773 735 818 733 1414 !355 Ethane Propane Ethylene Acetylene Methyl alcohol . Ethyl alcohol . . Amyl alcohol . . Glycerine Acetic acid Stearic acid .... Benzol Naphthalene . . . Phenol Benzoic acid . . . Salicylic acid . . . Aniline Nitrobenzene. . . Camphor 61.7 69.9 91.6 161.7 117.2 63-7 72.4 94-4 167.1 117.6 27.4 34-5 91.9 ^ 87.7 125-7 1 1.2- 5-i Cane-su^ar is usually the gram molecule. In engineering it is usually one gram or one pound, and the heat of combustion is often called the heat value or calorific power. Since most compounds are exothermic, the heat of combustion is usually less than that of the oxidation of the separate constituents. There are two rules which are often used for the approximate calculation of the heat of combustion of organic substances. The first rule (Welter's) states that the heat of combustion per gram molecule is equal to the heat of formation of the oxides of the elements which remain after all the oxygen and the equivalent amount of hydrogen for the formation of water have been subtracted. The second rule requires the subtrac- tion of the oxygen and the equivalent amount of carbon for 1 Reychler-Kiihn, pp. 177-181. t S lid. HEAT OF COMBUSTION. 1 95 the formation of carbon dioxide and then the heat of oxida- tion of the remainder is calculated. Illustration. Heat of combustion of stearic acid (C^H^O,,). By the first rule, we subtract H 4 O 2 , leaving C^H^. The heat of combustion of this carbon and hydrogen is i6X 97,600 + 16X68,400 = 2,600,000. By the second rule we would subtract CO 2 and the heat of combustion of the remain- der is 15 X 97, 600 + 18X68, 400 = 2,700,000. The experimental result is 2,700,000. 203. The heat of combustion will depend upon the physical conditions under which the combustion takes place. If the water vapor formed is allowed to condense, the heat of con- densation and that of cooling of the resulting water will be added to the true heat of combustion. If the combustion takes place at constant pressure, the heat of combustion per gram molecule will be greater than that at constant volume by wR6 = 2w(2 73 +/) (184), where w is the decrease in the number of gram molecules. For example, in the combustion of hydrogen H 2 +O=H 2 O w is 1/2 if the water remains as vapor and i 1/2 if it is liquid. Approximate values of the heats of formation may often be calculated from heats of combustion. Methane, CH 4 , for example, has a heat of combustion of 213,500 calories (Table XXIX). If the constituent hydrogen and oxygen were oxidized, the heat emitted would be C +O 2 =CO 2 +97, 600 ;H 4 + 2O 2 = 2H 2 O + 2X68400 or a total of 234,400 calories. Since, by Hess's law, the total amount of heat must be the same if the intermediate product, methane, is formed, the heat of formation of methane must be 234400 213500=20900 calories, which is approximately the value found by direct experiment. PROBLEMS XI. i. If a piece of iron is placed in a solution of copper sulphate, copper is deposited and an equivalent amount of iron goes into solution. Calculate from Table XXVI the heat emitted per gram of copper deposited. 196 THERMOCHEMISTRY. 2. The specific heat of liquid benzol is about .38 and that of the vapor is about .29. What is the approximate latent heat of vapor- ization at 20, if the latent heat at 80 is 93 ? 3. Assuming 12,000 as the heat of formation of ammonia (at con- stant pressure) at 100, calculate the heat of formation at 1000. 4. Calculate the heat of formation of a dilute aqueous solution of (a) sodium chloride, (6) sodium sulphide, from the ionic heats (Table XXVIII) and also from the combined heats of formation and solution (Table XXVI). 5. 450 grams of a solution which contained 9.12 grams of hydro- chloric acid, the temperature of which was 18.22, was mixed with 450 grams of a solution which contained 10 grams of sodium hy- droxide in a calorimeter whose water equivalent was 13. The initial temperature of the latter solution was 18.61. The final corrected temperature of the mixture was 22.17. Calculate the heat of neutralization per gram molecule. (Thomsen.) 6. Calculate the approximate heat of formation of (a) ethane, (6) acetylene, from their heats of combustion. 7. Calculate the heat of combustion of (a) ethane, (b) benzoic acid, by both rules of 202, and compare the results with the experimental values given in Table XXIX. EXPERIMENT XXIII. Heat of Combustion of a Solid Substance. Use of Bomb Calorimeter. Full directions for both the constant volume and constant pressure combustion calorimeters are given in 55 and 56. If a substance of indefinite composition, such as bituminous coal, is used in this experiment, a definite chemical compound, such as ethyl alcohol or benzol, should be used in the next experiment. Express your results in (a) calories per gram, (6) B. T. U. per pound (7), and (c), if the composition is definite, in calories per gram molecule. With (c), calculate the heat of combustion from the composition by both rules of 202 and state the difference in value for constant pressure and constant volume. QUESTIONS. 1. Calculate the heat value of (a) one kilo of this substance, (6) one short ton in B. T. U. per lb., (c) the mechanical energy equivalent to the latter. 2. What error would be caused by (a) an error of 20 in the water equivalent ? (6) allowing a current of 5 amperes to flow through a platinum wire of 2 ohms resistance for 5 seconds? (c) Neglecting the radiation correction ? EXPERIMENT XXIV. Heat of Combustion of a Liquid or Vapor. Use of Junker Calorimeter. Full directions for the use of the Junker calorimeter for both liquid and gaseous substances are given in 57 and 58. It is particularly interesting to use a liquid of known'composition, such as ethyl alcohol, benzol, etc., or a gas of definite composition. HEAT OF COMBUSTION. I 9 7 Express your results in (a) calories per litre (if a gas, the volume must be under standard conditions (4), (6) B. T. U. per gallon or cubic foot, and (c), if the composition is definite, in calories per gram molecule. With (c) calculate the heat of combustion by both rules of 202 and state the difference in value for constant pressure and constant volume. QUESTIONS. 1. Is the heat value of a gas, per gram, definite? 2. What difference would there be in the result vapor escaped without condensing? 3. Why is no radiation correction necessary? 4- Per litre? if all the water What is the heat value of 100 litres of this substance? CHAPTER V. LIGHT. 1 We shall confine this chapter to a study of certain optical phenomena which are of particular interest and importance to chemists. 204. Emission of Light. The electro-magnetic waves in the ether which produce in the eye the sensation of light are emitted by incandescent solids or liquids, by gases subjected to electric forces, and by bodies undergoing certain chemical changes. Incandescent, solid, or molten iron, the mercury vapor lamp, and oxidizing phosphorus may be cited as ex- amples. Secondary light waves are often emitted when bodies are subjected to light. The fluorescence of a solution of sulphate of quinine is an illustration. The emission of ether waves by physical or chemical causes other than high temperature is called luminescence. We shall consider the various types of luminescence after we have considered pure thermal radiation. 205. Thermal Radiation. We shall define a black body as one which completely absorbs all the ether waves which fall upon it. The absorbing power of any body is the fraction which it absorbs, of the energy of the ether waves falling upon it, and the emissive power or emissivity is the ratio of the amount of energy radiated by the body to the energy which would be radiated by a similar black body. In 1 859 KirchofI formulated the following law. " At a given temperature, the ratio between the emissive and absorbing powers, for a given wave length, is the same for all bodies." 2 Ritchie 3 had previously found 1 General references for Chapter V: Wood, "Physical Optics"; Drude, "Theory of Optics"; Preston, "Theory of Light"; Mascart "Optique"; Winkel- mann, 1906, vol. vi; Rapports Paris Congres, 1900, vol. ii; Kayser, "Spectro- scopie"; Landauer, "Spectrum Analysis." 2 Pogg. Ann., 1860, cix, p. 275. 3 Pogg. Ann., 1833, xxviii, p. 378. 198 THERMAL RADIATION. 1 99 experimentally that the greater the absorption of a body, the greater also was the emission. A black body therefore gives also greater emission than any other body. 206. Lamp-black and platinum-black are approximate black bodies. A small aperture in a hollow body, at a constant temperature, is a very perfect black body. Whatever the nature of the walls, any waves which enter the aperture are either absorbed, or suffer multiple reflections, without emerging to any appreciable extent. Radiations from within find even greater difficulty in escaping. Wood gives the following illustration. A fragment of decorated china shows the figure very clearly when heated to incandescence, because of the greater absorption and consequent greater emission of the pigment. If, however, the pigment is heated to the same temperature in the artificial black body just described and is examined through the aperture, the figure is not distinguish- able because the inferiority of emission of the plain china is compensated by greater reflection of the radiations from the interior walls. 207. The Stefan-Boltzman Law for the Total Thermal Radiation. Accompanying the ether waves which affect the eye are usually longer waves which can only be detected by their thermal effects and shorter waves which may be studied by their action on a photographic plate. Stefan, 1 from observations, and Boltzman, 2 from theoretical considerations, deduced the following law connecting the absolute temperature of a body and the total energy of the ether waves which it emits because of its high temperature. If W is the energy emitted by an area A, at absolute temperature 6, in T seconds, W=oAT6* (127) where a is a constant. Kurlbaum^ verified the law ex- perimentally and found that thers. The mean value of the above constant, for a black body, is 2940 (X m in /*) . 210. Planck's LaW for the Spectral Distribution of Energy. Planck3 has derived the following equation for B, the radiant energy, per second, per square centimeter; for wave lengths between A and A +dA, rhere d\ is a very small difference of wave length, at the absolute temperature 6. (129) /hen c-i and c 2 are constants and e is the base of natural logarithms. 211. Wien's Second Equation. If the wave lengths consid- ered are very short, as is the case in optical pyrometry, the parenthesis of Equation 129 may be considered unity. This simpler but less accurate equation was discovered by Wien, 4 >efore Planck's work. Taking logarithms of both sides of ds simpler equation (13, 14), we have InB I 5 ln>* - If we measure the radiation of a definite wave length, at two temperatures, O l and 2 , and subtract the two logarithmic [uations, B 2 _ e (130) 1 Ber. d. K. Akad., Berlin, 1893, p. 55; Wood, 2 Verb. Deutsch. Phys. Gesel., 1899, i, p. 218. 3 Verb. Deutsch. Phys. Gesel., 1900, ii, p. 202. 4 Wied Ann.. 1896, Iviii, p. 662. Phys. Optics," p. 470. 202 LIGHT. If Equation 129 is solved for the maximum value of B, c 2 will be found equal to 5 c (Equation 128) ; hence, c z = 14,700. 212. Optical Pyrometers. 1 Optical pyrometers are instru- ments for determining the temperature of distant bodies from the radiations which they emit. They may be divided into two types. In the first type (Fery thermo-electric telescope) the total radiation is concentrated upon a thermocouple by a fluorite lens and the total energy, B, is measured by the deflection of a galvanometer connected to the thermocouple. The ratio of the temperatures of two bodies is, by Equation 127, proportional to the fourth root of the energy. 213. The second type of optical pyrometer depends upon matching the intensity of the light from the hot body, of a particular color, with the similar light from a lamp in the instrument. These instruments are therefore based upon Equation 130, although all are calibrated empirically from a black body at known temperatures. Red glasses are usually used which limit the radiation to about .65^. In the Le Chatelier pyrometer the light from the hot body is reduced by a calibrated iris diaphragm, to equality with the light from a small gasoline lamp. The Fery absorption pyrometer substitutes absorption wedges for the variable diaphragm. The Wanner pyrometer uses a small incandescent lamp and varies the amount of light from the hot body by means of two Nichol's prisms. 214. The most accurate optical pyrometer is that devised by Holborn and Kurlbaum. 2 The current through a small incandescent lamp is varied until its light is equal to that from the hot body. When such equality has been attained, the filament and the hot body must be at the same temperature (if the radiations of both are similar to the radiation from a black body) . If necessary, one or more red glasses are inter- 1 Excellent discussions of optical pyrometers are given by Waidner and Burgess in Bui. Bureau of Stand., 1905, i, p. 189; and by Haber, "Thermo- dynamics," pp. 281-291. 2 Ber. Akad. d. Wiss., Berlin, 1901, p. 712. (The sale of this instrument in the United States is prevented by patent litigation.) UNIVER OPTICAL PYROMETERS. 203 posed to protect the eye. The instrument is calibrated by determining the current necessary to bring the filament to different temperatures. The current through the filament is adjusted until the filament has the same appearance as a standard black body, and the temperature or the black body is determined by an air thermometer, or thermocouple. A system of lenses assists the comparison. Having such a calibration, the instrument may be used to determine the temperature of any body whose radiation is similar to that of a black body. The error in determining the temperature of so extreme a departure from a black body as brightly polished platinum, amounts to about 74 at 950, but for most bodies it is very much less. I EXPERIMENT XXV. Study of Various Methods of High-temperature Measurements. Electric Furnace, Thermocouple, Platinum Resistance Thermometer, Optical Pyrometer. A hollow black body is heated electrically and the temperature of the interior is determined by means of a calibrated thermocouple. A platinum resistance thermometer is calibrated, and also an in- candescent lamp is calibrated for use as an optical pyrometer. Electric Furnace. The electric furnace (see Fig. 73) consists of a thin porcelain^ cylinder about 15 cm. long and 10 cm. in diameter upon which is wound about 5 m. of No. 22 "Nichrome"3 wire, if a 2 20- volt supply is to be used. Whatever the voltage, the winding must be such as to consume about half a kilowatt. The ends of the cylinder are closed by porcelain caps with proper apertures and the whole is surrounded by many layers of asbestos. Heating and cooling must be very gradual so that the thermo- couple and platinum thermometer may acquire the temperature of the furnace. The highest temperature should not exceed 1000. Thermocouple. A platinum, platinum, 10% rhodium, thermo- couple 4 should be connected to a galvanometer through a key and such a resistance as will keep the deflection on the scale at the highest temperature. The galvanometer with resistance should be calibrated as a voltmeter (49). (The potentiometer method described in 73 is more accurate, but does not permit as rapid observations.) The chart or table accompanying the couple gives the temperature of the 1 See end of articles by Waidner and Burgess, and Haber. 2 The author will be pleased to give any additional information desired in regard to porcelain, etc. 3 Driver-Harris Co., Newark, N. J. * Excellent, calibrated, Hereaus thermocouples and Hereaus platinum wire may be obtained from Charles Engelhardt, Hudson Terminal Building, New York City. 2O4 LIGHT. PLATINUM RESISTANCE THERMOMETER. 205 hot junction when the electromotive force is known. (The cool junction should be in ice and water.) Platinum Resistance Thermometer. The platinum resistance thermometer consists of a coil of fine platinum wire (for example, 50 cm. of No. 30) wound on a porcelain frame and surrounded by a glazed porcelain tube. The coil constitutes one arm of a Wheatstone's bridge (66-68). A pair of dummy leads are connected to an adjoining arm (see figure) and compensate for the heating of the lead wires. A suitable switch connects the galvanometer to either the bridge or the thermocouple. Optical Pyrometer. The optical pyrometer consists of a lens (object-glass) which focuses upon the tip of the filament of a mina- ture incandescent lamp, the interior of the nearly inclosed furnace (ideal black body). The current through the filament is adjusted until the tip of the filament is invisible against the image of the furnace. When this is true, both must be emitting similar light, and therefore (205) they must be at the same temperature. A small eye-piece aids in observing the tip of the filament. Calibrate the incandescent lamp filament, i.e., find the current necessary to heat the tip of the filament to different temperatures. The tem- perature of the filament is determined by finding the temperature of the furnace, by the thermocouple, when the two have the same temperature. Observations. While the furnace is slowly heating, and also while it is slowly cooling, observe at .frequent intervals, (^4) the galvan- ometer deflection with the thermocouple, and the resistance in the galvanometer circuit; (B) the resistance of the platinum ther- mometer; (C) the current through the filament. The three obser- vations should be made in succession and the times of each recorded. (D) Calibrate the galvanometer as described in 49. (E) If time permits, use the optical thermometer to determine the temperature of various distant, brightly-heated bodies, e.g., melted silver, iron, or copper. An image of the hot body is formed upon the tip of the filament, and the current through the latter is adjusted until the two are indistinguishable. The temperature corresponding to this current is obtained from the calibration (see / below) . Report. (a) Tabulate readings. (6) Plot the three sets of readings against the time, (c) From (B) make a plot giving the resistance of the platinum thermometer plotted against the time. Determine R and the two constants, a and 6, of the equation, >) (131) by choosing three values of t, and the corresponding values of Rt, substituting, and solving the three simultaneous equations, (d) Make a third plot with resistances as abscissas and, for ordinates, the plat- inum temperatures, as given by Callender's equation, pt = ioo * _j (132) where R is the exterpolated resistance at o and Ri is the resistance at 100. Transfer to this plot, also, the readings of the true tem- perature, t, and determine the mean value of Callender's difference constant, 5, by applying at several points the equation '- ('33) 206 LIGHT. For pure platinum, 5 is 1.50. The platinum resistance thermome- ter is the most accurate, convenient, method of measuring tem- perature below 1000. (e) Construct a curve which gives the temperature of the tip of the incandescent lamp filament plotted against the current. (/) Finally, determine by the latter curve the temperatures of any bodies tested with the optical pyrometer, and record the results. QUESTIONS. 1. Would you expect the platinum resistance thermometer to attain a slightly higher, or a slightly lower temperature than the thermocouple? Explain. 2. Is any correction required for the absorption of the lenses in such an optical pyrometer? Explain. 3. What small errors were disregarded in calibrating the gal- vanometer? 215. Spectrum of Gases. We have considered thus far the radiation from solids and liquids. It is doubtful if gases or vapors give off appreciable light at any attainable tempera- ture, unless they are simultaneously subjected to chemical changes or electrical forces (luminiscence) . x When a gas is subjected to proper electric forces, it emits light of certain definite wave lengths which are characteristic of the particular gas. If a light from a gas is analyzed by a spectrometer (61) narrow, isolated, bright images of the slit ("lines") are seen in different parts of what would be a continuous spectrum if the gas was replaced by an incan- descent solid. The most convenient method of producing electro-luminiscence is to inclose the gas in a tube provided with platinum electrodes. If the tube is exhausted to a partial vacuum, the gas will transmit a much greater current, at a lower potential, than it will at atmospheric pressure. 216. Spectrum of Vapors. The spectrum of vapors is often obtained in a similar manner, but there are also other methods which are available in many cases. The spectrum of a metallic vapor can be obtained by making a rod or block of the metal one pole of an electric arc. The metal is vaporized and the vapor emits the characteristic spectrum of the metal. Metals, such as sodium, or salts of such metals, can be introduced into a flame supplied with oxygen. The chemical reactions which take place in the hot flame cause the vapor to chemically 1 Fredenhagen, Phys. Zeit., 1907, p. 404, p. 729. r. KIRCHOFF'S LAW. 207 luminesce, and emit its "line" spectrum. Vapors of iodine luminesce where there are great changes of temperature or pressure, and give the characteristic spectrum of iodine. Such luminiscence is probably due to recurring dissociation and association. 1 The radiations from a gas or vapor are usually confined to such exceedingly limited groups of waves that while a por such as iron may emit several thousand such groups, the higher the resolving power of the spectrometer, the more isolated appear the wave lengths in each individual group. The great delicacy of spectrum analysis is due to the fact hat different gases or vapors emit waves of different wave gth, and an exceedingly small amount of gas gives intense diations under electric luminiscence. 217. Kirchoffs Law. Although Kirchoff's law of propor- ionality between absorption and emission has only been ved for pure thermal radiation, and although the emission m vapors and gases appears to be due largely to luminiscence, et gases and vapors generally absorb the radiations which ey emit. This principle has often been used as a method of alysis, in cases where the electric discharge required for an ission spectrum, would be likely to change the composition, e gas, or vapor, is inclosed in a long tube through which the ight from an incandescent source passes, before entering a trometer. The spectrum will be crossed by more or less w bands of all degrees of intensity. Warburg 2 has ently used this method in a beautiful qualitative and uantitative analysis of the various oxides of nitrogen, pro- uced by electric discharge. He worked with waves longer an those which affect the eye (infra-red) and measured the tensity of the radiations with a very narrow bolometer (48), hich was placed successively in different parts of the spectrum. Such bands of appreciable width are characteristic of mpounds, as the narrow lines, described in the previous ragraph are characteristic of the elements. 1 Fredenhagen, /. c. 2 Ann. der Phys., 1909, xxviii, p. 313. 208 LIGHT. 218. Absorption Spectrum of Liquids. Comparatively few liquids retain their characteristic properties at temperatures which are high enough to afford appreciable radiation. We are therefore obliged to study the degree to which they absorb the light from an incandescent solid. All liquids show some absorption, but it is generally extended over quite a range of wave lengths, and the transition between absorption and comparative transparency is usually gradual. Therefore, in the case of liquids, the absorption spectrum is not generally a delicate means of analysis. Solutions of the rare earths, erbium, didymium, europium, and neodymium, absorb limited groups of waves, and therefore, when light transmitted through such solutions is examined with a spectrometer, the spectrum is crossed by dark bands. Potassium permanganate, in a thin layer, of dilute solution, shows five dark bands in the yellow and green. All other .permanganates show the same identical bands, and it is there- fore concluded that the absorption is due to the negative, permanganate ion (168). The narrowing of absorption bands with dilution is explained by Jones 1 as due to increasing hydration (304) of the ions. The more an ion is loaded with water molecules, the more limited is the number of vibrations to which it can respond and which it can thereby absorb. Numerous other salts which have a colored ion (copper ion = blue, cobalt ion=red, ferrous ion=green, ferric ion=yellow, etc.) give more or less distinctive absorption bands, details of which are given in the references. 2 TABLE XXX. Wave Lengths of Ether Waves (mm.). Shortest waves investigated oooi Shortest waves ordinarily transmitted by air Shortest visible waves (violet) Blue Green Yellow . . .00018 .00038 .00045 .00052 .00057 Longest visible waves (red) 0007 5 Longest waves measured by heat effect 0612 Shortest waves measured by electric effect ... 6.0 1 "Elements of Physical Chemistry," p. 242. 2 See Carnegie Institution publications (60. no) of Jones and Uhler. SPECTROSCOPY. 209 EXPERIMENT XXVI. Spectroscopy. Emission and Absorption Spectra. The construction and adjustments of the spectrometer (61) must be studied carefully. The grating spectrometer (64) is prefer- able, since it measures wave lengths directly. (A) Emission Spectrum. The assigned spectrum tube 1 should be mounted in front of the slit of the spectrometer so that the capillary, in which the light is concentrated, coincides with the axis of the collimator. The terminals are connected to a small induction coil, capable of giving a spark of at least i cm. The slit is made as narrow as is consistent with sufficient illumination. The cross hair of the telescope is set successively on each of the more conspicuous bright lines in the spectrum and the position of the telescope is read on the graduated circle. After each prominent bright line in the spectrum has been located on both sides of the undeviated ray, a second set of readings is made on each side, and finally a third set, and the mean position of each line is calculated. The angular deviation of each line is half the angle between the positions on the two sides. If a grating is used, and some other spectrum than the first is brightest, this spectrum should be used and the proper value of the order, n, substituted in the formula (25) a sin 6 ^ n Tabulate the wave lengths and colors of the most prominent lines. (B) Absorption Spectra. The assigned liquid 2 is contained in a hollow glass prism which is mounted horizontally, in front of the slit of the spectrometer. An incandescent lamp, with a ground- glass bulb, is a convenient source of light. This is placed as close as possible to the prism and a little below the level of the slit, on account of the refraction of the prism. It is properly shielded to prevent any light entering the spectrometer without traversing the prism. The lower half of the slit is therefore illuminated with light which has traversed a considerable thickness of solution, while the light which enters the upper part of the slit has passed through very little of the solution. Therefore, a comparison of the top and bottom of the spectrum will show the effect of increasing the thickness of the solution. Set the cross hair of the telescope successively upon the center of each absorption band on each side, and read its position. Repeat the readings at least twice, and find the mean angular deviation, d, of each band (half the angle between the positions on the two sides), and from this, the wave length. Tabulate the wave lengths and the approximate, absorbed color. 1 Hydrogen, water vapor, ammonia, carbon dioxide, and carbon monoxide give satisfactory spectra. Excellent tubes may be obtained of Goetze, Leipsic, or Muller-Uri, Braunschweig. 2 It is interesting to have different students find the positions of the absorp- tion bands of different permanganates, e.g., sodium, potassium, calcium, etc., and compare the results, when the experiment has been completed by all. 14 210 LIGHT. QUESTIONS. 1. How would the appearance of the emission spectrum depend upon (a) the pressure of the gas? (6) the current through the tube? (c) the direction of the current? (d) the length of the capillary? 2. (a) Did the top of the spectrum correspond to a thick or narrow layer of solution ? (&) For which were the absorption bands narrow- est? Explain. 219. Velocity of Light. Refractive Index. Light travels in pure ether with a velocity of 3 Xio 10 cm. per sec. In all transparent material bodies the velocity is less, but the differ- ence is hardly appreciable for gases. (For air, under normal conditions, the ratio is 1.000293.) The ratio of the velocity in ether (or air unless extreme accuracy is required) to the velocity in the body, is called the refractive index of the body. We will designate this quantity by /*. It is shown in physics text-books that when a ray of light (direction of advance of waves) passes obliquely from air (or ether) into a body of refractive index JJL sm x is the angle between the ray in the air and the normal to the surface, and (f> 2 is the angle between the normal and the ray in the body. j is greater than < 2> and, if the ray passes from the body to air, Z is equal to 90 for a particular value of (j) 2 (called the critical angle, c ) . If the light passes from a body whose refractive index is to a body where refractive index is jj. 2 (I36 For, if U e is the velocity in ether and t7 x and U 2 are the velocities in the two bodies U e U e ^ = T7T' ^ = U7 /*! _ U 2 sin 2 H 2 Uj. sin < t PULFRICH REFRACTOMETER. 211 If a ray of light passes through a prism whose angle is A and whose refractive index is /*, the minimum angle of deviation of the ray, D, is given by the equation sin A + B (i37) sin The most accurate method of determining the refractive index of a solid is to cut it into the form of a prism and measure the angle of the prism and the angle of minimum deviation, and calculate JJL by Equation 137. Liquids may be inclosed in a hollow prism with sides of truly plane glass. A more convenient method of measuring the refractive index is to find the critical angle between the body and another body whose refractive index is known, and calculate /* by Equations 135 and 136. Such an instrument is called a refractometer. 220. Pulfrich Refractometer. Fig. 74 illustrates the prin- ciple of the Pulfrich refractometer. The liquid is contained in a glass cell which rests on the horizontal face of a right-angle prism. A horizontal beam of light , from a monochromatic source (60), is focused by a lens, upon a point in the surface between the liquid and the glass. A horizontal beam of light will enter the prism at the critical angle, e (see figure), and will emerge from the prism at the angle - 74 ' i, which is observed with a telescope. If N is the refractive index of the prism, and JJL that of the liquid, sin i sin sin ^ sin (90 e) cos e for sin e N (Equation 136) =\/N 2 sin 2 i 212 LIGHT. Values of N for different wave lengths (colors) are furnished with the instrument. It is well to test the instrument first, with a liquid whose refractive index has been carefully determined (see Table XXXI). Directions for obtaining the zero correction are given under Experi- ment XXVII. Instruments are often furnished with a closed tube which stands in the top of the liquid and through which passes a constant stream of water from a thermostat, which serves to keep the temperature of the liquid constant. 221. Abbe Refractometer. Fig. 75 represents a form of Abbe re- fractometer made by Zeiss, of Jena, which is very satisfactory for general laboratory use. A very thin layer of the liquid is inclosed between two prisms (Fig. 79) and the angle i is determined from the difference in the position of the prisms P (Fig. 75), when light traverses the liquid at grazing in- cidence, and when i is zero. The latter position is obtained when the reflection of a portion of the cross hairs which is illuminated by a small prism (a), Fig. 75, coincides with the cross hairs on the other side (see Fig. 76). The position of the prism for the grazing ray illustrated in Fig. 79 is the position where the cross hairs meet on the dividing line between darkness and light. Monochromatic light is necessary for accurate setting. The position of the prism is read by means of a vernier reading to two minutes, attached to the arm A . FIG. 75. ABBE REFRACTOMETER. 213 If /t is the refractive index of the film of liquid and N that of the glass fi = N sin e (Equations 135 and 136, and Fig. 79) (139) FIG. 76. We must determine e in terms of ^ the angle of the prism and i the angle observed. We have e = () r sin i sin r=- N (140) (141) If and N are not given, they can easily be determined. is measured by finding the positions of the single upper FIG. 78 FIG. 79. prism, for reflection of the illuminated cross hairs, from each of the two faces inclosing the angle. The angle between these two positions is evidently the supplement of (62). After (j> has been determined, N is determined by the above 214 LIGHT. equations, from the value of i for 139, 140 and 141 i', that is, for air. From sin 2 sn / -sin 2 *= A^ ---- AT C S i + sin i cos = .88oandM = 78. Substituting in Equation 143, = 26.13 224. Dispersion. The refractive index, and therefore the refractivity, varies with the wave length (or color) of the light. The difference in the refractive indices for two colors is called the dispersion for these colors, and the difference in refrac- tivities is called the dispersivity. The molecular and atomic dispersivities are analogous to the molecular and atomic refractivities. EXPERIMENT XXVII. Refractive Indices and Refractivities of Liquids. Use of Refractometer. First study carefully the construction and use of the refractometer. All the glass surfaces must be made scrupulously clean. A very soft clean cloth should be used. If a Pulfrich instrument is to be employed, determine the zero; that is, the position of the telescope when the axis of the telescope is parallel to the top of the prism. A portion of the cross hairs is illuminated by a small prism (Fig. 76). The telescope is adjusted until the image of this portion of the cross hairs, reflected from the vertical side of the prism, coincides with the cross hairs on the other side. The refractive index and the angle of the prism of an Abbe refractometer must be determined as described in 221. (A) Determine the refractive index of pure water and of an assigned solution. Determine also the density of the latter (36). The density of water at the temperature 'of the experiment may be obtained from Table LI. Calculate the refractivity of water and of the solution, and, finally, by Equation 109, determine the refrac- tivity of the dissolved substance. Monochromatic light (60) should be used. If possible, use several colors, but if only one monochro- matic source is available, make one determination with white light and find the approximate angle for both extremes of the spectrum, The difference in refractive indices (dispersion) should be calculated, and also the difference in refractivities (dispersivity). (B) Determine the refractive index and dispersion of an assigned organic liquid and also the density (36), unless it is given in Table LIV. Calculate its refractivity and molecular refractivity and com- pare with the value calculated from the atomic refractivities (Table XXXII). Estimate the dispersion, dispersivity and molecular dispersivity. (C) If time permit, determine the refractive indices of a series of normal or half-normal solutions similar to those used in Experiment XVI, and demonstrate that the refractive index is an approximate additive property for highly dissociated solutions. ROTATORY POLARIZATION. 217 QUESTIONS. 1. What is the velocity of light (a) in the first liquid? (6) in the second? 2. A ray of light strikes the liquid surface at an angle of incidence of 30. What is the angle of refraction in (a) the first liquid? (6) the second? 3. What is the critical angle of (a) the first liquid? (6) the second? 4. If the second liquid forms a layer upon the first, and a ray of light meets the boundary at an angle of incidence of 45 in the first liquid, what is the angle in the second? Rotatory Polarization. 225. The vibrations of ordinary light are in every direction and of every conceivable form. Certain instruments, particu- larly the Nichol's prism, resolve these heterogeneous vibra- tions into linear vibrations in one direction and the light is then said to be plane-polarized. Certain bodies have the property of changing the direction of vibration of such light; that is, as the plane-polarized light advances through the medium, the direction of vibration continuously rotates. This phenomenon is called rotatory polarization, and the bodies are said to be optically active. Optically active bodies have a type of dissymmetry il- lustrated by a screw or helix. For a given direction of ad- vance, the structure is different for one direction of rotation from what it is for the other. Just as there are right- and left-handed screws, so there are right- and left-handed opti- cally active bodies. If the direction of rotation appears clockwise to an observer receiving the light, it is called right- handed, and vice versa. A quartz crystal has such a dissymmetry in the arrangement of its faces, and, according to the form of the dissymmetry, it rotates the plane of polarization to the right or left. A similar condition exists among the atoms of a molecule having an asymmetric carbon atom; for example, dextro- or laevo- tartaric acid. When a transparent body is subjected to twist about an. axis coincident with the direction of the light, the mechanical structure acquires similar dissymmetry and the body shows rotatory polarization. 1 1 Ewell, Am. Jo. of Science, 1899, viii, p. 89; 1903, xv, p. 363; Phys. Zeit., 1899, p. 18; 1903, p. 706; Johns Hopkins Circulars, 1900, June. 2l8 LIGHT. In all these cases the structure is such that a light vibration, consisting of rotation in a circle about the direction of advance of the light, travels with different velocities according as the direction of rotation agrees with, or is opposite to, a direction which is determined by the structure. It is easily shown graphically and analytically that a linear vibration is equivalent to two opposite circular vibra- tions, and if one of these travels faster than the other, the direction of the resultant linear vibration rotates. 226. In physical chemistry we are particularly concerned with the optical activity of bodies having one or more assym- metric atoms and particularly with solutions of such bodies. The amount of rotation, 0, depends upon the length of the solu- tion, the mass of solute in unit volume of the solution, the temperature, and the wave length of the light employed. If m = mass of solute, m =mass of solvent, / =length of solu- tion, and p= density of the solution, the volume of the solu- tion is (m +m ) / p and the mass of solute in unit volume of the solution is mp - (i 4 6) The constant [<]*> is called the specific rotatory power or specific rotation. The lower suffix (D) states the kind of light employed and the upper (t) , the temperature. / is usually expressed in decimeters. If /=i, and _ mfj ' =i, or, the specific rotatory power is the rotation produced by one decimeter of solution which contains one gram of active sub- stance per cubic centimeter. For a pure active liquid, m = O and (i47) MAGNETIC ROTATION. 219 The specific rotatory power, 'multiplied by the molecular weight, r , is called the molecular rotatory power . For convenience, one lundredth of this constant is commonly employed. 227. For many substances, such as, for example, the sugars, the specific rotatory power is approximately constant ; that is, is quite independent of the concentration, and therefore :he rotation of the plane of polarization may be used as convenient method of measuring the concentration. With lany other substances, however, it varies with the concentra- tion, and, if dissolved, with the nature of the solvent. If, lowever, different salts of an active base or of an active acid ire dissolved in a common solvent, and a number of decreasing mcentrations of the resulting solutions are examined, the >tation at great dilution, for all the salts, has the same r alue (Oudeman's law). This obviously is in accord with ie dissociation theory ( 1 68) . TABLE XXXIII. Specific Rotatory Power (20). Yellow Sodium Light (D).* Active Substance Concentration (=c) (gr.in TOOC.C.) [0] 2C > ^ane-sugar, R / 3-28 \ 10-86 66.639 . 66.453-. 0208(7 000124^ nvert sugar, L 1-14 20.07 ~- 041(7 Glucose (dextrose). R (crystallized) 0-100% 4773 ~\~ 01 5 X % 7 ructose (levulose) L . . 0-40 *T I 1 J 100-3 + Milk-sugar, R 5-7 5^-53 Fartaric acid, R Quartz, R or L I 22-63 15.06 - 13.436-. 2 1. 70 (tor i mm I$IC ii gc . thickness) 228. Magnetic Rotation. It is explained in treatises on physical optics that a certain rotation is associated with a magnetic field, which in many bodies rotates the direction of the light vibrations of a ray of light parallel to the magnetic field. There is, however, no such dissymmetry associated with 1 Landolt and Bornstein. 220 LIGHT. this rotation as is illustrated by a screw. The light vibra- tions are rotated in the same direction, whether the ray is traveling in the direction of the magnetic field or in the opposite direction. The amount of the rotation is propor- tional to the integral product of the strength of the magnetic field and the length of the body. The magnetic rotatory power of a substance may be defined in either of two ways. The absolute unit is called Verdet's constant and is equal to the rotation, in minutes, of a column one centimeter long in unit (C, G, 5.) magnetic field (8). Often, however, the rotatory power is measured by the ratio of the rotation in the substance to that in a column of water, of equal length, in a similar magnetic field. This ratio, divided by the density of the substance, is called the specific magnetic rotation. 229. Rotatory Dispersion. Both the natural and the magnetic rotation of the plane of polarization are, approxi- mately, inversely proportional to the square of the wave length of the light employed. TABLE XXXIV. Magneto-optic Rotation (20). Yellow Sodium Light (D). Liquid Verdet's Constant in Minutes l Specific Magnetic Rotation Acetone Amyl alcohol Ethyl alcohol Methyl alcohol Benzol . .0113' .0128 .OI 12 .0093 1.080 1.204 1.070 9i3 2 ^O 2 Carbon bisulphide Chloroform Toluene Water .0441 .0164 .025 .0132 2-505 .839 2-354 i 230. Polarimeters. The simplest polarimeter consists of a Nichol's prism (polarizer) to resolve the light vibrations into one direction, a tube to contain the specimen, and a second Nichol's prism (analyzer) which locates the direction of vibra- 1 Smithsonian Tables, No. 305. POLARIMETERS. 221 tion of the light after it has traversed the specimen. The inalyzer is set so as to transmit no light. Such is evidently the case when the direction of vibration of the light incident >n the analyzer is perpendicular to the vibrations which it would transmit. The specimen is then removed and the analy- zer is reset for darkness. The angle between the two positions is obviously equal to the rotation of the specimen. The. setting of a Nichol's prism for darkness is usually uncertain by one or two degrees, and therefore more accurate instruments have been de- vised. : 231. We will first describe the bi- quartz polarimeter. The biquartz is a E double plate, one side being of right- handed quartz and the other of left- handed quartz, and the simplest mounting is illustrated in Fig. 81. The analyzer is rotated until both lives of the biquartz appear the FlG - 8o - tme (purple) color, first without the specimen, then with the specimen ; and the difference in readings gives the angle of rotation for yellow light. There are additional collimating lenses which render the light parallel before entering the solu- tion, and observing lenses which give a clear image of the bi- luartz. Fig. 80 explains the color changes. R and L FIG. 81. are the two halves of the biquartz, viewed from the analyzer. 'he two halves are of such a thickness (3.75 mm.) that the plane of polarization of yellow light is rotated through 90. )wing to the rotatory dispersion (229), the other colors will be rotated different amounts as shown by the letters R 222 ... LIGHT. (red) and B (blue). If the analyzer is set to transmit light vibrations parallel to those which left the polarizer, the yellow light will be omitted and each half of the biquartz will appear of a purplish color ("tint of passage"). If the analyzer is displaced slightly clockwise, more of the red component on the right will be transmitted and less of the blue, and there- fore this half will appear red and the other half will appear blue. If a dextro-rotatory specimen is placed between the bi- quartz and the analyzer, the directions of vibration of the different colors, will be rotated to the positions indicated by the dotted lines and the analyzer must be rotated to a new position (/'), perpendicular to the emerging yellow vibration, in order to have the two halves the same color. With the help of the biquartz the analyzer can be set within about a tenth of a degree. 232. The essential parts of the Lippich type of half-shade polarimeter are illustrated in Fig. 82. The smaller Nichol's prism of the polarizer is at a small angle with the larger FIG. 82. Nichol's prism, so that, unless the analyzer is properly placed, bisecting the angle between them, the two parts of the field appear of different shades. The analyzer is set so that both halves of the field appear equally bright, first without the specimen, then with the specimen, and the difference is the angle of rotation. The angle between the two Nichol's prisms of the polarizer can be varied. The smaller the angle, the greater is the sensitiveness, but the illumination is thereby reduced. There are also lenses for making the incident light parallel and for observing the line of separation of the compound polarizer. The addition of the half- shade device gives greater sensitive- ness than the biquartz (about .01 degree). SACCHARIMETERS. 223 In all polarimeters there are obviously two positions of the analyzer, 180 apart, where the two halves appear equally dark or the same dark color. There are also two intermediate positions where the two halves appear the same bright color or equally bright. The latter positions are not as sensitive as the former. Since the rotatory power of most substances changes with the temperature, in accurate work, the observation tube should be surrounded by a jacket through which flows water from a thermostat. 233. Saccharimeters. With some polarimeters, particularly those used for sugar analysis (saccharimeters) , the analyzer FIG. 83. is not rotated, but the rotation produced by the specimen is neutralized by a quartz wedge or wedges (see Fig. 83). The letters specify the rotations of the quartz. If the wedges are drawn apart, right-handed rotation will be neutralized, and vice versa. A scale is attached to one wedge and the unit is usually the Ventske, i.e., 100 divisions equal the rotation produced by 26.048 gr. of sugar in 100 c.c. of solution, at 17.5, in a tube 20 cm. long (i mm. of quartz produces the same rotation) . PROBLEMS XII. 1. (a). Calculate the amount of energy radiated in one hour by a carbon sphere i cm. in diameter at a temperature of 1000. (6) What is the wave length of the most intense radiation from such a source ? 2. Langley found the most intense radiations from the sun at wave length .0005 mm. Calculate the approximate temperature of the sun. 3. (a) At any instant how many red waves are comprised in a distance of one metre from a hydrogen tube in operation? (6) How many are issued per second ? [Remember that u =nX, (Eq. 88'")]. 4. What is the velocity of yellow light (a) in water? (6) in carbon bisulphide? 224 LIGHT. 5. A layer of water is poured upon carbon bisulphide. A ray of light enters the water at an angle of 30 in air. What is the angle in (a) the water? (b) in the carbon bisulphide? 6. Calculate the molecular refractivity of water (D light) and com- pare the result with that calculated from the atomic refractivities. 7. Calculate the rotation produced by 50 cm. of (a) a 2% solution of invert sugar; (6) a 2 % solution of dextro-tartaric acid. 8. What is the concentration of a sugar solution, if a tube of the solution 22 cm. long gives a rotation of io? 9. 10 cm. of a certain sugar solution gave 40 Ventske units in a saccharimeter. Calculate the concentration. 10. What is the rotation in a tube of carbon bisulphide, 20 cm. long, situated in and parallel to, a magnetic field of strength 100? EXPERIMENT XXVIII. Polarimetry, Specific Rotation. Study carefully the construction and operation of the polarimeter (230-233). Prepare the assigned solution by dissolving a carefully weighed amount of the active solute in a graduated flask which is filled with distilled water to TOO c.c. Fill one of the tubes with distilled water and make several readings of both zero positions, with both verniers (if the instrument has two). Pour the assigned solution into a carefully cleaned tube and make an equal number of readings of the position of the analyzer. If the instrument is not provided with a thermostat device, great care is necessary that the temperature does not change appreciably. Determine similarly the rotation of several other concentrations of the assigned substance. From the mean rotations, calculate the specific rotations and plot them against concentrations. If time permits and a Lippish instrument is used, determine the specific rotation for several other wave lengths (229). QUESTIONS. 1. Calculate the rotation produced by a meter column of the first solution. 2. What is the purpose of (a) both zero readings? (6) two verniers ? 3. What would be the effect of using white light? 4. Construct an equation from your observations which will represent the specific rotation for different concentrations. la^ I CHAPTER VI. CHEMICAL KINETICS. 1 234. The Law of Mass Action. With certain limitations discussed later, the rapidity of chemical or physical changes is proportional to the amount changing. The validity of this law in many systems is axiomatic, for we may imagine the system undergoing change to- be divided into equal portions, d the total change per unit time is obviously proportional to the number of parts. But if we mean by amount the amount per unit volume, that is, the concentration, which is the usual understanding in chemical problems, the validity of the law is not self-evident. It has, however, been demon- strated by experiments mentioned below, and we will accept it as the foundation of this chapter. In a crude fashion we can explain the law if we consider such changes from a mechanical point of view. We can regard the changes as due to the impact of particles or their proximity, and, therefore, the greater the concentration, the greater the rapidity of change. 235. A chemical or physical system of bodies may be regarded, or studied, from either of two points of view. One is the integral, where we study the total mass, m; volume, v, and ntropy T? (and sometimes energy and heat) ; the other is the differential, where a small portion of the system is considered. We then consider the so-called intensity factors which are the e for any part of the system as for the whole. The inten- sity factors are pressure, p\ temperature, t, and concentration, c. In place of concentration, we may use Gibbs' potential u, e potential of any system being the work required to intro- uce unit mass (compare electrical potential =work required 1 General references for Chapters VI and VII: Meyer, "Chemische Reaktions- ischwindigkeit "; Van't Hoff, Lectures, vol. i; Mellor, "Chemical Statics and Jynamics"; Chap. I-VI; Jiiptner, vol ii; Walker, Chap. XXIV; Nernst, iii, :hap. I, V. s 225 226 CHEMICAL KINETICS. to bring up unit charge). 1 Notice that the intensity factors are the derivatives of the energy with respect to the three magnitudes, volume, mass, and entropy. dW dW dW r - = p; j = t; -j = a (see Chap. II) (148) dv drj dm If the change is accompanied by alteration of the intensity factors, pressure or temperature, or alteration of the potential from without the system, the above simple law may obviously fail, since it considers only the integral factors. (Of course the potential does not remain constant, for the change is due to inequalities of potential and continues until the potentials are the same throughout the system.) 236. In chemical changes, the rapidity of change is deter- mined by the mass per unit volume, i.e., the concentration. If all of the substance does not take part in the reaction, that portion which does is called the active mass. 2 Suppose we have a chemical system where the temperature, total pressure, and total mass remain constant, so that the above law holds. We will suppose a reaction taking place which we will represent schematically as HiA + HzB+nf- n/A' + n 2 'B' + n 3 'C' - -(149) Where A, B, C, --- A', B' t C', - - are the reacting molecules and n lf n a , w 3 , etc., are the numbers of these molecules. The rapidity with which the left-hand side changes will be proportional to the number of each of the reacting molecules, and therefore to their product, or, c Xc 2 n2 Xc 3 M3 if the concentration of A is c lt of B is c a , etc., for n t A is equivalent to A . + A n times. Hence in the total product we have c x ni If the above are the initial concentrations, and after time, /, the change in the concentrations is x, the velocity at this time will be dx u = k(c l -x}^(c 2 -x} n *--- = -^ (150) 1 Phil. Mag., Nov., 1908, p. 818; Jiiptner, ii, 2, pp. 244, 245. Nernst, pp. 612, 614. 2 Walker, p. 257. MONOMOLECULAR REACTIONS. 227 where k is a constant called tbe velocity constant. The principle described above and expressed in this equation is known as the law of mass*action and was first formulated by Guldberg and Waage. 1 This differential equation can be integrated in a few simple cases. 237. (A] Monomolecular Reactions. The reaction con- sists of the decomposition of a single molecule; that is, it is monomolecular . dx .-. u = - = k(c-x) (151) (i53) We shall consider for the present complete reactions; that is, reactions where the final concentration of the original substance is practically zero, c, therefore, is both the initial concentration, and the total change in concentration. c #! is the concentration which is still to change at time / x and cx 2 is the unchanged concentration at time t 2 . In the experiments which follow, we do not measure the concentra- tions directly, but certain physical magnitudes proportional to the concentrations. If we plot these observations against the time, we can find the above ratios without working out the actual concentrations. It is customary to use the minute as the unit of time in chemical mechanics. If we can begin our observations at the beginning of the reaction, we can set t l = o, x l =o *-'-** ('545 and we only need the ratio of the total change, to the change remaining at time /. Notice that the equation for the velocity 1 Ostwald's " Klassiker," 104. 228 CHEMICAL KINETICS. constant of a monomolecular reaction does not involve the actual concentration. If we know k for a particular reaction, we can find the velocity of the reaction (change in concentration per minute) by multiplying the instantaneous concentration by k (Equa- tion 151). 238. Period or Time Constant. Let T be the time required for the reaction to be half completed T is often called the time constant or period of the reaction. 239. Exponential Formula. We may write Equation i 54 c x -kt=\n e-kt. c c x c . . c x = ce-kt and x = c(i e-ki) (156) There are comparatively few reactions whose velocity is neither too great nor too small for laboratory measurement and this is particularly true of monomolecular reactions. If the resources of an organic laboratory are available, a very good illustration is the change of acetochloranilide to the para-form. 1 The various radioactive transformations are monomolecular (3 49> 3 51), but these are complicated by successive reactions. The hydrolysis of an ester, the decomposition of benzol- diazonium chloride and the inversion of cane-sugar behave as monomolecular reactions. These are strictly bimolecular reactions, but the other component (water) has usually so high a concentration compared with the other substance that it may be regarded as constant or taking no part in the reaction. PROBLEMS XIII. i. In a certain monomolecular reaction, the initial concentration is 5. The concentration at 10 A.M. is three, and at 4 P.M. is one. Calculate (a) the velocity constant; (b) the initial velocity of the reaction ; (c) the period ; (d) when did the reaction commence ? 1 Blanksma, Rec. trav. Pays-Bas., 1902, xxi, p. 366; 1903, xxii, p. 290. THE CATALYSIS OF AN ESTER. 22Q 2. The period of a certain monomolecular reaction is one hour and the initial concentration is 10. Find (a) concentration after 30 minutes; (6) concentration after two hours; (c) velocity of the reaction at this time ; (d) plot a curve which will represent the progress of this reaction. 3. Derive an expression connecting T', the time when the fraction i /e remains unchanged, and k. e is the base of natural logarithms. (Answer: T' = i/k.) 240. The Catalysis of an Ester. 1 Comparison of Strengths of Acids. 2 If an ester, such as methyl acetate, is dissolved in water, a large portion of the salt ultimately breaks up into acid and alcohol, according to the equation CH 3 OOC 2 H 3 + H 2 O CH 3 COOH + CH 3 OH The change is greatly accelerated if an acid is present, and the so-called strongest acids, such as hydrochloric, have the greatest accelerating influence. In fact, if the different acids are tabulated in the order of their various properties, such as replacing power, dissociation, inversion of sugar, etc., this characteristic is in the same order. All of these prop- erties are therefore said to be a measure of the strength or affinity of the acid. We shall see later that the characteristic of an acid solution is the presence of free hydrogen ions, or atoms with positive charges, and that the strength of the acid is a measure of the number of hydrogen ions. The acid apparently takes no part in the reaction , but merely accelerates it . Such an accelerating agent is called a catalyser. EXPERIMENT XXIX. Catalysis of an Ester. We shall follow the above reaction by measuring the acid formed .at different times, and from the observation we shall calculate the velocity constant. Prepare the following apparatus. A thermostata (81) at about 25', containing a 75 c.c. Erlenmeyer flask with a paraffined cork, and a small bottle of methyl acetate. Both should 1 Ostwald, Journ, prakt. Chem., 1883, xxviii, p. 449; Hemptinne, Zeit. phys. Chem., 1899, xxxi, p. 35. * Walker, Chap. XXV. 3 A thermostat is recommended in this and following experiments, but a simple water-bath whose temperature is maintained within .5 gives fair results, and even this may be dispensed with if the temperature of the room is very constant and the liquids are not subjected to appreciable changes of temperature. 230 CHEMICAL KINETICS. be submerged to their necks by weights or frames. Two 100 c.c. Erlenmeyer flasks, three 2 c.c. pipettes. A burette and solution of approximately n/2o barium hydroxide ( 90), whose strength has been carefully determined by titration against a standard hydrochloric or other acid solution. An abundance of CO 2 free water (90). All the vessels should be scrupulously clean. Prepare a semi-normal solution of the assigned 1 acid and put 50 c.c. in the small flask. In each of the larger flasks pour about 30 c.c. of CO 2 -free water. When all is ready, fill a 2 c.c. pipette with the methyl acetate and discharge it into the acid solution. Mix thoroughly, and imme- diately withdraw 2 c.c. in one of the other pipettes and discharge into the water in one of the larger flasks. Note the exact time when the reaction is stopped by this dilution. Immediately titrate with the baryta solution, using phenolphthalein as an indicator. Ten minutes later withdraw 2 c.c. more, and repeat the dilution with observation of time and titration. So continue, increasing the length of time between the withdrawal of samples as the rate of change decreases. The final titration should be at least two days after the first. Plot your results with times as abscissae and titrations as ordinates, and draw a smooth curve. Since only the ratio of concentrations is required, titrations may be substituted. The total change in concentration, i.e., the initial concentration, c, will be equal to the total acetic acid produced which is measured by the total change in titration T^ T . T is the initial titre in c.c. and T^ the final. The concentration of the unchanged ester, c x, at any time / will be proportional to the remaining change in titration, T^Tt where Tt is the titre at that instant. .'., by Equation i 54 , 2 . "? i * 00 * O / .\ = ^log r Tt (i54') t 1 GO 1 1 If there is any uncertainty about T , the titre before any acetic acid has formed, find the titre of 50 c.c. of the assigned half-normal acid plus 2 c.c. of water. Or, Equation i 53 may be used. Choose 5 typical ordinates of the smooth curve, find the correspond- ing times and calculate the values of k. Take the mean. 2 QUESTIONS. 1. What was the initial velocity of the reaction? In what units is it expressed? 2. Calculate from the mean velocity constant the time when the reaction was one-half completed and compare with the experimental result obtained from the curve. (Time constant.) 3. Calculate the final concentration (gram equivalents per litre) of water, acetic acid, and alcohol. 1 This experiment may be varied by assigning different acids to successive students. When all have completed the experiment, the different values of the velocity constant may be given the entire class for comparison. 2 In almost all the experiments of this chapter a so-called constant is determined which by the theory should be invariable. The experiment may give values varying 10% or more, but such lack of agreement should be compared with the great variation in the individual factors from which it is calculated and their possible errors (see , 16-20). INVERSION OF CANE-SUGAR. 231 241. The Inversion of Cane-sugar. 1 Comparison of the Strengths of Acids. 2 Cane-sugar, dissolved in acidulated water, gradually breaks up into a mixture of glucose and fructose (dextrose and laevulose) , which is called invert sugar, the reaction being C I2 H 22 II +H 2 O = 2C 6 H I2 O 6 The cane-sugar on the left-hand side gives a right-handed rotation of the plane of polarization of polarized light (225) and the mixture of the two isomers on the right gives a net left-handed rotation. Therefore, the progress of the reaction can be studied by observing the rotation. The acid apparently takes no part in the reaction, but acts as an accelerating or so-called catalytic agent. A compari- son of the rates of inversion produced by different acids, shows that this property varies with the strength, or affinity, of the acid, which we will find later varies with the concentration of hydrogen ions (see preceding experiment). The rotations produced by both cane and invert sugars are closely proportional to the concentrations. Since, therefore, in the formula for the velocity constant we have only the ratio of concentrations, we may substitute total change in rotation $ for total change in concentration (or initial con- centration) , c, and change in rotation ^ at any time t, for the corresponding change in concentration x. Therefore, if we count time from the instant that we begin to observe the rotation, by Equation 154 k, the velocity constant, is the factor by which the concentra- tion of unchanged sugar must be multiplied to obtain the instantaneous velocity of inversion. 1 Wilhelmy, Pogg. Ann., 1850, Ixxxi, p. 413; p. 499. * Walker, Chap. XXV. 232 CHEMICAL KINETICS. EXPERIMENT XXX. Inversion of Cane-sugar. 1 We will use a comparatively dilute solution so that the change in concentration of the water may be inappreciable, and the reaction may behave as monomolecular. See 230-233 for a full description of the construction and operation of the polarimeter. The rotation changes considerably with the temperature and hence the rotation tube should properly be surrounded by a thermostat jacket, but this is not absolutely necessary if the room temperature is maintained very constant. Mix thoroughly equal volumes of the assigned sugar solution (e.g., 20% = 20 gr. in 100 c.c.), and the assigned half-normal acid solution. Fill a polarimeter tube as quickly as possible, and determine the rotation. If the instrument has a double vernier, there will only be time to read one. After a few minutes, read the rotation again, and so continue, observing carefully both rotations and time, and making the intervals longer as the changes become less. The later readings should be at intervals of several hours and the last after two days. Plot rotations against times as abscissae. The later rotations will of course be negative. Draw a smooth curve through the obser- vations, choose five points on the curve and for each calculate the velocity constant and take the mean. In the preceding experiment we showed how the reaction could be followed from the beginning. We could do the same b,ere by finding the rotation for a solution where the acid is replaced by water. It is simpler, however, to consider the time of the first observation as the beginning of the reaction. The initial concentration is then of course different from the original solution, but this is not material^ QUESTIONS. 1. How many grams of cane-sugar would be inverted per minute in a litre of 10% solution, if the acidification was the same as in this experiment ? 2. Compare the experimental and calculated values of the time constant of this reaction. 3. Show that no error is introduced by considering the change in rotation proportional to the change in concentration, although the specific rotation (226) of the mixture constituting invert sugar is less than that of cane-sugar. 242. Hydrolysis of a Salt. 2 A salt composed of a weak base and a strong acid, such as ferric chloride, copper sulphate or carbamide hydrochloride, partially breaks up when dis- solved, into the acid and base; for example, FeCl 3 + 3 H 2 O = Fe(OH) 3 + 3 HC1 1 The experiment may be varied by assigning different half normal acids (and the same sugar solution) to successive students. When all have completed the experiment the different velocity constants should be given the class for comparison. 2 See also Experiments XXXI and XXXIV; and 245, 261; Mellor, pp. 207-216; Juptner, ii, pp. 79-83; Walker, Chap. XXVII. HYDROLYSIS OF A SALT. 233 This phenomenon is known as hydrolysis or hydrolytic disso- ciation. The acid is much the stronger and the solution shows an acid reaction. Therefore, it should produce inversion of sugar and catalysis of an ester, and such will be found to be the case if the hydrolysis is sufficient. The degree of hydroly- sis is measured by the ratio of the acidity of the solution, to the strength of the acid, if the hydrolysis was complete. It must therefore equal the ratio of the velocity of inversion, or catalysis, in a solution of the salt, to the velocity in a solution of the resulting acid of strength equivalent to that of the salt. The ratio of the velocities will evidently be the ratio of the velocity constants. Little acid is formed unless the base is very weak, and therefore in this case only is the method accurate. PROBLEMS XIV. 1. Arseniuretted hydrogen decomposes, monomolecularly, at a moderately high temperature. The velocity constant at 367 is .0034. (a) How long a time will be required for 6 grams to be de- composed out of an initial mass of 10 grams? (6) At what rate is it changing at the end of this time ? (c) Plot a curve which will show the progress of the reaction. 2. The velocity constant of a 20% sugar solution in n/2 lactic acid at 25 is .000023. Find (a) the concentration one day after mixing ; (6) the velocity of inversion at this time ; (c) the time required for in- version of half the sugar, (d) If the velocity constant of n/2 sul- phuric acid is .005, compare the strengths of the two acids. 3. A certain sugar solution gave the following rotations, t minutes after an acid was added. t angle o 46.75 30 41.00 90 3-75 I2O 26.OO GO -18.70 4. The velocity constant of normal hydrochloric acid at 25 is .015, that of n/4 urea hydrochloride is .0006. What is (a) the degree of hydrolysis of the latter? (b) the concentration of free acid? 5. The activity (in arbitrary units) of a certain volume of radium emanation was as follows: Calculate the velocity constant. Time (hrs.) o 20.8 187.6 354-9 521.9 786.9 Activity. 100 85.7 24. 6.9 !-5 .19 Calculate the velocity constant (= radio-ac- tive constant) and the period (Meyer, p. 25). 234 CHEMICAL KINETICS. EXPERIMENT XXXI. Hydrolysis of Carbamide Hydrochloride. 1 In 100 c.c. of half-normal hydrochloric acid solution, dissolve an equivalent amount of carbamide. Repeat Experiment XXIX (catalysis of methyl acetate), with this solution substituted for the acid. Carry on a parallel experiment with half-normal hydro- chloric acid solution. From the ratio' of the two average velocity constants, determine the degree of hydrolysis. The degree of hydrolysis may also be determined by Experiment XXX (velocity of inversion of cane-sugar), the acid solution being replaced by an equivalent solution of carbamide hydrochloride. QUESTIONS. 1. It is shown in more complete treatises that the presence of a neutral salt retards the reaction. How could you experimentally correct for the effect of the neutral salt in the above experiment ? 2. Explain which method you consider preferable. EXPERIMENT XXXII. The Decomposition of Diazonium Salt. 2 In the previous experiment we have followed the reaction by chemical analysis or measurement of the rotatory polarization. In this experiment we shall use a third method, namely, measurement of the volume of gas produced. Benzol diazonium chloride, C6H 5 N 2 C1, is prepared at zero degrees, in aqueous solution. Upon raising the temperature of the solution, the salt reacts with water, forming phenol, hydrochloric acid, and nitrogen according to the equation: C 6 H 5 N 2 C1 + H 2 0=C 6 H 5 We shall use so large an excess of water that the reaction is prac- tically monomolecular. The amount of decomposition is determined from the volume of nitrogen liberated. V^ = final volume of nitrogen, Vu = volume at / : minutes, Vt 2 = volume at / 2 minutes. By Equation i 53 k is the velocity constant or, the velocity of the reaction at any instant is k times the instantaneous concentration of unchanged salt. A 100 c.c. Bunsen gas washing bottle, with a long wide neck, should be provided with a Witt stirrer (82) which passes through a mercury gas seal (85). The side tube should be connected to a gas burette (83). A thermostat (81) at about 30 should be filled with water to such a height that this bottle may be immersed to the 1 Walker and Bredig, Zeit. phys. Chem., 1889, iv, p. 319; 1894, xiii, p. 214; 1900, xxxii, p. 348. 2 Findlay, "Practical Physical Chemistry," p. 237. BIMOLECULAR REACTIONS. 235 neck. A small electric motor should be adjusted to drive the stirrer by a thread belt. An ice-water bath should also be ready. Having prepared the bottle, place it in the ice-bath, and also two 100 c.c. Erlenmeyer flasks and a litre graduated flask containing goo c.c. of water. Prepare the benzol diazonium chloride solution as follows: In one flask dissolve 6.64 gr. of aniline in 21.4 c.c. of hydrochloric acid (specific gravity 1.16). In the other dissolve 4.9 gr. of sodium nitrite in 75 c.c. of water. Pour the latter solution into the former very slowly, and, finally, pour the resulting solution into the large flask. Remove the stopper and stirrer of the bottle and pour in about 50 c.c. of this diazonium salt solution. Replace the stopper and stirrer, making sure that the mercury seal is tight, and transfer the whole to the thermostat. Do not connect the side tube to the gas burette until a few minutes have elapsed and the solution has acquired the temperature of the thermostat. Then connect to the gas burette, arrange the thread belt and motor so that stirring is uniform, and make an initial reading, Vti, of the gas burette, and notice the time. Read the gas burette and observe the time at intervals, at first short, and later longer as the rate of change de- creases. When the readings have become almost constant, transfer the gas bottle, still connected to the gas burette, to hot water, where the reaction will soon become complete. Return the bottle to the thermostat and record the reading of the gas burette. This will be FQC . Observe the temperature of the gas burette and the barometer. Plot the volumes against the time, in minutes, as abscissa?. Draw a smooth curve through the observations. Choose five well-distributed ordinates (volumes), find the corresponding times, and taking them by pairs, calculate k. Find the mean value of k. QUESTIONS. 1. Explain whether it would be better to reduce the volumes to standard conditions before substitution in the formula. 2. What would be the initial change, in grams per minute, in a fresh litre solution of 10 grams of this salt at this temperature? 3. Compare the experimental and calculated values for the time when the reaction was half completed (time constant). 243. Bimolecular Reactions. The next simplest case to a monomolecular reaction is one where two molecules are involved, and such is called a bimolecular reaction. This class of reactions may further be subdivided into (A) those where the initial concentrations of both molecules are the same and (B) those where the initial concentrations are different. (A) In Equation (150) let c z = c 2 , = c, n l = n 2 = i ' u=- = k(c-x) 2 (157) 236 Integrating CHEMICAL KINETICS. t, 2 ' f * - r^v J I - ) * ft I/ If we can follow the reaction from the beginning, c, the initial concentration is equal to the total change in concen- tration, for we are still considering reactions which are practi- cally complete. If we then count our time from the commence- ment of the reaction, and set x l and t l equal to zero, we have x *=te*F^ (I59) xf (c x} is merely a ratio and can be expressed in any conven- ient units, x is proportional to the change previous to the time t and c x to the change after this time. (B}. Different initial concentrations, c 1 and c 2 . For simplicity, we will commence to count time at the beginning of the reaction. x .(kit- \ -g- J I (c l -x}(c 2 -x) o /dx I dx ,-,'J - \J \S i r, c I -x~\x 2.3 , = - In = ^ log c l -c 2 \_ c 2 -x\ c l -c 2 .'. k = gf3- i-O* log C 2 (C I - X) Ci (C* - X) (161) SAPONIFICATION OF ESTERS. 237 :, is here the greater initial concentration. The action pro- jeds until the weaker substance is practically exhausted ; that ;, until x, the change in concentration, is practically equal c 2 , the smaller initial concentration. Most bimolecular reactions proceed so rapidly that their mrse cannot be followed, but there are a few reactions of >roper velocity, some of which are discussed in the pages following. 244. Saponification of Esters. 1 Strength of Bases. 2 When solution of an ester such as ethyl acetate is mixed with solution of a strong base, practically all of the ester is dtimately broken up into alcohol and the acetate corres- >onding to the base. This phenomena is called saponifica- m. The rapidity of the saponification depends upon the base ised and if the accelerating powers of various bases are deter- lined, comparative values are obtained similar to those given )y the replacing power, electrical conductivity, etc. There- fore, the accelerating power, that is, the velocity constant, is said to be the measure of the strength of a base. Just as he strengths of acids is proportional to the concentration of lydrogen ions, so the strength of bases is proportional to the mcentration of the radical OH', which, as we shall see later, exists in solutions, with a charge of negative electricity. Since ;he OH' ions have a marked effect upon the velocity of the ^action, they are said to act as pseudo-catalysers, the prefix ;ing added because, unlike true catalysers, they chemically ike part in the reaction. EXPERIMENT XXXIII. Velocity of Saponification of Ethyl Acetate.3 We will watch the progress of the reaction by the disappearance )f the alkali, and from our observations we will calculate the velocity mstant k; that is, the factor by which the product of the instanta- jous concentrations must be multiplied to obtain the instantaneous 1 Warder, Berichte, 1881, xiv, p. 1311. 2 Walker, Chap. XXV. 3 This experiment may be varied by assigning different strong bases to suc- jssive students. When all have completed the experiment, the class may be jiven all the velocity constants obtained, for comparison of the strengths of the lifferent bases. 238 CHEMICAL KINETICS. velocity of reaction. Let, for example, n/40 sodium hydroxide be the assigned alkali and n/ 50 ethyl acetate be the ester. Clean care- fully one 100 c.c. and three 75 c.c. Erlenmeyer flasks, a 10 c.c., a 2*0 c.c., and a 50 c.c. pipette, and two burettes. Prepare about 500 c.c. of approximately n/2o baryta solution which should be standardized with an acid solution of known strength. Prepare also 500 c.c. of n/5o HC1 solution and put 20 c.c. of the latter into two of the small flasks. Prepare the n/4o sodium hydroxide and n/$o ethyl acetate solutions. Put 50 c.c. of the latter into the remaining small flask, cork with a paraffined stopper and place in a thermostat at about 25. Put 50 c.c. of the sodium hydroxide solution in the 100 c.c. flask and set this also in the thermostat. When all is ready and the thermostat has come to a steady tem- perature, pour the ester into the alkali, mix thoroughly and note the exact time of mixing. As soon as possible, withdraw 10 c.c. of the mixture by means of the pipette and discharge into the 20 c.c. of w/5o acid, where the reaction will cease at once. Note the mean time of mixing with the acid. Five minutes later withdraw 10 c.c. more and discharge into the other flask, noting the time. Titrate each solution against the baryta solution, using phenolphthalein as an indicator. Empty and clean the flasks and refill them with 20 c.c. of the w/5o acid. After ten minutes, withdraw another 10 c.c. sample and titrate; then another sample 30 minutes later; another after one hour; another after two hours; another, if possible, after six hours, and, finally, one after twenty-four hours. Plot your titrations in c.c. of baryta solution against the times as abscissae, and draw a smooth curve through the points obtained. The initial concentrations c x and c 2 are known. Since we have assumed c 2 to be the smaller, it also represents the total change in concentration, hence c 2 x for any time t can be found from the difference between the titration at this time and the final titration. Suppose this difference is N c.c. and the concentration of the baryta solution is i/n (approximately /2o) AT Substitute in Equation 161. It is also possible to calculate k without knowing the strength of the baryta solution. c 2 is proportional to the total change of titre, c 2 x is proportional to the change in titre after time t. For d may be substituted the c 2 titre multiplied by the ratio d/c 2 which is known. c t x is the latter minus the change in titre before the time t. These four titres, or equivalent titres, may be sub- stituted for the concentrations in the logarithmic expression. For Ci c 2 the true value must be substituted (.0025, if the above con- centrations are used). If c l and c 2 had been equal, Equation 158 or Equation 159 should have been used. From the ordinate (titration) and abscissa (time) of four typical points on the curve, calculate the velocity constant and take the mean. In Experiment XLIX the velocity of saponification is determined by an electrical method. HYDROLYSIS. 239 QUESTIONS. 1. Calculate the velocity of reaction ten minute 1 after it com- menced (express in gram-equivalents, per litre, per minute). 2. Compare the experimental and calculated values for the time when the reaction was half completed. (Time constant.) 245. Hydrolysis. Strong Base and Weak Acid. 1 A salt composed of a strong base and a weak acid partly decomposes in aqueous solution into the original base and acid and shows an alkaline reaction. The degree of hydrolysis can be found by measuring the velocity of saponification when the salt solution replaces the base solution of the last experiment. The ratio of the velocity constant to that of an equivalent solution of the pure base is the degree of hydrolysis, for the velocity constant of saponification is a measure of the strength of an alkali (244). PROBLEMS XV. i. A 100 c.c. mixture of ethyl acetate and sodium hydroxide solutions gave the following titrations with ^723.3 hydrochloric acid. o. 4.89 IO -37 28.18 oo titre 61.95 50-59 42.40 29-35 14.92 Calculate (a) final concentration of base ; (6) initial concentration of The difference will evidently be the initial concentration of jster. (c) Calculate the velocity constant. 2. The velocity constant of methyl acetate and barium hydroxide at 9.4 is 2.14. What is (a) the initial velocity of saponification if normal base is mixed with half-normal ester? (6) What are the concentrations after 10 minutes? (c) When is the concentration of ester reduced to one-half? 3. .3% of normal potassium cyanide solution is hydrolyzed. What is the velocity constant of this solution for saponification, if "ic velocity constant of normal potassium hydroxide is 2.3? EXPERIMENT XXXIV. Hydrolysis of Sodium Carbonate. Sodium carbonate hydrolyzes in aqueous solutions, Na 2 C0 3 + 2H 2 0= 2 NaOH+H 2 CO 3 'repare tenth-normal solutions of sodium carbonate and ethyl :ate and place the solutions in a thermostat at about 2 5. Provide 1 See also Experiment XXXI and references for 242. 240 CHEMICAL KINETICS. all the apparatus used in the previous experiment except the baryta solution. The reaction is so much slower than when a base is used that it is not necessary to check the reaction by adding an excess of acid. The content of alkali is determined by direct titration with w/5o or w/ioo hydrochloric acid solution. When ready, pour 50 c.c. of one solution into the other, note the time, and thoroughly mix. Immediately pipette 5 c.c. of the mixture into one X)f the small dry Erlenmeyer flasks, note the time and dilute with about 20 c.c. of water. Add a few drops of methyl- orange and immediately titrate against the hydrochloric acid solution. Ten minutes later analyze similarly 5 c.c. more, and so continue, at longer and. longer intervals, until the readings change but little. Make the final analysis after two days. Plot titrations, against time in minutes. Take four well-distributed points on the curve, and for each calculate the velocity constant from Equation 159. If the above concentrations are used, =.05. Draw horizontal lines parallel to the time axis through the initial and final points on the curve. At the times corresponding to each of the points chosen on the curve erect perpendiculars. The ratio, x/c x, is obviously the ratio of the distance between the curve and the upper hori- zontal, to the distance between the curve and the lower horizontal. Find the mean value of k. If time permit, repeat Experiment XXXIII with tenth-normal sodium hydroxide and ethyl acetate. (Weaker concentrations are used in that experiment in order to secure a slower reaction and one which therefore can more easily be followed.) The ratio of the two mean velocity constants will be a measure of the degree of hydrolysis. If there is insufficient time for repeating Experiment XXXIII, an approximate value for the velocity constant of the base may be obtained by multiplying the value obtained in the previous experiment by the ratio of the concentration of the salt in this experiment to that of the base in the earlier experiment. QUESTIONS. 1. Devise an auxiliary experiment by which you could correct for the influence of the neutral salt. 2. What error is there in estimating the velocity constant of a reaction at a certain concentration, by multiplying the value obtained with a lower concentration by the ratio of the two concentrations? 246. Determination of the Order of a Reaction. 1 By the order of a reaction is understood the number of molecules taking part in the reaction. For example, the decomposition of calcium carbonate CaCO 3 =CaO+CO 2 is of the first order or monomolecular. The saponification of an ester C 2 H 5 OOC 2 H 3 + NaOH = NaOOC 2 H 3 + C 2 1 Van't Hoff, i, pp. 193-197; Mellor, .21. ORDER OF A REACTION. 241 is of the second order or bimolecular, etc. In many cases, however, it is difficult to determine the actual number of reacting molecules by inspection. If the reaction is sufficiently slow to enable one to follow it, several methods are available for determining its velocity. 247. (A) For several different times, calculate the velocity constant, using successively the formulae for monomolecular reactions, bimolecular reactions, etc. If reasonably constant values of the velocity constant are given by one of the formulae, the reaction may be assumed to be of that order. 248. (B) Suppose that the original concentrations of the reacting substances are the same, c, and the order of the re- action is n. The velocity of the reaction at any time / will be u = -j- = k (c x) n (162) where x is the change in concentration at this time. Transposing and integrating between the limits, o and t, o and x x Let n = 2 Let n = 3 If n = i, the above formula fails and we must reintegrate, when we shall obtain as before (Equation 154) 111 C X Let x be some fraction of the initial concentration, for ex- ample, 1/2. n= i t=-j-ln 2 (164) K 16 242 CHEMICAL KINETICS. (164') etc. Therefore, if the reaction is of the first order, the time re- quired for changing a definite fraction of the original concen- tration is independent of the initial concentration. If the order is the second, the time will vary inversely with the initial concentration. If the reaction is of the third order, the time will be inversely proportional to the square of the initial concentration, and, in general, it can easily be shown that the order is one higher than the power of the initial con- centration to which this time is inversely proportional. 249. (C) Suppose the change in concentration x is plotted against the time t. The velocity, dx U =~di at any point, is the tangent of 0, the slope of the curve. (Draw a short tangent to the curve at this point. Make this line the hypothenuse of a right triangle whose sides are parallel to the axes. Tan (f> is the ratio of the vertical side to the hori- zontal, but the vertical side is proportional to the small change dx and the horizontal side is proportional to the cor- responding small change dt.) Let U T be the velocity where the change is x t and u 2 the velocity where the change is x 2 . u^ = k(cx^) n U 2 = k(cx 2 ) n Take logarithms of both sides and subtract log Ut-log u 2 = n[log (c-xj-log (c-x,)] - - (165) ! C-X* log - & REACTION BETWEEN HYDRIODIC AND BROMIC ACIDS. 243 EXPERIMENT XXXV. Determination of the Order of Reaction Between Hydriodic Acid and Bromic Acid.* An aqueous solution of these two acids will be obtained by dis- solving their potassium salts in acidulated water and the progress of the reaction will be followed by measuring the iodine set free. The order of the reaction will be determined by method (B). Prepare the following apparatus: A thermostat at about 25. Four 100 c.c., one 300 c.c., and one 500 c.c. Erlenmeyer flasks. A burette with n/ioo sodium thiosulphate solution. Fresh starch solution. 2 One 25 c.c. pipette. Prepare decinormal solutions of potassium iodide, potassium bromate, and hydrochloric acid. Put 25 c.c. of the potassium iodine solution in the 300 c.c. flask and 25 c.c. of the potassium bromate solution in one of the 100 c.c. flasks and set them both in the thermostat. Pour 100 c.c. of the hydrochloric acid solution and 100 c.c. of water in the 300 c.c. flask. Into each of the other small flasks put 50 c.c. of cold water. When the reagents have attained the temperature of the ther- mostat, note the time, pour the bromate solution into the 300 c.c. flask, mix thoroughly and immediately pipette 25 c.c. of the mixture into one of the small flasks of cold water, noting the time when the reaction is stopped by the cold water. Add starch solution and titrate with the .01 n thiosulphite. After about three minutes, withdraw 2 5 c.c. more, note the time of mixing with the cold water, and titrate. Make the next interval about ten minutes and gradually increase the interval. The last interval should be about an hour. Allow the solution to stand a day before the final analysis. When the time intervals are sufficiently long, commence a second similar experiment with half the concentrations. The 500 c.c. flask (in the thermostat) contains initially 25 c.c. potassium iodine solution, 225 c.c. hydrochloric acid solution, and 225 c.c. water. 25 c.c. of the bromate solution are added from a flask which has also been standing in the thermostat and all the observations are repeated. Plot the observations in two curves, with times as abscissae and titrations as ordinates. From the two curves, find the ratios of the times required for one-half, one-third and two-thirds the total change, as represented by the titrations, and find the means. If the ratio is unity, that is, if the time for a definite fraction, is independent of the concentration, we know the reaction is of the first order. If the times are inversely proportioned to the concentrations, we know it is of the second order, etc. Write the equation for the reaction in accordance with your conclusion respecting its order. 3 QUESTIONS. 1. Choose three points on one of the curves and determine the order by method (A). Nij 2. Choose two points on one of the curves and determine the order by method (C). 1 Ostwald, Zeit. phys. Chem., 1888, ii, p. 127. 2 Kahlbaum's soluble starch, in paste form, is extremely convenient since it dissolves in cold water and keeps well. 3 See discussion by Ostwald, Zeit. phys. Chemie, 1888, ii, p. 127. 244 CHEMICAL KINETICS. 250. Determination of the Order of One Component of a Reaction. If, as is often the case, the number of reacting molecules of the different substances is not the same, the order for each kind of molecule may be determined separately by using such high concentrations of the other substances that they remain practically constant. If the initial concentra- tion of the component whose order we wish to determine is Cj, we make the other initial concentrations c 2 , c 3 , etc., so great that Equation 150 becomes u^kA(c l -x) n (166) where A is the product of the other concentrations raised to their respective powers, and is practically a constant, because c lf and hence x, is relatively very small. Therefore, methods (A), (J5), and (C) are available because it is immaterial if k is multiplied by a constant factor. PROBLEMS XVI. 1. Jiiptner, ii, i, p. 133, gives the following figures for the reaction between tenth-normal solutions of ferrous chloride, potassium chlorate, and hydrochloric acid. t x o o 5 .0048 Determine the order of 35 .0238 the reaction by methods no -0452 (A), and (C). 170 .0525 2. Prove that the reaction described in Problem XIV, 3, is of the first and not of the second or third orders. 3. Prove that the reaction described in Problem XV, i, is of the second and not of the first or third orders. 4. Determine the order of the following reaction: 2 Fed, + SnCl 2 = 2 FeCl 2 + SnCl 4 The initial concentration of each of the chlorides on the left was .0625. Time Change in Concentration. i. -01434 1.75 .01998 3- .02586 4-5 -37 6 7. .03612 n. .04102 25. .04792 40. .05058 (Meyer, p. 32.) ORDER OF ONE COMPONENT. 245 5. Determine the order of the following reaction: 6 FeCl 2 + KC10 3 + 6 HC1 = 6 FeCl 3 + KC1 + 3 H 2 O When the initial concentration of all three substances on the left was o.i the changes in concentration were as follows: Time Change in Concentration. 5 .0048 15 .0122 35 - 02 3 8 60 -0329 no -0452 170 .0525 (Meyer, p. 33.) EXPERIMENT XXXVI. Determination of the Order of the Reaction of Potassium Ferri- cyanide when Reacting with Potassium Iodide. 1 We shall make the concentration of the potassium iodide so great compared with that of the ferricyanide, that the concentration of the former may be regarded as constant and therefore we can use Equation 166 and methods (A), (B), and (C). Prepare the following. Burette supplied with n/ioo sodium thio- sulphate solution. Fresh starch solution, n/^o potassium ferricy- anide solution, n/2 potassium iodide solution, 25 c.c. pipette, 100 c.c. Erlenmeyer flask. If the temperature of the room is likely to vary much, a thermostat at about 2 5 should also be provided. Noting the time of mixture, pipette 2 5 c.c. of each solution into the Erlenmeyer flask, mix thoroughly and add a little starch solution. The solution will soon show color due to the liberated iodine. After about five minutes add thiosulphite solution from the burette until the blue color disappears and record the amount and the mean time of the titration. About ten minutes later add more thisulphite until the color disappears again, note the amount and the time, and so continue, increasing the intervals of time. The final titration should be two days after the initial mixing. Plot thiosulphite titrations against the time and draw a smooth curve. First apply method (A), using Equations 154, 159, and 163' c-x ' c-x ' (c-x)* are mere ratios, and therefore c and x in these expressions can be expressed in any units. We will therefore substitute the final titration for c, and for x we will substitute the titration at the corresponding time t. Where c occurs outside of these ratios, the actual value (1/80) must be substituted. In this manner calculate the velocity constant for three points on the curve by each formula. If one of the formulae gives values which agree closely, we can assume that the reaction is of the corresponding order as far as the ferri- cyanide is concerned. State your conclusions. 1 Donnan and Le Rossignol, Journ. Chem. Soc., 1903, Ixxxiii, p. 703. 246 CHEMICAL KINETICS. If time permit, repeat the experiment with .in potassium ferri- cyanide solution and n/4o potassium iodide solution, and thus deter- mine the number of molecules of potassium iodide taking part in the reaction. QUESTIONS. 1. Choose two points on the curve and calculate the order by method (C). 2. The thiosulphite is added to the entire solution rather than a small sample because an excess of free iodine disturbs the reaction. What other error is thereby introduced? Estimate its magnitude. 251. Incomplete Reactions. Equilibrium Constant. In the case of many reactions, possibly in all reactions, the chemical action ceases before the change is complete. The equilibrium finally obtained is undoubtedly kinetic, that is, the original action does not cease, but is counteracted- by the reverse reaction of the products formed. Therefore, at equilibrium, the velocity of the reverse reaction must be the same as that of the original reaction. If we represent the reaction as (Equation 149) n,A + n 2 B + nf - = nJA' + n 2 'B' + n 3 'C' c, c 2 c 3 cj c a ' c s ' with the respective initial concentration represented by the letters beneath, and, if equilibrium is established after the change of concentration on each side is x, then, the velocity of the original reaction (from left to right) is and the velocity of the counter reaction (from right to left) is u' = k' (c ' x} H1 '(c ' x} m ' - Since at equilibrium the two velocities must be equal u = u' -K- !-.-- (I67) k - -( c >- x ys(c'-xy*'- where K is a constant called the equilibrium constant. Ex- pressed in words, at equilibrium, the ratio of the products of the concentrations of the reacting molecules -on the two sides of the chemical equation is a constant. This theorem is INCOMPLETE REACTIONS. 247 often called the Mass Law. A more formal, thermodynamic, derivation of this equation will be given later, together with many illustrations. As an illustration of an incomplete reaction, we shall con- sider the catalysis of ethyl acetate when the water is not in great excess. 1 C 2 H 5 OOC 2 H 3 + H 2 O + C 2 H S OH + HOOC 2 H 3 The sign ^ signifies the reversibility of the reaction. Let c^ = concentration of water, c 2 =that of the ester, c x ' = that of the alcohol, and c 2 f =that of the acetic acid. If at any time t, the concentration of each substance has changed x, the velocity of catalysis is u = k (c l x) (c 2 x) and that of esterification is, u' = k f (c, f + x) (c 2 f + x} The actual net velocity of catalysis will be u - u' =~ = k (c, - x) (c 3 -x)-k' ( Cl f + x) (c 2 r + x) (i 68) At equilibrium, let x=~x, k' _ ( Cl -x)(c 2 -x) , } T >,'+*)(*,'+*) 25 ia. We wish to determine k and k' '. An obvious method is to plot the change in concentration x against the time /, and determine the net velocity, for a particular value of x, from the slope of the curve (29). Their ratio can be determined from the final concentrations and thus both can be found. It is also not difficult to integrate Equation 168, but this general result is not of particular interest. If all four substances are initially present in appreciable amounts, the reaction at ordinary temperatures is far too slow for a labo- ratory exercise. One case, however, offers no experimental difficulties and 1 Knoblauch, Zeit. phys. Chem., xxii, p. 268; Van't Hoff, i, p. 200. 248 CHEMICAL KINETICS. we shall integrate the above equation for the particular conditions of this case. Let one of the substances on each side be originally present in large excess, let one of the other substances be present in com- paratively small excess, and let the fourth substance be absent. Let d and d' be so large that x, in comparison, is negligible; let c 2 be small and c 2 ' =zero. The velocity at any time t is _ dx _ . . w , ,, , , , ( , lir T""" *& \& I ~~ %) \G 2 %) "^ \^I "T" "^) ^ \ ^ ^9 / = k[d(c 2 -x)-Kd'x] dx c t c 2 -(d + Kd')x o k' = Kk The corrected, equilibrium, values of c l and c/ should be used in calculating K by equation 167'. PROBLEMS XVI. 1. A bottle contains 500 c.c. of 50% alcohol. If 5 grams of ethyl acetate are added, how many grams of acetic acid must also be added to preserve the equilibrium? (The equilibrium constant of ethyl acetate is 4.) 2. What should be added to the former solution to (a) increase, (b) decrease the amount of ester? 3. When equivalent amounts of methyl acetate and acetic acid are mixed, 67.5% of each disappear. Calculate K. 4. Hydriodic acid partially dissociates at moderately high tempera- tures, (2HI=H 2 +I 2 ). Meyer and Bodensteini found that at 440 K = .02 and, also, the following figures are taken from this work. t (hours) x 5 .023 5 Plot, and determine k and k' 15 -755 by the first method of 2 5ia. 60 .19 EXPERIMENT XXXVII. Equilibrium of Ethyl Acetate, Water, Alcohol and Acetic Acid. We shall mix a large amount of water c lt a large amount of alcohol Ci', and a small amount of ethyl acetate, c 2 . We shall determine the velocity of the reaction and the final equilibrium concentra- 1 Berichte, 1893, xxvi, p. 1146; Zeit. phys. Chem., 1894, xiii, p. 56. ETHYL ACETATE, WATER, ALCOHOL AND ACETIC ACID. 249 tion, and, substituting in Equations 167' and 170, we shall determine k, the velocity constant of catalysis, and k', the velocity constant of esterification. The apparatus required and the proceedure, are the same as in Experiment XXIX, but the initial mixture consists of 25 c.c. n/io hydrochloric acid, 25 c.c. ethyl alcohol, and 3 c.c. of ethyl acetate. The titrations should be expressed in concentration of acid by multi- plying the titre, per c.c. of solution, by the standardized concentra- tion of the baryta solution. These concentrations should be plotted against the time and a smooth curve drawn. A second curve should be drawn to give the concentration of acetic acid. This curve will be below the other curve, an amount equal to the con- centration of hydrochloric acid. The latter may be taken as the initial ordinate of the first curve, or calculated. The first calculation is that of K by Equation 167'. The initial concentration of water, alcohol, and ethyl acetate should be deter- mined from the amount, total volume, density, and molecular weight. For example, the initial concentration of ethyl acetate is 3X. 905X1000^ 88X53 The final concentration of acetic acid, and the change in con- centration of the other three components, is the final ordinate of the second curve. Having calculated K, select three typical points on the curve and for each determine k by Equation 170. From the mean value, and K, calculate k' by Equation 167 (first part). QUESTIONS. 1. If we substitute total change in concentration for initial concentration and consider the actual velocity constant as k k', the reaction behaves as approximately monomolecular. Determine in this manner an approximate value for k k'. 2. One hour after the beginning of the reaction, what was (a) the concentration of each component (use curve) ? (6) velocity of catalysis? (c) velocity of esterification? (d) net velocity? CHAPTER VII. CHEMICAL STATICS. 1 252. Equilibrium. Variation of Equilibrium with Tempera- ture. 2 We have already (251) derived, from considerations of the kinetic equilibrium, the theorem that the ratio of the products of the concentrations on the two sides of a chemical equation is constant, at equilibrium. We shall now deduce this same "mass law" from a consideration of the mechanical work and heat involved in a chemical equation in order that we may find how the equilibrium varies with the temperature. To make our ideas definite we shall consider a particular reaction, namely, 2 H 2 + O,<=2H 2 O The sign <=^ is used because we shall consider that the three substances are present in their equilibrium proportions. At a high temperature, the concentrations of all three would be of the same order of magnitude. We shall devise a mechanical process which will carry on the above reaction from left to right, a device often used in physical chemistry. Suppose the mixture is under considerable pressure in a large gasometer, which has three openings closed by slides (Fig. 84). Each opening is covered by a diaphragm, one dia- phragm is only permeable to hydrogen, another is only per- meable to oxygen, and the third allows only water vapor to pass. (Compare the permeability of hot paladium to hydrogen , of copper ferrocyanide to water, etc.). Let the equilibrium concentration, the partial pressure, and the volume occupied by one gram molecule be, for hydrogen c lt p lt v lt respectively; for oxygen c 2 , p 2 , v 2 , and for water vapor c, p, v. Suppose we also have three great reservoirs containing these three gases at 1 General references for this chapter are given with those for Chap. VI. 2 Van't Hoff, i, pp. 98-103; Jiiptner, ii, Chap. I; Nernst, iv, Chap. III. 250 EQUILIBRIUM. 25 1 IH,, H 2 0j io 2 unit concentration (one gram molecule per litre). By Avogadro's law, the pressure in all three reservoirs will have the same value P. Let V represent the volume of one gram molecule, i.e., one litre. The temper- ature of the entire system is kept constant. Having placed a suitable cylinder, with piston, tight against the diaphragm permeable to water vapor, draw the slide, and allow the piston to move out so slowly that the pressure in the cylinder is always practically p. Allow two gram molecules to leave. Then close the slide and the cylinder, and allow the piston to move out still more until the pressure has fallen to P. Now connect the cylinder with the water vapor reservoir, and slowly moving the piston, force all the water vapor into the reservoir. The gasometer and reservoirs are supposedly so large that the addition or removal of two gram molecules does not appreciably change the pressure. 253. Let us calculate the work done by the gas. In the firs,t step the work done is pv (Equation 62) ; in the next it is 2V 2V FIG. 84.' /**-*/* 2V 2V >r, by the gas law (Eq. 57) pv = RwO .'. p 2 Rd\n [n the final compression into the reservoir the work done by te gas is PV. (The negative sign signifies work done upon ie gas.) But since the temperature and mass of the gas are mstant pv=PV, and therefore the total work done by the >ater vapor is 252 CHEMICAL STATICS. By means of a similar cylinder and piston, we will take two gram molecules of hydrogen from the hydrogen reservoir, at constant pressure P, compress it to pressure p lt and, removing the slide, force it into the gasometer through the diaphragm permeable to hydrogen. The work done upon the gas will be We shall introduce similarly one gram molecule of oxygen, and the work done upon the gas will be When the water vapor was removed, the hydrogen and oxygen formed more water vapor to maintain the equilibrium and this hydrogen and oxygen were replaced by that introduced. The initial and final conditions of the cylinder are therefore identical. Two gram molecules of water vapor have been formed from hydrogen and oxygen. The total amount of work done by the gas is (Twice the logarithm is the logarithm of the square.) Since the volumes are inversely as the concentrations and the concentration of the reservoirs is unity, we may also write this (172) Where K is our former equilibrium constant; that is, the product of the concentrations of the reacting molecules on one side of the equation divided by the product of the con- centrations on the other side. Since the water and hydrogen molecules occur twice, their concentrations are squared. 254. By Equation 101 in the chapter upon thermodynamics APPLICATIONS OF THE MASS LAW. 253 / is the decrease in internal energy produced by the reaction, id is evidently the heat emitted by the reaction when no external work is done and which we have represented by Q calories or JQ ergs (129, 184) dW T > . dlnK- dlnK .'. RfflnK +JQ = dO dO his is Van't Kofi's "isochore" equation. Notice that Q has been taken as the heat emitted in the ormation of the substance whose concentration appears in the umerator of K and the number of gram molecules is the num- er of molecules appearing in the chemical equation. For example, Q is the heat of formation T of two gram molecules of water. Since the amount of water, and therefore, K, decreases with rise of temperature, Q is negative, or heat is emitted when water is formed from hydrogen and oxygen. Equation 173 tells us that if the temperature is constant, In K and hence K is constant and thus Van't Hoff derived the mass law which Guldberg and Waage derived from nsiderations of the kinetic equilibrium. Applications of the Mass Law. 255. For convenience of reference, we will restate the general expression for the mass law (Equation 167) c I c 2 --- are the equilibrum concentrations, and n, n 2 are the numbers of the different kinds of molecules on one side of the reaction and the primed letters refer to the other side. If we increase a concentration in the numerator, some of the 1 Remember that positive heat of formation = heat emitted (Chap. IV). 254 CHEMICAL STATICS. other concentrations must decrease or some of those in the denominator must increase. 256. Equilibrium of Electrolytes. 1 Salts, acids, and bases, in aqueous solution partially dissociate into particles called ions, which possess electrical charges. This phenomenon, which has been mentioned previously, will be considered later in detail. Suppose we dissolve a weak acid, such as acetic acid, in water. It will dissociate according to the equation C a H 3 OOH<=Q ( H 3 OO' + H C C, C 2 (The dot signifies a positive charge and the prime a negative charge.) Add a little hydrochloric acid The increase in c 2 will require a decrease in c lt and a cor- responding increase in c, or, the addition of hydrochlori< acid, because it has a common ion, decreases the dissociatic and hence the strength of the acetic acid (240). The acetic acid will reciprocally decrease the dissociation of the hydro- chloric acid, but this strong, highly dissociated acid will be affected to a far smaller degree. The addition of sodium acetate would increase GI and similarly reduce the strength of the acetic acid. 257. Consider a solution of a weak base Walker, Chap. XXVI; Mellor, Chap. IX; Nernst, iii, Chap. IV. DISSOCIATION OF WATER. 255 The addition of a strong base, such as NaOH^OH' + Na- c' c, c 2 f increases c t and therefore decreases c 2 and increases c, thus decreasing the dissociation and strength of the weak base. The strong base will be affected to a far less extent. The addition of a salt, such as ammonium chloride, increases c 2 , and therefore has a similar effect. If the dissolved substance is only slightly dissociated and the concentration is near saturation, the addition of one of the ions may necessitate not only the reduction in dis- sociation, but the increase in undissociated salt may be so great that the solution may become supersaturated and the substance may be thrown out of the solution, or the solubility decreased. The best example of this is the so-called "salting out of soap." When sodium chloride is added to a solution of the slightly dissociated sodium salts of the higher fatty acids, the increase in the concentration of the sodium ions so greatly increases the concentration of the undissociated fatty acid salts, that the saturation concentration is exceeded and they are precipitated. 258. Dissociation of Water. lonization Constant. 1 Pure water suffers electrolytic dissociation to a very slight extent. C C t C 2 r, the concentration of the water, is practically constant. (175) K' is sometimes called the ionization constant (avoid confusion with the more common definition in 301). K f will be de- termined in Experiment LVI. For pure water its value is about io- J 4 (328) and 1 Jtiptner, ii, pp. 76-79; Walker, pp. 314-316. 256 CHEMICAL STATICS. Since K f is very small, the concentration of OH' ions in an acid solution is exceedingly low and the same is true of H* ions in an alkaline solution. 259. Indicators. 1 The mass law explains the action of indicators. For example, phenolphthalein is a weak acid with a pink negative ion. The pink color therefore appears when the concentration of the negative ions is appreciable, and the mass law tells us that this requires that the concentration of the hydrogen ion shall be very small, or the solution must be alkaline. If the concentration of the hydrogen ions is less than io- 9 normal, the pink color appears; if it is greater than io- 8 normal, the color is absent. 260. Dilution Law. Dissociation or Affinity Constant. 2 Degree of Dissociation. Suppose we have a solution of a weak acid, base, or salt, for example, acetic acid, and the concentration is such that one gram equivalent is dissolved in V litres. C 2 H 3 OOH<=C 2 H 3 OO' + H- c. Ct c 2 The fraction of the total acid dissociated, or the degree of dissociation, we shall represent by a. a " V V cx^ a 2 The law expressed in this equation was discovered by Ostwald. 3 It is often known as his dilution law. In Experi- ment L we shall prove that K is very approximately constant, however we may vary V. K is called the dissociation constant. It is also often called the affinity constant, because all th< properties which measure the strength of an acid or base are proportional to the dissociation (concentration of H', or OH' ions, 240). This subject is discussed further in 299, 300. 1 Walker, pp. 317, 323, 338; Mellor, pp. 215-216; Nernst, pp. 489-491. 2 Whetham, pp. 341-346; Walker, pp. 244-248; Mellor, pp. 189-193. 3 Ostwald, Zeit. phys. Chem., 1887, ii, p. 36. HYDROLYSIS. 257 261. Hydrolysis. 1 We can now explain the acidity or alkalinity in the hydrolysis of aqueous solutions of salts composed of a strong acid and a weak base, or vice versa. Take ferric chloride, for example. The equation for its disso- ciation is FeCl 3 + 3 H a O<=Fe + 3 Cl' + 3 IT + 3 OH" The dissociation constant of HC1 is so much greater than that of Fe(OH) 3 that the number of H' ions is vastly greater than the number of OH' ions, or the solution behaves as an acid. If the base is the stronger, the hydroxyl ions are in great excess. 262. Gaseous Dissociation. Calcium Carbonate. 2 At mod- erately high temperatures, calcium carbonate partially dis- sociates into calcium oxide and carbon dioxide gas, according to the equation CaCO 3 <=CaO + CO 2 Since both the carbonate and oxide are solids, c z and c 2 are practically constant, and therefore the concentration of the carbon dioxide is constant. In other words, if the temperature remains constant, the pressure of the carbon dioxide gas is independent of the amount of calcium oxide and carbonate >resent. 263. Nitrogen Peroxide. 3 Nitrogen peroxide exists in two molecular aggregations, the equilibrium between which may be determined by the mass law. N 2 4 : C 2 N0 2 C-, 1 See reference for 242. 2 Le Chatelier, C. R., 1883, 102, p. 1243. 3 Natanson, Wied. Ann., 1885, xxiv, p. 454; 1886, xxvii, p. 606. CHEMICAL STATICS. 2 S 8 Let a = degree of dissociation (260) and let V= volume occupied by one gram molecule (92 grams) of V (i -a) or Equation 176. PROBLEMS XVIII. 1. Derive Equation (173) from (172) by consideration of a thermo- dynamic cycle between temperature 6, where the reaction and work take place according to Equation (172), and 6-dO, where the same reaction occurs in the opposite direction. 2. (a) Above what concentration of OH' ions is the pink ion of phenolphthalein visible? Below what concentration is it invisible? (258, 259.) 3. The degree of dissociation of a normal solution of sodium chloride at 18 is .678. What is the dissociation constant? 4. The dissociation constant of acetic acid is i.8Xio-s. If a litre of water contains i gr. of the acid, (a) how much is disso- ciated? (6) What would be the approximate dissociation if the litre of solution also contains 100 gr. of hydrochloric acid? ( is so small that it may be neglected in comparison with unity, and Eq. 194 may be used in place of Eq. 176.) 5. The pressure of carbon dioxide over calcium carbonate and oxide at 740 is 25.5 cm. The density of calcium oxide is 3.20, that of calcium carbonate is 2.72. Calculate K. (First calculate the concentration of the The concentration of the CaO may be taken at 32 C , etc.) 5 6 EXPERIMENT XXXVIII. Variation in the Dissociation of N 2 O 4 with Change of Volume. The gas tube of a Boyle's law apparatus is filled with dry nitrogen peroxide, and the pressure is observed for different volumes, the temperature being maintained constant by a water-bath. The apparatus is illustrated in Figs. 42 and 420. The graduated tube, A, is removed from the slide and supported in front of the mirror glass of the slide. It is surrounded by a water jacket in which there is a stirrer F, and a thermometer T. The water jacket is covered by an asbestos jacket (not shown) with narrow, vertical windows. A and C are mounted on vertical slides separated by a vertical scale, upon which the mercury levels and the bottom of the stopper D are read by means of the sliding index /. A strip of mirror glass behind A and C will reduce error from parallax in reading. THERMAL DISSOCIATION. 259 A is filled with dry nitrogen peroxide in the following manner: About 20 gr. of lead nitrate are placed in a 15 cm. side-neck test- tube, which is closed by a paraffined stopper and connected through a drying tube, with a gas condensation vessel immersed in a freezing mixture of ice and salt. (The gas condenses at n.) The delivery tube of the condensation vessel is also supplied with a drying tube to which is connected a rubber tube leading to a hood or a window. A convenient form of vessel is described in 84, but a side-neck test-tube, with a tube passing through a paraffined stopper and reaching almost to the bottom, will answer. The lead nitrate is heated until a considerable volume of the dark brown gas has been produced and a considerable excess has escaped over what is condensed. The condensation vessel is disconnected 80 C 50 o .240 i-O 20 10 20 30 40 50 60 70 80 Temperature FIG. 85. from the retort, one end is closed, and the end of the drying tube connected to the other end, is placed almost against the mercury in A, which is in the mean position. The condensation vessel is now removed from the freezing mixture and warmed by the hand, until the tube A appears full of the gas and a considerable excess has escaped at the top. The end of the delivery tube is slowly removed, the mercury level in A is raised to within about 5 cm. of the top of the tube, and the paraffined stopper D is forced in as far as it .will go. A is then lowered about 10 cm., and E is filled with water at about 60. When the temperature has become fairly constant, the temperature and the positions of the mercury levels and the bottom of the stopper are read and recorded. C is now lowered about 10 cm., the water jacket is well stirred, and sufficient hot water is added to raise the temperature to the former value, and the readings are 260 CHEMICAL STATICS. repeated. 1 C is then lowered 10 cm. more, and the readings are repeated and so continued, until C is at its lowest level and A E has been raised to the highest possible position. "The readings shoulo be repeated at the same temperature. Read the barometer, and calculate and tabulate the pressures, and also the corresponding volumes of the gas. Since the cross section of A is constant, length of gas column may be substituted for the actual volume. Plot pressures against volumes (or lengths proportional to vol- umes). Find from the curve, the volume V T , corresponding to a pressure of 76 cm. The accompanying diagram 2 (Fig. 85) gives the degree of dissociation at different temperatures when the pressure is 76 cm. If a is tho degree ot dissociation, and N is the number of molecules if there were no dissociation, the actual number of undis- sociated molecules is (i ) N and the number of dissociated mole- cules is 2Na. Therefore, the total number of molecules is (j + a) N, or the number, and therefore the volume, if the pressure is constant, is increased in the proportion i +a Divide v l by (i + a) and thus find what would be the volume Vi jf there were no dissociation, and locate this point on the line of 76 cm. pressure. By assuming Boyle's law, find the volume v,' if there were no dissociation and the pressure was 66 cm 76 v l ' = 66v 2 ' Thus locate about six points between the highest and lowest pres- sures and draw a smooth dotted curve between them. For each of these points determine a, from the ratio (i +a) of the actual volume to the volume without dissociation, and calculate K= a2 V(i-a) V is the volume occupied by one gram molecule (92 grams). As the mass of gas, and the cross section of the gas tube are constant, and as we are principally interested in the constancy of K, we may substitute for V the actual volume or length of the gas column. QUESTIONS. 1. How could you determine the degree of dissociation at dif- ferent temperatures when (a) the volume is constant? (b) the pressure is constant ? 2. What else would you require to determine the true equilibrium constant for this temperature? 264. The Distribution Law. Partition Coefficient. Thus far we have only considered the equilibrium between molecules or ions in one medium. If two media are in contact, for ex- ample, liquid and vapor or two solvents, there will ultimately 1 If the required apparatus is available, a steady flow of water from a ther- mostat (81), through the water jacket, is much to be preferred. 2 From table in 1909 Chem. Kal., ii, p. 257. THE DISTRIBUTION LAW. 26l be kinetic equilibrium at the separating surface for each different kind of molecule. In any interval of time, the same number of any particular species of molecule will cross from medium one to medium two as travel in the opposite direction. Therefore, at equilibrium there must be a fixed ratio between the concentrations in the two media of any common molecule. This is called the distribution law and was discovered independently by Nernst and Aulich. 1 The constant ratio is called the partition or distribution coefficient. 265. As a general example, we shall consider the distribu- tion of benzoic acid between benzol and water. If it existed in similar molecular form in the two solvents, we should find a constant ratio between the concentrations, as we varied the total amount of benzoic acid which was distributed between the two solvents. We have, however, seen (168, 181) that such liquids as benzol tend to produce association of the molecules dissolved in them, while water and similar liquids produce dissociation. If therefore a fraction /? of the benzoic acid in the benzol is in the form of double molecules, the mass law requires that K B (177) should be constant. For two of the single molecules of con- centration C B (ijl) form one of the double molecules of which the concentration is C B {$. C B is the total concentration of benzoic acid in the benzol. In the water, where a fraction a is dissociated, we shall have (Eq. 176) __ -w / \ (i-a) ^urther, if K is the partition coefficient, a) (177') (177") 1 Zeit. phys. Chem., 1891, viii, p. 105; p. no. 262 CHEMICAL STATICS. for the only common molecules in the two solvents are those which are neither dissociated nor associated. Combining Equations 177 and 1 7 7 " For high concentrations, ft is practically constant, a is inappreciable, and hence C W 2 IC B is constant. If the concen- trations are reduced, ft decreases and a becomes appreciable. If a is determined by one of the methods described later, the variation in ft may be determined from the variation in the left- hand side of the equation. EXPERIMENT XXXIX. Partition of Benzoic Acid Between Water and Benzol. Into each of three carefully cleaned 75 c.c., labeled, glass- stoppered bottles introduce 25 c.c. of distilled water and 25 c.c. of benzol. To the first add 2 gr. of benzoic acid, to the second i gr. and to the third .5 gr. Shake thoroughly every minute for about fifteen minutes, and then allow the solutions to rest undisturbed for five minutes. Prepare a burette and an approximately n/2o baryta solution (90). Pipette 2 c.c. from the benzol layer of the first solution, dis- charge into a large excess of water in a clean Erlenmeyer flask, add a little alcohol, and titrate with the baryta, using phenolphthalein as an indicator. The solution should be vigorously agitated throughout the titration. Find similarly the titrations for the other two benzol layers. By means of a syphon of capillary tubing carefully draw off about 10 c.c. of the aqueous layer in the first bottle. Discard the first cubic centimeter or so which may be contaminated by the benzol. Pipette 5 c.c. of the remainder into a clean flask and titrate. Proceed similarly with the other water solutions. If carefully manipulated, a finely pointed pipette may be used in place of the syphon. Reduce the titrations to a common number of centi- meters, and tabulate. For each bottle calculate and tabulate CB' CB ' CB* Since we are only interested in the constancy of these ratios, titrations may be substituted for concentrations. State which ratio is most constant, and therefore what is the probable molecular state in each solvent. Explain the significence of any variation which you may find in this ratio. VAPORIZATION. 263 This experiment may be varied by substituting salicylic or succinic acid for benzoic acid and also by substituting ether for benzol. QUESTION. 1. Apply the distribution law to the solution of a gas in a liquid. 2. Apply the distribution law to the equilibrium between a saturated vapor and its liquid. Variation of Equilibrium with Temperature. 1 266. Van't Hoff's equation (173) will be in a more conven- ient form if we integrate it between the limits K r and K 2 and O l and 6 2 . K 2 2 JQ i dO^_ ^2_JQi_l_ 1_ 0* K, R (0, 2 /") /? /? /2 \ TTTr- (i79) f-- ff *J *J K, 0, We shall consider several applications of this equation. 267. Vaporization. Let c= concentration of liquid (this is practically constant for the volume changes little for small ranges of temperature) ; let the concentration of the saturated vapor =c t at absolute temperature d lt and c 2 at temperature 6 2 . If the temperature change is small, we can assume that the vapor obeys the gas law (103). pv = Rwd Since is the molecular concentration, v C - = W' C * = W'*'= ' /<(/! KU 2 etc. Q .' . 2.302 log Q- 1 Nernst, Gott. Nachricht, 1906, i, p. i; Van't Hoff's Lectures, i, p. 136, 149, 157; Mellor, Chap. XII. See also reference for 252. 2 In certain cases this equation gives results which are in error because Q is not constant as we have assumed. For a more accurate but more complicated expression which considers the variation in Q, see Nernst, "Thermodynamics and Chemistry." 264 CHEMICAL STATICS. Illustration. Determine the mean latent heat of vaporization of water between 95 and 105. From Regnault's tables the saturated vapor pressure at 95 is 633.8 mm. and at 105 it is 906.4 mm. Substituting these values and the absolute temperatures, Q comes out 9120. Now Q was the heat absorbed when no external work was done, but in the evaporation of water, the work pv=RO is done, where is the mean absolute temperature and v is the volume of one gram molecule of the vapor. (For the volume of the liquid is relatively so small that it may be neglected.) Adding Rd = 1.985 X 373, we have 9860 as the mean latent heat for one gram molecule. The ordinary latent heat per gram is this divided by 1 8, or 548 calories. 268. Heat of Solution. 1 If an excess of the dissolved sub- stance (solute) is present in the solution, there will ultimately be kinetic equilibrium between it and the saturated solution. In any time the same number of molecules will go into the solution as return and reunite with the undissolved solute. Therefore, both the mass law and Van't HofFs equation are applicable. The heat of solution per gram molecule replaces the heat of formation. Let c = concentration of undissolved substance. This is practically independent of the temperature, for the coefficient of expansion is usually extremely small. Let C T = concentra- tion of the saturated solution at absolute temperature 6 It and c 2 the concentration at 2 . K Cl K 2 K * = ' K *= Therefore, by Equation 179 \^ \ n s?fi /) \ (i 80) If the solubility increases with rise of temperature (the ordinary case) the left-hand side is positive and Q is positive, or heat is absorbed. If, however, the solubility decreases, as, for example, in the case of calcium hydrate, heat is emitted. 1 Jiiptner, ii, pp. 219-221; Nernst, pp. 552-554. HEAT OF DISSOCIATION OF A GAS. EXPERIMENT XL. Heat of Solution and Solubility. 265 In a thermostat at 2 5 place a glass-stoppered bottle containing 100 c.c. of hot water and an excess of benzoic acid, 1 a 5 c.c. pipette, and an Erlenmeyer flask containing about 25 c.c. of water. Shake the bottle vigorously every minute for fifteen minutes. After allowing it to rest undisturbed for five minutes, pipette 5 c.c. of the clear saturated solution from the bottle to the flask, and, removing the flask, titrate with approximately n/20 baryta solution (90), using phenolphthalein as an indicator. Repeat twice and take the mean. Raise the thermostat to about 65 and repeat the above procedure. The pipette must be at the temperature of the thermostat to avoid precipitation. The ratio of the mean titrations will be the ratio of the concentra- tions. From this ratio and the two absolute temperatures calculate the molecular heat of solution. QUESTIONS. 1. What is the heat of solution per gram? 2. Is the solution of the acid an endothermic or exothermic process ? 3. How would you change the above equation to allow for ion- ization? 269. Heat of Dissociation of a Gas. If p is the actual pres- sure of a gas and p' is what the pressure would be if it occupied the same volume but was undissociated p = p' ( z -f a] (181) where a is the degree of dissociation. For the number of molecules, and therefore the pressure, is increased in the ratio (i+a) (see Experiment XXXVIII). If v, the volume, is constant the total concentration is constant and equals i/v By 263 and Equation 176 K = V(i-a) .'. 2.30 log q 2 a (i-q) = Q 0,-Ot a x (i-a a ) 1.98 6,6, (182) a l is the degree of dissociation at absolute temperature d lt and o: 2 is that at 2 . 1 Salicylic, succinic, or boric acid may be used in place of benzoic acid. 266 CHEMICAL STATICS. PROBLEMS XIX. 1. Prove that the potential of any type of molecule is the same in each of two adjoining media, when there is equilibrium (235). 2. Succinic acid was dissolved in varying amounts in a mixture of 10 c.c. of water and 10 c.c. of ether. The following concentrations were found. Water. Ether. .024 .0046 .070 .013 .121 .022 Compare the molecular weights in the two solvents. 3. Benzol boils at 80. i at 76 cm. The latent heat is 93. Cal- culate the vapor pressure at 85 by Eq. 179'. 4. The molecular heat of solution of succinic acid is 6700. The saturation concentration at 8.5 is 4.22%. Calculate the mass in grams of a liter of saturated solution at 20. 5. The degree of dissociation of water vapor is 1.89X10-4 at 1207 and 18.1X10-4 at 1531. Calculate the heat of dissociation. 6. Calculate the temperature centigrade at which 10% of oxygen is associated into ozone, assuming the following approximate figures. 34,100 calories are absorbed when one gram molecule of ozone is formed. Concentration of ozone at i9io=.oi%. (The application of Eq. 182 is simpler if the decomposition of ozone is considered, e.g., the degree of dissociation at 1910 is .9999; at what temperature is it .9?) 7. The percentage dissociation of carbon dioxide is .0042 at 1027 and .03 at 1205. Calculate the heat of formation. (Nernst and Wartenberg.) 8. The equilibrium constant of dibromosuccinic acid is .0000967 at 15 and .0318 at 101. (a) What is the ratio of the velocities of decomposition? (6) What is the heat of the reaction? 9. Calculate the latent heat of water at 75 from the vapor pres- sures at 70 and 80 (a) as given in Table LVII ; (6) as determined in Experiment IX. 10. Calculate the heat of dissociation of N 2 O 4 at constant pressure (Fig. 85). EXPERIMENT XLI. Heat of Dissociation of Nitrogen Peroxide, Variation of Dissociation with Temperature. 1 We shall use the air thermometer apparatus described under Experiment III. Fill the bulb with dry nitrogen peroxide in the following manner: Surround it by a freezing mixture and connect it, .through a drying tube, with a condensation vessel (84) which is also in a freezing mixture, and in which nitrogen peroxide has been condensed as described in Experiment XXXVIII. Gradually remove the condensation vessel from the freezing mixture, so that the nitrogen peroxide may distill over into the bulb. Then remove the bulb also from the freezing mixture and warm it to about 20, so that most of the air may be expelled. Return it to the freezing 1 Richardson, Jour. Chem. Soc., 1887, ^> P- 397- THE PHASE RULE. 267 mixture, refill the condensation vessel, and again condense nitrogen peroxide in the bulb. Finally, disconnect the bulb, heat it to about 20, and immediately connect it to the manometer of the air thermometer. The mercury should be at such a level that there is little air space between it and the bulb. Surround the bulb with ice and water and make a number of independent readings of the mercury levels. Since the volume is to be kept constant, the mercury on the side next the bulb must always be brought to the same position. This should be as high as possible to reduce the air space. Replace the ice by water at about 20 and adjust, and read the mercury levels. So continue, 'for about every 20, until the water boils, when several observations should be made. (See Experiment III.) Read the barometer and calculate the pressures. Plot pressures against temperatures as abscissae. Find the temperature, t, for which the pressure is 76 cm., and from Fig. 85 find the degree of dissociation corresponding to this temperature and pressure. From Equation 181 calculate the pressure p' for this temperature, if there were no dissociation. Find the corresponding undissociated pressure p" for 100 by Gay Lussac's law. P" 373 Locate these two points on the plot and connect them by a dotted straight line. For five temperatures, calculate the degree of dissociation from the ordinates of the two curves and Equation 181, and plot the values obtained. From one of the first and one of the last values of a and the cor- responding absolute ^temperatures, calculate the heat of formation of NO 2 from N 2 O 4 at constant volume. Remember that Q is the heat absorbed, or Q is the heat emitted per gram molecule of N 2 O 4 , in the reaction QUESTIONS. 1. What is the heat of formation of one gram of NO 2 ? 2. Is the formation of NO 2 endothermic or exothermic? 3. From Q, and the degree of dissociation at some particular temperature, calculate the temperature centigrade at which 99% of the gas is dissociated. The Phase Rule. 1 Thus far we have considered the relations between the con- centrations of different molecules in one state, and of the same molecule in different states. We have also considered 1 Gibbs, Trans. Conn. Acad., 1874-1878,11!, pp. 108-303; Collected Memoirs, I, p. 96; Findlay, The Phase Rule; Bancroft, The Phase Rule; Juptner, ii, Chap. VII; Whetham, Chapters II, III. 268 CHEMICAL STATICS. how the concentrations must change if the temperature and pressure (or volume) change. But we have not learned in how many different states a molecule may exist in equilibrium, nor what changes a system may surfer without losing one or more states. 270. We must first define several terms. By "phase" we will understand a physically homogeneous state; for example, in the system consisting of water and salt, the solution, the vapor, and the undissolved salt" at the bottom are three distinct phases. If some ice were present, there would be a fourth phase. By "components' 1 we will understand the substances composing the system. In the above illustration, the components are salt and water. As the phases are physical divisions, so the components are chemical divisions. If in any case there is uncertainty, as to what, or how many, components should be chosen, we shall always take those which are indispensable in describing each phase, and whose composition in each phase may be independently varied. In the above example we take salt as one component rather than sodium and chlorine, because the concentrations of the latter cannot be varied independently. 271. In some cases the particular choice of components is uncertain and unimportant, for example, in the equilibrium between calcium carbonate, calcium oxide and carbon dioxide, CaCO 3 ^CaO+CO 2 any two of the three substances may be chosen, for two are necessary and sufficient to chemically describe each phase and may exist in independent proportions. We saw in 235 that the state of a system may be defined by the intensity factors, temperature, pressure, and poten- tial of each component, and that the potential in a particular phase is proportional to the concentration. It was also pointed out that the intensity factors are the same throughout the system, and do not depend upon the actual amount of any phase or component. 272. Let P be the number of phases in a certain system. THE PHASE RULE. 269 Let N be the number of components. There are therefore N-\-2 intensity factors in each phase (N potentials and pres- sure and temperature). How many of these can be varied without disturbing the number of phases? The mass law gives us one necessary relation between the concentrations (and therefore potentials) in each phase. There remain N i possible variations in the concentrations in each phase, or, with temperature and pressure, a total number of independent variables (N-i) P + 2 for the entire system. The potential of a component must, at equilibrium, be the same in every phase. To express this equality mathematically requires N equations between any particular phase and the other P i phases, or a total of N (P i) equations. The number of undetermined variables, F, is therefore equal to the number of variables, less the number of equations, or F=(N-i)P + 2-N(P-i) = N + 2-P (183) This is the famous Phase Rule of Willard Gibbs. In words, it states that the number of possible variations of. concentra*- tion, pressure, and temperature, without changing (reducing) the number of phases, is two more than the difference between the number of components and the number of phases. Con- versely, if we determine the maximum number of possible variations, we can judge of the number of phases present. 273. By variations are understood arbitrary, independent, assignments of particular values to intensity factors. If a particular variation involves a change in one or more other factors, the two or more together constitute but one variation. The variations of concentration must be variations of the concentration of one or more phases, not simply variations in the total concentration. For concentration is used as a convenient measure of potential, and the total concentration may vary on account of a change in the relative amounts of the different phases which would not affect the concentration (and potential) in each phase. 270 CHEMICAL STATICS. 274. The phase rule is of particular utility in conjunction with a graphical representation of the system, with the inten- sity factors as coordinates. If there is one component, the axes are temperature and pressure, and the different phases are represented by areas, the coexistence of two phases by lines, and of three phases by points. 275. Illustrations. One component. F=$P. Water. 1 The different phases are represented by the areas designated in Fig. 86. Two phases are coexistent at the p (cm.) i. E Solid ID* Liquid FIG. 86. !0 C temperatures and pressures corresponding to the lines OA, OB and OC, and at 0, where the temperature is .0076 and the pressure is 4.6 mm. (154), three phases coexist. At a point E, when there is but one phase, F = 2, or the system is bivariant; that is, we may independently change both temperature and pressure, as is evident from the figure. At a point on one of the lines, F = i, or the system is uni- variant, that is, we may arbitrarily change either the pressure or the temperature, but not both, if the two phases are to be preserved. For if we change the temperature, there must be 1 Jiiptner, ii, pp. 204-5; Whetham, pp. 39-44. ALLOYS. 271 an accompanying change in pressure which is not arbitrary, but is such that it and the new temperature give a point on that line. At O, F=o, or the system is invariant. The dia- gram shows that at this point, any change in the temperature or pressure will reduce the number of phases. 276. Two Components. F=4P. Since there are three intensity factors, temperature, pressure, and concentration, a figure in three dimensions is required. We shall usually find it most convenient to lay off the temperature and concen- tration along horizontal rectangular axes, in which case the pressure axis is vertical. The conditions for equilibrium of 1000 500 Ag+ Eutectic Cu -*- Eutectic 1000 Ag Cone FIG. 87. Cu 500 vapor and solid, or vapor and solution, or vapor and both, will lie upon a surface. Above the surface the pressure is so great that the vapor phase is absent, below the surface is only the vapor phase. 277. Alloys. Silver Plus Copper. 1 Fig. 87 represents the surface viewed from above, that is, along the pressure axis. Consider the point D on this surface. Here there are two phases, solution and vapor, and therefore there are two possible 1 Whetham, pp. 59-63. 272 CHEMICAL STATICS. variations. We shall choose to lower the temperature and keep the concentration the same. The pressure will therefore change in a definite manner, out of our control, if we wish to preserve the vapor phase. (The exact mode of variation of the pressure would be shown by a section of the surface, perpendicular to the c t plane, and through the line DE.) At E solid silver separates out, there are three phases, and the system is univariant. If we lower the temperature, the concentration of the solution is beyond our control and varies with the temperature to give a line such as EO. At a point such as F, the total concentration has not changed, but the concentration of the liquid phase has changed as just described, and it is such variations of concentration which are contem- plated in the phase rule and not variations in the total con- centration (273). The concentration at F is given by an amount of pure silver proportional to FG and of solution proportional to HF. The solution has the proportions, Ag: Cu=GI: GH At O solid copper begins to appear from the solution, and four phases are present vapor, solution, silver, and copper. The system at this point is therefore invariant. This point is called the eutectic point, and the alloy which separates out upon further cooling, of the concentration of the point O [40 (atomic) parts of copper] is called the eutectic alloy, and evidently has a definite melting point. At any point M we have a mixture (solid solution, 182) of solid silver and solid eutectic alloy of the concentrations indicated. Similar diagrams for iron and carbon are somewhat more complex, but are of great industrial importance. 1 278. Dissociation of Calcium Carbonate. Upon heating, calcium carbonate dissociates into calcium oxide and carbon dioxide (262). We shall consider a vertical section, perpen- dicular to the concentration axis, of such a figure as is described in 276. The axes are pressure and temperature, and the 1 Roozeboom, Journ. Iron and Steel Inst., 1900, ii, p. 311; Zeit. Elektro- chem., 1904, x, p. 489; Juptner, i, pp. 135-138; Roberts-Austin, "Intro, to Metallurgy," 5th ed., p. 802; Findlay, "Phase Rule," pp. 224-228. DISSOCIATION OF CALCIUM CARBONATE. 2 73 curve A B, Fig. 88, is the section of a suface which separates the carbonate above (high pressures) and the oxide and gas below (low pressures). Along A B three phases are present, two solids and gas, and therefore the system is uni variant. We may arbitrarily change the pressure, but unless the tempera- te (cm) I50| 100 50 CaCO 500 600 700" FIG. 88. 800 900 ture is also changed to correspond with a point on the curve, one, or two phases will be lost. Other sections, parallel to this one, would correspond to a greater or less concentration of CO 2 in the lower part of the figure, and therefore the curves would be somewhat different. EXPERIMENT XV. This experiment should now be reviewed and the results inter- preted with the help of the phase rule. PROBLEMS XX. 1. When CuSO 4 ' sH 2 O crystals are heated, we obtain successively CuSO 4 ' 3H 2 O, CuSCV H 2 O and the anhydrous salt. Determine qualitatively how the temperature will vary. 2. Prove that the vapor pressures of ice and water are equal at -.0076. 3. Could two of the above copper sulphate salts remain in excess, in equilibrium, in an aqueous solution? 18 274 CHEMICAL STATICS. 4. When hydrogen is forced into paladium, within a certain range, the volume absorbed is proportional to the pressure. Upon increasing the pressure further, a point is reached where a very slight increase in pressure is accompanied by a great increase in the volume absorbed. Decide by the phase rule how many phases are present in each stage. 5. Decide by the phase rule whether the eutectic alloy is a com- pound or a mixture. EXPERIMENT XLII. Construction of a Model to Represent the Equilibrium of Salt and Water.' Upon a board or other smooth surface mould a block of modeling clay or plaster of Paris, making the base about 10 cm. by 15 cm. NaCI. H 2 Salt + Cryo- hydrate Cryo- j hydrate; Salt +- Saturated So.lution W -30 A -20 -10 temp FIG. 89. 10 20 While the clay or plaster is sufficiently soft to cut easily, form the surface which will show the equilibrium between the vapor and other phases within the limits of about 30 and 20 and o and 1.5 cm. 1 Van't Hoff, i, pp. 32-38; Findlay, "Phase Rule," pp. 126-132; Juptner. ii, pp. 225-227; Whetham, pp. 49-52.' CRYOHYDRATES. 275 pressure. Choose one of the bottom corners as the origin. Make the longer horizontal edge the axis of concentration, the other horizontal edge the temperature axis, and the vertical edge the pressure axis. Fig. 89 represents roughly the appearance of such a surface if it is viewed from above. The face inclosed by the temperature and pressure axes should appear like the upper curve of Fig. 71, since the concentration of the salt is zero. The surface will slope away from this curve since the greater the amount of salt, the less the pressure. The boundaries between different phases, represented by the lines OA, OB, OC, OD, OE, will appear as more or less abrupt changes in slope. Below the surface the pressure is so low that there is only vapor, while above the surface the vapor phase is absent. A point P in such a region on the surface as OAD represents the coexistence of three phases vapor, unsaturated solution, and ice. The amounts of the two latter are in the proportion PN : MP. The point O, where CO and OD meet, represents the coexistence of salt, saturated solution, ice, and vapor. Since there are four phases, the system is invariant. The temperature is 22, the concentration is 23.5%, and the pressure is .079 cm. This point is called the cryohydrate point. If the system is cooled from the point O, salt and ice solidify in the above proportions, and the mixture is called the cryohydrate. A point such as Q represents a mixture of ice and cryohydrate in the proportions QT : QS. OC is evidently the solubility curve and OD is the freezing-point curve. The lower pressures are so small that they should be exaggerated in the model. Designate the phases present in the different portions of the surface. QUESTIONS. 1. What is the ratio of the concentration of, (a) salt and cryo- hydrate, (b) salt and water, corresponding to a point such as X? 2. (a) What are the relative concentrations of salt and saturated solution corresponding to a point such as Wf (b) of salt and water? 3. Explain how and where the phases change when a mixture of salt and water is cooled from +10 to 30, if the initial state cor- responds to (a) the point V, (b) the point U. 4. What are the phases at a point a little above M? below M? EXPERIMENT XLIII. The Melting Point of an Alloy. If an alloy is melted and is allowed to cool, while its temperature is continuously observed and a curve be then drawn with times as abscissae and temperatures as ordinates, it will be found that at certain points the curvature abruptly changes, the fall of temperature being decreased or even ceasing. At the moment corresponding to such a point, the alloy is radiating heat to the room, and the fact that its temperature does not fall as rapidly indicates that heat is being produced internally by some change of state of the material. Such a point is therefore a solidifying point of some constituent of the alloy or of the eutectic alloy (277). 276 CHEMICAL STATICS. The assigned 1 metals are carefully weighed and melted in an iron cup. A copper-constantin thermo couple (49) is plunged into the liquid metal and kept there until the rentie mass is solid. A porcelain tube 2 should cover one wire for some distance from the junction. The terminals are connected to a galvanometer through a resistance such that the maximum deflection will keep on the scale. The galvanometer is read every half minute and the time of each reading is noted. When the readings are commenced, the metal should be considerably above the melting point and the readings should be continued for some time after the metal is apparently solid. Find the number of volts or millivolts corresponding to unit deflection of the galvanometer by applying a known small electro- motive force to the galvanometer, with its resistance, and observing the deflection. (47,77.) Plot the galvanometer deflections against the time. Determine the electromotive forces corresponding to the gal- vanometer deflections where the curvature changed, and from the con- stants of the thermocouple, or a chart giving the temperature for dif- ferent electromotive forces, determine the temperatures of these points. Tabulate the observed temperatures of these transition points and your opinion of what they represent. QUESTIONS. 1. Explain why the second transition point is represented by a horizontal portion of the cooling curve, .while the first transition point is merely represented by a change of curvature. 2. Will the temperature of the first point vary with the initial concentration? 3. Will the temperature of the second transition point vary with the initial concentration? 279. Transition Points. The points where several phases coexist are of considerable importance. We have already considered the eutectic alloy and the cry ohy drat e. Other examples will be found in special treatises. In some cases it is difficult to observe such a point directly, but we can find it by slightly varying the temperature or pressure, and observing the effect on the volume, temperature, or pressure caused by the disappearance of one phase, or the appearance of another, or both effects. These points of coex- istence of several phases are often called transition points. 1 Tin and lead are suitable metals. The changes of curvature are more dis- tinct if the former is in excess. It is interesting to have different students use different alloys and compare the results when all have completed the experi- ment. The eutectic of tin and lead is composed of 37% lead, 63% tin, and melts at 182.5 (Rosenhain and Tucker, Roy. Soc. Phil. Trans., 1908, A. 209, p. 89). For further interesting information regarding this alloy see Zeit. elect. Chemie, 1909, xv, p. 125. 2 Fine porcelain tubes may be obtained of the Royal Berlin Porcelain Factory or American Agents. TRANSITION POINT OF SODIUM SULPHATE. 277 280. Transition Point of Sodium Sulphate. 1 If we have a saturated solution of sodium decahydrate, together with an excess of hydrated salt, and heat it gradually, at 32.384, 2 the hydrate changes to the anhydrous salt plus water, and the solution of the anhydrous salt has a slightly larger volume than the solution of the hydrate. Above this temperature the anhydrous salt and its solution are stable, if the pressure is suitable. At the above temperature, the two salts, their common solution, and vapor coexist, and this is the transition point. EXPERIMENT XLIV. Transition Point of Sodium Sulphate. Prepare a dilatometer as follows: Procure a "weight thermom- eter " ; that is, a glass bulb with a long capillary stem. The capacity of the bulb should be about 5 c.c. and the stem should have an internal diameter of about .7 mm. and a length of about 2 5 cm. By means of a one-hole rubber stopper and a large glass tube, provide a reservoir at the top of the capillary and fill it with crystals of sodium decahydrate, together with a very little water. (See Fig. 90.) Warm very gently the bulb, stem, and reservoir. The hydrate will be melted and the warmed air will bubble out through the liquid. Be careful not to heat the stem and reservoir too hot, otherwise considerable anhydrous salt will separate out. When some of the melted salt has been col- lected in the bottom of the bulb, it may be heated until all of the air has been expelled by the vapor. Now cool gradu- ally. When the bulb is nearly full, replace the remaining liquid in the reservoir with kerosene, which will prevent evaporation of the liquid below and serve as an index in the capillary. Adjust by suitable heating and cooling until the level of the kerosene is in the lower half of the capillary. Remove the reservoir and attach a paper scale. Place the bulb in a vessel of water provided with a 1/10 ther- mometer. Gradually raise the temperature of the bath and read the level of the meniscus at every half degree between 30 and 32, every fifth degree between 32 and 35, and every half degree between 35 and 37. Repeat with de- scending temperatures. Plot your results with temperatures as abscissae and posi- ^^ tions of the meniscus (volumes) as ordinates. The two p IG ^ . curves will show a lag. Explain. State the mean value of the temperature of the transition point. Another method which should be employed, if time permit, is to place the bulb in a thermostat at about 32 and see if there is any 1 Findlay, "Phase Rule," pp. 134-142; Whetham, pp. 53-56; Juptner, ii, pp. 233-235. 2 Dickinson and Mueller, Bui. Bu. Stand., 1907, iv, p. 641. 278 CHEMICAL STATICS. change of volume, and then successively at 32.5, 33, 33.5, 34, etc. There is likely to be some of the unstable salt present and therefore there will be a continuous change of volume except at the transition temperature. This experiment may be varied by substituting for the sodium decahydrate an approximately equimolecular mixture of sodium decahydrate and magnesium sulphate heptahydrate. At about 21, astrachanite, Na 2 Mg(SO 4 ) 2 ' 4H 2 O, and water separate out and the transition point can be determined with a dilatometer. For the solubility, thermometric, and tensimetric methods of de- termining the transition temperature, see special treatises. 1 QUESTIONS. 1. What other invariant point has sodium sulphate and water? 2. Explain which dilatometer method you prefer. iFindlay, "Prac. Phys. Chem," Chap. XV; "Phase Rule," Appendix; Juptner, ii, pp. 205-207; Nernst, pp. 588-589. CHAPTER VIII. ELECTROCHEMISTRY, 1 ELECTROLYTIC CONDUCTION. 281. Faraday's Law. The greatest contributor to our knowledge of this subject was Michael Faraday (1791-1867). The most important law which he discovered will be stated in his own words : 2 " The chemical decomposing action of a current is constant for a constant quantity of electricity, notwithstanding the greatest variation in its sources, in its intensity, in the size of the conductors used, in the nature of the conductors (or non-conductors) through which it is passed, or in other circumstances." Faraday also invented our present termin- ology. "I propose to call bodies of this the decomposable class, electrolytes. The anode is ... that surface at which the electric current enters the electrolyte, it ... is where oxygen, chlorine, . . . etc., are evolved. . . . The cathode is that surface at which the current leaves the decomposing body . . . metals, alkalies . . . are evolved there." "Then, again, the substances into which these divide under the influence of the electric current form an exceedingly important general class. They are combining bodies, are directly asso- ciated with the fundamental parts of the doctrine of chemical affinity, and have each a definite proportion in which they are always evolved during electrolytic action . I have proposed to call these bodies generally ions, or particularly anions or cations, according as they appear at the anode or cathode, and the numbers representing the proportions in which they are evolved electrochemical equivalents. Thus hydrogen, 1 General references "Electrochemistry," Lehfeld, Longmans; "Electro- chemistry," Arrhenius, Longmans; "Electrochemistry," LeBlanc, Macmillan; "Electro-chemie," van Laar, Engelmann, Leipsic (founded upon thermo- dynamic potentials); Winkelmann, 1905, iv, I. 2 Experimental Researches, vol. i, ser. Ill, VII; also in "Fund. Laws of Electrolytic Cond.," Goodwin. 280 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. oxygen, chlorine, iodine, lead, tin, are ions . . . and i, 8, 36, 125, 104, 58, are their electrochemical equivalents." "Electrochemical equivalents coincide, and are the same, with ordinary chemical equivalents." 282. To avoid this unnecessary duplication of names, the term electrochemical equivalent is now applied to a fraction, one ninety-six thousand five hundred and thirtieth of the above numbers. This fraction is the mass of hydrogen, in grams, liberated by one coulomb (io). x Therefore 96,530 coulombs (which, for convenience, is often called one faraday) will liberate one gram of hydrogen, eight grams of oxygen, 35,5 grams of chlorine, or, in general, a mass numerically equal to the chemical equivalent. The chemical equivalent is the atomic (or ionic) weight divided by the valency and the electrochemical equivalent is the chemical equivalent, divided by 96,530. Table L gives the atomic weights of the more common elements. The corresponding weight of a radical ion is the sum of the atomic weights of the constituents. The valencies are so familiar that they are not tabulated. 283. Faraday's description (see reference) of the experiments by which he substantiated his law is very interesting and in- structive. Since Faraday's time the law has been subjected to more exact experimental tests. The discrepancies do not exceed the possible experimental errors. Perhaps the most accurate work is that of Richards and Stull 2 who sent the same current through an aqueous solution of silver nitrate at 20 and a solution of silver nitrate in melted sodium potassium nitrate at 260. The mean difference in the mass of silver liberated in the two solvents was .005%. Kahlen- berg3 compared the deposition of silver from an aqueous solution of silver nitrate with that from various organic sol- vents, such as pyridine, aniline, etc., and found the differences less than the experimental errors. Richards, Collins, and 1 Van Dijk, Arch. Neerl., 1905, 10, 287. 2 Zeit. phys. Chem., 1903, xlii, p. 621. 3 Jour. Phys. Chem., 1900, iv, p. 349. DISSOCIATION THEORY. 281 Heimrod 1 found the ratio of the masses of silver and copper deposited in two solutions, traversed by the same cur- rent, to be 3.3940, while the ratio of their chemical equivalents was 3. 3938. 284. Dissociation Theory. Thus far we have only considered the liberation or, as Faraday termed it, the decomposition, at the electrodes. Arrhenius suggested, in i88y, 2 a theory which is now generally accepted, namely, that the substances which were evolved at the electrodes existed in the solutions as independent ions before the electric current passed through, and before the solution was subjected to any electric forces. For example, according to the theory of Arrhenius, when silver nitrate is dissolved in water, a certain portion remains as molecules of silver nitrate, but the remainder (usually the larger portion) breaks up into its constituents, silver and the nitrate radical, with equal opposite electric charges. 285. Electric Charge on Ions. We understand by the direction of a current, the direction in which positive electricity moves, and since the cations follow the current, they must carry positive charges. Hydrogen and all metallic ions are cations. A solution has no free charge of electricity, and therefore the sum of the positive charges on the cations must equal the sum of the negative charges on the anions. As required by Faraday's law, each ion has always a definite charge in whatever combination it may occur. Therefore, since a cation such as sodium occurs singly with such an anion as chlorine and twice with the sulphate radical, the charges on the two anions cannot be the same, but must be proportional to the valencies . Evidently a similar law must be true for cations . Therefore, the charge on a copper ion is twice that on a silver ion and equal to that on a ferrous ion. - The charge on a ferric ion is three times that on a silver ion. The kinetic theory of gases enables us to estimate the approximate number of ions in a given mass, and thus we can J Zeit. phys. Chem., 1900, xxxii, p. 321; 1902, xli, p. 302. 2 Zeit. phys. Chem., 1887, i, p. 631. 282 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. determine the order of the charge on a single ion. The number of molecules in a cubic centimeter of gas, under standard conditions (4), is probably of the order io I9 .( x ) 96,530 coulombs liberate, and are therefore carried by, one gram of hydrogen, which, under standard conditions, occupies 11,120 c.c. The number of ions will equal the number of atoms or twice the number of molecules. The charge on a univalent ion is therefore of the order 9 53 _ = 4 xio- 19 coulombs 1120X2 Xio'9 286. Voltameter. Faraday's law suggests a simple and accurate method for determining the quantity of electricity which traverses a circuit. A suitable electrolyte is made a part of the circuit and the mass liberated at one of the electrodes is determined. The quotient of this mass divided by the electrochemical equiva- lent is obviously the quantity of electricity in coulombs. Such an instrument is called a voltameter or coulometer. The electrochemical equivalent of silver has been deter- mined with the greatest care and the mean result in grams per coulomb is .oouiyS. 2 Although the silver voltameter is the more accurate, a voltameter where copper is liberated from copper sulphate is more convenient (see 79). The mean cur- rent, in amperes, is the quantity, in coulombs, divided by the time (10). PROBLEMS XXI. 1. A current of 5 amperes flows for one hour through a copper voltmeter, (a) How many coulombs traverse the electrolyte? (6) How much copper is deposited? (c) How much copper is dis- solved from the anode ? 2. If 10 volts are applied to the electrodes of a certain silver plating bath, 20 grams are deposited in half an hour. Find (a) number of coulombs; (6) average current; (c) average power ex- pended; (d) work done by current. 3. Five Edison cells ( 340) in series send a current of 10 amperes for one hour through a gold-plating bath. Find (a) total zinc dissolved I Meyer, "Kin. Theory of Gases," 120; Boynton, "Kin. Theory," pp. 278-280. 2 Guthe, Bui. Bureau of Standards, 1905, i, 3, p. 362. COPPER VOLTAMETER. 28 3 in cells; (6) gold deposited. If the electric motive force of each cell is .9 volts, calculate (c) the average power and (d) the total work done (10). 4. Calculate the approximate number of ions in i c.c. of a .01 normal solution of sodium chloride if 92% of the molecules are dissociated. 5. Calculate the electrochemical equivalents of (a) zinc; (6) ferrous iron; (c) ferric iron; (d) SO 4 ; (e) NO 3 . EXPERIMENT XLV. Copper Voltameter, Joule's Law. This experiment is an application of the laws of Faraday and Joule and it affords practice in the use of a copper voltmeter and in interchanging electrical, thermal, and mechanical units. A current is sent for a definite time, T, through a copper volt- meter and through a coil of resistance, R, immersed in m w gr. of water in a calorimeter whose total water equivalent is m c . If the mass of copper deposited is m, the quantity of electricity, e (in coulombs), which has traversed the circuit is m divided by the electrochemical equivalent of copper, or .0003292, and the mean current, i, is this quotient divided by the time, T. The work done in the calorimeter, W, is e multiplied by the fall of potential in volts and the latter, by Ohm's law, is the product of the resistance in Ohms multiplied by the current in amperes, or Ri. .'. W = eiR =i 2 RT joules (Joule's law, 10) The heat produced in the calorimeter (in calories) is (m w +mc) (t 2 t l ) where t t and t 2 are the initial and final corrected tempera- tures. If ]' represents the number of joules in one calorie eiR=J' (184) The mechanical equivalent of heat, usually represented by J t is the number of ergs equivalent to one calorie, or / = 10? ]' . Fig. 91 illustrates the connections. The construction and operation of the copper voltameter is fully described in 79 of the introduction. The heating coil and calorimeter are shown on the left. The latter should consist of a thin-walled, brightly polished metal vessel of about 200 c.c. capacity, which is supported on corks inside a larger vessel, the space between the two being filled with cotton wool. The heating coil should consists of a spiral of constantin or other resistance wire of low- temperature coefficient. The ends of the coil should be attached to heavy leads, which pass through a wooden top, which covers both calorimeter vessels, and which has a hole in the center for a i /io thermometer. The resistance of the coil should be determined with great care (65-67). Between i and 2 ohms is a convenient value. The inner calorimeter vessel should be filled with distilled water from a burette to such a height that the coil will be well covered. The water should preferably be several degrees below the room temperature. The storage battery supply is represented at 284 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. the bottom of the figure; a regulating rheostat on the left, and an ammeter or tangent galvanometer at the top. If the latter is used, connections must be made through a reversing switch. Some such instrument is needed to obtain a rough idea of the magnitude of the current and to see that it remains constant. The current should be such as will give a rise of 10 to 15 in half an hour. When everything is ready, read the temperature, to tenths of a degree, every minute for five minutes, and then, noticing the exact minute, FIG. 91. close the switch. Continue minute readings of the temperature and keep the current steady by adjustments of the rheostat. When the temperature has risen about 10 or 15 degrees, note the exact time, open the switch and take five more readings of the tempera- ture at minute intervals. Correct for radiation as described in 59. Calculate from your observations and the above equations, a value for the mechanical equivalent of heat. The true value in terms of the 15 calorie is 4.187 X io7. (*) QUESTIONS. 1. Calculate the mean voltage at the terminals of the heating coil. 2. What error would be introduced if this voltage was excessive (333)? 1 Ames, Rap. Paris Cong., 1900, i, p. 204. CONDUCTION THROUGH AN ELECTROLYTE. 285 3. Why was it necessary to keep the current constant? (Note that the heat produced is proportional to i*.) 4. What percentage error would be introduced by neglect of the radiation correction? 5. If a tangent galvanometer has been used, calculate the hori- zontal component of the earth's magnetic field. 287. Conduction Through an Electrolyte. Let us examine more minutely the process by which electricity is transported through an electrolyte. For definiteness, we shall consider a solution of silver nitrate, in which dip two silver plates. A moderate difference of potential is applied to these plates; for example, by connect- ing them to a storage cell. The positively charged plate, the anode, will attract the negatively charged NO 3 ions and repel the positively charged Ag ions, and a current of elec- tricity will result. We consider as the direction of an electric current, the direc- tion in which positive electricity moves, but the magnitude of the current is the sum of the current in the positive direc- tion plus the current of negative electricity in the opposite direction. At the cathode the entire current is carried from the solution by the positively charged silver ions to the silver plate, and at the anode an equal amount of positive electricity is carried by an equal mass of silver ions from the anode silver plate to the solution. In the solution the total current is the positive current carried by the Ag ions plus the negative current, in the opposite direction, carried by the NO 3 ions. As the silver ions are deposited on the cathode, they must change from the ionic to the neutral metallic condition. A positive univalent ion may be considered as a neutral atom or radical from which one electron (345) or ultimate particle of negative electricity has been removed. The negative charge on the cathode restores the electron and we have Ag' + =Ag (One dot signifies an ion with a single positive ionic charge, and a dash signifies an ion with a single, negative, ionic charge. 286 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. is the symbol for an electron). A negative univalent ion may similarly be considered as a neutral atom or radical plus an electron. 288. Velocity of Ions. Consider the current through a centimeter tube of an electrolyte which dissociates into two univalent ions. If the concentration is n gram equivalents per litre, the number of equivalents in this cubic centimeter is n/ 1000. If the fraction a is dissociated, the ionic charge on either positive or negative ions must be 96530^071000 for one gram equivalent of ions has a charge of 96,530 coulombs. Let HI = velocity of positive ions, u 2 = velocity of negative ions, i = total current For, the current is the charge which passes through one face of the cube per second. Since we are considering a centimeter cube, the current is also equal to the specific conductivity, k (10), multiplied by the difference of potential. E (which is also the potential gradient, since the distance is i cm.) /. i ooo &= 965307*0: (u I -\-u 2 ) If E is in volts and k in reciprocal ohms, HI and u 2 are in centi- meters per second. For, to change to absolute electromagnetic units (Table III), the factor for k is 10-9, that for E is io 8 , and that for 96,530 is io- 1 ; therefore the total factor is unity. k .'. 1000 = 96,530 a (/! + U 2 ) =A ( J 86) n where U \ and U 2 are the velocities of the ions for unit potential gradient (i volt per cm.). 289. Equivalent and Molecular Conductivity. 1000 k/n is called the equivalent conductivity, and will be designated by A. The reason for the factor 1000 is that in electrical units (such as specific conductivity, specific resistance, etc.) the cubic DEGREE OF DISSOCIATION. 287 centimeter is the unit rather than the cubic decimeter or litre and n/ 1000 is the concentration in gram equivalents per cubic centimeter. The molecular conductivity is, similarly, one thousand times the specific conductivity divided by the concentration in gram molecules per litre. It is therefore equal to the equiva- lent conductivity multiplied by the valency. We can obtain a physical idea of ^ if we imagine one gram equivalent of the solution contained in a tank, two of whose sides are parallel conducting plates i cm. apart. Since the concentration of i c.c. is n/iooo, IOOO/H c.c. of solution must be between the plates. The conductivity of one cubic centi- meter is k (10) and the total conductivity between the two plates must be or, the equivalent conductivity is the conductivity of sufficient solution to contain one gram equivalent, inclosed between two parallel plates i cm. apart. 290. Degree of Dissociation. It is found by experiment that if we add distilled water to such a solution, in such a tank, the conductivity between the conducting sides, and therefore the equivalent conductivity, increases. Therefore, by Equa- tion 1 86, dilution must increase a or increase / x and U 2 or increase both. We know that the increase in conductivity comes almost entirely from increase in a, the degree of dis- sociation. For we saw in 181 and Experiments XVIII and XIX that the degree of dissociation of a dissolved substance increases with the dilution, and we know that the fluidity (reciprocal of viscosity, 127) upon which U^ and U 2 must depend does not change appreciably. 1 We should therefore expect that if the dilution was carried far enough, a point would be reached where all the electrolyte would be disso- ciated (i.e. a = i), and further dilution would not appreciably increase the conductivity. Such is found experimentally to 1 Spring. Pogg Ann., clix, p. i; Wagner, Zeit. phys. Chem., v, p. 36. 288 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. 'OS^Of H H s M cs n to rt- CO >OSu Z f M 1 1 1 CN) (N M^f H d M M 00 1 00 >OS<* * IO * H to oq -COK> H d H M M s csi WO 'ON*N vo O H 5 oq M M ON rj- oo S 1 TJ s 'ON* 00 10 H H to IH M M H oo' M i oq c J} m M d H 2 S" *? M 00 ON ctf _> w ITO 1 M oq H oq M ON 2 HO*HN 00 S 5 S s vO ON S ON 00 to HO*N H 1 8 f O M 'OS^H? CO GO M I to M o O'H'O S o" H M J 4 H E ONH 00 JC g to M to NO I3H oo s M to M * UOI^-BJJ -U3DU03 8 H 8 M O H ^ o X HI DEGREE OF DISSOCIATION. 289 be the case with a large number of electrolytes, and it is undoubtedly true in all cases where the nature of the ions is independent of the concentration. We will designate by ^ the limiting value of >1, corresponding to infinite dilution (a = i). Hence, by Equation 1 86, ^= 96330 (U T +U a ) (186') Therefore, dividing Equation 186 by 186', we find that the degree of dissociation when the equivalent conductivity is >l, is 1 Table XXXVI, compiled from the observations of Loomis, 2 Kohlrausch and Maltby, 3 and Ostwald, 4 illustrates the close agreement between the values for the dissociation calculated from the lowering of the freezing point and those calculated from the equivalent conductivity. TABLE XXXVI. Degree of Dissociation. Potassium Chloride. Concentration Fr. Pt. Cond. .01 .946 94 .02 9i5 .92 03 9 .91 05 .89 .89 .1 .862 .86 4 .802 .80 Tartaric Acid. Concentration Fr. Pt. Cond. .0106 .0200 .26 .18 .27 .20 .0499 .0997 13 .09 3 .09 1 Arrhenius Zeit. phys. Chem., 1887, i, 631. 2 Wied. Ann., 1894, li, p. 500. s Wiss. Abh. Reichsanstalt, iii, 151. 4 Zeit. phys. Chem., 1889, iii, p. 371. 2QO ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. 291. Temperature Coefficient. If the temperature of an electrolyte is raised, the equivalent conductivity generally increases, but the explanation is quite different from that for the similar effect of dilution. The velocity of the ions increases enormously with rise of temperature, owing, to a great de- crease in the viscosity, 1 while the dissociation generally de- creases. 2 If, as a first approximation, we regard the increase of conductivity as proportional to the increase of temperature, we may write k t =k io [i+a(t-t )] (188) where k to is the specific conductivity at a standard tempera- ture and a is the temperature coefficient. The temperature coefficients of a number of the more common electrolytes are given in Table XXXVII. The conductivity is not, how- ever, a simple linear function of the temperature (see 120, note, and 303), and Equation 188 and these temperature coefficients give only the approximate resistance at different temperatures. TABLE XXXVII. Temperature Coefficient (i8).3 HN0 3 0163 H 2 SO 4 0164 HC1 0165 KOH 0190 KNO S O2I I KI 0212 KBr O2l6 KC10, 02l6 AgN0 3 Kl 02l6 O2I7 NH 4 C1 O2 19 K 2 SO 4 0223 CuSO 4 022 =; NaCl 0226 Na 2 SO 4 0234 ZnSO 4 025 1 Thorp and Rodger, Zeit. phys. Chem., 1894. xiv, p. 361; 1896, xix, p. 323. 2 A. A. Noyes and Coolidge, Zeit, phys. Chem., 1903, xlvi, p. 323; Proc. Am. Acad., 1903, xxxix, p. 163. 3 KohlrausJi Sitz. Ber. Berlin Akad., 1901, p. 1026; 1902, p. 572; Proc. RoyJ Soc., 1903, !xxi, p. 338. Deguisne, Strassburg Dissertation, 1895, SPECIFIC AND EQUIVALENT CONDUCTIVITIES. 291 PROBLEMS XXII. 1. 10 gr. of anhydrous CuSO 4 were dissolved and diluted until the solution at 18 filled a tank 20 cm. long and 5 cm. cross section. The resistance between the ends was 125 ohms. Calculate (a) specific resistance, (6) specific conductivity, (c) equiva- c^ lent concentration, (d) equivalent conductivity, (e) molecular conductivity. 2. What is the degree of dissociation of this solution (Table XXXV)? 3. If the above tank has a resistance of 97 ohms at 28, what is the temperature coefficient of the solution? 4. The equivalent conductivity of a tenth-normal sodium chloride solution is 92.5. Calculate (a) specific conductivity, (6) specific resistance, (c) the resistance of the above tank when filled with this solution. EXPERIMENT XLVI. Absolute Determination of Specific and Equivalent Conductivities. Temperature Coefficient. The conductivity vessel consists of a glass tube about i cm. internal diameter and i 5 cm. long, fitted with rubber stoppers, through which pass copper rods. A copper disk which nearly fills the interior of the tube is attached to one end of each rod and the other end is provided with a transverse hole for a wire connector and a longitudinal binding screw (see Fig. 92), or a spring connector (95) is attached. The electrolyte is a solution of copper sulphate of assigned strength. The vessel is nearly filled with the solution. There are marks on the edge of each elec- trode and three similar marks on the tube. The elec- trodes are first placed so that their marks exactly coincide with the outside marks on the tube. Both electrodes must be covered by the solution, all air bubbles being carefully excluded. The vessel is then mounted vertically in a thermostat (81, and note, Experiment XXIX) and when the temperature is con- stant, the resistance is determined as described in 69. The upper electrode is then lowered until its mark coincides with the middle mark on the tube, and the resistance is again determined. The difference between the two resistances is the resistance of a column of the solution whose length is the distance between the two upper marks on the tube, and whose cross section is that of the tube. The latter is afterward determined by very carefully filling the tube with water from a burette, and finding the exact volume contained between two of the marks. The FIG. 92 distance between the marks is obtained with a comparator (28) or a vernier beam caliper (26). Several measurements should be made of both quantities. The conductivity tube should now be surrounded by ice and water, and when the temperature has become constant, the resistance should be redetermined. Calculate and tabulate for both temperatures (i) resistance, (2) 292 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. specific resistance, (3) conductivity, (4) specific conductivity, (5) equivalent conductivity, (6) molecular conductivity; and, finally, calculate (7) the temperature coefficient of resistance and (8) the temperature coefficient of conductivity, taking o as the standard temperature. QUESTIONS. 1. Explain use of (a) alternating current, (b) telephone, (c) two lengths of solution, (d) electrodes of the same metal as the salt dissolved. 2. Calculate the resistance of a tank filled with the solution you have used, if the tank and electrodes are twenty cm. square and the electrodes are i m. apart and (a) if the temperature is o, (6) if the temperature is 50. 292. Ratio of Ionic Velocities. The sum of the velocities of the positive and negative ions can be calculated from the equivalent conductivity and the degree of dissociation (Eqs. 186, 187). We shall show that the ratio of the velocities of the two kinds of ions can be found from the changes in concen- tration of the electrolyte at the two electrodes. Suppose we have, first, two platinum electrodes dipping in an electrolyte and that we send through the solution 96,530 coulombs of electricity. Consider the solution in the vicinity of the anode. One gram equivalent of anions has been liber- ated. In the solution, the current is divided between the anions and cations, each kind of ion carrying a portion pro- portional to its velocity, since the total charges on the two are equal. Therefore the mass of anions carried into the vicinity of the anode is the fraction of a gram equivalent, u^ and u 2 being the velocities of the ca- tions and anions, respectively. The net loss of anions is therefore The mass of cations which have left the vicinity of the anode is RATIO OF IONIC VELOCITIES. 293 Therefore there is a loss of anions and cations of of a gram equivalent, or this amount of electrolyte disappears from the vicinity of the anode when 96,530 coulombs traverse the liquid. Similar reasoning will show that the fraction of a gram equivalent of electrolyte disappears from the vicinity of the cathode. Observe that the ratio of these two fractions is the ratio of the velocities of the two types of ions, or, the losses at the two electrodes are inversely proportional to the velocities of their respective ions. u^ _ Loss at anode u 2 ~ Loss at cathode This law was discovered by Hittorf ,* who named the above fractions "transport numbers" since they represent the share of transport of electricity. The transport number for the anion is the one usually given in tables, and is generally understood unless the transport number for the cation is specified. We will represent the (anion) transport number by The transport number for the cation is obviously i-N . . (190) u 2 N From Equations 186, and 189 or 190 we can calculate U l and U 2 - Table XXXVIII gives the transport numbers of the more common electrolytes (see also 295 and Table XXXIX). Ann. 1853, Ixxxix, p. 177; also, "Fund. Laws of Elec. Cond.," Goodwin. 294 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. TABLE XXXVIII. Transport Numbers (20). l gr. mol. liter 5 5- HC1 .i6s I 7 3 .176 .2*8 H 2 SO 4 .167 . IQO .2OO .270 NaOH 80 82 8^ KC1 . ^i CQ ^o ^o NaCl . .60 .62 .6^ .64 CaCl 2 S6 .60 .67 .68 CuSO 4 62 60 7 2 AgNO., 53 51 49 47 ZnSO 4 .64 .78 293. If the anode is a metal of which the electrolyte is a salt, the anions are not liberated, but an equivalent of metal cations goes into s.olution. Instead of a loss of electrolyte at the anode there will therefore be a gain. The amount of metal dissolved at the anode will equal that deposited at the cathode, and therefore, before substituting in Equation 189, we must find what the loss would have been with a platinum electrode, by subtracting from the apparent gain in electrolyte at the anode the equivalent of the cathode deposit. 294. Direct Determination of Ionic Velocities. The velocities of certain ions have been determined directly and the values obtained agree well with those calculated by Equations 186 and 189. The electrolyte consisted of two or more solutions in series, separated by either a jelly or gravity. In the methods of Whetham 2 and Masson one of the solutions pos- sessed a colored ion, and the progress of this ion was watched and its velocity determined. Lodge 3 followed hydrogen 1 Compiled from the exhaustive tables in Winkelmann, 1905, IV, i. 2 Phil. Trans., 1893, A - clxxxiv, p. 337; 1895, ccxxxvi, p. 507. 3 Brit. Ass. Rep., 1886, p. 389. IONIC CONDUCTIVITIES. 2 95 ions by their decoloration of a phenolphthalein solution. Steele 1 observed the change in refractive index as the ions migrated. The original papers should be consulted for details. The actual velocities of the ions are of interest, but are not, however, of as much importance as the ionic conductivities to which they are proportional. 295. Ionic Conductivities. Returning to Equation 186', we see that the equivalent conductivity of a completely dissociated solution is made up of two parts, one of which, 96,530 t/j, is contributed by the positive ions, and the other portion, 96,530 U 2 , is contributed by the negative ions. TABLE XXXIX. Ionic Conductivities (i8). 2 Cations Anions H . 318 OH K . NH 4 . . . iPb . . . JBa ... Ag JCd ... 64.7 64- 61.5 55-9 54- 47-4 47-2 a 2 4 '. C 4 H S 4 C 4 H S 6 v .... NO, 68.7 66. 63- 62. 38. 39- 59. T 7 4.6 6 C 2 HO 4 47- fef.::: 46.1 4.7 C C 4 H,0 6 C 7 H,O, . . 39- 79. 38. C!H!O! 3 ?. These two components of the equivalent conductivity, X x , are called the ionic conductivities j l and j 2 /. ^=a(j l +j 2 ) (192) Kohlrausch and Ostwald 3 have demonstrated that the ionic 1 Phil. Trans., 1902, A, cxcviii, p. 105. 2 Compiled from the excellent tables in Van Laar, Chap. Ill; and Winkel- mann (1905), IV, i, except for Cl and NO 3 which are taken from Goodwin's paper in Phys. Rev., 1904, xix, p. 369. 3 Gott. Nach., 1876, p. 213; Wied. Ann., 1898, Ixviii, p. 785; also in "Fund. Laws of Elec. Cond.," Goodwin. 296 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. conductivity of a particular ion is independent of the presence of other ions if the solution is very dilute, and that this law is also approximately true for moderate concentrations. 1 We would naturally expect the ions would be mutally inde- pendent in a solution which was so dilute that the electrolyte was almost completely dissociated. The ratio of the ionic conductivities of a salt is the ratio of the velocities of the ions at great dilution and from this ratio corresponding transport numbers can be calculated by Equation 190. EXPERIMENT XL VII. Velocity of Ions. (A) Determination of Sum of Velocities, and Degree of Dissociation 3 Fill a standardized conductivity vessel (70) with the assigned, electrolyte and determine the resistance (69). Dilute the electro- lyte until the concentration is about .0005 and redetermine the resistance. Calculate the equivalent conductivities for both concentrations. The dissociation may be considered complete in the more dilute solution. The ratio of the two equivalent conductivities will there- fore equal the degree of dissociation a of the more concentrated solution. Finally, calculate (Ui + U 2 ) by Equation 186. (B) Determination of Ratio of Velocities. Ionic Conductivities. Place in a beaker two porous cups of about 75 c.c. capacity and pour in the assigned solution until the level is the same in the two cups and outside in the beaker. In each porous cup place a plate elec- trode of the metal whose salt was assigned. The electrode which is to be the cathode should have been carefully cleaned before immersion and weighed to tenths of a milligram (32). Connect the two electrodes to storage-battery terminals through an ammeter, a switch and a variable rheostat (see Fig. 93). Be careful to connect the cathode plate to the negative pole. If the electrolyte is a copper salt, the current per 100 cm. 2 of cathode should not exceed one ampere, and with a silver salt the current density must be much less. When the current has continued sufficient time to give a suitable deposit on the cathode (for example, .05 gr. in 40 minutes), remove and carefully dry the cathode, and weigh it to tenths of a milligram. Measure the volumes of the three solutions. Take equal volumes of each (e.g., 25 c.c.) and determine the amount of the salt in each solution by determining the amount of metal. If copper is the metal, determine the amount either by iZeit. phys. Chem., 1888, ii, p. 841. 2 The most convenient electrolyte is copper sulphate of concentration between .1 normal and normal. Silver nitrate with silver electrodes offers no difficulties if the current density is low and the time correspondingly greater, but the porous cups must be sufficiently dense to prevent appreciable diffusion during the in- creased time. VELOCITY OF IONS. 297 (a) depositing the copper on a platinum cathode, using a low- current density and platinum cathode and anode, and continuing the current until all the copper is deposited, or (b) determine the copper by iodimetry. 1 This is much more rapid and sufficiently accurate for a laboratory experiment. .Acidify each solution with acetic acid, add an excess of potassium iodide, and titrate with .1 n sodium thiosulphite. Remembering that one molecule of thio- sulphite corresponds to one molecule of copper, calculate the con- centration of each solution from the titrations and the volumes. Rheostat FIG. 93. From the original volumes of the solution in the porous cups, calcu- late the total amount of copper in each, before and after the passage of the current. Subtract from the value for the anode cup the amount deposited on the cathode (293). Finally, from the ratio of the losses in the two cups, calculate the ratio of the velocities (Equation 189) and the transport number (Equation 190). If silver is the metal, the amount of silver in each solution may be obtained by electrical deposition, using platinum electrodes and a very small current density, or by volumetric analysis with potas- sium or ammonium sulphocyanide. 2 Combining the results of (A) and (B) calculate the ionic con- ductivity and the actual velocity of each ion. QUESTIONS. 1. What is the velocity of each ion in cm. per hour? 2. What would be the average velocity of each of the ions of this solution between two fine wires 5 cm apart, if the difference of potential of the two wires was 500 volts? Button, "Volumetric Analysis," p. 176. 2 Treadwell, Vol. ii, p. 540. 298 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. 3. With the help of Table XXXIX and Equation 186' calculate the velocities in cm. per sec. of hydrogen and hydroxyl ions for unit potential gradient. 4. Calculate the velocities of the latter ions if the solution of (2) was replaced by pure water. 296. Relative Velocities of Ions. Table XXXIX shows that hydrogen is the swiftest ion and the hydroxyl ion comes next in order of speed. Suppose we have an alkaline solution, and gradually add an acid solution, for example, imagine HC1 solution added to NH 4 OH solution. Up to the neutrallization point the mixture is alkaline and therefore practically none of the hydrogen added remains in ionic form (258). The only effect therefore is the substi- tution of the other ion of the acid, Cl', for the faster moving OH' ions and hence the conductivity decreases to the neutrali- zation point. The further addition of acid beyond the neutralization point increases the .number of the rapid hydro- gen ions and thus increases the conductivity. Analogous effects are observed when a solution of a strong base is added to a solution of a strong acid. PROBLEMS XXIII. 1. Calculate Van't Hoff's coefficient, i, for in solutions of AgNO 3 , ZnSO 4 , CuSO 4 , and Na 2 SO 4 . (Equations 112 and 187 and Table XXXV.) 2. Hittorf found that after the current had passed through a normal solution of CuSO 4 , ,29 58 gr. of copper had been deposited on the cathode while the solution in its vicinity had lost .2114 gr. of copper. Calculate (a) ratio of velocities; (b) transport number. With the assistance of Table XXXV calculate (c) the degree of dissociation; (d) the ionic conductivities, and (e) the velocities for unit potential gradient. 3. A current was passed through a solution of silver nitrate between silver electrodes. While the cathode gained 96.6 mg. of silver, the electrolyte in its vicinity lost 50 mg. of silver. Calculate (a) ratio of velocities of ions, (6) transport number. 4. From Tables XXXV and XXXVIII determine (a) the degree of dissociation of a normal solution of hydrochloric acid ; (b) the ionic conductivities; (c) the actual velocities of the ions under unit potential gradient. 5. Calculate the actual velocity of the acetic acid radical in cm. per sec., for one volt per cm. 6. .in HC1 is gradually added to .in NaOH, until the volume of the solution is three times the initial volume. Construct a curve which will illustrate qualitatively the change in conductivity (two values may be obtained from Table XXXV). ELECTRICAL MEASUREMENT OF RATE OF SAPONIFICATION. 299 7. From Tables XXXV and XXXVII calculate the temperature at which a .01 normal solution of CuSO 4 has the same specific con- ductivity as a .001 normal solution of Pb (NO 3 ) 2 at 18? EXPERIMENT XLVIII. Conductivity of Acid, Alkaline, and Neutral Solutions. 1 As an illustration of the difference in the velocity of various ions, we shall follow the change in resistance, or conductivity, of an alkaline solution while an acid is gradually added. Fill a conductivity vessel (70) with the assigned 2 alkaline electrolyte so that the electrodes are well covered. Add a few drops of phenolphthalein. Determine the resistance as described in 69, preferably using a slide-wire bridge. Add from a burette a small measured amount of the assigned acid solution and redeter- mine the resistance. Add more acid and again determine the resistance, and so continue until well beyond the neutralization point. There should be at least five observations on each side of this point. In the vicinity of the neutralization point, add the acid slowly so that a determination of the resistance may be made as close as possible to this point. Plot the observed resistances against the total volume of acid solution added, and draw a smooth curve through the points. The curve should show a sharp change of curvature at the neutralization point. This method of determining the neutralization point is sometimes useful in determining the strength of an acid or alkaline solution which is so turbid or colored that an indicator cannot be observed. QUESTIONS. 1. From considerations of the progressive changes in ionic con- centrations deduce the form of curve obtained when (a) a weak acid is added to a weak base; (6) when a strong acid is added to a weak base ; (c) when a strong base is added to a weak acid. Explain why the change of curvature is indistinct in these three cases. 2. From the constant of the cell (72) calculate (a) the specific conductivity of the neutral salt at the neutralization point, and (6) its equivalent conductivity. 297. Electrical Measurement of Rate of Saponification. In 244 we saw that when an alkali is added to a solution of an ester both gradually disappear and the corresponding ace- tate and alcohol are formed. In experiment XXXIII we followed the reaction by determining, at intervals, from titra- tions, the unchanged alkali. From the previous paragraphs it is evident that the dis- appearance of the rapidly moving hydroxyl ions of the base, 1 Findlay, "Practical Physical Chemistry," p. 179. 2 A solution of any one of the more common strong bases is satisfactory and the particular acid is immaterial. It is convenient to have the strength of the acid solution about twice that of the alkaline solution. 300 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. and the substitution of the little dissociated alcohol and acetate for the highly dissociated base, must decrease the conductivity, and Walker has shown * that the conductivity is very closely proportional to the amount of base unchanged. EXPERIMENT XLIX. Study of Saponification by Change in Conductivity. Prepare a conductivity vessel and Wheatstone's bridge so that a resistance determination may be made immediately after filling the conductivity vessel. The latter should, preferably, be in a thermo- stat (81). Prepare the assigned 2 solutions of ester and base and, noting the exact time, mix the two solutions. Immediately fill the conductivity vessel with the mixture and determine the resist- ance (69). About three minutes later make another observation of the resistance. Notice the exact time when a balance is secured. So continue, gradually increasing the intervals. The last observation but one should be about three hours after the first, and the final determination after about twenty-four hours. Plot observed resistances against the time and draw a smooth curve through the observations. Choose five points on the curve and calculate the velocity constant for each. If the initial concentrations were equal, Equation 1 59 must be used and x/c x for any point is the difference between the ordinate at that point and the initial ordinate divided by the difference be- tween this ordinate and the final ordinate. If the initial concentrations are unequal, Equation 161 must be used. c 2 , the smaller concentration, is proportional to the total change in resistance. At any one of the points in the curve (c 2 x) is proportional to the change in resistance beyond that point. Ci is proportional to the resistance corresponding to c 2 , multiplied by the ratio of the initial concentrations, and x for any point is proportional to the change of resistance at that point. Thus all the factors c 2 , (GI -x), c lt (c 2 -x) may be expressed in terms of resistances. The actual concentrations must of course be substituted in the factor (d c 2 ). Find the mean velocity constant and compare it with the value obtained in Experiment (XXXIII), if identical solutions have been employed. . Royal Soc., 1906-7, Ixxviii, p. 157. 2 Ethyl acetate is the most convenient ester, and the solution may have any strength between .O2 and .iw. The alkali may be any one of the more common bases and its concentration may be the same as that of the ester or slightly different. EQUIVALENT CONDUCTIVITY FOR INFINITE DILUTION. 301 QUESTIONS. 1. (Time constant.) Determine from the curve when the reaction was half completed, and compare it with the time calculated from the velocity constant (Equation 155). 2. What was the initial velocity of the reaction? In what units is your answer expressed? 3. What advantages and what disadvantages has this method over that of Experiment XXXIII? Determination of the Equivalent Conductivity for Infinite Dilution. 298. The most obvious method of determining the equiva- lent conductivity at infinite dilution is to determine it for a large number of concentrations, the last being as dilute as possible, and then, by exterpolating, determine what would be the conductivity at infinite dilution. A convenient method of exterpolating is to plot the observed conductivities against the concentrations (or, preferably, the cube root of the con- centration, since this will give a. more convenient scale) and extend the curve obtained until it cuts the axis of conductiv- ities at zero concentration. This method is applicable to acids, bases, and salts which are strongly ionized. , Some electrolytes are so little dissociated that it is impossible to determine the equivalent conductivity for infinite dilution in this manner. In such a case we must find some highly dissociated combination of each one of the ions, and determine the ionic conductivities. By Kohlrausch's law (295) the equivalent conductivity for complete dissociation is always equal to the sum of the ionic conductivities of the constituent ions. For example, acetic acid is only dissociated to a small degree at great dissociation. We can, however, find the ionic conductivity of the hydrogen ion from the equivalent conduc- tivity and transport number of HC1 at great dilution, and we can similarly find the ionic conductivity of the other ion, the acetic acid radical, by measurements upon sodium acetate which is highly dissociated. 302 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. The Dilution Laws. 299. We saw in 260 that K= V(i - a) where V is the volume (litres) which contains one gram equivalent, i.e., the dilution, a is the degree of dissociation, and K is a constant called the dissociation constant (Ostwald's dilution law, 260). Substituting for a its value given by Equation 187, we have K=~ ; (193) If a is very small, we may neglect it in comparison with unity and :.K = ~ (194) Equation 193 holds well for weak electrolytes, but when we apply it to strong electrolytes we find that K is not a constant but depends upon the dilution. It is almost impossible to believe that the law of mass action, upon which this equation is based, is inapplicable to strong electrolytes. It seems probable that there are forces between the ions themselves, and between the ions and the neutral molecules of strong electro- lytes, which make it impossible to apply the mass law directly to the ions and molecules. The papers of Jahn 1 and Nernst 2 should be consulted for a full discussion of the subject. 300. Two empirical modifications of the above dilution law apply quite satisfactorily to strong electrolytes. In place of the first power of the dilution, V, Rudolphi's^ formula substitutes the square root of the dilutiojn and Kohlrausch's 4 formula has 1 Zeit. phys. Chem., 1901, xxxvii, p. 490; 1902, xli, p. 257. 2 Zeit. phys. Chem., 1901, xxxviii, p. 487. s Zeit. phys. Chem., 1895, xv > P- 385. 4 Zeit. phys. Chem., 1895, xv i> 662. DISSOCIATION CONSTANT. 303 the cube root. Noyes and Coolidge 1 found that the latter formula K = v*T~(T ( ig ^ I/MX (Xoo A) gave values of K which were constant, within the experimental errors, for the highly dissociated salts KC1 and NaCl, through- out a wide range of concentrations (.3 to 100 normal), and an extreme range of temperature (i 8 to 306) . 301. Dissociation Constant. The dissociation of an electro- lyte is often quite complex and may take place in stages. For example, sulphuric acid may dissociate as follows: 2 H 2 SO 4 ^H' + HSO 4 '; HSO/ = H- + SO/ and water may dissociate as In such cases there will evidently be two dissociation constants which will not be independent, since they involve common ions. As has been previously pointed out, all the different methods of measuring the strengths of acids or bases give values which are proportional to the dissociation. The dissociation constant is perhaps the most convenient measure of the dis- sociation, and is therefore of great importance. It is also often called the ionization constant, and, for reasons just explained, another name for it is affinity constant. TABLE XL.3 Dissociation Constants (25) Acetic acid ......................... oooo 1 8 Benzoic acid. . : ..................... 000073 * Succinic acid ....................... 000066 Formic acid ........................ 0002 14 Tartaric acid ....................... 00097 Salicylic acid ....................... 00102 Ammonia .............. -. ........... 000023 *lx. 2 Perkin, "Electrochemist," 1901, i, p. 189. 3Landolt and Bernstein's Tables. 4Bauer, Zeit. ph. Chem., 1906, Ivi, p. 215. 304 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. 302. Isohydric Solutions. Two solutions are called iso- hydric if the total number of each kind of ion is unchanged upon mixing. We will only consider one case, namely, the mixture of two binary electrolytes which have a common ion ; for example, two univalent acids. Let the dilution of one solution be V (volume occupied by one gram equivalent) and its degree of dissociation a (= fraction of gram equivalent of each ion in volume V) and let the corresponding quantities for the other solution be V and a'. If the electrolytes are weak, we may apply Oswald's dilution law and for the first electrolyte we must have K- 2 V(i-a) After mixing, the total volume, or dilution, is V -\-V' y and if the ions are to be unchanged, the amount of the common ion in this volume is (a + a') . The dissociation constant of the first solution must therefore also agree with the equation (a+a'}a Dividing one equation by the other, we have (a+a')V = . a+a' ^V + V (V+W)a~ a V a a' (196) V V or two binary electrolytes having a common ion are isohydric, if they have equal concentrations of the common ion. 1 1 For an excellent discussion of isohydric solutions, see Walker, 4th Ed. Chap. XXVI. THE DILUTION LAW." 305 PROBLEMS XXIV. 1. Velocity df reaction between n/2$ solutions of ethyl acetate and sodium hydroxide. Change in electrical conductivity. Time (min.) .Resistance o 270 3 3 M 35 22 390 44 425 75 45 2 240 520 720 567 Calculate (a) velocity constant, (6) initial velocity of the reaction, (c) time when the reaction is half completed. 2. Calculate from Table XXXIX the equivalent conductivity at infinite dilution of (a) oxalic acid; (6) tartaric acid; (c) ammonium hydroxide. 3. Calculate the degree of dissociation of a .005 normal solution of acetic acid from the dissociation constant (Table XL). 4. Calculate (a) the degree of dissociation of a .001 normal solution of tartaric acid (Eq. 176 and Table XL); (6) the equivalent conduc- tivity; (c) the specific resistance, and (d) the resistance of a tube of this solution i metre long and i square decimeter cross section. 5. Calculate both Rudolphi's constant and Kohlrausch's constant for a low solution of (a) HC1; (6) NaOH. 6. We have a .1 normal solution of potassium chlorate. Estimate from Table XXXV and Equation 196 the concentrations of iso- hydric solutions of (a) KI; (6) K 2 SO 4 . 7. From Tables XXXIX and XL calculate (a) the degree of dissociation; (b) the molecular conductivity, and (c) the specific resistance of a i % solution of benzoic acid. EXPERIMENT L. The Dilution Law. Prepare with great care a sufficient quantity of a .05 normal solution of the assigned electrolyte. 1 Choose such a pipette that the standardized conductivity vessel (70, 72), may be properly filled with two transfers of the pipette. Determine the conductivity of the solution, following the directions given in 69. By means of this pipette remove half of the solution and in its place introduce from a similar pipette an equal amount of pure water. Determine the resistance as before. Continue replacing half of the solution by water and determining the resistance until the concentration is 1/256 of what it was initially. For each observation, calculate (i) the concentration in gram equivalents per litre; (2) the specific conductivity; (3) the equivalent conductivity; (4) the degree of dissociation (Equations 187 and 191) and, finally, (5) the dissociation constant. i Suitable electrolytes are any of those whose constants are given in Table XL. 20 306 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. QUESTIONS. 1. (a) Calculate the number of grams of (a) undissociated solute (6) of each ion, in one litre of the original solution. 2. For each ion calculate (a) the ionic conductivity, and (b) the actual velocity for unit potential gradient. 3. Could one determine ^ by exterpolation ? Explain. 303. Electrolytic Conductivity and Temperature. It was pointed out that Equation 188 is only approximate. Kohl- rausch 1 found that he could express the equivalent conductivity for infinite dilution, at any temperature t, in terms of the conductivity at 18, by the empirical equations l*^ ^ I8 [i+a(t-i&)+b(t -i&)*]; b = .oi6 3 (a-. 0174), (197) Upon substituting the values of ^ l8 , a, and b, which he had determined for a great number of electrolytes, he found that ^* would be equal to zero at some temperature between 37 and 41, for every electrolyte.tested. It is interesting to note that the empirical formula for the viscosity of pure water at different temperatures (127) gives a minimum within this range of temperature. 304. Hydrates. This coincidence suggests that each ion in an aqueous solution attracts a number of water molecules, which more or less completely surround the ion and that the resistance to the motion of the ion is therefore simply the viscous resistance between bodies of pure water. Further evidence of the formation of such hydrates is given in the papers of (Nernst 2 Buchbock,^ Jones, 4 and Washburn. 5 The latter has shown that the minimum hydration ranges from .3 of a molecule of water for hydrogen to 4.7 molecules for lithium. 305. Conductivity at High Temperatures and Pressures. Noyes and his co-workers 6 have measured the conductivity of aqueous solutions of the common salts, acids, and bases over a range of temperature extending to about 300. The solutions were kept liquid by great pressure. A platinum-lined, steel 1 Berichte, Ber. Ak., 1901, p. 1026; 1902, p. 572; Proc. Roy. Soc., 1903, 338. 2 G61t, Nach., 1900, pp. i and 68. sZeit. phys. Chem., 1906, Iv, p. 563. 4 Am. Chem. Journal, 1905, xxxiv, p. 294; 1907. xxxvii, p. 126; 1909, xli, p. 19. s Jour. Am. Chem. Soc., 1909, p. 322. 6 Z. c. CONDUCTIVITY OF NON-AQUEOUS SOLUTIONS. 307 bomb was used and the joints were made tight with gold bushings. Quartz was used where an insulating material was required. They found that the conductivity was very great at high temperatures. The conductivity for infinite dilution (estimated by Kohlrausch's Equation 195) showed even a greater increase, and, therefore, by Equation 187, the dissocia- tion must have decreased. Moreover, the limiting value of /l x , as the temperature was increased, was approximately the same for all binary electrolytes (about noo). The conductivity generally increases as the temperature rises, because the velocity of the ions increases more rapidly than the dissociation decreases. (Compare Equation 185.) This explanation suggests the possibility of some tempera- ture where the dissociation begins to decrease more rapidly than the velocity of the ions is increasing. This would result in a maximum of conductivity at this temperature. Such is undoubtedly always the case near the critical temperature. Noyes and Coolidge 1 found such maxima- for fairly concen- trated aqueous solutions of sodium and potassium chloride. Kraus 2 has demonstrated such a temperature maximum for ethyl and methyl alcohol solutions, and Hagenbacks for solutions in sulphur dioxide. A few solutions show such a maximum of conductivity at moderately low temperatures, e.g., copper sulphate at 95. 4 306. Conductivity of Non-aqueous Solutions. A great amount of work has been done upon the electrical conductivity of solutions in other solvents than water, but it is only possible to give a brief summary. For more detailed information, the reader should refer to the original memoirs of Walden, 5 Kraus 6 and Kahlenberg. 7 'Proc. Am. Acad., 1903, xxxix, p. 163. 2 Phys. Rev., 1904, xviii, pp. 40, 89. 3 Ann. de Phys., 1901, v, p. 276. 4 Sack, Ann. d. Phys., 1891, xliii, p. 212. s Zeit. f. Anorg. Chem., 1900, xxv, p. 209; 1902, xxix, p. 371; xxx, p. 149. Zeit. f. phys. Chem., 1903, xliii, pp. 396, 464; xlvi, p. 103; 1906, liv, p. 129; Iv, pp. 207, 281, 683. 6 Am. Chem. Jo., xxiii, p. 277; Jour. Am. Chem. Soc., xxvi, p. 499; xxvii, p. 101. 7 Jour. Phys. Chem., 1902, vi, p. 447; 1903, vn, p. 254. 308 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. Liquid sulphur dioxide, liquid ammonia, and hydrocyanic acid are the best known inorganic solvents, while among organic solvents, ethyl and methyl alcohol, pyridene, and formic acid have been carefully studied. Solutions in all these solvents show, in general, the electrical characteristics of aqueous electrolytes. The equivalent conductivity of a dissolved substance increases with the dilution, indicating an increase in the dissociation. TABLE XL!.' Degree of Dissociation, a, of i/io Normal Solutions of Potassium Iodide and Potassium Acetate in Water, and Ethyl, and Methyl Alcohol ; and Equivalent Conductivity at Infinite Dilution, ^ . K [ KC 2 H 3 2 *QC a ^ H 2 O I2O 7 88 OO 8^ CH 3 OH 95-2 5 2 77.8 36 C 2 H 5 OH 48 o 2 ^ 12 8 16 The dissociation even at great dilution is however, generally much less than in aqueous solutions, but the equivalent con- ductivity is often much greater. We see by Equation 186 that the velocity of one or both the ions must be much greater than in solutions in water. Kraus has shown that in liquid am- monia solutions the anion is apparently an electron (345), which, on account of its diminutiveness, travels with great speed. Solutions in liquid ammonia obey the dilution law (299). Non-aqueous solutions often do not show the same degree of dissociation by the freezing-point method (Eq. 112) and by the conductivity (Eq. 187); and Kohlrausch's law (295) usually fails. They resemble aqueous solutions (305) in showing an increase of conductivity as the temperature is raised until a certain temperature, beyond which the con- ductivity falls off. 1 Vollmer,5Wied. Ann., 1894, Hi, p. 328; and Jones, Zeit. phys. Chein., 1899, xxxi, p. 114. CONDUCTIVITY OF FUSED SALTS. 309 Skaupy has applied Oswald's dilution law to solutions of metals in mercury (amalgams) and has shown that the ions are similar to the ions which Kraus found in ammonia solutions, namely, the anion is an electron and the cation is the metal. 1 For the conductivity of salts in mixed solvents, the reader is referred to the papers of Jones and his co-workers. 2 307. The Conductivity of Fused Salts. Faraday discovered that salts which conduct electricity when dissolved in water also conduct when they are melted, even though no water is present, and that they obey his law (28i). 3 The specific conductivity (10) of a fused salt may greatly exceed the specific conductivity of the most concentrated solutions, but the concentration is so high that the equivalent conductivity is much less. Goodwin and Mailey 4 studied not only the conductivity, but also the fluidity (127) of a large number of the more common salts in the molten state, and they found that conductivity and fluidity increased as the temperature rose, but that the fluidity increased somewhat faster, showing that the increase of conductivity was due to an increase in the ve- locity of the ions rather than to an increase in the dissociation. 5 TABLE XLII.6 Fused Silver Nitrate. Temp. k A F 218 (Melt.pt.) .681 29.2 250 .834 36.1 27.7 300 1.049 46.2 36-7 350 1.245 55-4 45-5 'Zeit. phys. Chem., 1908, Iviii, p. 580. 2 Am. Chem. Jo., 1902, xxviii, p. 329; 1904, xxxii, pp. 409, 521; 1906, xxxvi, pp. 325, 427. 3Exp. Res., iv, 380; vii, 669. 4 Phys. Rev., 1908, xxvi, p. 28. s See also the papers of Arndt; Zeit. f. Electrochemie, xii, p. 337; xiii, p. 59; xiv, p. 662. 6 Goodwin and Mailey, /. c. 3IO ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. Table XLII gives the specific conductivity, k, the equivalent conductivity, X, and the fluidity, F, of fused silver nitrate at different temperatures. The specific conductivity of a 60% aqueous solution at 18 is but .208. 308. Electrolytic Conductivity of Solids. Hot non-metallic solids, such as glass, porcelain, etc., conduct appreciably. Warburg 1 inclosed a glass plate at 300 between sodium amalgam electrodes and found that it conducted electricity, and that the products liberated (Na 2 SiO 3 at anode) were in accordance with Faraday's law. If a lithium amalgam was used the progress of the colored lithium ions through the glass, could be observed. Practically all the current was carried by the cations, sodium, or lithium. Warburg found that a hot crystal of quartz showed enormously greater conductivity parallel to the axis than at right angles. Nernst considers that the conductivity of the metallic oxide glower, which he invented and which is used in Nernst lamps, is electrolytic. He explains the small amount of decomposition, -even with direct current, by the great rapidity of diffusion of the products of the electrolysis at the high temperature employed. 2 309. Dielectric Constants. The attraction between the two ions of a binary molecule is given by the fundamental electrostatic equation F- e - ~td* Where F is the force in dynes, e is the ionic charge in electro- static units, d is the distance between the ions in centimeters, and e is the dielectric constant (specific inductive capacity) of the medium surrounding the two ions. The greater e, the less the attractive force, and therefore we should expect that the higher the dielectric constant of a solvent, the easier the ions of a molecule would separate, and the less frequently would they recombine; in other words, the greater would be the dissociation. 'Ann., 1884, ii, p. 622. 2 Zeit. f. elec. Chem., 1899, vi, p. 41. DIELECTRIC CONSTANTS. TABLE XLIII.i Dielectric Constants. IJ Hydrocyanic acid 96 Water 80 Methyl alcohol 33 Ethyl alcohol 25 Ammonia (liquid) 22 Acetone 17 Sulphur dioxide 14 Pyridene 12 Ether 4.5 Xylol 2.26 Benzol 2.2 Toluol 2.2 Petroleum 2.07 310. Nernst -Thomson Rule. In general, such is the case, as is illustrated in the following table. The liquids in column I give conducting solutions while those in column II do not. All the values are either for static charges or for very low frequencies. While the dielectric constant is evidently a very important factor in determining the dissociation, there are other modifying influences which are occasionally more important. For example, the strong acids conduct better in hydrocyanic acid than in water, while the reverse is true of potassium salts. 2 PROBLEMS XXV. 1. Calculate the equivalent conductivity of a .001 normal solution of ZnSO 4 at o. Use Kohlrausch's formula (197) and the value of a given in Table XXXVII. 2. How would you interpret Noyes' observation that at high temperatures and great dilution the equivalent conductivities of all binary electrolytes approach a common value ? 3. What is the transport number for (a) the anion; (b) the cation in the ammonia solution of Kraus described in 306? 4. Compare the degree of dissociation given in Table XXXVI with the dielectric constants as given in Table XLIII. 5. Calculate (a) the concentration; (6) the specific resistance of melted silver nitrate at 300 (Table XLII, Density of fused salt =4.3 5). 6. How many milligrams of sodium silicate should Warburg have found (308) after the passage of i milliampere for an hour? 7. Two parallel plates, 12 cm. in diameter are separated by 2 mm. of benzol. Calculate the force drawing them together when their difference of potential is (a) 10 electrostatic units; (6) 1000 volts 1 From Winkelmann, iv, i, p. 135. 2 Kahlenberg, Jour. Phys. Chem., 1902, vi, p. 447. 312 ELECTROCHEMISTRY, ELECTROLYTIC CONDUCTION. ( 10, 12 and 309) calculate the force on unit charge from the poten- tial (9, 10), and the charge from the capacity (9). EXPERIMENT LI. Determination of the Dielectric Constant of a Liquid by DeSauty's Method. Determine the dielectric constant of a highly insulating liquid such as kerosene or benzol by the method described in 80. Make repeated careful determinations of the proper resistances for the largest distance between the plates which will give a distinct minimum of the sound. Then surround and cover the plates with the liquid and again determine the proper resistances. Check your observations by changing the resistances back to their values for air and then adjusting the distance between the plates for minimum sound. The ratio of the distances apart of the plates should be (approximately) inversely proportional to the ratio of the resistances when the distance was kept constant. QUESTIONS. 1. Calculate the force in dynes, between two ions .01 mm. apart in this liquid, if the charge on each is 3 X io- 10 electrostatic units. 2. Calculate the capacity of the two plates when separated by (a) air; (6) liquid, the distance apart being the same as in the first part of the experiment (9). 3. Calculate the charge for each case if (a) 100 electrostatic units of potential are applied; (6) 100 volts (9, 12). CHAPTER IX. ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. 311. Difference of Potential Between a Metal and a Solution of One of its Salts. A metal dips in a solution of one of its salts. The ions in the solution tend to increase their volume; i.e., they exert a pressure which we call the osmotic pressure, p (169.) Nernst has suggested 1 that we may consider that there are also ions in the metal and that they are under a similar pressure which he calls the solution pressure, and which we will designate by P. If P is greater than p, ions will go from the metal into the solution, and since metal ions have a positive charge (285-287), the solution will become positively charged (Fig. 94). Since the removal of a positive charge is equivalent to the addition of a negative charge, the metal will become charged negatively. This negative charge will attract the FIG. 94. po'sitive metallic ions which will be repelled by the positively charged solution. Equilibrium will be attained when this electric force opposing the solution of the metal, is equal to the force equivalent to P p, which tends to produce solution. We will show that (198) where E is the potential of the solution above the metal, in volts, J is the number of joules in one calorie (4.187, 7), v is the valency of the metal, m is the number of ions in a 'Zeit. phys. Chem., 1889, iv, p. 129. 314 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. molecule, Q is the heat absorbed from surrounding bodies during the transfer of this electricity, k is a factor defined later, R is the gas constant (in calories), and is the absolute temperature . P and p have already been defined . 312. At equilibrium, the energy of the metal ions must be the same in metal and solution (equal thermodynamic potentials, 235) and a transfer of ions between the two requires no work. The energy gained by the system when one gram molecule of ions is carried from the metal to the solution is the charge, 96,5301^, multiplied by E, or joules (10) The mechanical energy lost by the system, when one gram molecule of ions is transported from the pressure P to the lower pressure p is Cpdv = - Cvdp = -kRO C^P- = kROln (198') y / * / P i if we assume that Boyle's, Gay Lussac's, and Van't Hoff's laws are applicable. For, since the temperature is constant, pv= const. .'. pdv=vdp According to Van't Hoff's law (Equation in), the equation of state for one gram molecule of solute is Since, however, we are considering the ions in both solvent and electrode, we shall use the constant k which we will define later. Furthermore, to make the case general we will let Q be a quantity of heat which is absorbed from neighboring bodies during this isother- mal transfer of one gram molecule. If we express the three forms of energy in joules, the electrical energy gained must equal the mechanical energy lost plus the heat energy absorbed, or, p kROln +7^-96530 vmE=o .'. ^- -(/ + kROln - P \ (198) For convenience, we have considered one gram molecule of ions. So great a transfer would usually disturb the equilibrium and properly we should have considered a small fraction, w, of a gram molecule. This factor would, however, cancel from the equations. NULL ELECTRODES. 315 313. In order to test this equation, we must find some electrode which will acquire the potential of the electrolyte. If metal and electrolyte are initially uncharged, and p=P, there will be equilibrium between the ions in each when they come together, and the difference of potential will be zero. P must therefore equal the osmotic pressure, p, of a solution of such concentration that no charges and no difference of poten- tial appear when the two come in contact. 314. Null Electrodes. Metallic ions of the more "noble" metals are usually deposited on the metal from the solution; for example, if a copper plate is placed in a solution of copper sulphate, copper ions will leave the solution even if it is very dilute, and, depositing on the copper, give it a positive charge. But if we add potassium cyanide, the almost undissociated salt K 2 Cu 2 (CN) 4 is formed and by the addition of a proper amount, the concentration of copper ions may be reduced until the metal and solution are at the same potential. Further addition of KCN will cause solution of the copper, giving it a negative charge. By this means, the concentration of the copper ions may be so reduced that the copper is even more negative to the solution than zinc is to a solution of one of its common salts. Mercury is another noble metal whose cyanide salt solution may have an osmotic pressure equal to its own solution pressure, so that there is no difference of potential between metal and solution. Such a combination is called by Billitzer a null electrode. 1 315. Dropping Electrodes. A second means of reducing the concentration of the ions of a noble metal, until the metal and the solution are at the same potential, is to exhaust the ions by presenting fresh increasing surfaces as, for example, in the dropping electrode of Kelvin and Hemholtz. 2 The dropping electrode consists of a very fine capillary through which a stream of the metal flows into the electrolyte. The extremely fine stream breaks into individual drops at J Ann. der Phys., 1903, ii, p. 902; Freundlich and Makelt, Zeit. elect. Chem., 1909, xv, p. 161. 2 Paschcn, Ann. der Phys., 1890, xliv, p. 42. 316 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. the surface of the electrolyte. The mercury ions in the solution are deposited upon the fresh expanding surfaces of the drops, giving the drops a positive charge. This positive charge attracts the negative ions of the salt (electric double layer} and drags them down with itself. When a drop reaches the mercury in the bottom, its surface and capacity are reduced and some of the mercury ions leave the mercury and unite with the negative ions which were carried down. This exhaustion of the salt at the end of the mercury column continues until the osmotic pressure of the re- maining ions is equal to the solution pressure of the metal, and the mer- cury, both in the stream and in the reservoir, has the potential of the solution. If, now, we measure the difference of potential between the mercury in the reservoir (A) (see Fig. 95) and the mercury in the IFlG 95 bottom of the electrolyte (F), we shall obtain the difference of potential between mercury and this particular solution. EXPERIMENT LIL Dropping Electrodes. A dropping electrode will be used to determine the difference of potential between mercury and a saturated solution of calomel. A funnel is drawn out to the finest point which will permit a flow of mercury when the funnel is nearly full. A platinum wire is sealed into the bottom of a large test-tube or tall beaker so that only a very short length projects inside. Sufficient mercury is poured into the bottom to cover the platinum, and the vessel is nearly filled with a normal solution of potassium chloride to which an excess of calomel has been added. The funnel is mounted so that the capillary tip just touches the solution and is filled with mercury, connection to which is made by a platinum wire. The two platinum wires are connected to a compensation apparatus (73), and their difference of potential is determined, when the stream has run for ELECTROCAPILLARY PHENOMENA. 317 a sufficient time for a steady state to be reached. The result obtained will probably be low on account of the errors due to the limitations of facilities and time which are imposed upon a laboratory exercise. 316. Electrocapillary Phenomena. Another method of reducing the mercury ions, so that the metal and electrolyte are at the same potential, is to force the ions from the solution upon the mercury by the electric current. The electrolyte is in a fine capillary tube so that new ions only slowly diffuse in from the rest of the solution. Under ordinary circumstances, mercury ions are deposited upon mercury and give it a positive charge, and the electrolyte a nega- tive charge. Since the like charges repel and the opposite charges attract, both tend to increase the surface; that is, they oppose the surface tension. Therefore, when the surface tension effects are a maximum, the mercury and solution must be at the same potential. Since glass is not wet by mercury (Table XV) the surface tension will cause it to con- tract in a capillary, and the maximum con- traction will be obtained when the surface tension is unopposed by the electric forces. 317. Let us see how the position of the mercury meniscus in the capillary will change as we vary the applied electromotive force. Let E= difference of potential between mercury and electrolyte, C= capacity of surface per square centimeter. The electrical energy of unit area is one-half the product of the potential, E, and the charge, CE, or i/2CE*. The surface tension is numerically equal to the energy per unit area (122). Let r = surface energy when the difference of poten- tial is E and T m = maximum or true surface energy or tension. .'. T=T m -\CE* (199) If T, which is proportional to the contraction in the capillary, is plotted against E, the curve will evidently be a parabola, whose maximum corresponds to the point E=O. This assumes FIG. 96. 318 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. that T m is independent of E, which is not strictly true, but the correction is small and will be found in specific treatises. 1 318. Standard Calomel Electrode. If by either of these last two methods, the dropping or the capillary electrode, we make the difference of potential between the electrode and the electrolyte zero, and if we measure the potential difference between this electrode and any other in contact with the electrolyte, the observed difference of potential will be that between this second metal electrode and the electrolyte. Having in this manner obtained the potential difference between some particular electrode and its solution, we may use this electrode as a standard. A very convenient standard is the calomel electrode which is described in 75. Its difference of potential is usually taken as E= .s6o[i + .0006 (/ 18)] for a normal solution, and for a decinormal solution E = .6i3[i + .oooo8(/- 1 8]) The mercury is of course positive. TABLE XLIV.' Potentials of Electrodes in Normal Solutions of their Ions (18). (The positive sign signifies that the electrode is at a higher poten- tial than the electrolyte.) Electrode Polential (volts) Electrode Polential (volts) K . 2 t; Hg 2 . + 1.027 -Na ' j 2 . H K .. ...... +1.048 Zn + i 306 Cd I A 3 Cl + i 604. Ni . OAQ NO, + 1.7=; Pb H w ^y + .129 + 277 OH SO 4 +i-94 +2.2 Cu + 606 HSO 4 + 2 Q 'Van Laar, Chap. XII; Whetham, Chap. XI. 2 Largely from Wilsmore and Ostwald, Zeit. phys. Chem., 1901, xxxvi, p. 92; CALOMEL ELECTRODE. 319 These values are probably too high, 1 and therefore the potential differences given in Table XLIV which are based on these values are probably somewhat in error, but the relative values, which are far more important than the absolute values, quite accurate. In Table XLIV the ions of the electrode are present in ie electrolyte in normal concentration, except in the case >f O and OH, where the value given is for normal concentra- :ion of hydrogen ions. Many of the values have, however, >een exterpolated by Equation 202 from observations at lower mcentrations. 319. The gas and radical electrodes are either platinum-black (71) electrodes saturated with the gas (for example, the tydrogen electrodes of Experiment LVI) or compounds from which these ions are liberated. For example, the calomel electrode, Hg + Hg 2 Cl 2 , reversibly receives or gives up chlorine ions. When chlorine ions arrive, mercury dissolves. When they leave, mercury is precipitated. Such a reservoir of negative ions is called an electrode of the second class, while positive electrodes are said to be of the first class. 320. The capillary electrometer 2 which depends upon the displacement of mercury in a capillary is a very convenient and sensitive instrument for detecting small potential, differ- ences. It is described in 74. PROBLEMS XXVI. 1. Why must the mercury stream from a dropping electrode break into drops inside the electrolyte? 2. Would it be possible for the electrolyte about a dropping electrode to become so exhausted that the mercury acquired a potential below that of the solution? 3. Calculate the difference of potential between (a) a "null electrode." and a zinc rod dipping in a normal zinc solution; (6) an electrode of mercury which drops into a normal silver solution and a silver rod dipping in the same solution ; (c) a lead plate in a normal lead solution and a column of mercury showing maximum con- traction in a capillary tube filled with the solution. (The potential difference between solutions may be neglected in this and the following problems.) r Smith and Moss, Phil. Mag., 1908, xv, 478; Palmaer, Zeit. phys. Chem., 1907, iv, p. 129. 2 Lippmann ; Ann. der Phys., 1873, cxlix, p. 547. 320 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. 4. An earthed copper rod dips in a normal copper solution. If the solution is joined by a syphon successively to normal solutions of silver, lead, mercury, and zinc, find the potentials of rods of (a) silver; (b) lead; (c) mercury, and (d) zinc, dipping in the respective solutions. 5. A normal calomel electrode dips in a normal zinc solution and a zinc rod dips in the latter. What is the difference of potential between the zinc and the mercury? (b) What would have been the difference of potential if the rod and the solution had been of copper? EXPERIMENT LIII. Potential Difference Between Mercury and Sulphuric Acid. Capillary Electrometer. Set up a capillary electrometer (74) with a scrupulously clean new capillary tube and fresh pure (1:6) sulphuric acid solution and mercury. Connect it to a compensation apparatus (73) through a key with upper and lower contacts which keeps the electrometer short-circuited except when depressed (see Fig. 2o a and 74). Make the mercury in the capillary negative and apply various electromotive forces. For each potential, observe the position of the meniscus and also its position before and after applying the e.m.f. Subtract the mean of the two latter from, the reading when the potential is applied. Gradually increase the applied e.m.f. until the deflection (above difference) begins to decrease. Also, make several observations of the position of the meniscus for very low voltages, when the mercury in the capillary is positive. Plot your results, making applied e.m.f.'s abscissae and deflections ordinates. Determine from your curve the natural potential difference between mercury and the sulphuric acid solution. QUESTIONS. 1. Why must potentials which give continuous electrolysis be absolutely excluded (i.e., potentials several tenths of a volt above that corresponding to maximum deflection, or which make the mercury positive by several tenths of a volt) ? 2. Is the curve obtained a parabola? Explain. ENERGETICS OF A CELL. 321. Heat of Reaction. Let us further consider Equation 198. We have seen that kRdln P is the mechanical work accompanying the solution of one gram molecule of the electrode. If no electrical energy is produced, this work which accompanies the solution appears as an equivalent amount of heat and in Chapter IV, we have seen how this can be determined. CONCENTRATION CELLS. 321 There remains the term Q which represents the heat exchange with the surroundings. We shall first consider several cases where this term is eliminated. 322. Concentration Cells. If we have two soluble electrodes of the same material, dipping in either the same or different connected electrolytes, the passage of the current will be accompanied by solution of one electrode and an equal deposition upon the other, and, therefore, if we find the dif- ference of potential of the two electrodes, Q will be plus for one and negative for the other and will cancel out. 323. (A) The two electrodes are of different concentrations but dip in a common electrolyte. For example, the two elec- trodes may be amalgams of different concentrations or plati- num-black saturated with gas under different pressures. The resultant electromotive force may be found by considering Equation 198 for both electrodes. We shall use the prefix i for one electrode and 2 for the other, remembering that the two differences of potential oppose each other and that the solution is the same for both, and hence p is common E = = 1.99x4.187x2.30 M i , P, _ j PA 96530?^ p P ' k c = 1.98X10-4 01og- (200) v^n c For the solution pressures in the two electrodes will evidently be proportional to the concentrations c t and c 2 . k was the provisional factor in the equation for one gram molecule of ions (312). In this case we are only concerned with the ionic state in the electrodes. Let us assume that k = i . Such an assumption would seem natural for electrodes consisting of absorbed gas (since it is unity in the gaseous state, Equation 57). The following representative example shows that it is also permissible with amalgams. 322 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. The difference of potential between two mercury-zinc amalgams of concentrations .003366 and .00011305 was found to be .0419 volts at u.6 . 1 From equation 200, E= i.gSX lo- 4 log = i.pSX 10-* - log 29.7 = .0416 WYl C 2 2 (Vapor pressure measurements have shown that zinc is monatomic (m = i) when dissolved in mercury.) 324. (B) Two identical electrodes in solutions of the same electrolyte of different concentrations. Let x = potential of the electrode in the more concentrated solution, E 2 = po- tential of the other electrode above its solution, and 3 =the difference of potential between the two solutions. Since the electrodes are identical, P is the same in each and cancels out. Moreover, the osmostic pressures p t and p, are pro- portional to the concentrations c t and c 2 (169-171). Van't Hoff's equation for solutions (173) tells us that if we consider one gram molecule of solute k=i and m = 2, for both the posi- tive and the negative charges are included in the gram mole- cule of solute. E = E, - E 2 - 3 = i .98 X 10-40 log - E 3 (200') 2 "V C i Determination of the Difference of Potential Between Two Similar Electrolytes of Concentrations d and C 2 . 325. Let u-i be the velocity of the cation and u 2 that of the anion. When one gram molecule of ions is dissolved at one electrode and deposited at the other, the share transported between the two solutions by the cation is u l lu l + u 2 , and that by the anions, in the other direction, is u 2 /u l + u 2 (292). If the electrodes are of the same substance as the principal cation of the electrolyte, the current due to the difference of concentration will flow from the weak to the strong solution, in the electrolyte, for it must equalize the concentration [principle of stable equilibrium (188)]. The excess transported by the cations is fti ffe/ttr+tta of a gram molecule, and since the cations travel with the current, it is carried from the weak concentration, Ci, to the strong concentration, c 2 (see Fig. 97). 1 G. Meyer, Ann., 1892, xvi, p. 292. CONCENTRATION CELLS. 3 2 3 The work represented by this transfer is (Equation 198' and 3 2 3 324)- 2.30 log But Ul ** 2 XT XT-. -y = i 2N (Eq. 1 90) .'. E 3 = i.gSX 10-4(1 2Af) log (201) - ,C 2 FIG 97. Observing that E 3 opposes the potential difference due to the electrodes, Equation 200' becomes Ni0 1 c 2 E = i .98 X 10-4 log (202) If the electrodes are of the second class (319), E 3 must be added instead of subtracted. 325a. If the potential difference between a metal and a solution is known for one concentration c^ (e.g., Table XLIV), the potential difference for any other concentration c 2 may be found by substituting in Equation 202 and adding (alge- braically) the result to the potential for the concentration c l . 324 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. EXPERIMENT LIV. Difference of Potential of Metal and Electrolyte. Influence of Concentration. Clean carefully two electrodes of the assigned metal * and prepare the two assigned solutions. Place an electrode in a beaker or tumbler and pour in one of the solutions. Connect a normal calomel elec- trode (75) to the electrolyte (if necessary, using an intermediate electrolyte) and determine the difference of potential between the metal and the mercury in the calomel electrode by the potentiometer method (73 and Fig. 21). After all the adjustments are completed, and before the final determination, it is well to clean the electrode and stir the solution. Observe carefully which electrode is positive and follow the directions regarding the addition or subtraction of the potential of the calomel electrode (76). Find similarly the potential difference for the other concentration. Finally, place one electrode in a porous cup and place the cup in a tumbler or beaker. Put the other electrode in the tumbler, outside the cup. Pour one solution into the porous cup and the other into the tumbler outside. Determine the difference of potential of the two electrodes by the potentiometer method. . In the report, give the difference of potential between the metal and each concentration, the difference in these values, the difference as determined directly and the difference as calculated by Equation 202. i should be calculated from Equations 112 and 187 together with the data given in Table XXXV. An approximate value of N may be obtained from Table XXXVIII. QUESTIONS. 1. What would have been the difference of potential of the electrodes at (a) o; (b) ioo? 2. Why does this difference of potential change upon standing? 3. What would be the change in the concentrations of the two solutions if the cell delivered one-hundredth of an ampere for one hour? 326. Determination of Solubility. We can determine the concentration of a very slightly soluble salt by measuring the electromotive force of a concentration cell, one of the solutions of which contains this salt. For example, suppose we wish to determine the solubility of silver chloride at a given temperature. We set up a cell with two silver electrodes separated by a porous cup. In the cup we pour a saturated solution of silver chloride, outside the cup a known solution of some soluble salt, for example .oin AgNO 3 . The observed electromotive force is substituted in Equation 202 and the J Silver, copper, zinc, and lead are satisfactory metals and the electrolyte may be .in and .oiw concentrations of any of their common salts. DETERMINATION OF SOLUBILITY. 325 unknown concentration C L is calculated. If the porous cup also contains a known solution of a soluble chloride salt, for example, .in KC1, the concentration of the chlorine ions, c', is approximately known. If C is the concentration of the dissolved silver chloride. KC is called the solubility product. If we dissolve silver chloride in pure water the concentra- tion of both ions will be the same and will equal \/KC =\fcj' This will also equal approximately the concentration of salt dissolved or the solubility, for such a very insoluble salt is almost completely dissociated. EXPERIMENT LV. Determination of the Solubility of a Salt of Low Solubility. If silver chloride is the salt, a few drops of silver nitrate added to a .in potassium chloride solution will give a solution saturated with silver chloride, without seriously disturbing the chlorine concen- tration. If iodide of potassium is substituted for the chloride, the concentration of silver iodide may be determined. The solubility of lead sulphate may be determined by setting up a cell with two lead electrodes, one of which is in a porous cup. Out- side the cup is a solution of .oin Pb(NO 3 ) 2 , and in the cup is a solution of .in ZnSO 4 , to which a few drops of Pb(NO 3 ) 2 are added. Calcu- late the actual concentration of the metal ions, the normal concen- tration in pure water, and the solubility of the salt. QUESTIONS. 1. How jnany grams of the salt dissolve at this temperature in one litre of water? 2. What was the potential difference between the metal and the soluble salt solution? (Table XLIV and 3250.) In the last experiment we neglected the difference of poten- tial between the two different electrolytes which were sepa- rated by the porous cup. We shall now consider the simplest case of such a junction. 326 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. 327. Difference of Potential Between Two Different Solutions of Equal Concentrations. If the velocities of the ions are unequal, the solution with the faster moving cations will thereby lose some positive electricity which will be gained by the other solution. The same effect will be produced if the other solution has the faster anions. Planck 1 has calculated the difference of potential due to these charges and finds that for two binary electrolytes, of like ionic concentration, it is equal to r^ ( 2 3) FIG. 98. where u I and x ' are the velocities of the cations and u 2 and u 2 are the velocities of the anions. The reader is referred to Planck's paper for the formal proof of this equation, since only a quasi-proof is given below. We have seen previously (Equation 202) that the difference of potential between two identical electrodes in solutions containing common, binary, univalent (v=i), completely dissociated (1=2} ions, whose transport number is approximately .5, is given by the equation E= 1.98 X 10-4 log where c 2 and d are the concentrations in the two solutions. Let Ui^>Ui f and u 2 <^u 2 '. Consider a portion of each solution adjacent to the boundary (a porous wall for example, see Fig. 98). 1 Wied. Ann., 1890, xl, p. 561. DISSOCIATION OF WATER. 327 Owing to diffusion, the right-hand solution will gain an excess of positive ions which is directly proportional to u lt the velocity of the positive ions which enter and u 2 ' the velocity of the negative ions which leave, or u^ +u 2 f . This gain in positive ions is also evidently inversely proportional to the velocities of the positive ions which leave the right-hand solution, and the negative ions in the other solution, or u/ +u 3 . Therefore, the ratio of concentra- tions of positive ions is Ct Uj + U z This same expression evidently also gives the proportion in which negative ions are in excess on the left side The ionic conductivities (Table XXXIX) may be used in place of the actual velocities of the ions. 328. Dissociation of Water. The molecules of pure water are dissociated to a slight extent (258). If c= concentration of undissociated water, c x = concentration of hydrogen ions, c 2 = concentration of hydroxyl ions, and K is the equilibrium or dissociation constant (251). CjCt = Kc K may be determined from the potential difference of two hydrogen electrodes, one of which is in a known acid solution and the other is in a known alkali solution. The potential difference will give the concentration of H', c lf in the alkali (258) and the concentration of OH/c 2 , is known, c is 1000 - = in In pure water The values of K at different temperatures are given in Table XLV. TABLE XLV. Dissociation of Water. 1 Temperature o 25 100 200 Dissociation constant io- i s io~ l6 6XIO- 1 ? 5Xio- 18 1 Heydweiller, Ann., 1909, iii, p. 503. 328 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. PROBLEMS XXVII. 1. What is the difference of potential at 30 between two hydrogen electrodes dipping in a common electrolyte but under pressures of i and 20 atmospheres, respectively? 2. What is the change in the potential at 20, between a metal and a solution when the concentration of the solution is increased tenfold, if (a) the metal is univalent ? (6) if it is bivalent ? (Assume N =.5 and a = i.) 3. What is the potential difference at 10 between two silver electrodes which dip in connecting solutions of silver nitrate, if one solution contains 50 grams of salt to the litre and the other 2 ? (Obtain i from Equations 112 and 187, and Table XXXV, and N from Table XXXVIII or XXXIX. The dissociation may be considered complete.) 4. What is the difference of potential at 22 between (a) .00 in and .000 1 w solutions of silver nitrate? Similar solutions of lead nitrate? 5. What is the difference of potential at 20 between two silver plates, one of which is in a .01 normal solution of silver nitrate and the other is in a saturated solution of silver bromide, the two solutions being separated by a porous cup ? (The concentration of the silver bromide -solution may be taken as 7 Xio-7.) 6. Calculate the concentration of OH ions at 20 in a .1 normal solution of (a) sulphuric acid ; (6) acetic acid. [Calculate first the con- centration of H' from the degree of dissociation (Table XXXV.)] 7. Calculate the concentration of hydrogen ions in a .in solution of (a) potassium hydroxide; (6) ammonium hydroxide, both at 15. 8. What is the potential difference at 20 between .oin solutions of (a) potassium chloride and sodium chloride ? (6) potassium nitrate and sodium chloride? 9. Calculate the difference of potential at 25 between .in and .oin solutions of HC1. EXPERIMENT LVI. Gas Electrodes. lonization of Water. Prepare the following cell: H 2 1 .oin HC1 1 .oin NaCl | .oin NaOH | H 2 Each hydrogen electrode consists of a platinum black plate sealed into an adapter (see Fig. 99). A continuous stream of hydrogen bubbles from a small orifice, D, below the plate, and escapes through a second small tube B. E dips in the intermediate NaCl solution. One electrode contains the acid solution and the other the alkali solution. Determine the e.m.f. of this cell by the potentiometer method (73). Observe carefully which electrode is positive. Calculate the difference of potential at the two junctions of unlike solutions (Equation 203 and Table XXXIX) and carefully decide whether these potential differences are in the same direction as that due to the electrodes or in the opposite direction. Substitute the algebraic difference in Equation 202 and determine the concen- tration of hydrogen ions in the alkali solution. The concentrations of hydrogen ions in the acid, and hydroxyl ions in the alkali, may ENERGETICS OF A CELL. 3 2 9 be obtained from the concentrations and the degree of dissociation, calculated from their equivalent conductivities as given in Table XXXV. Calculate the dissociation constant, K, of pure water, the concentration of hydrogen and hydroxyl ions, and the degree of dissociation. FIG. 99. QUESTIONS. 1. Calculate the number of grams of (a) hydrogen ions? (b) hydroxyl ions in one cubic meter of pure water. 2. What percentage error in your result would be caused by neglect of the potential differences between the solutions? 3. Why must both electrodes be in a constant stream of hydrogen? 329. Energetics of a Cell. Temperature Coefficient. We shall now consider the first term of Equation 198 which we have eliminated hitherto. We have seen in 321 that the mechanical work corresponding to the second term kRftn may be expressed in terms of its heat equivalent. Let E! be the potential of one electrode of a cell with reference to its solution. Let Q l be the heat absorbed during the passage of 16,530 mv coulombs, and Q/ be the heat equivalent of the energy represented by the accompanying solution or deposition . 330 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. For the other electrode The total electromotive force of the cell is [(Q '- Q ' ) + (G/ - G *' )] (2 4) Let E' equal a similar expression for the electromotive force at a lower temperature /'. A cycle (143) between these two temperatures will eliminate the second term of this equation. For, allow the cell to furnish 96,530?^ coulombs at t, then cool it to t f and, from some outside source, send the same amount of electricity -through the cell in the opposite direction. Finally, restore the cell to its initial temperature t. The total amount of chemical change is zero, and there- fore, the second term of the above equation, which represents the net heat value of the chemical reactions, will not appear in the expression for the energy produced by this cycle. The net work done by the cell is W= 96530 mv (E E f ) joules For any cycle, the work W and the heat absorbed at the higher temperature (Q I Q 2 ) are connected by the relation (Equation 96) W_ - 6 ~ e ' - 96530 vw (-') ~Q = 'TI^TH^T . n n 96530 E-E' 'U'-y*- 4.187 0-0' .' . Equation 204 becomes ENERGETICS OF A CELL. 331 where Q f is the net thermal value (calories) of the reactions accompanying the passage of 96,530 mv coulombs, E-E' = E-E' = dE Q^ == /- /' : ~ dt is the temperature coefficient, and is the absolute tempera- ture. If Q' represents the energy of the reactions in calories for the deposition or liberation of one gram equivalent e ^ (206) dt This equation is often called the Gibbs I -Helmholtz 2 equation from the names of the discoverers. If the second term is neglected, it is often known as Thomson's rule. EXPERIMENT LVII. Temperature Coefficient of a Cell. Energetics of a Cell. Prepare either of the following cells: Ag | - 5 *AgN0 3 1 , 5 nPb(NO 3 ) 2 1 Pb or Ag .5ttAgNO 3 |.5wCu(NO 3 ) 2 |Cu The two solutions should be separated bv :\ porous cup. The cell should be placed in a thermostat or in a water-bath whose tempera- ture can be maintained constant. Determine the e.m.f. (73) at two different temperatures. Calculate the temperature co- efficient dE E-E' dt t-t' Calculate Q' by Equation 206 and compare it with Qi QS as calculated for one gram equivalent from the data given in Table XXVI. QUESTIONS. 1. Calculate the e.m.f. of the cell at (a) o; (6) ipo. 2. Would this cell grow colder or warmer when in operation? 3. What would be the percentage error if E were calculated by Thomson's rule? 4. Will the electrode for which the heat of solution is the greater be the positive or the negative pole for external connections? Explain. 1 Trans. Conn. Acad. 1875, iii, pp. 108, 343. 2 Berl. Sitz. Ber. 1882, 22. 332 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. Polarization. 330. To send a current, i, through an electrolyte, a difference of potential E must be applied which is sufficient to overcome the resistance R of the circuit and the differences of potential E! and E 2 at the electrodes E = iR + E> + E 2 .-.i= E ^ E ~ E ^ (207) is called the polarization electromotive force. E l and E 2 have the values given in Table XLIV (Le Blanc's law), and may be either positive or negative. We shall consider a few cases. 331. Electrolysis of Copper Sulphate. Copper Electrodes. At the cathode copper is deposited; at the anode copper dis- solves. Evidently E^ = E 2 , or the polarization electromotive force, is zero. "If, however, the e.m.f. is so great that the copper ions are insufficient to carry all the current, hydrogen (from the dissociation of water, 258 and 328) will also be liberated at the cathode. Table XLIV shows that while copper is so desirous of depositing from a normal copper solution that it continues to do so until the potential reaches .606 volts, hydrogen, in normal concentration, is not spon- taneously deposited at the cathode after the potential reaches .277 volts. At the anode the potential of .606 volts must be overcome if copper is to dissolve, therefore the polarization e.m.f. is .329 if hydrogen from a normal solution is liberated with the copper. The actual concentration of the hydrogen is much less and therefore (3250) the polarization e.m.f. is greater. 332. Platinum Electrodes. The cathode is soon covered with copper, and, being indistinguishable from a copper plate, shows a potential difference of .606 volts above the solution (Le Blanc's law). If the current is weak, the oxygen ions can convey it to the anode. 1-396 volts would be required (see note*at end of 334) and the minimum polarization e.m.f. would be .79 volts. If the current is gradually increased, OH' jons, SO 4 " ions, and possibly HSO/ ions will also be liberated ELECTROLYSIS OF SULPHURIC ACID. 333 and Table XLIV shows that these will give greater polariza- tion e.m.f.'s. Since these radicals are liberated in the presence of water, they will change to equivalents of oxygen by obvious reactions, before they leave the solution. 333. Electrolysis of Sulphuric Acid Between Platinum Plates. Suppose we have normal ionic concentration. The liberation at the anode will be identical with that described in the preceding paragraph. Hydrogen is liberated at the cathode giving a difference of potential of + .277. Ac- cording to the magnitude of the current, the polarization e.m.f. will therefore be about 1.396 .277 =1.119 volts, 1.94 .28 =1.66 volts, 2.2 .28 = 1.92 volts, or 2.9 .28=2.62 volts. There is little evolution of gas until the OH' ions are liberated. 334. Electrolysis of Sodium Hydroxide Between Platinum Electrodes. Oxygen will be liberated at the anode if the current is extremely small, otherwise hydroxyl ions will also be liberated and about 1.94 volts must be overcome. At the cathode there are both the sodium ions and the hydrogen ions from the dissociation of the water. The hydrogen ions, however, will be liberated unless the current is very great and consequently the fall of potential is very high, for normal hydrogen ions give a potential of .277 which assists the elec- trolyzing current making the polarization e.m.f. 1.66 volts, while a cathode fall of potential of two volts is necessary to liberate sodium, making the total polarization e.m.f. 2.28 volts. In all these examples, values of the potential have been used which are only correct for one particular concentration and therefore the results are only approximate. If the concentrations are known, the true potential differences may be calculated from Table XLIV and 3250. EXPERIMENT LVIII. Polarization. Pour the assigned electrolyte into a large crystallizing dish, mount in it two platinum electrodes, and connect them to a source of current through a regulating rheostat, a switch, and, preferably, 334 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. an ammeter (see Fig. 100). Arrange also a compensation apparatus and a normal calomel electrode (73, 75) so as to determine the potential difference between each electrode in succession, and the solution at its surface. Determine also the total fall of potential between the electrodes. Repeat for several other current strengths. Calculate the potential drop at each electrode, the total e.m.f. , and the polarization e.m.f. Careful attention must be paid to signs (76). ^AAA/WVWV\AMAA/VW r Rheostat AAMM/WV Storage Battery FIG. 100. QUESTIONS. 1. What was the fall of potential (a) between the electrodes? (6) in the electrolyte? (c) the resistance of the electrolyte? 2. What mass of metal would have been deposited on the cathode in one hour? 3. Does the fall of potential at the anode help or hinder the cur- ent? at the cathode? 335- Galvanic Cells. The earliest arrangement for producing an electric current from the difference of potential of two dissimilar metals, dipping in an electrolyte, consisted of a copper and a zinc plate dipping in dilute sulphuric acid. When the metals STANDARD CELLS. 335 were joined, a current flowed through the circuit, the direction in the solution being from zinc to copper. The copper plate soon became covered with the readily liberated hydrogen which lowered the potential of the cell from about .493 +.606 to about .493 +.277 (Table XLIV) and interposed great resis- tance to the passage of the current. Various methods were devised to remove this hydrogen, and the cells which have accomplished this, without introducing other serious faults, will be described below. 336. (A) Cadmium Cell (Reichsanstalt Form). Cadmium amalgam CdSO 4 crystals CdSO 4 solution Hg 2 SO 4 paste amalgamated platinum + The chemical reactions consist of solution of cadmium and deposition of mercury. E t 1.01843 ~~ .00004075 (t 20) .00000095 (^~ 2o) 2 * (208) 337. (B) Cadmium Cell (Weston Form). The cadmium sulphate crystals are omitted. Its e.m.f. may be taken as 1.0190 volts. f 338. (C) Clark Cell. Zn - ZnSO 4 7 H 2 O crystals - ZnSO 4 solution - Hg 2 SO 4 - Hg + Solution of zinc, deposition of mercury. e.m.f. = 1.4328 .00119 (/ 15) .000007 (^~ I 5) 2 t ( 2 9) 339. (D) DaniellCell. Zn - ZnSO 4 x H 2 O |CuSO 4 x H 2 O - Cu + Solution of zinc, deposition of copper. The division A may be a porous cup. or, since the CuSO 4 solution is heavier, the two solutions may be separated by gravity. E.m.f. =1.105 vo l ts (approximate). The internal resist- ance is generally high (i-io ohms) . *Jager and Steinwehr, Zeit. Inst., 1908, p. 327; Wolff, Bui. Bu. Stand., 1908, P- 309- f Winkelmann, 1905, iv, I, p. 208. tjager and Kahle, Ann., 1898, Ixv, p. 926. 336 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. (A), (B) and (C) give very constant electromotive forces when the current is inappreciable. 1 A and B have the advan- tage of having a very small temperature coefficient. All three have very high internal resistances and cannot be used to supply current. The e.m.f. of (D) is sufficiently constant for ordinary laboratory use even if the cell is supplying an appreciable current . 340. (E) Edison Cell. Zn - KOH - Cu 2 O + Solution of zinc, reduction of copper oxide, e.m.f. = 8. Very low internal resistance (e.g., about .05 ohm). 341. (F) Leclanche Cell. Zn concentrated NH 4 C1 solu- tion (MnO 2 + C) -f . Solution of zinc, reduction of manganese dioxide. e.m.f. = 1.46 Moderate internal resistance (e.g., .5 ohm). 342. The dry cell is a Leclanche cell in which the liquid is absorbed by plaster of Paris or some similar absorptive. The Leclanche* cell is cheap and very satisfactory when a current is only required for short times, at infrequent intervals. 343. Lead Storage Cell. Pb - H 2 S0 4 x H 2 (density =1.2)- PbO 2 + The reaction at the positive pole (the cathode as regards the passage of the current through the electrolyte during dis- charge) is (287) Pb0 2 + 2 H- + 28 + H a S0 4 5FPbS0 4 + 2 H 2 O and the reaction at the other pole is Pb + SO/ = PbSO 4 + 20 E.m.f. = 2.0 to 2.2 volts. Very low internal resistance. The weight of lead storage cells is about 10 kilos per 100 watt hours. 1 Directions for setting up these cells are given by Wolff and Waters, Bui. Bu. Stand., 1907, p. 623. Also Watson, "Practical Physics," p. 487. EDISON STORAGE CELL. 337 As the storage cell discharges, both >plates change to lead sulphate and the concentration of sulphuric acid decreases. To charge the cell a current is sent through in the opposite direction and the reactions are reversed. Evidently the positive terminal when the cell is discharging is the terminal to which the positive side of the supply current should be connected. The positive pole is obviously an electrode of the second class (31 9).* 344. Edison Storage Cell. (Fe + C) - 20% KOH - (Ni(OH) 3 + C) E.m.f. = 1.2. The internal resistance is even less than that of the lead storage cell. Other advantages are; a more constant e.m.f., it may be both charged and discharged at much higher currents, and the weight per 100 watt hours is only about 3.5 kilos. 2 PROBLEMS XXVIII. 1. Derive Equation 206 directly from Equation 101. (Notice that 7=0' (321) and fP-*-o6co.) 2. Derive Equation 206 directly from Equations 172 and 173. (Notice that W =Ee. Find the complete differential of Equation 172, substitute from Equation 173, and reduce.) 3. Calculate the electromotive force of a Daniell cell from the heat values of the chemical reactions. (Table XXVI.) What error has the result ? 4. What proportion of the energy of a lead storage cell comes from the energy of the chemical reactions? [Pb + PbO 2 + 2 H 2 SO 4 +aq = 2 PbSO 4 +2H 2 O + aq + 85ooo calories (Van Laar)] 5. Explain the liberation of hydrogen when a storage cell is being overcharged. 6. Two platinum electrodes dip in a normal solution of silver nitrate. Calculate the different polarization electromotive force as the current is gradually increased. 7. Is the mercury electrode of the cadmium cell an electrode of the first or second class? Of the Clark cell? 8. If the solubility of cadmium sulphate changes with the tempera- ture, which form of cadmium cell will have the smaller temperature coefficient? Explain. 'For further information consult Dolezalek, "Theory of the Lead Accumu- lator," Wiley, New York. 2 For further information consult Foerster, " Electrochemie, " pp. 153-159. 338 ELECTROCHEMISTRY. POTENTIAL DIFFERENCES. 9. What changes would be produced in the e.m.f. of a normal Daniell cell if (a) the concentration of the copper sulphate was reduced to one-tenth of its value? (6) If the concentration of the zinc sulphate was reduced instead? 10. If zinc costs 15 cents per pound, copper oxide 40 cents, copper 20 cents, caustic potash 15 cents a pound, calculate the approximate cost of one-horse-power hour obtained from Edison cells. (Neglect the value of the zinc salt formed.) EXPERIMENT LIX. Study of a Storage Cell. Observe the current, voltage, and time as a storage cell is charged and also as it is discharged through a known resistance. The current should not exceed .01 ampere per cm. 2 of either electrode, and if the cell is valuable, the discharge should not be continued after the e.m.f. of the cell falls below 1.5 volts. Plot all the observations against the time. If two channeled or pocketed lead plates are available, it is interesting and instructive to prepare the cell- which is tested. The process of forming the plates .is greatly hastened if the positive plates are filled with red lead, Pb 3 O 4 , and the negative with litharge, PbO. These oxides should be prepared as thick pastes, by mixing thoroughly with dilute H 2 SO 4 (s. g. = 1.2).. When all reaction has ceased, the pastes should be pressed into the carefully cleaned plate pockets. After having dried for at least one day, they are placed in a suitable jar filled with dilute H 2 SO 4 (s. g. = 1.2). The positive and negative plates must be carefully insulated. QUESTIONS. 1. Calculate (a) the initial and (6) the final activity (watts) of the cell during charging and discharging. 2. Why are the curves for charging and discharging dissimilar? 3. Calculate by Faraday's law, the amount of lead sulphate which disappeared during charging. CHAPTER X. GASEOUS IONS. RADIOACTIVITY. 345. Conduction of Electricity Through Gases. When gases are subjected to radioactive bodies, X-rays, ultra-violet light, hot metals, or flames, or intense electric forces, the molecules break up into ions. These ions resemble electrolytic ions (284, 285) in that they have a charge which is usually equal to that on either a univalent or bivalent electrolytic ion. At very low pressures the positive ions are usually atoms or molecules with a univalent charge, while the negative ion is a so-called "electron" with a univalent electrolytic charge (285) and a mass of about 1 7 70 Xio 8 -1-96530 = T 1 ^ TF that of an hydrogen atom. 1 At ordinary pressures, these ions become the nuclei of clusters of several molecules. This very brief introduction is preparatory to the considera- tion of the equilibrium of certain endothermic compounds under particular forms of electric discharge. Ozone and the oxides of nitrogen are endothermic com- pounds, and therefore (191) the stable concentration increases with the temperature. At ordinary temperatures, under natural conditions, it is negligible, but under the influence of a silent, luminous, electric discharge the natural constructive forces are strengthened and the decomposing forces are re- duced, so that the equilibrium concentration is enormously increased, particularly at low temperatures. If oxygen, for example, is subjected to such a silent dis- charge, a considerable portion may be transformed into ozone. The ozone will only slowly return to the negligible equilib- rium concentration when removed from the electric field, for at moderate temperatures the decomposing forces are very weak (although much greater than the constructive, if the concentration is large) . 1 Classen, Phys. Zeit., 1908, ix, p. 762. 339 340 GASEOUS IONS. RADIOACTIVITY. 346. The silent electric discharge is an extensive, quiet, low temperature conduction of electricity through a gas. The gas through which the electricity is passing has a violet hue. It differs from the spark discharge in that the latter is confined to a very narrow path through the gas, while the silent dis- charge always occupies an appreciable volume of gas and in commercial ozonizers it often involves a large volume. If the potential is not excessive, electricity will pass between a point (preferably positive) and a plate by the silent discharge. If a high, alternating, electromotive force is applied to two conductors which are separated by the gas, and a dielectric plate (for example, glass) is interposed anywhere between the two conductors, the gas may be subjected to a sufficient electric force to produce the ions which carry the silent discharge, and the dielectric will prevent sparks. 347. Production of Ozone. Table XLVI gives the efficiency of different methods of producing ozone. The thermal method depends upon the principles of 191 and 269, and has been TABLE XLVI. Grams of Ozone per Kilowatt Hour by Different Processes. 1 Concentration (gr. per cu. m.) Thermal ! Thermal (blast) (liq. air) Electrolysis Silent Discharge Points Dielectric 37 1.8 14 290 i.-3 3-5 2 7 + 60 5 40 37 10 70 55 fully worked out by Franz Fischer. 2 The electrolytic method depends upon the fact that in the electrolysis of acidulated water, ozone as well as oxygen is liberated at the anode, par- ticularly if the current density is very great. 348. Production of Oxides of Nitrogen. The silent discharge I Ewell, "Electrochemical and Metallurgical Industry," 1909, i, p. 23. 2 Berichte deutsch. Chem. Gesell. xxxix, pp. 940, 2557, 3631; xl, pp. 443, ii n; xli, p. 945. RADIOACTIVE BODIES. 341 through air, at atmospheric pressure, at 20, oxidizes about 10 litres of nitrogen per ampere-hour. 1 The most efficient means of oxidizing the nitrogen in the air is to raise it to a very high temperature by means of an electric arc and then quickly remove it from the hot region by giving both the air and the arc a rapid motion at right angles. The large commercial plants in Norway which use the Birkeland process yield about 1.5% to 2% of nitrogen oxides which, when absorbed by water give 1 20 grams of 50% pure nitric acid per kilowatt hour. 2 A cheaper method of obtaining the same amount of nitrogen in a suitable form for fertilizers is to absorb the pure nitrogen produced by the Claude or Linde process (138, 139) in calcium carbide. Calcium cyanamide is formed according to the reaction CaC 2 + N 2 = CaCN 2 + C One kilowatt hour yields 130 gr. of CaC 2 and about 1000 gr. of N 2 , or about 180 gr. of CaCN 2 .3 349. Radioactive Bodies. The rays emitted by radio- active bodies as they disintegrate consist of electrons at enor- mous velocities (some have nearly the velocity of light), helium atoms with the charge on a bivalent electrolytic ion 4 and a velocity which may be as high as one-fifteenth that of light, and X-rays. These rays are often designated as /?, a, and j- rays, respectively. The a rays, or helium atoms, are absorbed by a few centi- meters of air, or a few hundredths of a millimeter of aluminum. Therefore, a large part of the a rays emitted in the interior of a radioactive body never reach the surface. The mass of a rays is so much greater than the mass of the /? rays that they have much more energy, and when they are stopped they give up this energy in the form of heat and light. One gram of radium develops about 100 calories per hour. The /? rays (electrons) have the mass stated in 3 45 (1/1830) 1 Warburg and Leithauser, Ann., 1906, xx, p. 743. 2 Haber, "Thermodynamics," p. 267. 3 Elec. Chem. Ind., 1907, pp. 77, 491. 4 Rutherford, Proc. Roy. Soc., 1908, A, 81, p. 162. 342 GASEOUS IONS. RADIOACTIVITY. that of an hydrogen atom provided the velocity is far re- moved from the velocity of light (3 X io 10 cm/ sec) . 350. Variation of Mass with Velocity. If the velocity is increased above about one-tenth the velocity of light, the mass, as defined by Newton's second law, increases also. If m =mass for moderate velocities, m u =mass when the velocity has a high value, u, and U = velocity of light. = (2IO) "' If this equation represents the mass of any body of matter rather than simply that of an electron (and there are good grounds for believing that such is the case) the mass of a body cannot be regarded as absolutely constant. However, u/U is inappreciable in terrestrial mechanics and for all practical purposes the mass of a body may still be regarded as constant. The student is urged to read Lewis' derivation of this equation and discussion of its consequences. 1 351. Table XL VI I illustrates the series of changes of uranium, radium, etc., and the values of the time constant or period (i.e., the time required for the subtance to be half-trans- formed). The time constant is determined from the velocity constant as described in 238. The calculation is often com- plicated by the successive reactions. The emanation is a gas under ordinary conditions. Ruther- ford found that its boiling point is 68 under atmospheric pressure and that its molecular weight is 222. By compressing the emanation into a capillary tube and cooling it with liquid air, Rutherford obtained visible amounts of liquid which glowed with a brilliant phosphorescence. 2 Notice that the difference between the atomic weights of radium (226) and that of the emanation is the atomic weight of the expelled a particle -(helium). Sufficient helium accompanies the disin- tegration of the emanation to be detected spectroscopically T Phil. Mag., xvi, p. 705 2 Phil. Mag., 1909, xvii, p. 723. DISINTEGRATION PRODUCTS OF URANIUM. 343 within one day. 1 The product formed, radium A, collects on the walls of the containing vessel, but if any body in the vessel has a negative charge, all of the radium A will collect upon it. This phenomenon is known as excited activity. TABLE XL VII. Disintegration Products of Uranium. 2 Radioactive Products. Period Nature of Rays Emitted. Uranium 5 X 100 years a I Uranium X j 22 days /? and l Ionium : ? a * Radium 2,000 years a 4- Emanation 375 days a I. Radium A 3 minutes a i Radium B 26 minutes a * Radium C j 19 minutes a, /?, and f I Radium D (radio-lead) | 40 years No rays Radium E 6 days No rays I Radium F 45 days /? and f Radium G (polonium) 140 days a i Radioactive changes are best followed by studying the conductivity of gases produced by the three types of rays. They may also be studied by their effect on a photographic plate and by the fluorescence which they produce. Most of the elements are probably disintegrating, but very much slower than radium, thorium, actinium, etc. For further information respecting the conduction of electricity through gases, and radioactivity, see the treatises of Thomson, Rutherford, Strutt and McClung. Rutherford, Phil. Mag., 1909, xvii, p. 281. 'McClung, in "A Text-book of Physics," Duff. 344 GASEOUS IONS. RADIOACTIVITY. PROBLEMS XXIX. 1 . It is desired to produce one kilo of ozone of such a concentration that 1.8 gr. are contained in i cubic meter, (a) How many calories are required by the thermal process? (6) How long a time would a one-horse-power dielectric ozonizer require? 2. Calculate the amount of oxides of nitrogen produced by a looo-horse-power plant in one year if the plant is in operation 300 complete days. Air+0, \ FIG. 101. 3. Assuming the validity of Equation 210, calculate the true mass of a 20 gram bullet traveling with a velocity of 1000 m. per sec. 4. A vessel filled with radium emanation showed the following activity (in arbitrary units) at different times. t (hours) Activity o 100 20.8 85.7 187.6 24 355- 6.9 5 22 - i-S 787. .19 ELECTRICAL PRODUCTION OF OZONE. 345 Calculate (a) the velocity constant, (6) the time in which half the emanation is transformed (Meyer, p. 25). EXPERIMENT LX. Electrical Production of Ozone. 1 For a description of more efficient apparatus and for extensive general details, see the references below. Siemens (dielectric) ozonizers are sold by glass instrument makers under the name of ozone tubes (see Fig. 101). A point ozonizer may be constructed by sealing several platinum wires into a large glass tube and mount- ing opposite them a platinum plate (see Fig. 102). This latter type of ozonizer should be connected to a plate electric machine. The former (dielectric) type requires a suitable induction coil or a suitable transformer. The latter is preferable except for Air Air t 3 FIG. 102. the danger from serious shocks. Connect a series of drying tubes and a tube filled with glass wool to the side of the ozonizer at which the air or oxygen enters. Connect to the other end, two gas absorption vessels, preferably of the Gray type, 2 one of which contains water to absorb oxides of nitrogen, and the other contains .in KI solution. The fall of potential in the tube is determined by a Braun electrom- eter which is connected across the terminals. A non-inductive resistance, for example, a potassium iodide solution, or a non- inductive coil, is put in series with one of the terminals. If a point tube and a plate machine are used, a galvanometer is connected 1 Warburg, Ann., ix, pp. 781, 1287; xiii, p. 464; xvii, p. i; xx, p. 134; xxiii, p. 209; xxviii, pp. i, 17. Ewell, Phys. Rev., 1906, xxii, pp. 3, 232; Am. Jo. of Science, 1906, xxii, p. 368; Phys. Zeit., 1906, xxv, p. 927; Elec. Chem. Ind., 1907, p. 264; 1909, p. 23. 2 Ann. 1904, xiii, p. 466. 346 GASEOUS IONS. RADIOACTIVITY. across the non-inductive resistance, and a Dolezalek electrometer (idiostatically connected) is used, if a dielectric ozonizer is employed. The instrument and non-inductive resistance are calibrated together, as an ammeter (78). The current is adjusted until the proper purple silent discharge is obtained. The time is then noted and a steady current of air or oxygen is forced or drawn through the apparatus. The velocity of the gas is determined either with a gasometer or by collecting a certain volume over water and noting the time required. When sufficient ozone has been produced and absorbed, the time is noted and the current stopped, and a few moments later the gas current is also shut off. The amount of ozone is determined by acidulating the .in KI solution with an equivalent of H 2 SO 4 , adding starch and titrating with .O2n Na 2 S 2 O 3 . i c.c. of the latter =.48 mg. of ozone. Calculate (a) total yield of ozone ; (b) yield in grams per coulomb ; (c) yield in grams per kilowatt hour; (d) concentration in grams per cubic meter. QUESTIONS. 1. Calculate the amount of ozone which would have been liberated by the quantity of electricity which traversed the tube if the process were electrolytic. 2. What electrical reason is there for carefully drying the gas? (Other objections to moisture are given in Warburg's paper, Ann., 1906, xx, P- 75 1 -) TABLES. All the tables in the book, whether they appear here or earlier, are listed in the following pages under their respective subjects. 1 Mathematical Tables, Densities, etc. Symbols, (I) p. i. 1 For more detailed information, consult the tables of Landolt and Bornstein, the Smithsonian Tables, and Winkelmann's Handbuch. 348 TABLES. TABLE XL VIII. Logarithms of Numbers from i to 1000. No. i 2 3 4 5 6 7 8 9 10 0000 0043 0086 0128 0170 O2I2 02 53 0294 0334 0374 ii 0414 4<3 0492 Q53 1 0569 0607 0645 0682 0719 755 12 0792 0828 0864 0899 934 0969 1004 1038 1072 1106 13 IJ 39 JI 73 1206 1239 1271 !33 J 335 J 3^7 J399 143 14 1461 1492 1523 1553 1584 1614 1644 !673 J 73 J 73 2 15 1761 1790 1818 1847 1875 1903 J93 1 1959 1987 2014 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 17 2304 233 2 355 2 3 80 2405 2430 2455 2480 2504 2529 18 2 553 2577 2601 262 5 2648 2672 2695 2718 2742 2765 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 20 3010 3032 3054 3075 3096 3118 3*39 3160 3181 3201 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 22 3424 3444 3464 3483 3502 3522 354i 356o 3579 3598 23 3617 3636 3655 3674 3692 37 11 3729 3747 3766 3784 24 3802 3820 3838 3856 '3874 3892 3909 3927 3945 3962 25 3979 399? 4014 4031 4048 4065 4082 4099 4116 4i33 26 415 4166 4183 4200 4216 4232 4249 4265 4281 4298 27 43 X 4 4330 4346 4362 4378 4393 4409 4425 4440 445 6 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 2Q 4624 4639 4654 4669 4683 4698 47*3 4728 4742 4757 30 477 1 4786 4800 4814 4829 4843 4857 4871 4886 4900 31 4914 4928 4942 4955 4969 4983 4997 501 1 5024 5038 32 5051 5065 579 5092 5!5 5H9 5132 5 r 45 5159 S 1 ? 2 33 5185 5*98 5211 5224 5237 5 2 5o 5263 5276 5289 5302 34 53i5 5328 5340 5353 5366 5378 539i 5403 54i6 5428 35 544i 5453 5465 5478 549 5502 5515 55 2 7 5539 555i 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 37 5682 5694 575 57 J 7 57 2 9 5740 5752 5763 5775 5786 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 39 59U 5922 5933 5944 5955 5966 5977 5988 5999 6010 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 44 6 435 6444 6454 6464 6474 6484 6493 6503 6513 6522 45 6 53 2 6542 6 55 J 6561 657 1 6580 6590 6599 6609 6618 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 49 6902 691 1 6920 6928 6937 6946 6 955 6964 6972 6981 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 5i 7076 7084 7093 7101 7110 7118 7126 7 J 35 7 J 43 7 I 5 2 52 7 1 60 7168 7i77 7185 7 J 93 7202 72 10 7218 7226 7235 53 7243 7 2 5i 7259 7267 7275 7284 7292 7300 73o8 73 J 6 54 7324 7332 7340 | 7348 7356 7364 7372 738o 7388 7396 No. o i 2 3 4 5 6 7 8 9 TABLES. TABLE XLVIIL Continued. Logarithms of Numbers from i to 1000. 349 No. 1 i 2 3 4 5 6 7 8 9 55 7404 7412 7419 7427 7435 7443 745 1 7459 7466 7474 56 7482 7490 7497 7505 75*3 7520 : 7528 7536 7543 755 1 i *j *j 57 7559 7566 7574 7582 7589 7597 i 7604 7612 7619 7627 58 7 6 34 7642 7649 7657 7664 7672 7679 7686 7694 7701 59 7709 7716 77 2 3 773 1 7738 7745 1 7752 7760 7767 7774 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 62 7924 793 1 7938 7945 795 2 7959 7966 7973 7980 7987 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 66 8i95 8202 8209 8215 8222 8228 8235 8241 8248 8254 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 7i 8513 8519 8525 853i 8537 8543 8549 8555 8561 8567 72 8573 8579 8585 859i 8597 8603 8609 8615 8621 8627 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 79 8976 8982 8987 8993 8998 9004 9009 9oi5 9020 9025 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9*33 82 9*38 9M3 9149 9!54 9i59 9165 9170 9175 9180 9186 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 84 9 2 43 9248 9253 9258 9263 9269 9274 9279 9284 9289 85 9294 9299 934 939 93 T 5 9320 9325 933 9335 9340 86 9345 935 9355 9360 9365 937 9375 938o 9385 939 87 9395 9400 9405 9410 94i5 9420 9425 943 9435 9440 88 9445 945 9455 9460 9465 9469 9474 9479 9484 9489 89 9494 9499 9504 9509 95 r 3 95i8 9523 9528 9533 9538 90 9542 9547 9552 9557 9562 9566 957 1 9576 958i 9586 9i 959 9595 9600 9605 9609 9614 9619 9624 9628 9633 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 93 9685 9689 9694 9699 9703 9708 97 J 3 9717 9722 9727 94 973 1 9736 974i 9745 975 9754 9759 9763 9768 9773 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 98 9912 9917 9921 9926 993 9934 9939 9943 9948 9952 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 No. i 2 4 5 6 * 8 9 350 TABLES. TABLE XLIX. Natural Sines and Cosines. Sine >i 1 Cosine >i 1 o o.oooo 90 I.OOOO I 0.0175 i75 89 0.9998 02 2 0.0349 J 74 88 0.9994 04 3 0.0523 J 74 87 0.9986 08 4 0.0698 I 75 86 0.9976 IO 5 0.0872 J 74 85 0.9962 14 6 0.1045 J 73 84 0.9945 J 7 7 0.1219 X 74 83 0.9925 20 8 0.1392 J 73 82 0.9903 22 9 0.1564 172 81 0.9877 26 10 0.1736 172 80 0.9848 29 1 1 0.1908 172 79 0.9816 32 12 0.2079 171 78 0.9781 35 J 3 0.2250 171 77 0.9744 37 14 0.2419 169 76 0.9703 41 15 0.2588 169 75 0.9659 44 16 0.2756 168 74 0.9613 46 *7 0.2924 168 73 o-9563 50 18 0.3090 1 66 72 0.9511 52 J 9 0.3256 166 7 1 0-9455 56 20 0.3420 164 70 0-9397 58 21 0-3584 164 69 0.9336 61 22 0.3746 162 68 0.9272 64 2 3 0.3907 161 67 0.9205 67 24 0.4067 1 60 66 0-9*35 70 25 0.4226 J 59 65 0.9063 7 2 26 0.4384 158 64 0.8988 75 27 0.4540 156 63 0.8910 78 28 0.4695 J55 62 0.8829 81 2 9 0.4848 J 53 61 0.8746 83 3<> 0.5000 152 60 0.8660 86 3 1 0.5150 I 5 59 0.8572 88 32 0.5299 149 58 0.8480 92 33 0.5446 J 47 57 0.8387 93 34 0.5592 146 56 0.8290 97 35 0-5736 144 55 0.8192 98 36 0.5878 142 54 0.8090 IO2 37 0.6018 140 53 0.7986 104 38 0.6157 139 52 0.7880 106 39 0.6293 136 5' 0.7771 109 40 0.6428 i35 50 0.7660 in 4i 9.6561 133 49 0-7547 Ir 3 42 0.6691 130 48 Q-743 1 116 43 0.6820 129 47 o-73M 117 44 0.6947 127 46 o-7 J 93 121 45 0.7071 124 45 * 0.7071 122 Cosine >i 1 Sine D i TABLES. TABLE L. International Atomic Weights (Oxygen =16), 351 Aluminum Antimony .. 27.1 . . I2O.2 Magnesium .... Manganese 24.36 55- Arsenic 75- Mercury .... 200. Barium J 37-4 Nickel .... 58.7 Bismuth . . 208. Nitrogen .... 14 01 Boron ii. Oxygen . 16. Bromine . . 79.96 Phosphorus .... 31. Cadmium . . 1 12.4 Platinum 194.8 Caesium i3 2 -9 Potassium .... 39.15 Calcium -. . . . . . 40.0 Radium 226. Carbon . . 12. OO Selenium .... 79.2 Chlorine 35-45 Silver .... 107.93 Chromium 52.1 Silicon .... 28.4 Cobalt 59- Sodium .... 23.05 Copper .. 63.6 Strontium .... 87.6 Fluorine . . . . . 19 Sulphur .... 32.06 Gold . . 197.2 Tantalum .... 181. Helium . 4 Thorium .... 232.5 Hydrogen . . 1.008 Tin .... 119. Iodine ' . 126.97 Tungsten .... 184. Iron 55-9 Uranium .... 238.5 Lead .' . 206.9 Zinc .... 65.4 Lithium 7.03 Reduction of Weighings to Vacuum. (IV) p. 23, Barometer Correction. (V) p. 28. 352 TABLES. TABLE LI. Density and Volume of One Grain of Water at Different Temperatures. Temp. Density Vol. of i. gr. Temp. Density Vol. of i. gr. 0.999878 .000122 21 0.998065 .001939 i -999933 .000067 22 0.997849 .0021 56 2 0.999972 .000028 23 0.997623 .002383 3 Q-999993 .000007 24 0.997386 .00262 T 4 I.OOOOOO .000000 2 5 0.997140 .002868 5 0.999992 .000008 30 0-99577 .00425 6 0.999969 .00003 J 35 0.99417 .00586 7 0.999933 .000067 40 0.99236 .00770 8 0.999882 .0001 1 8 45 0-99035 .00974 9 0.999819 .000181 50 0.98817 .01197 10 0-999739 .000261 55 0.98584 .01436 1 1 o 999650 .000350 60 0-98334 .01694 12 0.999544 .000456 65 0.98071 .01967 13 0-99943 .000570 70 0.97789 .02261 M 0.999297 .000703 75 0-97493 .02570 15 0.999154 .000847 80 0.97190 .02891 16 0.999004 .000997 85 0.96876 .03225 X 7 0.998839 .001162 90 0.96549 03574 18 0.998663 .001339 95 0.96208 .03941 19 0.998475 .001 527 100 0.95856 04323 20 0.998272 .001731 TABLE LII. Density of Gases (o, 76 cm.). 1 'Hydrogen 00008987 Oxygen 0014290 Nitrogen 0012507 Air 0012928 Chlorine 003167 Carbon monoxide 0012504 Carbon dioxide 0019768 Ethane 001341 Ethylene 001252 Steam (at 100) 00060315 Largely from Guye, J. Ch. Phys., 1907, p. 203. TABLES. 353 TABLE LIII. Density (o), Specific Heat (o), and Coefficient of Linear Expansion. Element *y \ s ifm c Coef. of Lin. Exp. Multiplied by io 6 Aluminum 2.60 .22 23.1 Antimony 6.62 .049 Bismuth 9.8 .031 Cadmium 8.61 055 3-7 Carbon, diamond 3-52 .IO 1.18 Carbon, graphite 2.25 J 5 7.8 Carbon, gas carbon ... 1.90 5-4 Cobalt 8.8 .106 12.4 Copper 8.92 .094 16.8 Gold 19-3 .032 14.4 Iron 7.8 .1 1 12. I Lead 1 1.36 .029 29.2 Magnesium i 74 Mercury I3-596 -0333 181 (cub. exp.) Nickel 8.9 .108 12.8 Phosphorus, yellow. . . V 1.83 .20 Phosphorus, red 2.19 - 1 ? Phosphorus, metallic . 2 T.A. Platinum * O'T 21.4 33 9.0 Silver IO. S3 .0 =;6 19.2 Tin JO 7-3 v o .056 22.3 Zinc 7.2 .094 29.2 354 TABLES. TABLE LIV. Density, Specific Heat, and Coefficient of Cubical Expansion of Liquids. (o unless otherwise specified.) Liquid r^ ., Specific Coef. of Cub. Exp. Density J^ Multiplied by ii Acetone .792 1.080 .8! 83 .81 956 1.04 .899 1.293 i-53 74 905 1.2(4 .64 .914 464 07 9 i-i35 79 1.025 J 52 54 .69 59 "I" 23 53 ".58" 348 057 .048 .89 8 5 .28 .817 .176 .14 .1 1 5 1 .28 Acetic acid Ethyl alcohol Amyl alcohol Methyl alcohol Methyl acetate Aniline Benzol Carbon bisulphide .... Chloroform Ethyl ether Ethyl acetate (17). .? Glycerine Ammonia (liq ) Carbon dioxide (o) . . . Carbon dioxide (31.3). Hydrogen (liq. , 252) Oxygen (liq., 130) . . Oxygen (liq., -183) . . Nitrogen (liq., 145) . Air (-liq., 190) 6. 24. 4-6 43 5-6 TABLE LV. Density, Specific Heat, and Coefficient of Expansion of Miscellaneous Substances (o). Substance Density Specific Heat Coef. of Lin. Exp. (Xio*) Castor oil 969 Cork . Glass, green 2 6 I O 8 o Glass, crown 2 7 I O 8 8 Glass, crystal . . 2 o 18 7 7 Glass, flint Hard rubber 3- 1 5~3-9 i.i < .19 7-3 7-7 Marble . . 2 7 C T I 7 Paraffin J -75 .89 Quartz, crystal II .... Quartz, crystal J_ . . . . Quartz, fused .... Wax 2-653 2 - 6 53 2.20 7 .19 7.2 I 3 .2 54 TABLES. 355 .11 ii CC 00 O . t^ CM ON rj- t^ O O O O .Q -3-00 co CO M . ON -00 CO t^OO 00 vO -00 -00 M r#5 H M 1-1 0) CO ^ O t^ Y J 00 T 10 co CO VO ^ t^ O * O O 00 O O CO t^. 00 rj- 10 . 10 . co to P S 1l -COON!IH. NO. ..I | ] '.'.'. ."'.*'.'. O H t^ . . < ^-.... . VO COOO O W OO ' Cl t** VO CO " t^ VO M CO VO */} O ON vo *3- ' 00 O ON ON " COOO O ON W 00 ON VO N N VO (S M vovo oo \OVOVON cow't M 01 H T!- i-t o oo d cooo { S ' '21C'' '' o^ 1 ^ I *>. v o' ; I ; ; I I ; ; ; ; i i : : :. : : : : ' w ' *'x ' ' '. ' '. !iS 'x ! ! -<'p ! ! Ill lag ll|| -11 356 TABLES. Gases, Vapors, and Liquids. Deviations from Boyle's Law (XI), p. 97 Coefficient of Increase of Volume of Gas (XII), p. 98. Coefficient of Increase of Pressure of Gas (XIII), p. 88. TABLE LVII. Pressure of Saturated Water Vapor (Regnault). (mm.) Temp. Pressure Temp. Pressure Ice Water 29 29.782 30 31-548 10 1.999 2.078 31 33-405 8 3 2 2-379 2.456 33 3 5 3 59 37-4io 34 39 565 6 2.821 2.890 35 41.827 40 54.906 4 3-334- 3-387 45 r . 7 I -39 I 5 Q I . Q o 2 2 3-925 3-955 55 117.479 1 60 148.791 65 186.945 O 4.600 70 233-093 + I 4.940 75 288.517 2 5-302 80 354-643 3 5-687 85 433-41 4 6.097 90 525-45 5 6-534 545-78 6 6.998 92 566.76 7 7.492 93 588.41 8 8.017 94 610.74 9 8-574 95 633-78 10 9.165 96 657-54 1 1 9-792 97 682.03 12 10.457 98 707.26 13 1 1.062 98-5 720.15 14 11.906 99-o 733-9 1 15 12.699 99-5 746.50 16 13.635 100. o 760.00 1 7 14.421 100.5 773-7 1 18 J 5-357 IOI - 787-63 19 16.346 102.0 816.17 20 17.391 104.0 875-69 21 18.495 105 906.41 22 19.659 I 10 1075-4 23 20.888 I 20 149 1.3 24 22.184 I 3 2030.3 25 23-55 I 5 3581.2 26 24.998 175 6717 27 26.505 200 1 1690 28 28.101 225 19097 TABLES. TABLE LVIII. Vapor Pressure of Mercury (mm.). 357 JL Clllp. J. V-11J.L/. o O.O2 170 8.091 + 20 O.O4 i So I l.OOO 40 0.08 ' 190 14.84 60 o.'i6 200 19.90 80 o-35 210 26.35 IOO 0.746 220 34 7 I IO I -73 230 45-35 120 i-534 240 58.82 130 2-i75 250 75-75 140 3.059 260 96.73 J 5 4.266 270 123.01 1 60 5.900 280 I55-I7 358 TABLES. TABLE LIX. Vapor Pressure of Alcohols. (Pressure in cm. of Mercury.) Temperature Ethyl * Propyl 2 Isobutyl? Amyla 10 6 1 o 1.2 < .-1 Z 10 2.42 .78 4 20 4-47 1.48 9 qo 7 n } 2 8l I 7 40 13-53 5-n 3- 2 9 5 22.26 8.90 5.6 1.8 60 35-38 14.90 9.6 3-2 70 54.67 24.04 15.8 5.6 80 81.71 37-53 25.1 9-4 90 1 19.64 56.81 38-7 i 5.2 IOO !7-33 83-58 57-8 2 3-7 I I O 237 3 <\ 11982 3 c 7 120 323-47 167.70 52.2 130 433- 1 229.6 74-4 140 C7i.i 308 IOV3 Batslli. 2 Ramsey and Young. 3 Schmidt. TABLES. TABLE LX. Vapor Pressure of Benzol (Benzene), Regnault. 359 Temp. Pressure (cm.) Temp. Pressure (cm.) 20 10 58 1.29 70 80 54-74 75-19 2-53 90 101.27 IO 4-52 IOO 134.00 20 3 40 12. 02 18.36 I IO 120 I 3 174.4 223-5 282.4 5 . 60 27.14 39-01 I4O 352 433 TABLE LXI. Vapor Pressure of Carbon Bisulphide (Regnault). Temp. Pressure (cm.) Temp. Pressure (cm.) 20 4-73 50 85-7I 10 7-94 60 116.45 12.79 7 !55-2I 10 19.85 80 203.25 20 29.80 90 261.91 3 43-46 IOO 332. 5 1 40 6i-75 J 5 909.6 * Comparison of Corresponding States (XIV), p. 108. Surface Tension of Liquids (XV), p. 117. Coefficient of Viscosity (XVI), p. 120. Solutions. Coefficient of Absorption (Henry's Law) (XIX), p. 151. Solubility of Partially Miscible Liquids (XX), p. 154. Valson's Moduli (XXI), p. 159. Density of Ammonium Chloride (XXII), p. 160. Coefficient of Diffusion (XXIII), p. 168. Molecular Elevation (XXIV), p. 174. Molecular Lowering (XXV), p. 177 Thermochemistry. Specific Heat of Water (II), p. 5. Specific Heat of Gases (XVII), p. 126. Molecular Specific Heats at Different Temperatures (XVIII), p. 1 27. 360 TABLES. TABLE LXII. Melting Point of Metals. (Holborn and Day and Waidner and Burgess. 1 ) Tin 232 Cadmium 3 21 Lead 327 Zinc 419 Antimony ". 631 Aluminum 657 Silver 961 Gold 1063 Copper 1084 Platinum 1770 Heat of Formation (XXVI), p. 184, 194. Heat of Dilution (XXVII), p. 186. Heat of lonization (XXVIII), p. 192. Heat of Combustion (XXIX), p. 194. Light. Wave Lengths of Different Types of Ether Waves (XXX), p. 208. iPhys. Rev., 1909, p. 467. C. R., 1909, cxlviii, p. 1177. TABLES. TABLE LXIII. Wave Lengths in Angstrom Units (io- 8 cm.). 3 6i Line Element Wave Length Color c, H a -;\J; D z Hydrogen Sodium 6563.054 c8o6 i ^ ? Red Yellow D 2 ! F.H0 G' H r .. Sodium Hydrogen Hydrogen 5890.182 4861.527 4. 74.0 634. Yellow Blue Violet T H Calcium Helium 3968.625 7O6 Z..2 Violet Red Helium Helium 6678.1 cg7 c 6 Red Yellow Helium Helium 50!5-7 AQ2 I Q Green Blue Helium Helium * 47I3' 2 A.A.7 I c; Blue Violet Mercury Red Mercury Mercury 5790-7 Yellow Yellow Mercury Mercury 31 v*t- v 5460.7 Green Green Blue Mercury Mercury 4y iy- / 4916.4 AT. 8 T. Blue Blue Mercury <+o 3-6 407 8 i Violet Mercury Violet K,v Potassium 7 6OO 3 Red K B . Potassium <:8^2.2 Yellow K r . Potassium 4.O4. 7 4. Violet T ^ Li- Lithium 6708 2 Red Li/? . Lithium 6107 8 Orange Cadmium 6/178 c Red Cadmium U 4o- o 508 s- 8 Green Cadmium Blue 1 Light Filters (VIII), p. 146. Refractive Indices (XXXI), p. 214. Atomic Refractivities (XXXII), p. 215. Specific Rotatory Power (XXXIII), p. 219. Magneto-optic Rotation (XXXIV), p. 220. 362 TABLES. Electro-chemistry. Conversion of Practical to C. G. S. Units (III), p. 8. Slide Wire Bridge (Ratios) (IX), p. 51. Specific Conductivity of Potassium Chloride Solutions (X), p. 57 Temperature Coefficient (XXXVII), p. 290. Equivalent Conductivities (XXXV), p. 288. Transport Numbers (XXXVIII), p. 294. Ionic Conductivities (XXXIX), p. 295. Degree of Dissociation (XXXVI), p. 289. Dissociation Constant (XL), p. 303. Dissociation of Water (XLV), p. 327. Conductivity of Non-aqueous Solutions (XLI), p. 308. Conductivity of Fused Silver Nitrate (XLII), p. 309. Dielectric .Constants (XLIII), p. 311. Electrode Potentials (XLIV), p. 318. Production of Ozone (XLVI), p. 340 Radioactive Transformations (XLVII), p. 343 INDEX. Abbe, refractometer, 212, 216 Abbreviated arithmetic, 14 Absolute temperature, 86, 87, 141 zero, 86, 142 Absorbing power, 198 Absorption spectra, 207-209 Accumulators, 336, 337 Aceto-chloranilide, 228 Acids, strength of, 229, 231 Active mass, 226 substances, optically, 217 Additive properties, 158 Adiabatic changes, 127, 129, 130 Affinity constant, 256, 303 of acid 229 of base, 237 Alcohols, vapor pressures, 358 Alloys, 271, 272, 276 Amagat, gas laws, 97, 98 Amalgams, 309, 322 Ames, mechanical equivalent, 284 Ammonia, solutions in liquid, 308 Ampere, definition, 7 Angstrom unit, 3 Anion, definition, 279 Anode, definition, 279 Approximation formulae, 15 Arrhenius, conductivity cell, 55 degree of dissociation, 289 dissociation, 281 vapor pressure, 170 Association, 162, 178 Atomic dispersion, 216 heats, 124 refractivities, 215 weights, 351 Avogadro's law, 89 Aulich, dilution law, 261 Balance, air buoyancy, 22 correction of weights, 23 directions for use, 20 ratio of arms, 22 weighing by oscillations, 21 Barometers, 27 corrections, 28 Bases, strengths of, 237 Batschinski, mean density, 113 Beckmann, boiling point apparatus, 35 freezing point apparatus, 35 thermometers, 33 Bender, von, refractive indices, 160 Berkeley and Hartley, osmotic pres- sure, 163 Berthelot, calorimeter, 38 principle of maximum work, 186 Billitzer, null electrodes, 315 Bimolecular reactions, 235-240 Black body, 198, 199 Boiling, in Boiling point, apparatus, Beckmann, 35, 175 elevation of, 173 Landesberger- Walker, 36, 175 of liquids, 355 of liquid mixtures, 153-175 of water, 33 Bolometer, 34 Bomb colorimeter, 39 ' Boyle's law, 79, 82 deviations, 96 British thermal unit, 4 Briihl, atomic refractions, 216 Buckingham, absolute temperatures, 142 Bunsen, effusion apparatus, 95 Burette, calibration, 76 Cadmium cell, 335 Calcium carbonate, dissociation, 257, . 268, 272 chloride, heat of formation, 189 Callender and Griffith's bridge, 53 Calomel electrode, 60 Calorie, definition, 4 Calorific power, 5, 193-197 Calorimeter, Berthelot's, 38 bomb (Hempel's), 39 gas (Junker), 42, 196 liquid (Junker), 43 fuel (Rosenhain), 40 water equivalent, 39, 40, 41 Cane-sugar, inversion, 231, 232 363 3 6 4 INDEX. Cane-sugar, osmotic pressure, 163 Capacity, definition, 6 Capillary electrometer, 59, 319, 320 Carbon-dioxide-free vessels, 77 Carbon monoxide, heat of formation, 189 Carnot cycle, 138-140 Catalysis, 229, 231 of ester, 229 Cathetometer, 19 Cathode, definition, 279 Cation, definition, 279 Cell, constant of, 57 energy of, 320, 331 primary, 334, 336 Charge on ions, 281 Charles' law, 85 Chemical dynamics, 225-249 equilibrium, 246-254 equivalent, 280 statics, 250-278 Clapeyron's equation, 146 Clark cell, 335 Clausius, equation, 147 kinetic theory, 87 thermodynamics, 137, 143 Claude, liquid air, 131 Cleaning glass, 78 Clement and Desormes' apparatus, i33-*36 Coefficient of absorption, 150-152 cubical expansion, 354 diffusion, 168 increase of pressure, 98 increase of volume, 98 linear expansion, 353, 354 Coefficient, temperature of cell, 329 of conductivity, 290, 306 Comparator, 18 Compensation method, 57 Component, phase rule, 268 Concentration cells, 321-324 Conductivity, cells, 55 equivalent, 288, 308 . maximum, 307 molecular, 286 of fused salts, 309 of non-aqueous solutions, 307 specific, 8 and temperature, 306 Connectors, clip, 78 Conrody, atomic refractions, 216 Constantin, wire, 34 Conversion factors, electrical units, 8 Copper voltameter, 64-66, 283 Corpuscle, 339, 341, 342 Corresponding states, 106, 108 Cosines, 350 Coulomb, definition, 7 Coulometer, 64, 282 Critical angle, 210 data, 355 pressure, 104 state, 103, 1 08 temperature, 104 volume, 104, 113 Cryohydrates, 275 Cubical expansion, 354 Dal ton's law, 84, 102, 153 Daniell cell, 335 Degree of dissociation, 287, 289, 308 Density, definition, 3 of gases, 352 of liquids, 24, 354 of solids, 353, 354 De Vries, osmotic pressure, 163 Dew point, 29, 103 Diazonium salt, decomposition, 234 Dickinson and Mueller, sodium sul- phate, 277 Dielectric constant, and dissociation, 310 definition, 6 measurement, 66, 311, 312 Difference of potential of cells, 329, 334 of electrodes, 313, 334 Diffraction grating, 48 Diffusion, 167 Dilatometer, 277 Dilution law of Kohlrausch, 303, 306 of Ostwald, 256, 302 of Rudolphi, 302 Dispersion, refractive, 216 rotatory, 220 Displacement law, 201 Dissociation, 162, 178 constant, 256, 302, 303 degree of, 287, 289, 308 electrolytic, 281, 285 of gases, 257, 265-267 Distillation of liquid mixtures, 154, 157 Distribution constant, 261 law, 260 . Dolezalek electrometer, 63 Donnan, order of reaction, 245 osmotic pressure, 164 Dropping electrode, 315, 317 Drude, dielectric constant, 68 Dry^cell, 336 Drying tubes, 74 INDEX. Dulong and Petit's law, 124 Dumas, vapor density, 91 Dyne, definition, 4 Edison cell, 336 storage cell, 337 Efficiency, 141 Effusion, 94, 95 Electric charge, 6, 7, 64 charge on ions, 281 current, 6, 63 furnace, 203 quantity, 64 Electrical measurements, 49 thermometers, 34 units, 5, 8 Electro-capillary phenomena, 317 Electro-chemical equivalent, 279, 280 Electrode, calomel, 60 classes, 319 dropping, 315 gas, 328 null, 315 potentials, 313-334 Electrolysis, 285 Electrolytes, equilibrium, 254 resistance, 54 Electrolytic conductivity at high tem- perature, 306 conductivity of solids, 310 Electromagnetic units, 5 Electrometer, capillary, 59, 319, 320 Dolezalek, 63 electrostatic, 63 Electromotive force, measurement of, 57 small known, 63 unit of, 6, 7 Electrons, 339, 341, 342 Electrostatic units, 6 voltmeter, 63 Emanation from radium, 342 Emissive power, 198 Emptying bulb, 77 Endosmosis, 170 Endothermic reaction, 187 Entropy, 142 Eotvos' law, 115 Equilibrium, constant, 246 effect of temperature on, 250, 263 of electrolytes, 254 principle of stable, 183 Equivalent conductivity, 8, 286, 288, 291, 308 conductivity at infinite dilution, 301 Erg, definition, 4 Errors, estimation of, 10-14 Ester, catalysis of, 229 saponification of, 237-240, 299 Eutectic alloy, 272, 276 Ewell, ozone, 340, 345 rotatory polarization, 217 Excited activity, 343 Exner, molecular refractivity, 215 Exothermic reaction, 187 Expansion of liquids, 354 of solids, 353, 354 Exponential equations, 9 formula, 228 Earad, definition, 8 Faraday, law of, 279 Fery pyrometer, 202 Frick's law of diffusion, 167 Filling bulb, 77 First law of thermodynamics, 123 order reactions, 227-233 Fischer, F., ozone, 340 Fluidity, of fused salts, 309 Foote, regulator, 72 Fractional distillation, 157 Fredenhagen, spectra, 206, 207 Free energy equation, 144 Freezing point, apparatus, 35 effect of pressure, 145 lowering, 176 of liquids, 355 molecular weights, 176-179 Fused salts, conductivity, 309 Gas, burette, 72 condensing vessel, 73 electrodes, 328 equation, 86 seal, 73 Gases, density, 352 dissociation, 257, 265-267 electrical conductivity of, 339- 346 kinetic theory of, 80-82 liquefaction of, 103, 131-133 solubility in liquids, 150-152 specific heats, 124-127 spectra, 206, 209 Gay Lussac, law of, 85, 88 deviations, 97-99 Gibbs, phase rule, 267-275 potentials, 225 theory of cell, 331 Goodwin, conductivity of fused salts, 39 3 66 INDEX. Gram atom, 3 equivalent, 3 molecule, 3 Gray, absorption vessels, 345 Groshans, molecular volume, 160 Guldberg and Waage, mass law, 247, .253 Guthe, silver voltameter, 282 Hagenbach, sulphur dioxide solutions, 37 Heat of combustion, 5, 193, 197 of dilution, 183, 186 of dissociation, 265 of formation, 181, 184-186, 191, . 320 t of lomzation, 192 of neutralization, 191, 193 of solution, 182, 184-188, 264, 265 of vaporization, 191, 263 units, 4 Helium, liquefaction, 133 from radium, 341 Helmholtz, double layer, 316 dropping electrode, 315 energetics of cell, 331 Hempel, calorimeter, 39 gas burette, 72 Henry's law, 150 Hess, law of, 188 thermo-neutrality, 190 Heydweiller, dissociation of water, 327 Hittorf, velocity of ions, 291 Holborn-Kurlbaum pyrometer, 202 Horsepower, 4 Hydrates, 306 Hydrogen ions, catalytic action of, 229, 231 Hydrolysis, general, 257 weak base, 232 weak acid, 239 Hygrometer, chemical, 31 Regnault, 29 wet and dry bulb, 29 Hygrometry, 29, 103 Ice, vapor pressure, 356 Incomplete reactions, 246-249 Indicators, theory, 256 Internal energy, 123, 145, 182 Invariant system, 271, 272 Inversion of cane-sugar, 231, 232 Ionic conductivity, 295 lonization constant, 255, 303 heat of, 192 Ions, charge on, 281 gaseous, 339 velocity of, 286, 291, 294, 296, 298 Irreversible processes, 142 Isochore equation, Van't Ho IT, 253 Isohydric solutions, 304 Isothermal cycle, 140 Isothermals, 99, 108 Isotonic solutions, 164 Jager and Steinwehr, cadmium cell, 335 water equivalent, 39 Jahn, dilution laws, 302 absorption spectra, 208 Jones, hydrates, 306 mixed solvents, 309 non-aqueous solutions, 308 Joule, definition, 4 Joule's law, 283 Junker calorimeter, 42, 196 Kahlenberg, Faraday's law, 280 non-aqueous solutions, 307 theory of solution, 183 Kammerlingh-Onnes, Boyle's law, 96 liquefaction of helium, 133 Kelvin, absolute temperature scale, 141 dropping electrode, 315 thermodynamics, 137 Kilowatt, definition, 4 Kinetic energy of molecules, 87 theory of gases, 80-82 Kirchoff, radiation law, 198, 207 Kohlrausch, degree of dissociation, 289 dilution law, 303 ionic conductivity, 295 temperature coefficient, 290, 306 Konowalow, liquid mixtures, 154 Kraus, alcohol solutions, 307 ammonia solutions, 307, 308 Kundt, velocity of sound, 128 Kurlbaum, pyrometer, 202 radiation constants, 199 Fused salts, 309 Landesberger-Walker, boiling point apparatus, 36, 175 Landolt, light filters, 46 Latent heat, effusion, 355 of vaporization, no, 114, 355 Lebedew, radiation pressure, 200 Le Blanc, polarization, 332 Le Chatelier, calcium carbonate, 257 law of equilibrium, 187 INDEX. 3 6 7 Le Chatelier, pyrometer, 202 specific heats, 127 Lerlanche cell, 336 Lewis, mass and velocity, 342 thermodynamics, 123 Light, 198-224 emission of, 198-202 filters, 46 monochromatic, 45 plane-polarized, 217 velocity of, 210 wave lengths, 361 Linde, liquefaction of gases, 132 Lippich, polarimeter, 222 Lippmann, capillary electrometer, 319 Liquefaction of gases, 103, 131-133 Liquid cells, 326 Lodge, velocity of ions, 294 Logarithms, common and natural, 9 table, 348 transformations, 10 Loomis, degree of dissociation, 289 Lorentz-Lorenz, refractivity, 160 Lubricant, cock, 78 Lummer, radiation, 200, 201 Luminescence, chemical, 198, 206 electric, 198, 206 Magnetic force, unit of, 5 rotation, 219 Manometers, 26, 27 Mass action, law of, 225-227, 247, 253 Mass and velocity, 342 Masson, velocity of ions, 294 Mathias' rule, 112 Maximum work, principle of, 186 Maxwell, radiation pressure, 200 viscosity, 119 Measuring vessels, calibration, 75 Mechanical equivalent of heat, 1 23 Mechanical units, 4 Melting points of metals, 360 Membranes, semi-permeable, 163 Mercury, purification, 74 . still, 74 Meyer, Victor, vapor density, 93 Micrometer microscope, 18 Micron, definition, 3 Mixed solvents, conductivity, 309 Mohr-Westphal balance, 25 Molecular conductivity, 286 dispersion, 216 elevation, 174 gas equation, 107 heat, 124 lowering, 177 Molecular, refractivily, 214 rotatory power, 219 weights, in solution, 178 of liquids, 115, 118 of gases, 90, 95 of vapors, 91-94 Morse, osmotic pressure, 163, 169 Monomolecular reactions, 227-233 Natanson, nitrogen peroxide, 257 Nernst, dilution laws, 302 dielectric constant, 68 dissociation of water, 187 distribution law, 261 free energy, 145 glower, 310 hydrates, 306 molecular weights, 94 solution pressure, 313 Nernst-Thomson rule, 311 Neutralization, heat of, 191, 193 Nichols and Hull, radiation pressure, 200 Nitrogen oxides, absorption spectra, 207 dissociation, 257-260 electrical production, 339-341 Non-aqueous solutions, 307 Normal electrode, 60 solution, 3 Noyes, ethyl alcohol, 155 conductivity arid temperature, 290, 306 dilution laws, 303 maximum conductivity, 307 Null electrode, 315 Ohm, definition, 7 Olszewski, Boyle's law, 96 Optically active bodies, 217 Optical pyrometers, 202-205 Order of a reaction, 240243 of one component, 243-246 Osmotic pressure, experimental results, 163, 169 thermodynamic study, 165-167 Ostwald, catalysis of ester, 229 degree of dissociation, 289 dilution law, 256, 302 ionic conductivity, 295 order of reactions, 243 pyknometer, 25 Oxygen, separation from nitrogen, 132 Ozone, electrical production, 339, 340, 344-346 thermal production, 266, 340 3 68 INDEX. Oudemann, rotatory polorization, 161, 219 Palmaer, electrode potentials, 319 Partition Jaw, 261 Period of reaction, 228 Pfeffer, osmotic pressure, 163 Phase, definition, 268 rule, 267-269 applications, 268-275 Plane-polarized light, 217 Planck, liquid cell, 326 radiation law, 201 Platinum-black, 56 resistance thermometer, 34, 205 Polarimeters, 220-224 bi quartz, 221 half -shade, 222 Polarization, electrolytic, 332-334 rotatory, 217-224 Potassium choride solutions, con- ductivity, 57 Potential, chemical, 225, 269 of electrodes, 313-334 measurements, 57-62 signs, 62 Potentiometer, 57-59 Prefixes, meaning of, 8 Pressure, measurement of, 26 of light, 200 units, 4 Prism spectrometer, 47 Pulfrich, refractometer, 211, 216 Pyknometers, 24 Radiation correction, 43-45 pressure, 200 pyrometers, 202-205 thermal, 198-202 Radioactivity, '341-343 Radium, 341, 343 Raoult, vapor pressures, 172 Ratio of specific heats of gases, 125, 128 Refraction, index of, 210 Refractivity, atomic, 215 molecular, 214 Refractometers, 211-216 Regnault, hygrometer, 29 vapor pressures, in Relative humidity, 103 Resistance, box, 49 electrolytic, 54 measurement, 50-57 specific, 8 unit of, 6, 7 Reversible processes, 140 Richards, Faraday's law, 280 electrochemical equivalent of silver, 281 Ritchie, radiation, 198 Roberts-Austen, alloys, Roozeboom, alloys, 272 Rosenhain, calorimeter, 40 alloys, 276 Rotation, magnetic, 219 specific, 218 Rotatory polarization, 217-224 dispersion, 220 Rudolphi, dilution law, 203 Rutherford, radioactivity, 342 Saccharimeters, 223 Saponification of esters, 237-240, 299 Second law of thermodynamics, 137 Second order reactions, 235240 Semi-permeable membranes, 163 Share of transport, 293, 294 Siemen's ozonizer, 345 Silent discharge, 340 Silver voltameter, 282 Sines, table, 350 Single potential differences, 60-62 Skaupy, amalgams, 309 Slide wire bridge, 50 Sodium flame, 45 Solids, electrolytic conductivity of, 310 Solid solutions, 178 Solubility constant or product, 325 measurement of, 324. Solution, heat of, 182, 18^4-188, 264, 265 pressure, 313 Solutions. 150-180 additive properties of, 158 colloidal, 178 of gases, 150-152 of liquids, 153-157 of solids, 158 solid, 178 Sound, velocity of, 128 Specific conductivity, 8, 291 heat, of gases, 124-127 of liquids, 354 of solids, 124, 353 of water, 5 inductive capacity, 6, 66, 310- 312 resistance, 8 rotation, 218 Spectra, absorption, 207-209 of gases, 206, 209 INDEX. 369 Spectra, of vapors, 206 Spectrometer, adjustments, 46 grating, 48, 209 prism, 47 Stable equilibrium, principle of, 183 Standard conditions for gases, 3 Steele, velocity of ions, 295 Stefan-Boltzman law, 199 Storage cells, 336, 337 Stirrers, 72 Straight diameter, law of, 113 Strengths of acids, 229 of bases, 237 Surface tension, 114, 117 measurement of, 116, 117 Symbols, table, i Temperature, absolute, 86, 141 Temperature coefficient, of cell, 329 of conductivity, 290 effect of, on conductivity, 306 on equilibrium, 250, 263 on heat evolution, 190 units, 4 Thermal neutrality, 190 radiation, 198-202 Thermochemistry, 181-197 Thermocouple, 34, 203 Thermodynamics, 123-149 first law, 123 second law, 137 Thermometers, Beckmann, 33 bolometer, 34 calibration, 31 mercury, 31 platinum resistance, 34 thermocouple, 34 Thermoneutrality, 190 Thermostats, 69-72 Thomson, James, isothermals, 101 Thomson's rule, 331 Transition points, 275, 277, 278 Transport numbers, 293, 294 Trigonometrical functions, 350 Trouton's rule, 147 Uhler, absorption spectra, 208 Units, electrical, 5 mechanical, 4 thermal, 4 Universal wax, 78 Uranium, disintegration, 343 Valson, moduli, 159 Van der Waals' equation, 97 applications, 100 24 Van der Waals' constants, 355 reduced equation, 104-107 Van Dijk, value of faraday, 280 Van't Hoff, coefficient, 167 equation, 167 equilibrium and temperature, 250 isochore equation, 253 order of reactions, 240 solid solutions, 178 study of osmotic pressure, 164- 167 Vapor density, Dumas, 91-92 Victor Meyer, 93 mean, 112 Vapor pressure, and boiling points, measurement of, 101, in of alcohols, 358 of benzol, 359 of carbon bisulphide, 359 of liquid mixtures, 153-158 of mercury, 357 of solutions, 170 of water, 356 Vaporization, heat of, 147, 263 Vapors, 99-110 Velocity constant, 227 and mass, 342 of ions, 286, 291, 294, 296, 298 of light, 210 of reactions, 226, 246 of sound, 128 Ventske unit, 223 Verdet's constant, 220 Vernier, use of, 17 caliper, 17 Viscosity, 118, 121 measurement of, 120 Volt, definition, 7 Voltameter, copper, 64-66, 282, 283 silver, 282 Volumenometer, 83, 84 Walden, non-aqueous solutions, 307 Walker, diazonium salt, 234 electrical measure of saponifica- tion, 300 vapor pressure, 36 Welter's rule, 194 Wanner, pyrometer, 202 Warburg, absorption spectra, 207 solid electrolytes, 310 Washburn, hydrates, 306 Water, boiling point, 33 density, 352 dissociation of, 255, 327, 328 370 INDEX. Water, equivalent, 39-41 Wheatstone's bridge, box type, 52 phases, 270 Callender and Griffith's, 53 specific heat, 5 slide wire, 50 Watt, definition, 4, 7 Wien, radiation, 200, 201 Wave lengths, of ether waves, 208 Wilhelmy, inversion of sugar, 23 1 of light, 361 Witt stirrer, 72 Wax, universal, 78 Wolff, standard cells, 335 Weighing pipette, 25 Wood, radiation, 199 Weston cell, 335 Westphal balance, 25 Zemplen, surface tension, 116 Whetham, velocity of ions, 294 RETURN CIRCULATION DEPARTMENT TO * 202 Main Library LOAN PERIOD 1 HOME USE 2 3 4 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS Renewals and Recharges may be made 4 days prior to the due date. Books may be Renewed by calling 642-3405. DUE AS STAMPED BELOW JUL 07 1989 UNIVERSITY OF CALIFORNIA, BERKELEY FORM NO. DD6 BERKELEY, CA 94720 s YC u.c. C 0fe7-Ul3 7 '