PRACTICAL PHYSICAL CHEMISTRY J.B. FIRTH GIFT OF MICHAEL REESE PRACTICAL PHYSICAL CHEMISTRY PRACTICAL PHYSICAL CHEMISTRY BY JAMES BRIERLEY FIRTH (M.Sc. MANGH.) LATE DALTON CHEMICAL SCHOLAR, MANCHESTER UNIVERSITY ASSISTANT LECTURER AND DEMONSTRATOR IN CHEMISTRY, ARMSTRONG COLLEGE, NEWCASTLE-ON-TYNE WITH SEVENTY-FOUR DIAGRAMS NEW YORK D. VAN NOSTRAND COMPANY 25 PARK PLAGE 1916 Printed in England PREFACE DURING recent years it has come to be more widely recognized in the various schools of chemistry that a study of physical chemistry is necessary for all those who wish to study chemistry with any degree of thoroughness. The theoretical significance of physico-chemical constants, and the fact that they find their application in almost every branch of chemistry, renders it essential for all students of the science to become familiar to some extent, at any rate with physico-chemical methods. It is not possible within the limits of a small volume such as this to deal with every phase of the subject. I have, therefore, chosen such experiments as will demonstrate the fundamentals of the subject, in order that, in the first place, the student may familiarize himself with physico-chemical measurements, and secondly, that he may fix more firmly in his memory the knowledge that he has already gained in the lecture theatre. If a science is to really live, it is essential that theory and practice should go hand in hand. One principle demonstrated by the student himself is of far more value to the student than pages of lecture notes. The importance of spectrum analysis seems to have been overlooked in the past, but it is the opinion of the author that the student should at least be familiar with the principal features of the subject, such as " mapping of spectra " and " determination of wave-lengths," etc. ; therefore a short chapter on this subject finds a place in the present volume. Short chapters of Electrochemical Analysis, Electrolytic Preparations, have also been included, because, besides their purely academic value, they have their industrial applications. vi PRACTICAL PHYSICAL CHEMISTRY I have thought it necessary, in certain sections at any rate, to introduce just sufficient theory to enable the student to understand the principles of his experiment, because, owing to the fact that many experiments require special apparatus, it is not possible for all the students to do the same experi- ment at the same time, and it frequently happens that a student's practical work is in advance of his theory. Hence the introduction of a little theory prevents the experiment becoming mechanical. It will not be usually possible for students to perform ex- periments in all the sections, nor is it possible to say what sections should be omitted where the time is limited, because so much will depend upon the particular requirements of the student. For example, it may seem advisable for a student who intends to pursue certain industrial work to study thoroughly electro-analysis, electrolytic preparations, etc., at the expense of some of the more academic sections. Therefore, the actual experiments selected must be left to the discretion of the demonstrator. In every case the student should read up the corresponding section in some theoretical textbook as soon as possible. Senter's " Outlines of Physical Chemistry " admirably meets the requirements of most students. A slight knowledge of advanced mathematics (elements of calculus, etc.) has been assumed. It is not possible to acknowledge all the textbooks which have assisted in compiling the present volume, but, in con- clusion, I should like to acknowledge my indebtedness to Ostwald-Luther's "Physical Chemistry Measurements," Traube's " Physicochemical Methods," Elbs' "Electrolytic Preparations," Watts' " Spectroscopy." J. B. F. CHEMICAL DEPARTMENT ARMSTRONG COLLEGE NEWCASTLE-ON-TYNE January ', 1915 CONTENTS CHAPTKR PAGE INTRODUCTION ix I. THERMOSTATS 1 II. DENSITY OF GASES, LIQUIDS, AND VAPOURS 6 III. DETERMINATION OF VISCOSITY AND SURFACE TENSION - 15 IV. DETERMINATION OF SOLUBILITY- 21 V. DETERMINATION OF MOLECULAR WEIGHTS - 23 VI. DETERMINATION OF TRANSITION POINTS - 35 VII. OSMOTIC PRESSURE 41 VIII. REFRACTIVITY MEASUREMENTS - 46 IX. ROTATION OF THE PLANE OF POLARIZATION - 55 X. SPECTRUM ANALYSIS - 62 XI. DETERMINATION OF PARTITION COEFFICIENTS 71 XII. THERMO-CHEMICAL MEASUREMENTS 74 XIII. DETERMINATION OF TRANSPORT NUMBERS 87 XIV. ELECTRICAL CONDUCTIVITY 91 XV. ELECTROMOTIVE FORCE - 107 XVI. VELOCITY OF CHEMICAL REACTION - 137 XVII. QUANTITATIVE ELECTROLYTIC DETERMINATIONS- 144 XVIII. ELECTROLYTIC PREPARATIONS - - 151 XIX. PREPARATION OF COLLOIDS - 158 APPENDIX 163 INDEX ------ 176 VII INTRODUCTION The Balance : Rules for Weighing The balance should be placed so that it is protected from direct rays of the sun or other sources of heat, which would produce inequality of tem- perature in the different parts. It should rest on a firm bench, which is free from vibration. The balance must be kept horizontal by means of the foot screws. This position is indicated by a spirit-level or plumb-line. The interior of the balance case should be kept dry by means of calcium chloride, etc. The weights should be placed on the pan only after the arrestment of the beam, picking up the weights in all cases by means of forceps. Rapid swinging of the beam is not con- ducive to accurate weighing, and the final weighings should be made with the case closed. Adjustment of the Balance The sensibility, and hence the period of vibration, are regulated by means of a gravity bob, situated near the middle of the pointer. The adjustment is so made that the period of vibration for a short-armed balance is from six to ten seconds, and from ten to fifteen seconds for a long-armed balance. The adjustment, so that the pointer swings equally on both sides of the middle division of the scale, is made by movable weights attached to the end of the beam ; when these fail, the unsymmetrical weight in the middle of the beam is given such a position that the adjustment can be made. Determination of the Zero-Point It is not necessary nor desirable in weighing that the weights be so adjusted, so that the pointer will swing equal on both sides of the middle x PRACTICAL PHYSICAL CHEMISTRY division of the scale. The actual resting-point is determined from the several turning-points of the pointer. The zero is determined by releasing the beam and allowing it to swing freely (free from any load). Then, neglecting the first swing, observe the extreme points on the scale, taking two readings on one side, and one on the other. Suppose the readings on the right are called positive, and those on the left negative, and the readings on the right were -t-6'5 and +5*6, and the reading on the left 5 '8, then the mean reading on the right was +6-01, and the zero will be halfway between + 6-01 and -5'8 i.e., +0-10, that is, (H of a division to the right. It frequently happens that this zero changes after the weighing of heavy loads, therefore it must be frequently redetermined. As before mentioned, it is not desirable to have to adjust the weights so that the pointer moves " symmetrically " about this zero ; such a process would be tedious, and is absolutely unnecessary. To avoid this the sensibility of the balance is determined. By the sensibility of a balance is meant the change of position of the zero, for an increase of 1 mgm. on one side of the balance. The weighing on the pan is only made to within 1 cgm., the milligrams being determined by means of a rider working on a graduated beam. Suppose, when the weight has been practically determined, the resting-point calculated from the swings is 2'40. Now move the rider so as to increase the weights by, say, 2 mgms., and the resting-point now be 1*8. The resting-point has moved through 4*2 divisions for a change of 2 mgms. i.e., 2*1 divisions for 1 mgm. This is the sensibility of the balance for the load used. The sensibility changes, however, with the load, and it is therefore necessary to determine the sensibility for different loads, say for every 10 grams. Then plot a curve so that the sensibility can be determined for any load ; plot the loads as abscessse and the corresponding sensibilities as ordinates. INTRODUCTION xi Knowing the sensibility of the balance, it is possible to weigh to the fourth decimal place. Suppose the zero of a balance is found to be + 1, and that in a certain weighing the resting-point is found to be +1*5, also let the sensibility for this particular load be 3-5. In the weighing we have a change of resting-point of + 0*5. Now, we know from the sensibility that 1 mgm. produces a change of 3 '5, hence a change of 0*5 is 0*5 produced by =0-14 mgms. Thus, if the weights plus o'O rider on the balance read 21-693 grams, the true weight is 21'69314 grams. It is usual to take the nearest fourth decimal place, as without additional precautions the fifth place is of no value. Calibration of a Set oj Weights Let the larger set of weights be designated 50', 2(X, KX, 10*, 5', 2', 1', 1", 1'". Place the 50-gram weight on the left-hand pan and exactly balance it by the others, the final adjustment being done by the method of oscillation. Then place the 50-grain weight on the right-hand pan, and repeat the weighing. Suppose we have Left. Right. (1) 50' 20'+ 10' + 10" + - + . .-ha, mg. (2) 20' + 10' + 10"+ . . + b, mg. 50' then 50' = 20' + 10' + 10"+ . . +\(a + l)mg. Similarly we obtain and so on. Putting a, /3, y, . . . for J(a + b), J(c + d), \(e +/) respectively, we get- 50 7 =20'+ !(/+ 10"+ . . . +a 20' = 10' + 10" +J3 10"=1(X + y 5' + 2' + l' + r+l"' = 10' +8 in which a, (3, y, 8, can be either positive or negative. xii PRACTICAL PHYSICAL CHEMISTRY Then, comparing all weights against the 10' -grain weight, we have 10"= 1x10' + 7 10' = 10' _ S = 50' + 20' + 10' + 10" + 5' + 2' + 1' + 1" + 1'" = Let T V (a + 2/2 + 4y + 28) = o-, then 10' = 10 grams -o- 10* = 10 grams = o- + y 5' + 2' + 1' + 1* + 1"'= 10 grams - a- + 8 20' =20 grams -2 and carefully note the time with a stop-watch for the liquid meniscus to move from a to b. This should be repeated four or five times, and the mean result taken. The viscosity varies considerably with temperature; it is therefore essential that the temperature should be kept constant to at least 0'1 during a series of experiments. A suitable tempera- ture to work is 25 C. A suitable exercise is the determina- tion of the viscosity of benzene relative to water. The influ- ence of temperature on viscosity is determined approximately by repeating the experiment at intervals, say, of 5 between 25 C. and 50 C. and plotting the results, from which the temperature co- efficient ^r? for 5 can be calculated. The absolute value in C.Gr.S. units of the viscosity co- efficient of water at 25 C. is 8-95 x 10- . 2 FIG. 12 18 VISCOSITY AND SURFACE TENSION Calculation The force which drives the liquid through the capillary will be equal to hgp, where h is the mean difference of level of the liquid in the two limbs of the tube, p is the density of the liquid, and g gravity acceleration. Now, if the experiment is repeated with a second liquid, we get the " driving force " in this case hgp v from which we see that the driving force is proportional to the densities of the liquids, since h and g are constants. The " co-efficients of viscosity "- therefore 17 for the same apparatus is proportional to the driving force p. Hence we get Tl z 7 7l gp^ pj This gives the viscosity of the second relative to the first, which is all that is usually required. Water is usually taken as the comparison liquid. The co efficient in absolute units may be calculated by substituting the absolute values in the equation for 77. Surface Tension Capillarity If a clean glass tube of fine bore is dipped into water, the water rises inside the tube. This elevation is due to the angle of contact between the glass and water being less than 90, so that the surface tension tends to raise the water near the glass. The resolved part of the force parallel to the axis of the tube is 27mr cos a where r is the radius of the tube, o- the surface tension, and a the angle of contact. Now, the weight of liquid up the tube must be equal to this resolved force, and this latter is equal to irfihpg, h being the height in the tube, and p the density of the liquid. /. 2 TITO- cos a = 7rr 2 A/o<7. Now, cos a is usually taken as 1 in cases where the liquids wet the glass : SURFACE TENSION 19 The value of o- is dependent on the nature of the liquid and also on the temperature. Now, the molecular surface of different liquids will contain the same number of molecules, hence the product of the surface tension and the molecular surface of different liquids should be comparable quantities. Now the molecular surfaces are proportional to V$ where V is the molecular volume ; therefore o-VS represents the molecular surface energy, or substituting Mv for V where M is the molecular weight of the substance and v is the specific volume, we get o-Mv*. Now, o-(Mv) is a linear function of the temperature where T& is the critical temperature. Therefore at temperatures T x and T 2 ^ The value of K is the same for different liquids with certain exceptions, and has a value 2-12. In certain cases, particularly when the liquid contains hydroxyl groups, the value obtained for K is less than 2*12. If, how- ever, the molecular weight is multiplied by a factor x greater than one, the value 2- 12 can be obtained. The factor x is termed the association factor, and represents the number of times the mean molecular weight of the liquid is greater than the normal molecular weight. Determination of Surface Tension of Benzene Fit up apparatus as indicated in Fig. 13, which consists of a boiling- tube with side arm, fitted with a tight rubber stopper, through which passes a stout capillary tube. A graduated scale is fixed on to the capillary tube. Put some benzene into the boiling- tube, and place the whole FIG. 13 20 VISCOSITY AND SURFACE TENSION into a thermostat at 25 C. When the apparatus has attained the temperature of the bath, blow slightly through the side tube so as bo cause the benzene to rise up the capillary, and completely wet the sides. Then by means of a telescope read off the height of the benzene in the capillary tube. Three or four readings should be made, both after the benzene has been made to rise above (by blowing) and below (by sucking at the side tube) its final position. Then from equation rpgh The density of benzene at 25 C. may be taken as 0-8736. r may be conveniently found by measuring carefully a thread of mercury in the capillary and then weighing it, and calculating r. w where w is the weight of the mercury, A the density of the mercury, and I the length of the thread. From these data the surface tension can now be calculated. To Determine the Molecular Surface Energy and Association Factor of Ethyl Alcohol Repeat the above experiment with ethyl alcohol at 20 and 40, and calculate, as before given. The density of alcohol at 20 = 0-7894, at 40 = 0-7722. From which the molecular surface energy can be calculated thus : Na 1 S0 4 + 10H 2 0. Experiment to Determine the Solubility Curve of Sodium Chloride up to 50 C. The method is as in the previous experiment. Experiment to Determine the Solubility Curve of Potassium, Chloride up to 50 C. Observe carefully the different characteristics of the three curves obtained from the above experiments. CHAPTER V DETERMINATION OF MOLECULAR WEIGHTS IN the experiments about to be described it is necessary to use a thermometer which would be accurate to 0*002 of a degree. At the same time it is not usually necessary to know the exact temperature, but only changes in temperature. For experiments of this type a Beckmann thermometer is used. It usually has a range of five or six degrees, and is graduated in tenths and hundredths. The thermometer is so constructed that the amount of mercury in the bulb can be to a certain extent controlled. This is rendered possible by having at the upper end of the capillary a reservoir, into which any excess of mercury can be driven, or from which further mercury can be drawn, as desired. To set a Beckmann Thermometer First invert the thermometer, and collect the mercury in the reservoir at the end which joins on to the capillary (see Fig. 15). Then carefully (so as not to dislodge the mercury in the reservoir) place the thermometer in a beaker of water ; the actual temperature of the water is measured by an ordinary accu- rate thermometer, graduated at least in tenths. Now regulate the tempera- ture of the bath until the column of mercury in the capillary joins com- pletely the mercury in the reservoir. FIG. 15 Then control the temperature of the bath until it is about two degrees above the highest tem- perature to be recorded in the actual experiment. Allow the thermometer to remain at this temperature for several minutes, and then strike the top of the thermometer sharply 23 24 DETERMINATION OF MOLECULAR WEIGHTS with the palm of the hand, thus causing the mercury in the reservoir to fall, thereby becoming disconnected from the mercury in the capillary. Now allow the temperature of the bath to fall to the highest temperature to be reached in the actual experiment. If the setting has been successful, the mercury in the capillary should stand on the scale. If the mercury stands above the scale, there is too much mercury in the bulb ; if too low on the scale, the mercury in the bulb is insufficient. In either case repeat the above operation, slightly raising or lowering the temperature of the bath at which the mercury column is separated from the reservoir, until the mercury stands at a convenient height on the scale at the highest temperature to be reached in the experiment. Elevation of the Boiling-Point When a non-volatile sub- stance is dissolved in a liquid, the vapour pressure of the liquid is diminished ; further, this diminution is proportional to the amount of solute added. Raoult, in 1887, after much experi- mental work, came to the following conclusions : 1. Equimolecular quantities of different substances, dis- solved in equal volumes of the same solvent, lower the vapour pressure to the same extent. 2. The relative lowering of the vapour pressure is equal to the ratio of the number of molecules of solute, and the total number of molecules in solution. A liquid boils when its vapour pressure is equal to that of the atmosphere. In the presence of a solute the difference between the vapour pressure of the solution and the atmo- sphere is greater than in the case of the pure solvent, hence in , the case of a solution a slightly higher temperature is required than for the pure solvent to produce the slightly extra pressure. It follows also that the elevation in temperature will be proportional to the lowering of the vapour pressure. Hence Raoulfs law may be re-interpreted thus : Equimolecular quantities of different solutes, in equal volumes of the same solvent, produce the same elevation of the boiling-point. It is therefore possible to determine the molecular weight of any soluble substance by comparing its effect on the boiling-point of a solvent with that of a substance of known molecular weight. If x grams of the substance of molecular weight m (where m is to be determined) be dissolved in W grams of solvent, raise the boiling-point by 8 degrees, whilst m grams in ELEVATION OF THE BOILING-POINT 25 100 grams of solvent give a rise of K degrees, then we have x . m K- W 5 ' ' TOO ' K ' KalOO Van't Hoff has shown that K (which is termed the molecular elevation, constant) can be calculated from the latent heat of vaporization of the solvent, and its boiling-point on the abso- lute scale : _ 0-02T2 ~H~' where T is the boiling-point, and H the latent heat of vaporiza- tion ; hence we get 0-02T* Method I: Beckmanrfs Method The apparatus, as is shown in Fig. 16, consists of a boiling-tube, A, to the side arm of which is attached a coiled condenser, K v and through the upper stopper of which is introduced a Beckmann ther- mometer. A stout bit of platinum wire is fused through the bottom of A, and a few glass beads are introduced to ensure uniform ebullition. This boiling-tube is surrounded by a jacket, B, which is made of glass (porcelain or copper for high tempera- tures), which is also fitted with a coiled condenser, K 2 . The vapour jacket is supported by a small asbestos box, C, which is so constructed that the flames do not come directly under the boiling- tube A (see section). Two chimneys, S t carry the hot gases from the flames away from the apparatus. If the solvent boils below 60 C., the coiled condensers should be replaced by small water condensers, which may be joined up in series. For hygroscopic solvents, calcium chloride tubes should be attached to the condensers. Experiment to Determine the Molecular W 'eight of Camphor in Ethyl Alcohol Weigh out carefully into the boiling-tube 15 grams of ethyl alcohol, introduce also a few clean dry glass 20 DETERMINATION OF MOLECULAR WEIGHTS beads. See that bulb of the thermometer is just below the surface of the liquid. Introduce into the outer jacket a con- venient quantity of alcohol (containing a little water, or a few drops of higher boiling liquid). Put in also one or two pieces of FIG. 16 porous tile. Then bring the liquid in the outer jacket to a steady boil, this will eventually cause the pure alcohol in A to boil. When the Beckmann reading has remained steady for at least five minutes, note the reading, and allow the apparatus to cool down ; and then introduce into A a small tabloid of camphor ELEVATION OF THE BOILING-POINT 27 (about 0-5 gram) accurately weighed. Now bring the liquid to boiling again, and when the reading on the thermometer is constant, note the temperature. It is essential that the rate of boiling should be as near equal as possible in both cases ; this may be judged by noting the rate at which the drops fall back from the condenser attached to A. The thermometer should also be tapped before each reading, as the mercury column is very liable to stick. The barometric height should also be taken at each reading, and corrections applied, if neces- sary. Repeat the experiment, using 0*75 gram of camphor. Latent heat of vaporization of ethyl alcohol is 216*5 cals., FIG. 17 B.P. 78-4 ; benzene may be used instead of ethyl alcohol as a solvent. Experiment to Determine the Molecular Weight of Ethyl Benzoate in Benzene In this case the liquid is introduced by means of a special pipette (see Fig. 17). The pipette contain- ing the ethyl benzoate is first accurately weighed, and then a quantity introduced into the apparatus, and then weighed again. The loss represents the amount of solute used. Latent heat of vaporization of benzene, 93 cals., B.P. 80. Method II: Electrical Heating A modified and much more convenient form of apparatus is indicated in Fig. 18. It consists of a boiling-tube fitted into a Dewar flask. Two narrow tubes, t, t, pass through cork, W, through the lower end 28 DETERMINATION OF MOLECULAR WEIGHTS of each is sealed a piece of fairly stout platinum wire, and from these two wires is suspended the heating-coil. The coil consists essentially of a glass spiral, which is broken in the middle at M. Through this spiral is threaded fine platinum wire (about 0*25 mm. diameter). The two ends of this wire are then fastened to the two stout wires, so that the coil hangs vertically, and also symmetrically with respect to FIG. 18 the thermometer. A quantity of mercury is introduced into the tubes t, t, so that by means of copper wires inserted into the open end, so as to touch the mercury, the heating-coil may be connected with the source of electricity. A current from four or five accumulators, giving a current of 6 to 8 amperes, will usually be sufficient. By having a glass spiral surrounding the wire the bulk of the liquid is eventually heated by its own vapour as it vaporizes within the spiral. In order to prevent superheating ELEVATION OF THE BOILING-POINT 29 it is essential to see the bubbles are issuing from the opening in the middle M and at the bottom. If bubbles come only from the middle and top, superheating is very probably taking place ; this can be remedied by tapping the apparatus. The experiment described under Method I may be carried out with this apparatus in a similar manner. Landsberger's Method In this method the solution is brought to boiling-point by passing into it the vapour of the solvent. In FIG. 19 this case there can be no fear of superheating, as the tempera- ture of the vapour is lower than that of the boiling solution. The apparatus consists essentially of a graduated tube, T, with a small outlet at 0. This tube is surrounded by a wider tube, L, which has a tube at the bottom to lead the vapours to a condenser. The thermometer E should be graduated in tenths. The pure solvent is boiled in flask H, from which the vapour is led into T by tube K. The tube X is merely a safety valve. Experiment Fit up the apparatus as shown in Fig. 19. Introduce into H a quantity of pure alcohol (also a few pieces 30 DETERMINATION OF MOLECULAR WEIGHTS of porous tile). Place about 10 c.c. of alcohol in T. Boil the alcohol in H, and pass the vapour into the alcohol in T. Regulate the heating of the liquid in H so that when the alcohol boils in T the condensed vapour issues from the con- denser at about one drop in two seconds. When the tempera- ture is constant, read off the boiling-point of the solvent. Remove some of the solvent which has accumulated in T until about 6 or 7 c.c. remain Fill up, if necessary, flask H. Now introduce into T a small tabloid of camphor, and repeat the above process, taking care that the rate at which the solvent issues from the condenser is similar to that in the pre- vious case. Note the temperature when practically constant. Then turn out the flame under the boiler, and rapidly discon- nect from the rest of the apparatus. Then read off accurately the volume of liquid in T to a tenth of a centimetre. Reconnect with the boiler, and repeat the experiment three times. On each occasion the volume of solution in T will change, but for each volume there will be a corresponding temperature ; for in each case the concentration of the solute will be different, hence the change in the boiling-point. Note It is advisable to renew the porous tile in H after each disconnection. Calculation In this the equation will be KzlOO where V is the volume read off, and S the density of alcohol at the temperature at which the reading is made (boiling- point). The ratio -g is sometimes known as the constant of Landsberger's method. 17- Hence, if we put C = -Q, we get CslOO ~V8~* C for alcohol =15-6. Compare the results obtained by this method with those obtained by Beckmann's method. DEPRESSION OF THE FREEZING-POINT 31 Experiment to Determine the Molecular Weight of Benzoic Acid in Ether by the Method described above : Depression of the Freezing-Point Where possible, this method is used in preference to the boiling method, because much more accurate determinations can be made. The apparatus is due to Beckmann, and is as shown in Fig. 20. The inner tube A, which is provided with a ther- mometer and stirrer, and also a side tube, contains the solvent, the freezing- point of which is to be determined. A is fastened to the wider tube B by means of a cork, which is in turn supported by a metallic cover in the bath (7, in which the freezing mixture is placed. The vessel C is provided with a stirrer and also vessel A ; in the latter case it should be of platinum, but, without any serious error it may be of glass. The depression in freezing- point is determined by means of a Beckmann thermometer, which is fitted by means of a cork in A. Between B and A is an air mantle, which controls the fall in temperature by causing the solvent to cool gradually. In carry- ing out an experiment the tempera- ture of the freezing mixture should not be more than 3 or 4 below the freezing-point of the solvent, and, further, the temperature of the bath should be kept as constant as possible. Method In an experiment about 20 grams of solvent are introduced into A ; stir the solvent uniformly (not too vigorously), and from time to time stir the freezing-bath. Owing to the supercooling this temperature falls below the freezing- point of the solvent, but as soon as any solid begins to separate out the temperature rises again, owing to the evolution of the latent heat of fusion of the solvent. The amount of supercooling can be reduced by the introduction of a crystal of solvent as soon as the temperature falls below the FIG. 20 32 DETERMINATION OF MOLECULAR WEIGHTS freezing-point. The highest temperature observed after the formation of solid is taken as the freezing-point, because the temperature cannot rise naturally above the melting-point of the solid while solid is still present. (A slight error is intro- duced due to the friction of the stirrer in A, and also conduc- tion from outside by stirrer, thermometer, etc., but this need not be considered here.) A is now removed and accurately weighed, a quantity of the solute added, and the determination of the freezing-point repeated. If the temperature of the freezing-bath has also been carefully adjusted, the solvent will separate out slowly, and the highest temperature reached soon after the formation of a little solid is taken as the freezing- point. If, however, the temperature of the bath is too low, or there is considerable supercooling, the separation of solid solvent will be too great, and the temperature of this equil- ibrium will be that of a much more concentrated solution than that originally prepared, and the more concentrated the solu- tion, the greater is the depression produced. Calculation The calculation is made by a similar method to that used in the case of boiling-point determinations. KzlOO -WA m ' where A is the depression. 0-02T 2 K, as before, Experiment to Determine the Molecular freight of Acetone in Acetic Acid Introduce into A 25 grams of pure glacial acetic acid. Use as a bath water at about 12 to 13. Determine the freezing-point as described above. Now introduce by means of a pipette (see Fig. 17) about 0-5 gram of acetone (determine weight by difference), and redetermine the freezing- point. Experiment to Determine the Molecular Weight of Napthalene in Benzene Use a bath of ice and water giving a temperature of about 2 C. Where the temperature of the solvent is a fair way off its freezing-point, preliminary cooling may be done by immersing tube A directly in the freezing-bath until the solvent is within 1 or 2 of its freezing-point. Use 0*25 gram of napthalene in 25 grams of solvent. ABNORMAL MOLECULAR WEIGHTS 33 Abnormal Molecular Weights It frequently happens the molecular weights obtained by the above method do not agree with those obtained by other methods. They are in some cases greater and in other cases less. Now, the depression of the freezing-point is proportionate to the number of molecules dissolved in a given volume of solvent. Hence the only conclusion is that the number of molecules in solution is greater or less than it should be i.e n dissociation or association has taken place. Consider the case of association : Let x be the degree of association, then 1 - x represents the unassociated molecules. If n represents the complexity of the associated / molecules, then will represent the number of associated molecules. Hence in a molecular solution the number of /j* molecules will have been reduced in the ratio 1 : ].-x + -- 71 Therefore the decrease of the observed depression from the theoretical depression will be in the ratio of where A is the observed depression, and A, the calculated depression. Hence x = or since we get M -M ( 34 DETERMINATION OF MOLECULAR WEIGHTS If dissociation takes place, the equation becomes or M t -U Mo(n - 1)' By applying the above, the degree of association or dissocia- tion of a solute may be determined. Suppose in equation KzlOO /1X m= WA~ . . . (1) we assume m from other sources and calculate K, and compare it with the value obtained from Van't HofFs equation K H If association has taken place, K will be less ; if dissociation, greater in equation (1) than in equation (2). Example K for cane sugar in water is 18 '6, for sodium chloride in water 36*0, for methyl iodide in benzene 50 -4, for benzoic acid in benzene 25*4. The normal values are 18-6 and 51*2 in water and benzene respectively. Note One value of K is approximately double the other for each solvent. Experiment to Determine the Apparent Molecular Weight of Potassium Chloride in Water, and from the Result Calculate the Degree of lonization Carry the determination as in previous experiment. Introduce a crystal of ice to prevent excessive supercooling. CHAPTER VI DETERMINATION OF TRANSITION POINTS MANY substances are capable of existing in two or more crystallized forms, but the various forms are not equally stable under the same conditions. Sulphur is one of the best known examples. Rhombic sulphur is stable at ordinary temperatures, and on heating melts at 115 C. On being kept for a time at about 100 C. it changes completely into the monoclinic variety, which has a melting-point of 120. Monoclinic sulphur can be kept for an indefinite period at temperatures, say, 100 to 110 C. with- out undergoing any further change. Rhombic sulphur however, changes to monoclinic at these temperatures. Monoclinic sulphur is therefore the stable form under these conditions. Thus there is a temperature above which mono- clinic sulphur is the stable form, and below which rhombic sulphur is the stable form, and at which the two forms are in equilibrium with their vapour i.e., a temperature at which neither form changes into the other on keeping. This tem- perature is termed the transition temperature, or transition point, and is in the case of sulphur 95'6 C. When a salt combines with water to form more than one hydrate, it is found that only one hydrate is stable under any given conditions of temperature, etc., or conditions may arise when the anhydrous salt is the stable variety. Thus, we find transition points in the case of salt hydrates, that is to say, on passing a certain temperature the composition of the salt hydrate changes to another definite composition, while at this temperature the two definite hydrates (or anhydrous salt) can co-exist. Thus on heating sodium sulphate decahydrate to a tempera- ture above 33 C. it is found that decomposition occurs into 35 36 DETERMINATION OF TRANSITION POINTS anhydrous sodium sulphate and a saturated solution of the anhydrous salt. If, on the other hand, a saturated solution of sodium sulphate, at say 40 C., in presence of an anhydrous salt, be allowed to cool, when the temperature has fallen below 33 C. the anhydrous salt takes up water and forms decahydrate crystals. 33 is therefore approximately the transition-point for the change. Na 2 S0 4 10H 2 0^ == >Na 2 S0 4 + 10H 2 0. Determination of the Transition-Point (1) Thermometric Method When one system changes into another, the change is almost invariably accompanied by some heat effect, either absorption or evolution of heat. Thus, on heating, say Na 2 S0 4 10H 2 O, the temperature rises normally until the decahydrate begins to change into the anhydrous form; at this point the temperature remains practically stationary until the transformation is complete, since heat is absorbed by this change. Hence, by noting the temperature at which this /? retardation occurs, the transition-point may be determined. When the reverse change is allowed to take place, there is an evolu- tion of heat. In actual experiment it is usual to plot both the heating and cooling curves. Experiment to Determine the Transition-Point of Sodium Sulphate Take about 40 grams of pure sodium sulphate decahydrate in a thin glass boiling - tube. Hang a ther- mometer, which should be graduated in tenths of a degree, so that the bulb is com- )letely surrounded by the decahydrate. support the tube in a large beaker of FIG. 21 water, which can be heated very gradually with a small flame. The temperature of the bath should be kept uniform by means of a stirrer (see Fig. 21). Eaise the temperature of the bath to about 31 C., and then keep the temperature constant for a short time. Now very slowly raise the temperature until the salt becomes partially liquid. At this stage the salt should also be kept constantly stirred. The rate of rise in temperature at DILATROMETR1C METHOD 37 this stage should not be more than about 1 in 10 minutes. When the salt has begun to liquify, the temperature should be read every minute. A point is reached at which the temperature is practically stationary for an interval. This is due to the absorption of heat during the transition from the decahydrate to the anhydrous salt and solution. After a time the temperature begins to rise gradually again. When the temperature has reached about 36 C., allow to cool, stirring constantly, the bath and the salt. Again take readings every minute ; a period of approximate constancy will be noted, in this case due to the evolution of heat, owing to the reformation of the decahydrate. Now plot these temperature readings against time, and draw the two curves, one for rising temperature and the other for falling temperature. Theoretically one would expect these two curves to be identical. They are both of the same type, but the vertical portions do not coincide. This lack of coincidence of the two curves is due to what is termed suspended transformation. At the higher tempera- ture we are dealing with a solution of the anhydrous salt, and after passing below the transition-point, it is possible for the solution of the anhydrous salt to exist, if the stable phase, in this case the decahydrate, is entirely absent. Such a solution is, however, unstable. The amount of lag can be considerably reduced by vigorous stirring in the neighbourhood of the transition-point. The amount of lag can also be reduced by allowing the temperature to change very slowly in the neighbourhood of the transition -point. The general type of such curves is as indicated at Fig. 22. (2) Dilatrometric Method This method depends upon the fact that change from one system to another on passing through the transition-point is accompanied by an appreciable change in volume, and it is only necessary to determine the temperature at which this change of volume occurs in order to ascertain the transition-point. This variation in volume is studied by means of a dilatometer, which consists of a long capillary tube about 0*5 mm. internal diameter, to which is attached a long bulb (Fig. 23). Experiment to Determine the Temperature of Foi'mation of Astra- canite from the Simple Salts Take equimolecular weights of sodium sulphate decahydrate, and magnesium sulphate hepta- DETERMINATION OF TRANSITION POINTS hydrate ; powder each up, and mix them by stirring with a glass rod. Protect the capillary tube by a small glass bead, Temperature FIG. 22 V FIG. 23 and then introduce some of the mixture into the bulb, filling it about three-quarters full ; then seal off the open end of the bulb; invert and shake the solid mixture down to the bottom of the bulb. It now remains to fill the rest of the bulb and part of the capillary with some suitable liquid. To do this fix an adapter to the capillary (as shown in Fig. 24), and intro- duce a quantity of xylene. Attach the adapter to a water-pump and exhaust the dilatometer, then, on suddenly admitting the air, the xylene will be driven down into the bulb. This operation is repeated until all the air has been removed. It is neces- sary to tap the tube to remove any air which is entrained in the solid mixture. Fix some suitable scale to the capillary, and adjust the meniscus by pushing a piece of thin platinum wire down the capillary, and thus driving out some of the xylene. Immerse the bulb of the FIG. 24 VAPOUR PRESSURE METHOD dilatometer in a beaker of water at 16 C., and note the height of the meniscus. Raise the temperature 1 at a time, and take reading of the height of the meniscus, each degree each time waiting until the meniscus has come to rest ; con- tinue up to 25 0. Now allow the bath to cool, and again take readings every degree, and so obtain a cooling curve. Plot the results obtained i.e., plot the heights of the meniscus as ordinates against temperature readings. An abrupt increase in volume will be noted about 21 to 22 on the heating curve, and an abrupt contraction on the cooling curve at about the same temperature. The two curves, however, do not coincide, the expansion taking place at a slightly higher temperature, and the contraction at a slightly lower temperature, than the true transi- tion-point. The curves are very similar to those obtained in the previous experiment. (3) Vapour Pressure Method When one system can be trans- formed into another, the vapour pressures of the two systems are identical at the transition-point. This method has, so far, only been applied to systems contain- ing water or other volatile com- ponent. For the purpose of making these measurements a differential manometer is used. The most convenient form is known as Bremer-Frowein tensi- FIG. 25 meter, which is as shown in Fig. 25. It consists of a U tube, the limbs of which are bent close together, and backed by a millimetre scale. The bend is filled with oil, or bromnaphthalene, or some other suitable liquid. The substances the vapour pressures of which are to be com- pared are placed in the bulb a, b, and the necks then sealed off. The apparatus is then inclined so that the liquid in the bend -=- 40 DETERMINATION OF TRANSITION POINTS collects in the bulbs c, d. The open end e is then connected to a mercury pump, and the apparatus completely evacuated. The tube e is then sealed off. The apparatus is then placed perpendicularly in a thermostat, and the differences in level read. Experiment to Determine the Transition of Sodium Sulphate In this case fill the bend of the tube with bromnaphthalene, and into the bulbs a, b respectively introduce pure dry powdered crystals of the decahydrate, and crystals moistened with a little water so as to make a saturated solution. Exhaust the apparatus and seal off as previously indicated, and place the tensimeter perpendicularly in the thermostat at 25 C., allow the difference in pressure to become constant, and then read it off. Then slowly, as before, raise the temperature, noting each degree the difference in pressure. At the transition - point the vapour pressure of the crystals of decahydrate must become equal to that of a solution saturated with the deca- hydrate and anhydrous salt. (4) Solubility Method The transition-point of Glauber salts may be determined by plotting the solubility for the an- hydrous salt and the decahydrate respectively. The point of intersection of the two curves gives the transition-point. The experimental details of this method are indicated in the chapter on Solubility. CHAPTER VII OSMOTIC PRESSURE WHEN a dilute solution of a substance in water is placed in a vessel closed with an animal membrane, such as a bladder, and the whole immersed in water to a depth that the level of the water outside is the same as the level of the solution inside, it is observed that the volume of the liquid in the inner vessel increases, and this is made manifest by the rise of the liquid in the vessel. It is obvious from this experiment that water must have passed from the outer vessel through the membrane to the inner vessel But if the outside liquid is examined, a quantity of solute will be found to be present. Hence some of the solution must have found its way through the membrane. After the solution has risen to a certain height in the vessel, the liquid begins to fall gradually, due to the fact that the solutions continues to pene- trate the membrane. Many attempts were made to find some general relation- ship between the height the liquid rose in the vessel and the concentration of the solution. But at first this was found impossible, since the amount of solution which escaped varied with different membranes. Later, however, it was discovered (Traube 1867, Pfeffer 1877) that artificial membranes could be prepared which, while allowing the passage of water through them just as in the case of animal membranes, unlike these materials, they offered a perfect barrier to the passage of many substances in solution in the water. If a solution of copper sulphate is brought very carefully in contact with a solution of potassium ferrocyanide, a delicate film of copper ferrocyanide forms where the two liquids come into contact. The student can see this very effectively by performing the following experiment. 42 OSMOTIC PRESSURE Experiment Let a drop of a cold saturated potassium f erro- cyanide solution run from a fine glass capillary into a 0-5 molar solution of copper sulphate contained in a glass vessel. Detach the drop by a slight motion of the tube so that it sinks to the bottom of the vessel. The drop at the moment of its entrance into the solution became surrounded with a thin film of cupric ferrocyanide, which keeps growing in thickness at the expense of the dissolved components. The concentration of the solute within the membrane is greater than that of the copper sulphate outside, hence water passes into the globule and the membrane expands, because of the pressure caused by the entrance of the water through the walls. The membrane is at first transparent and traversed by brown veins. As the expansion of the cell continues, the specific gravity of the contents diminishes until it becomes less than the copper sulphate solution ; then the cell rises to the surface of the solution. In time, however, the walls become sufficiently thick to cause the cell once more to sink to the bottom, where it remains permanently. The copper ferrocyanide film, however, is very delicate, and, to be of any practical value, has to be supported. This is most conveniently done by precipitating the copper ferrocyanide within the walls of an unglazed porcelain vessel. By this means an area of film which can be utilized is obtained. In reality it is built up of a very large number of very small films, each of which is supported by the porcelain particles round it. The membrane thus obtained is almost completely unpermeable to a great many solutions, and for our purpose be regarded as a true semipermeable membrane. Preparation of a Semipermeable Membrane Take an unglazed porcelain pot 8 or 10 cms. high and 2 to f cms. diameter. Soak it in water for several hours, then fill up the pot to near the top with a solution of copper sulphate containing 2-5 grams per litre, immerse this in a beaker containing a solution of potassium ferrocyanide of a strength 2-1 grams per litre, so that the levels of the liquid, both inside and outside the pot, are about equal. Allow to stand for several hours. The salts diffuse through the walls, and where they meet a copper ferro- cyanide membrane is formed, which, since it is impermeable to the salts from which it is formed remains quite thin, but is capable of withstanding fairly large pressures since it is sup- ported by the walls of the porous pot. The porous pot is then taken out and thoroughly washed. DETERMINATION OF OSMOTIC PRESSURE Experimental Determination of Osmotic Pressure A suitable form of apparatus is shown in Fig. 26. A tube B, of such a diameter that as near as possible it just fits inside the porous pot, is fixed to the porous pot by surrounding the junction with a glass collar, C, the whole being held in position by filling the surrounding space with cement or sealing-wax, the joint being perfectly air-tight. The top of the tube B is closed by a stopper, through which passes a glass tube E, which is drawn out at the end. To the side tube F is attached a graduated manometer, provided with a reservoir bulb, H. Experimental Determination of the Osmotic Pressure of Cane Sugar Solu- tion Fit up the apparatus as previ- ously described. Prepare a 1 per cent, solution of cane sugar, and fill up the porous pot to near the top by removing cork E. Then attach the manometer and make joints E and F perfectly air-tight by coating the junctions of the stoppers with the glass with a layer of some suitable cement or sealing-wax. The tube E has up to now been open to the air, thus preserving atmospheric pressure throughout the apparatus until all joints were tight i.e., the mercury in the manometer is the same in both limbs. Now seal off E in a blowpipe (note E has been already drawn out to a fine point, so that the sealing off is only a matter of a second or so), and note carefully the mano- meter reading. Now immerse the porous pot in a beaker of distilled water at room temperature. Water gradually passes into the cell, and the air in the upper part of the apparatus is compressed, and thus drives up the mercury in the mano- meter, thus measuring the pressure inside the cell. Take readings every hour, then allow to stand over night, and take readings again until no alteration occurs. The actual time required depends upon the particular cell. If the cell has FIG. 26 44 OSMOTIC PRESSURE been well prepared, the maximum pressure will be retained for several days. Make a note of the maximum pressure. According to Pfeffer the osmotic pressure of a 1 per cent, solution of cane sugar is 535 mm. of mercury. For higher concentrations the osmotic pressure of cane sugar solutions rises to considerably more than an atmosphere, and a manometer of the closed type has to be used for example, a 6 per cent, solution of cane sugar has an osmotic pressure of 3075 mm. of mercury at room temperature. Osmotic pressure measurements do not make suitable laboratory exercises, but students ought to be familiar with the method by performing the experiment described above. The apparatus once set up, other experiments may be done while equilibrium is being established. Where necessary, five or six students may take readings from one apparatus. The following laws relating to osmotic pressure have been established : 1. Temperature and concentration being the same, different substances, when in solution, exert different pressures. 2. For one and the same substance, at constant temperature, the pressure exerted is proportional to the concentra- tion. 3. The pressure for a solution of a given concentration is proportional to the absolute temperature, the volume being kept constant. 4. Equimolecular quantities of different substances, when dissolved in the same volume of solvent, exert equal pressures under the same conditions of temperature and pressure. Note This is only true of those substances whose mole- cules neither dissociate into simple forms (i.e., non-electro- lytes), nor associate into more complex molecules when in solution. It will be observed that the second statement is analogous to Boyle's law ; the third corresponds to Charles's law ; while the last is an extension of Avagadro's hypothesis. Hence Van't Hoff came to the following conclusion : " The osmotic pressure exerted by any substance in solution is the same as it would exert if present as a gas in the same volume as that occupied by the solution, provided that the solution is so dilute that the volume occupied by the solute is negligible in comparison with that occupied by the solvent." DETERMINATION OF OSMOTIC PRESSURE EXAMPLES FROM PFEFFER'S RESULTS 45 Percentage of Sugar in Solution Osmotic Pressure in Mm. of Mercury = P. Volume of Solution containing 1 Gram of Sugar =V. P.V. C.c. 1 535 99-6 53286 2 1016 49-6 50394 4 2082 24-61 51238 6 3075 16-34 50245 CHAPTER VIII REFRACTIVITY MEASUREMENTS Refractive Index When a ray of light passes from one medium to another, and the densities of the two mediums are different, the direction of the ray is altered, except when the ray is perpendicular to the boundary between the two media, in which case no change occurs. This latter position is called the normal. Consider Fig. 27. Let A and B repre- sent the two media where B is denser than A, also let a b represent the normal, then a ray of light passing through A at an angle " i" to a b will be deflected on entering B in such a manner that angle "e" is less than angle "i." In other words the angle of incidence, "i," will be greater than the angle of refraction, "e." The relation between these two angles is termed the refrac- tive index, and further it can be shown that sin i _ N sin e~~ n' where N is the refractive index in the denser medium, and n the refractive index of the less dense medium. It will be seen that the maximum value for i is 90, in which case sin i = 1 ; then n sin = Tr. b FIG. 27 46 REFRACTIVE INDEX 47 Determination of the Refractive Index of a Liquid The principle indicated above is used in determining the refractive index of a liquid, the index of refraction being found by comparison with a glass prism of known refractive index, which must be greater than that of the liquid. In actual practice monochromatic light is used, since white light would give spectrum effects, thereby preventing the obtaining of sharp and definite images. Consider Fig. 28, which represents a glass cell containing the liquid to be examined, mounted on a right-angled glass prism of refractive N N FIG. 28 FIG. 29 index, N. Then a ray of light (Fig. 28) entering at A will have a path somewhat as indicated, and the relation sin e' N = exists, ouppose now the angle e is gradually sin e n increased : a point is reached when no light is visible at B, this occurs when angle e' becomes 90. At this point the light is totally reflected. The ray of light is entering horizon- tally, as shown in Fig. 29, and in actual practice it is the position at which this occurs that is determined. Thus, when e' = 90 we have n Sin e = TTn n being the refractive index of the liquid, and N that of the prism. 48 REFRACTIVITY MEASUREMENTS Further, N= ^^ sin i" But sin e = cos i ; n cos * = j^ i.e., n = cos i N. FIG. 30 SPECIFIC AND MOLECULAR REFRACT1VITY 49 But cos 2 i = 1 sin 2 * ; sn *. Substituting S H for sin 2 i, we get n = JN 2 - sin 2 i'. Hence we see that to find n we have to determine the value of i' when the incident ray is horizontal. In actual practice it is not usually necessary to go through the above calculation, since the makers supply tables giving values of n for each value of i'. Specific and Molecular Refractivity The refractive index varies with the temperature of the liquid, and according to Gladstone and Dale 3 = constant, where d is the density of the liquid ; Lorentz and Lorenz, however, find the expression 71 2 -1 1 y 2.0 ' ~d gi yes a better constant. The value of this expres- sion is termed the specific refractivity of the liquid. This value is dependent only on the nature of the liquid, and is a characteristic property of it. Molecular Refractivity is found by multiplying this value by the molecular weight of the substance. 2 ^ -y- gives a constant, where M is the molecular weight of the substance. Method of Determination of the Refractive Index The best instrument to use for this purpose is the Pulfrich refracto- meter, which is somewhat as shown in Fig. 30. L is a refracting prism, on which is mounted a glass cell ; this is clamped in position by the screw K, so that the flat face of the prism faces the telescope F. Since a constant temperature is required, the temperature of the liquid in the cell is con- trolled by heater S (see section, Fig. 31), through which water from a thermostat is circulated. A thermometer screwed into the heater indicates the actual temperature inside the cell. At the end of the telescope nearest to the prism is a cap, in which is an oblong slit, through which the light passes after refraction. With a single cell the whole slit is used, but with a divided cell half the slit is used. 50 REFRACTIVITY MEASUREMENTS Near the eyepiece end of the telescope is a large graduated metal disc, Z>, which is graduated in degrees and half -degrees. A vernier is also provided, by means of which a single minute can be read off. This vernier read- ing is made by the aid of a telescope, which can be rotated round the disc. To make the final adjustment the disc is fixed by screw H, and the fine adjustment made by means of screw 0. N is a reflecting prism on a movable arm, and P is a lens by means of which the light can be focussed on to the centre of the cell. In any experiment it is essential that the ray of light should be monochromatic and of a definite wave length. There are three spectrum lines, which are generally used for this purpose. D line (given by sodium flame), C line (red line of the hydrogen spectrum), and the F line (the blue line of the hydrogen spectrum). The D line is obtained, say, from sodium chloride in a bunsen flame, C and F lines are obtained from Geisler tubes. Determination of the Zero- Point A small right angle prism is let in the telescope tube near the eyepiece for the purpose of determining the zero of the instrument. This prism is illuminated by some strong source of light, such as an electric lamp. This light is reflected along the telescope. Here it emerges through the slit at the other end and strikes the face of the prism, thereby being reflected back along the telescope. Hence, on looking through the eyepiece, the small prism, and also an image of it, are seen on the right and left of the field of view respectively. On the image are seen two dark lines running parallel to the cross wires; these are the reflected images of the cross wires (see Fig. 32). Rotate the graduated disc until the cross wires and their images coincide as near as FIG. 31 SPECIFIC AND MOLECULAR REFRACTIVITY 51 possible. Tighten screw H, and make the final adjustment by means of screw G- Now observe the vernier reading, and the difference of this from zero is the correction which has to be applied to every subsequent reading. It sometimes happens that the simultaneous coincidence of the cross wires with their images cannot be obtained. In this case the true zero is obtained by taking the reading when the upper wire coincides with the upper image, and again when the lower wire coincides with the lower image, and then taking the mean of the two readings. The drum on the fine adjustment screw is divided into 200 divisions, and moves along a horizontal FIG. 32 scale, which is divided into degrees and thirds of a degree. One complete turn of the drum corre- sponds to a third of a degree (20'), therefore one division on the drum is equal to 0-1'. Experimental Determination of the Refractive Index of Alcohol for D line The sodium flame is placed about 2 feet from the reflecting prism N, which must be arranged so as to throw an image of the flame on the cell which is mounted on the re- fracting prism. Usually a wooden cap, W, with a side slit, is placed over the cell to exclude extraneous light ; it also serves to keep the temperature constant. Introduce a layer of alcohol about 5 mm. deep by means of a pipette, taking care not to touch the polished surface of the prism. Now bring into position the heater, lower- ing the movable flange until it is in contact with the top of the cell. Circulate the water from the thermostat at 25 C. through the heater, and when the temperature becomes con- stant to 0'1, a measurement may be made. Rotate the graduated disc until a bright yellow band crosses the field of view. Then clamp it by means of screw H, and then by means of screw G arrange the intersection of the cross wire on the upper edge of the yellow band. The reading then gives the angle of emergence, from which the index of refrac- tion can be obtained from the tables. The tables are usually divided into six columns ; i f is the angle of immergence obtained as above, nv is the value calcu- lated from n= VN 2 - sin 2 *', & is the amount in units to be 52 REFRACTJVITY MEASUREMENTS subtracted from the last decimal place for a rise 1' in the value of i. The last three columns are corrections when C, F, G lines are used. Having obtained the refractive index n, the specific refradivity can be calculated from the formula of either Glad- stone and Dale j- = R, where R is the specific ref ractivity, or that of Lorentz and Lorenz, in which case 2 11 E-j^gy the value of d being obtained either from tables, or directly by the method given for the determination of the density of liquids. The molecular refradivity will be MR: MandMR = respectively, where M is the molecular weight of the liquid. It has been found from measurements on a large number of organic liquids that the molecular refraction may be repre- sented as an approximate summation of the atomic refractivi- ties, so that the refractive power is largely an additive property. The values given for n in the tables are usually for a tem- perature of 20 C., so that if the experiment is done at 25, it is necessary to make a correction. This correction will be found in another table. CORRECTION FOR TEMPERATURE, THE UNITS TO BE ADDED TO THE FIFTH DECIMAL PLACE n C D F 1-60 0-25 0-29 0-40 1-50 0-26 0-30 0-42 1-40 0-28 0-33 0-45 1 30 0-30 0-35 0-49 The value in second, third, and fourth columns are the cor- rectness to be applied per degree for the spectrum lines C, D, F SPECIFIC AND MOLECULAR REFRACTIVITY 53 respectively. The first column n is the value obtained from the value of i in actual experiment given for 20. Suppose an experiment at 25 using D light gave a value of n 1-53107, then the correction would be (25 - 20) x 0-30= 1-5. This has to be added to the fifth decimal place of the original value of n, hence n D (at 25)= 1-531085. Exercise Given the following atomic refractivities for D line : = 2-501, H = 1-051, (in OH)= 1-521. Compare the molecular refractivity calculated from the above with that obtained in actual experiment. When hydrogen lines are used, the reflecting prism is not required. The Geissler tube is clamped in position and the beam of light focussed by means of lens P on to the slit in the wooden cap over the cell. The visible lines may be made sharp by means of a diaphragm fitted on to the lens. On looking through the telescope the chief lines visible are on the extreme right, the red line C, a pale blue line F ; and on the extreme left two violet lines, G', and G" ; other lines (green) are usually also visible, due to mercury vapour. Only C and F lines are used experimentally. The values of i' are determined for C and F separately by arranging the intersection of the cross wires on the upper edge of the respective lines. Having fixed the graduated disc force for, say, line C, the measurement for F can be made by means of the fine adjust- ment G. Experiment to Determine the Refractive Index of Acetone for C and F Lines On examining the tables it will be observed that corrections have to be made for C and F lines, in units of the fifth decimal place. Example, where the correction is given, 0-589, the correction to be made is 0-00589. In the case C line the correction must be subtracted from the value of W D . In the case of F (or G') line the correction value must be added to the value of W D (the values of n for D, C, and F lines respectively are usually indicated thus : n^ n c , TI F ). Note Whether the correction is added or subtracted from the value for %, depends on the relative positions of C and F lines with respect to D in the spectrum. Refractivity of Substances in Solution The refractivity of a soluble substance can be determined from the refractivity of its solution and solvent, provided the solution is not too strong. 54 REFRACTIVITY MEASUREMENTS Let %, n 2 , n B be the refractive indices of the solute, solvent, and solution respectively ; and d v d 2 , d 3 the corresponding densities, and x the percentage of solute in solution. Then using Lorentz and Lorenz formula n i 2 1_ l 1 = 100 V-l I n* - 1 _!_ 100 -a; w x 2 + 2 ' d t ~ x w 3 2 + 2 d s ~ n 2 ' \ 2 ' d z x or Gladstone and Dale's formula, we get AI Experiment to Determine the Molecular Refr activity of Sodium Chloride Make up a 10 per cent, solution, and first determine its density at 25 relative to water at 25. Then determine the refractive index of pure water and solution respectively for the D line at 25. Calculate the specific and molecular refractivities of sodium chloride, using Gladstone and Dale formula. CHAPTER IX ROTATION OF THE PLANE OF POLARIZATION THE ref ractivity of liquids and dissolved substances is general ; but when we come to the polarization of light, we are dealing with a property possessed only by comparatively few liquids and dissolved substances. This property depends entirely on the arrangement of the atoms in the molecule for example, isorneric substances have usually very similar refractive pro- perties, but it often happens that they behave very differently with respect to polarized light. Polarized light (light in which the vibrations lie all in one plane) is obtained by passing monochromatic light through a Nicol prism (or tourmaline plate), which cuts off all rays except those vibrating in one plane. This prism is termed the polarizer. The light then passes on, and is examined by a second Nicol prism, termed the analyzer. When these two prisms have their axes at right angles, the field of view is totally dark. If when such conditions exist a tube containing cane sugar solution be interposed, the field becomes illuminated, but it becomes dark again on rotating the polarizer through a certain angle. What has happened is, the plane polarization has been twisted through a certain angle by the cane sugar solution. The analyzer has therefore to be turned through a certain angle, in order to take up the previous position relative to the plane of polarized light. The actual angle depends on the nature of the liquid, on the wave length of the light used in the measurements and on the temperature, and is proportional to the length of the tube containing the liquid under examination. Specific rotation is defined as the angle of rotation produced by a liquid, which in a volume of 1 c.c. contains 1 gram of active sid)- 55 56 ROTATION OF THE PLANE OF POLARIZATION stance, when the length of the column is 1 dcm., and is represented thus where a is the observed angle, I is the length of the column in decimetres, d is the density of the liquid at temperature t ; D indicates that sodium light was used as a source of illumina- tion. For solutions the specific rotation is lOOa where x is the number of grams of solute in 100 grams of solution. Polarimeter The types now largely in use are those designed by Lippich and Laurent. The two forms only differ in the mode of production of the half-shadow. The sodium light enters through a diaphragm, which is provided with a plate (or solution) of a crystal of potassium bichromate, which filters out any extraneous light which accompanies the yellow light. On leaving the lens E the rays pass parallel into the Nicol prism Z), and then enters the second diaphragm, F, half of In G) ^ EH tn 9 \z\ o ! IH I G P F D E ' FIG. 33 which is covered with a quartz or mica plate of definite thick- ness, and cut parallel to the axis. From here the rays pass through the liquid tube P into the analyzer G, and then through the lenses 1 and H of the telescope through which the observations are made (see Fig. :33). The characteristic part of the apparatus is the quartz or mica plate, the thickness of which is chosen so that the rays of sodium light which passes through suffers a change of phase of half a wave length, but still remains plane polarized. Thus we have two beams of polarized light, one double the wave length of the other. If the polarizer is adjusted so that the plane of polarization of light is parallel to the axis of the POLARIZATION 57 quartz, then for each position of the analyzer the two halves of the field of view will be equally illuminated. If, however, the polarizer is placed at an angle with this axis, the plane of polarization of the rays of light which pass through the quartz plate will suffer a like displacement, but in the opposite direction. m FIG. 34 When such conditions exist, the circular field appears divided into two halves, which are, with two exceptions, unequally illuminated. For two positions, however, 180 apart, both halves are equally illuminated. The apparatus (see Fig. 34) is so constructed that the analyzer, fastened to the telescope and vernier n, can be moved by means of an arm, T, on a fixed circle, K; the vernier can be read by means of a telescope. As already mentioned, the plane of the polarizer must form an angle with the axis of the quartz plate, thereby producing unequal illuminations of the two halves of the field. This is 58 ROTATION OF THE PLANE OF POLARIZATION accomplished by means of a contrivance, h, by means of which the polarizer can be rotated. The apparatus is first adjusted to the parallel position, so that for any position of the analyzer the two halves of the field view are equally illuminated. The polarizer is then rotated through an angle, 6, by means of h (see note). The smaller the angle is, the more sensitive is the instrument ; the more brilliant the light and the clearer the liquid, the smaller can be made. The proper adjustment of the polarizer is that position corresponding to the greatest change of the shade in the field of view for a slight movement of the analyzer. At the beginning of an experiment the telescope F is focussed sharply on the diaphragm, so that the dividing line at the edge of the quartz plate appears quite sharp. In determining the zero-point the tube should be filled with distilled water, in order that the intensity of the light may be the same as when the active liquid is observed. In case the field of view is too dark, on account of the liquid being coloured or not clear, the illumination may be increased by a slight rotation of the polarizer; this, however, as before mentioned, renders the instrument less sensitive. The angle 6 through which the polarizer is rotated is called the half -shadow angle. Since the quartz disc is fixed, only one wave length of light can be used with any one instrument, and the quartz disc being definitely gauged to just half this wave length. The apparatus described above is the Laurent type. The Lippich differs in that the quartz plate is replaced by a third Nicol prism, which covers half the field of view. This appar- atus has the advantage over the Laurent type, in that homo- geneous light of any wave length can be used. The observation tubes in which the liquid is placed usually consists of a thick- walled glass tube, with accurately ground ends closed by circular glass plates. These plates are held in position by means of screw caps. The tubes are either 1 dcm. in length, or some simple multiple of a decimetre. In constant temperature experiments the tube is surrounded with an outer jacket, through which water from a thermostat can be circulated (see Figs. 35, 36). Experiment to Determine the Specific Rotation of Cane Sugar Dissolve 10 grams of cane sugar in a little water and make up to 100 c.c. Then, having determined the zero with distilled POLARIZATION 59 water in the observation tube, fill up the tube completely (free from air bubbles) with cane sugar solution (first wash the tube out with the solution). Then determine the angle of rotation i.e., redetermine the position of equal illumination. Then from this angle calculate the specific rotation. For accurate experiments ; a jacket tube should be used, through which water is circulated from a thermostat. For ordinary purposes the temperature of the room is sufficiently constant. FIG. 35 FIG. 36 To Determine the Amount of Pure Cane Sugar in a Sample of Sugar The sugar will contain mainly cane sugar and a small amount of invert sugar, also traces of optically inactive sub- stances which do not materially affect the experiment. Weigh out the two samples of sugar, each 10 grams weight. One sample dissolve in distilled water, and make up to 100 c.c. The other dissolve in about 50 c.c. of water, add 10 c.c. of strong hydrochloric acid, and heat up to about 70 for ten to fifteen minutes, and then make up to 100 c.c. Now deter- mine the angle of rotation of each sample separately. In the first case the value will be for impure cane sugar, and in the second case for invert sugar only. 60 ROTATION OF THE PLANE OF POLARIZATION For cane sugar [a]j- 66-5 -0-0184(i? -20). For invert sugar [ a ]^ = - 19-66 - 0-0361 C' - 0-304( - 20). The influence of concentration is greater in the second case, and has therefore to be taken into consideration (C'). Suppose C grams of cane sugar in the sample. Then C' grams of invert sugar result ; then C /_360 C since If a' is the angle after inversion a'= - {19-66 + 0-0361C'- 0-304(i?- 20)} yj^ + A CY a= {66-5 -0-0184(i?- 20)} ^ Q + A where a is the angle of the original solution, and (3 the angle due to the presence of impurity (invert sugar) in the initial sugar, t is the temperature of experiment, then [/"*1 7 ^ YOO {66-5 -0-01 84(i? -20)} + r r'/n {19-66 + 0-0361 C'- 0-304(i?- 20)} y^Q Substituting C' = ~ C, we get rv - of = iQQ[{66-5 - 0-0184(^ - 20)} + {19-66 + 0-0380 C - 0-304^ - 20)} 1-0526], from which C can be calculated, and hence C'. Note The action of the quartz plate may be explained as follows : The plane of polarized light falling on the plate is decom- posed into two rays. The two rays traverse the plate with POLARIZATION 61 different velocities, and the thickness of the plate is so arranged that a difference in phase of half a wave length is produced. The effect of this is, that if the light passing through the un- covered portion of the field polarized in direction B, making an angle 6 with A (the edge of the quartz plate), then that which has passed through the plate is polarized in a direction FIG. 37 B', so that B A = A B f . On looking through the eye- piece the two halves of the field will be unequally illuminated, unless the principal plane of the analyzing Nicol in the eye- piece make equal angles with B and B' i.e., is parallel to or perpendicular to A. In the former case the field will be equally bright, in the latter equally dark (see Fig. 37). CHAPTER X SPECTRUM ANALYSIS THE spectroscope, next to the balance, is the most im- portant instrument of the chemist. By its aid a chemist is able to identify substances which heretofore were entirely beyond his ken. It has long been known that certain chemical substances, when strongly heated in the almost colourless flame of a bunsen or blowpipe, impart a charac- teristic colour to the flame. For example, sodium salts colour the flame intense yellow, while potassium salts impart a violet colour to the flame. If, however, sodium and potassium are present in the same substance, then the intensity of the sodium yellow completely masks the violet of the potassium. Hence by this method it is impossible to detect potassium in pres- ence of sodium with the naked eye. This difficulty is over- come by regarding the flame through a prism instead of with the naked eye. By this means the light is refracted, each differently coloured ray having its own specific refractivity. If the source of light be white, then a continuous band of differently coloured rays is observed, the white light being resolved into its various coloured constituents. The coloured band thus obtained is called a spectrum, and white light gives a continuous spectrum, stretching from red (which is the least refrangible) to violet (the most refrangible). If, now, the light from a coloured flame be allowed to fall through a narrow slit on to the prism, we get a spectrum which consists only of a few bright-coloured bands. Thus the yellow sodium flame, when treated in this way, gives two bright yellow lines close together, while the violet flame of potassium gives two bright lines, one in extreme red and the other in extreme violet. These peculiar lines, or sets of lines, are absolutely characteristic of the chemical element in question, and are 62 THE SPECTROSCOPE 63 exhibited by no other substance ; further, the position of each line in the spectrum is definitely fixed, and never alters for any given apparatus. Hence, suppose we examine the flame given by a mixture of sodium and potassium salt, we see the red and purple lines in their respective portions of the spec- trum, and the yellow sodium lines in between, just as distinctly as when only one element is there alone. Some elements give a great many coloured bands, but no matter, the same element will always give exactly the same number of bands, in precisely the same position, no matter what the source of the element originally may be. If a number of elements are present, then the spectrum is made up of the spectrum of each separate element, and in most cases the spectrum can be analyzed into groups, and the elements in this way identified ; in other words, an analysis of the mixture can be made. A great advantage of this method of analysis is its extreme delicacy, as well as in the great facility with which the pres- ence of particular elements can be detected with certainty. Thus the y^^.^o.^o^ f a sodium salt can be detected ; lithium to the extent of 1 part in 6,000,000. In this way the presence of substances can be made manifest where hitherto they have eluded detection. For example, lithium, which was formerly supposed to exist only in four minerals, has been detected in almost all spring waters, in tea, tobacco, milk, and blood. Again, certain samples of sodium and potassium exhibited certain lines which were entirely absent in other samples, yet the additional lines did not belong to any then known sub- stance. What was the result of this observation 1 The dis- covery of the alkali metals, rubidium and caesium, in 1860 by Bunsen. These metals had previously eluded detection simply because they occurred in such minute quantities that it was absolutely impossible to detect them by ordinary ana- lytical methods. Since Bun sen's discovery of rubidium and cgesium the spectroscope has been the means of revealing quite a number of previously unknown elements. It is not only those bodies which have the power to impart colour to a flame which yield characteristic spectra, this property belongs to every elementary substance, whether metal, non-metal, solid, liquid, or gas ; and it is always observed when such an element is heated to the point at which its vapour becomes luminous, for at this point each 64 SPECTRUM ANALYSIS element emits its own specific light, and the characteristic bright lines are apparent on observing the spectrum. The majority of the metals require a much higher tempera- ture than the ordinary flame in order to make their vapours luminous ; they may, however, be easily heated up to the required temperature by means of an electric spark, which volatilizes a little of the metal in passing between two points, and heats it to an intensity sufficient to enable it to emit its own peculiar light. Thus, all metals (including iron, platinum, gold, silver, etc.) can be recognized by means of their spectra. FIG. 38 The permanent gases, such as hydrogen, can be rendered luminous by means of an electric spark, and their spectra mapped out. Thus the red light of the incandescent hydrogen is resolved into one bright red, one blue, and two violet lines. There are two distinct types of spectra namely, line spectrum, which is made up of a number of sharply defined coloured lines (really images of the slit), and band spectrum, which consists of bands which are broad, even with a very narrow slit. These bands are often sharp on one side, and gradually fade away on the other. The Spectroscope This instrument is somewhat as shown in Fig. 38. It consists of a prism, A, which is firmly fixed on an iron base ; a collimator, B, which carries an adjustable slit at one end and a lens at the other end, by means of which the THE SPECTROSCOPE 66 light from the coloured flame E is rendered parallel before falling on the prism A. The light, having been refracted by the prism, is received by the telescope F, and the image magni- fied before reaching the eye. In many instruments the slit is half covered with a small prism. By this means it is possible to obtain two spectrum bands at the same time from two different flames. One is arranged so that the rays pass directly through the uncovered portion of the slit. The rays from the second flame first strike the small prism, and are then reflected through the slit and along the collimator on to the prism. Usually one flame gives a standard spectrum, which helps to emphasize any special characteristics of the substance tested. The tube G contains a scale which is illuminated by the white light from H. This scale is distinctly visible in the telescope, and by it the position of any coloured spectrum line can be definitely fixed. Adjustment of the Spectroscope. It has already been pointed out that the rays of light leaving the collimator should be parallel. This is achieved by adjusting the distance between the slit and the collimator lens. First bring the spectroscope near a window, and observe through the telescope some distant object ; focus the telescope by means of the adjusting screw until that object is seen clearly. The telescope is then focussed for parallel light. Now bring the telescope into the dark-room, and illuminate the slit of the collimator by means of a sodium flame ; then adjust the collimator by sliding it in or out until the image of the slit is seen quite sharply. Now illuminate the scale, and adjust it so that the sodium line is about a third the distance from the left-hand side of the scale. Remember it is necessary to have the spectra as bright as possible. This depends upon the position of the sodium flame relative to the slit. The importance in securing the correct position of the flame will be better understood from Fig. 39. Let A, Bj C, D represent a section of the collimator, B^ D the lens, and S the slit, also &, E"^ E three different positions 5 66 SPECTRUM ANALYSIS of the flame. At position E' only part of the flame is used to illuminate the collimator ; at position E' ff the outside portions of the lens are not illuminated at all. It is only at the position E" that the lens is illuminated with the maximum amount of light. This position must in all eases be determined by trial. Mapping oj Spectra Prepare several pieces of platinum wire (thickness 1 mm.) sealed into glass tubes. Clean them thoroughly by moistening with pure concentrated hydro- chloric acid and heating white heat in bunsen. Repeat this process until the wire imparts no coloration to the bunsen flame. The student should also provide himself with a sheet of paper on which are ruled lines divided into millimetre divisions. Now take one of the wires and moisten it with pure concentrated hydrochloric acid, dip the wire into a little solid sodium chloride, causing a little to adhere to the wire. Now place the wire in the hottest part of the flame i.e., just above the cone (this portion of the flame should be adjusted so as to be opposite to the slit) and observe the position of the sodium line on the scale. Mark the position on one of the lines on your scale-paper, each division on your scale corre- sponding, say, to 1 mm. on your paper. On a second wire, moistened with hydrochloric acid, place a small quantity of barium chloride, and in a similar manner map out the spectrum. One, and perhaps two, bright green lines should be visible in this case ; if this is not so, the slit requires adjusting. Repeat this with fresh platinum wires with the chlorides of lithium, thallium, strontium, calcium, and potas- sium. In the case of potassium there is a very distinct red line and also a line in the violet, but this is often very difficult to see, except by experienced observers. The violet can usually be seen by removing the light which illuminates the scale and readjustment of the slit ; then, having noted its approximate position, it can often be detected on illuminating the scale again, and hence its position obtained. In the case of calcium and other salts it will be observed that the spectrum changes. The first spectrum is due to the chloride, which is gradually replaced by that of the oxide. The spectrum of an incandescent solid is continuous ; a dis- continuous spectrum of bright lines is only produced by an incandescent gas. The yellow line seen when a salt of sodium is heated on a platinum wire in the bunsen flame is due to the THE SPECTROSCOPE 67 vapour of sodium set free by the temperature of the flame, or by chemical change taking place between the substance and the hot gases of the flame. The carbonates, chlorides, or nitrates of the alkaline earths are convenient to use, but the chlorates, where possible, are preferable, since as a consequence of the liberation of oxygen the flame is hotter. The actual number of lines visible depends upon the tem- perature of the flame. Thus a flame of hydrogen burning in chlorine does not give the sodium line when sodium is intro- 20 30 4O 5O 60 70 00 90 WO HO 120 130 OO ISO 160 10 JO 4-0 50 60 70 80 90 100 I/O 120 130 140 ISO 160 H 20 3O 40 50 60 7O QO 90 100 HO 120 130 140 ISO 160 FIG. 40 duced into it ; or, again, the sodium line is hardly visible in a flame of sulphuretted hydrogen burning in air. If, on the other hand, much hotter flames are used, such as the oxy- hydrogen flame, then new lines are revealed. Thus, with such a flame sodium gives five lines at 43'2, 5OO, 56'0, 76'0, 83-6, whereas in the electric spark spectra of sodium eight lines are visible. Bunsen flame spectra are somewhat as follows (Fig. 40) : 68 SPECTRUM ANALYSIS Sodium A bright yellow line at position 50*0. This line is a standard, and is known as the D line. Lithium salts colour the flame crimson. The spectrum con- sists of two lines, a very brilliant one at 31'7, and a much feebler line at 45-0. The red line should be quite distinct. Potassium gives one line in the extreme red at 17 '5, and another in the extreme violet at 153-0. Alkaline Earths The spectra of the alkaline earths are not so simple as those of the alkalies. When first introduced into the flame there are seen certain bands which are "X different according to the particular salt of the metal >^> used, and which are supposed to be due to the com- pound employed, but the final spectrum is the same with all salts, which is partly due to the oxide, besides which the brightest lines of the metal are also visible. Calcium is recognized by its characteristic orange band, 40-0-43-0, and the green band, 61-0-63-0. Chloride, chlorate, bromide, give the best results. Non-volatile salts should be treated with hydro- chloric acid if it decomposes them, or heated with ammonium fluoride. Strontium gives an orange band at 44 f O-47'0, red lines 30-0-35-0, but the most characteristic is the blue line at 107 -6. The best salts to use are chloride or chlorate ; the lines are not visible with silica, silicate, phosphate, etc. Barium gives brilliant green bands at 73-0 and 78-0. \\J Hydrogen Spectrum In the case of hydrogen, the iir spectrum is obtained by using exhausted tubes, such fc as Geissler or Plucker tubes. Such a tube is shown FIG. 41 j n -ffig. 41 1 The electrodes of platinum are sealed into the glass, one at each end of the tube, and the central portion is a capillary tube. It is the capillary portion which is placed in front of the slit of the spectroscope, while a discharge is passed through the tube by means of an induc- tion coil. If the tube contains " rarefied " hydrogen, then the discharge is red, which, when observed through the spectroscope, shows the red (C line) at 34-0, blue (F line) at 92-0, and two violet (' G" lines) at 127-5 and 151-0 respec- tively. The red and blue are the most conspicuous. REDUCTION OF SPECTROSCOPIC MEASUREMENTS 69 The student should obtain such a tube and map out the spectrum as before. Reduction of Spectroscopic Measurements to an Absolute Scale When the spectrum of a given substance is mapped, the relative positions of the lines will be found to differ according to the instrument used. Even if the sodium line is at the same scale division in each, the readings of the other lines will differ in the different instruments, since they depend upon the dispersion of the prism and on the distance between the divisions of the scale. The student must not, therefore, expect his readings to coincide with the scale number here given as examples, as this, except by mere coincidence, will not be the case. The numbers and positions of the lines on the diagrams are for one particular prism and for one particular scale. The student will therefore at once see the importance of being able to standardize his readings so that they may be comparable with the readings obtained on any other instru- ment. In other words, the student must be able to represent his results in a manner which is entirely independent of his instrument. This is done by reducing the measurements taken on the arbitrary scale to wave lengths. There are several methods by which this may be done, but only one need be considered here namely, what is known as the graphical interpolation method. In this method the positions of three (or more) lines, the wave lengths of which are known, are observed on the arbitrary scale of the spectroscope, and the unknown wave lengths of other lines are obtained by interpolation. For our purpose we will take six standard lines of known wave length, whose position on the scale of a certain instru- ment are as quoted viz. : The Chloride of Line taken Wave Length Scale Reading Potassium Red 7669 17'5 Lithium ... Red 6708 31-7 Strontium Orange 6409 40'0 Sodium ... Yellow 5893 50-0 Thallium Green 5351 69-0 Strontium Violet 4608 107-6 The wave lengths are given in Angstrom units, where 1 unit mm< (0*1 w)' Having noted the position of the 70 SPECTRUM ANALYSIS above six lines on the scale, and given their wave lengths, it is only necessary now to draw a curve, the scale readings taken as the abscissae, and the corresponding wave lengths as ordi- nates (see Fig. 42) ; connect the separate points by a smooth curve, 1 mm. representing one division on the scale, and, say, 1 mm. on the ordinate representing 40 wave-length units. From this curve the wave length may be read that corresponds to each division on the scale. 10 20 JO 40 50 60 70 80 90 100 HO 120 /30 140 Scale Reading. FIG. 42 Exercise : Determine the Wave Lengths of (a) Hydrogen (C and F lines). (b) Barium (green lines). (c) Calcium (orange lines). The student should now try one or two " unknowns," selected from those whose spectrum he has already mapped, by first mapping the spectrum of the unknown, and then, by comparison with the spectra previously prepared, determine what the metal is. If time permits, he should map the spectrum of a mixture of two or three metals. CHAPTER XI DETERMINATION OF PARTITION COEFFICIENTS Distribution of a Substance between Two Non-Miscible Solvents When succinic acid is shaken up with two immis- cible liquids, such as ether and water, the distribution which takes place is very similar to the distribution of a substance between a liquid and a gas phase (solution of a gas in a liquid), and therefore similar rules apply to the distribution of a sub- stance between two immiscible solvents as to the solution of gases. These may be expressed as follows : 1. If the molecular weight of the solute is the same in both solvents, the distribution coefficient (i.e., the ratio in which the solute distributes itself between the two solvents) is constant at constant temperature (Henry's law). 2. In the presence of several solutes the distribution of each solute separately takes place as if the others were entirely absent. (This corresponds to Dalton's law of partial pres- sure.) 3. The ratio in which the solute is distributed between two solvents depends, however, not only on its solubility in each solvent, but also on whether it possesses the same molar weight in the two solvents. Hence a study of these relation- ships is of vital importance, in so far as they afford a means of determining the state of association or dissociation of a sub- stance in solution. This will be better understood from a consideration of the following results given by Nernst : Distribution of Succinic Acid between Ether and Water Varying quantities of succinic acid were shaken up with water and ether and the distribution coefficient determined where C T is the concentration in water and C 2 the concentra- 71 72 DETERMINATION OF PARTITION COEFFICIENTS tion in ether. The approximate constancy of this ratio shows that Henry's law applies. Ci (Water) C 2 (Ether) Si Co 0024 0-0046 5-2 0-070 0-013 5'2 0-121 0-022 5-4 When, however, benzoic acid is shaken up with benzene and water , Nernst gives the following results : Ci (Water C 2 (Benzene) C 2 Ci 0-0150 0-0195 0-0289 0-242 0-412 0-970 0-062 0-048 0-030 0-0305 0-0304 00293 It will be observed that in this the ratio *r is not constant, *r i but the ratio JL is constant. V 2 These results show that while benzoic acid has a normal molecular weight in water, it consists almost entirely of double molecules in benzene. In such a case the concentration of the single molecules in benzene is proportional to square root of the total concentration. Since a constant ratio should be found between the concentration of the single molecules in the first solvent and the single molecules of the second solvent, it follows that = must be a constant (Law of Mass Action, Dilution Law, etc.). Generally this law may be stated, that if in one solvent the solute is present as simple molecules, and in the second solvent in " n " simple molecules are associated as PARTITION COEFFICIENTS 73 and C t is the concentration in the first solvent and C 2 in the pi second, then the ratio JL should be a constant. V 2 Experiment to Determine the Distribution Coefficient of Succinic Acid between Ether and Water Take a well- stoppered bottle, and introduce 100 c.c. of distilled water (free from CO 2 ) in which 1 gram of succinic acid has been dissolved. Add an equal volume of ether. Fix the stopper securely, and immerse the bottle up to the neck in a thermostat at 25 C. Shake the bottle vigorously every five minutes for about forty minutes. Determine the concentration of acid in each layer by carefully removing 25 c.c. of solution with a pipette. The titration should be done with-^ baryta solution, using phenolphthalein as an indicator. Repeat the experiment, using 2 per cent, and 5 per cent, solutions respectively, and determine in each case the value of r\ the ratio ?y . Experiment to Determine the Distribution Coefficient of Benzoic Acid between Water and Benzene Prepare three solutions of benzoic acid in benzene containing 12, 6, and 3 per cent of benzoic acid respectively. To 100 c.c. of benzene solution add 100 c.c. of distilled water, and proceed exactly as in the previous experiment. Since at the concentrations used in these experiments benzoic acid exists mainly as (C 6 H 6 COOH) 2 i,e., associated molecules in the benzene solution the ratio -= should be constant. V^2 Experiment to Find the Degree of Association of Benzoic Acid in Chloroform Repeat exactly the previous experiment, using chloroform instead of benzene, and find what value of n in the p ratio _ gives a constant. This value is the number of molecules which are associated in the chloroform solution. CHAPTER XII THERMO-CHEMICAL MEASUREMENTS Hess's Law When the same chemical change takes place between two definite amounts of two substances under the same conditions, the same amount of heat is always given out, pro- vided that the final products or product are the same in each case. The actual heat effect, absorbed or evolved, depends on (a) the nature of the reaction, (6) the physical conditions of the reacting substances, and (c) the amounts of the substances present. Usually the heat of a reaction is measured by the method of mixtures. The value of the thermal effect measured in calories (cal.) is usually too large, and the last figure uncertain, so a larger unit is used, equal to 100 cals. This larger caloric is usually represented by K, and is practically equal to the amount of heat required to raise 1 gram of water from to 100. A larger caloric still, due to Berthelot, is now considerably used, and is equal to 1000 calories, and is represented by Cal., as distinguished from cal. Heat of Neutralization By the heat of neutralization of a monobasic acid and a base is meant the amount of heat given out when 1 gram molecule of acid and 1 gram molecule of the base, dissolved in water, are mixed. For polybasic acids, as many heats of neutralization are possible, as there are basicities for each acid. The reaction is caused to take place in a calorimeter, which should be preferably of platinum or silver, but nickel, copper, or aluminium may be used. It should have a capacity of about 600 c.c. The outer surface of this calorimeter should be polished. This is then surrounded by at least two other vessels, polished on the inside, and, if possible, a water-jacketed 74 HEAT OF NEUTRALIZATION 75 vessel should surround these. In each case the respective calorimeters are insulated from one another by wooden blocks. The two inner vessels should be fitted with non-conducting lids, with two holes in each, to admit a stirrer (glass) and a thermometer, reading at least in tenths(better use a Beckmann). Experiment to Determine the Heat Neutralization of Hydro- chloric Acid by Caustic Soda Prepare 250 c.c. of a semi- normal solution of caustic soda and hydrochloric acid, and determine accurately the strength. The caustic soda should \ V//////////////////////A FIG. 43 be free from carbonate. Fit up the apparatus as shown in Fig. 43, and measure out into the inner calorimeter 250 c.c. of caustic soda. Into a flask (previously washed out with i> HC1), protected with at least two polished metal cylinders, to reduce loss by radiation, introduce 250 c.c. of hydrochloric acid. A sensitive thermometer (graduated at least in tenths) is sup- ported in the hydrochloric acid. This thermometer must have been previously compared with that in the alkali. In order to allow for the loss of heat by radiation, it is necessary to determine the rate of change of temperature of both acid 76 THERMO-CHEMICAL MEASUREMENTS and alkali before mixing, and then of the mixture by taking readings, say every minute, for about seven minutes before the solutions are mixed, then mix the solutions quickly, con- stantly stirring, and again take readings for a similar period. (Note /j should be as near as possible equal to t 2 .) In order to determine the true temperature which should have resulted, it is necessary to plot the above readings. This is illustrated in Fig. 44. The curves ^ and t 2 give the temperatures for alkali and acid respectively. After seven minutes, the solutions are 2 3 456 Time 89 W II 12 13 14- FIG. 44 mixed, then the temperature continues to rise, rapidly at first, for about three minutes, after which it falls gradually. The bend in the curve is obviously due to loss by radiation whilst the mixture was becoming heated, since a time-cooling curve would be straight. The direction of the true curve is, however, given by the last few readings. Hence, by extra- polation, the true elevation temperature, t y can be found by drawing a perpendicular at the point which indicates the instant of mixing (seventh minute), and reading off the tem- perature at the point where this line cuts the extrapolated HEAT OF NEUTRALIZATION 77 cooling curve i.e., the temperature reading thus obtained is used in calculating the result. Calculation The heat evolved is represented by the follow- ing equation ~^) J, where m v m^, ra 3 , m v are the masses of the solution, calori- meter, thermometer, and stirrer respectively, and a, ft, y, 8, their respective specific heats. As regards the solution, it will be sufficiently accurate in this case to take the water equivalent of the solution as equal to the mass of water contained in it i.e., equal to the volume of the solution approximately. In the case of the thermo- meter we do not know the relative weights of the glass and mercury, but we may make use of the fact that, volume for volume, the specific heats of glass and mercury are practically identical, and equal to 0*47 per c.c. To find the volume of the thermometer immersed in the solution insert it in a burette, partially filled with water, up to the depth it is immersed in the solution, and measure the displacement. If the thermometer is not solid, as in the case of a Beckmann, the volume of the bulk and the requisite portion of the stem must be found separately, and the volume found for the stem divided by five, and this value added to the volume for the bulb. In place of the ordinary calorimeter a Dewar vacuum vessel may be conveniently substituted, to reduce the loss of heat. Repeat the above experiments, using ammonium hydroxide and sulphuric acid, also caustic potash and acetic acid. In accordance with the theory of electrolytic dissociation, the heat of neutralization of any completely dissociated base is constant, since the reaction consists solely of the union of H* and OH' ions giving unionized water. In the ease of hydro- chloric acid and caustic soda it may be represented thus H- + Cl' + Na- + OH' = Na- + Cl' + H 2 0. The value of this constant is 13*7. When it is required to determine the heat of neutralization of a polybasic acid with a monovalent base, or vice versa, the thermal effect must be calculated for each basicity separately. In case precipitates are formed, the heat of precipitation 78 THERMO-CHEMICAL MEASUREMENTS must be subtracted from the heat evolved (see later section). If the acid or base is a solid or gas, a correction for heat of fusion-solution, or absorption must be applied when possible. For example, when caustic soda solution is neutralized by gaseous CO 2 , we get a certain heat effect, 2NaOHAq + C0 2 ; but to get the true heat of neutralization the heat of absorp- tion of C0 2 must be subtracted i.e., C0 2 Aq. .-. 2NaOHAq.C0 2 - C0 2 Aq. = 2NaOHAq.CO 2 Aq. Heat of Solution The heat of solution of a substance is the thermal effect produced by dissolving 1 gram molecule of a substance in a given number of molecules of solvent. The heat of solution may be sometimes positive and some- times negative, that is, heat may be evolved or absorbed. It varies with the quantity of solvent used. If further dilution produces no further heat effect, the heat measured for 1 gram molecule is known as the heat of solution at infinite dilution. Experiment to Determine the Heat of Solution of Sodium Chloride The method is similar to that employed for heat of neutral- ization. Into the calorimeter introduce 500 grams of water, and fit up the apparatus with thermometer and stirrer as before, taking the same precautions as to temperature read- ings. Weigh out into a dry test-tube 10 grams of finely powdered dry sodium chloride. Place the test-tube in a beaker filled with water at a known temperature (which should, as near as possible, be at the same temperature as the water pre- viously weighed out). When the salt has acquired the tem- perature of the bath, remove the test-tube, dry it roughly, and empty the contents into the calorimeter and stir rapidly, and take readings every minute for seven or eight minutes. Plot the temperature readings against time, and eventually determine the maximum elevation. The method of calculation is similar to the previous experi- ment. Consider the solution as pure water for calculation. Repeat the above experiment with MgSO 4 7H 2 O and ZnS0 4 7H 2 0. Heat of Hydration The heat of hydration is the quantity of heat liberated when 1 gram molecule of substance combines with a definite number of molecules of water to form a hydrate. HEAT OF DILUTION 79 The heat of hydration is obtained by determining the heat of solution of the hydrated and anhydrous forms of the salt, and subtracting the latter from the former. The method of experiment is therefore essentially that for determining the heat of neutralization and solution. Experiment to Determine the Heat of Hydration of Copper Sulphate (a) Determine the heat of solution of GuS0 4 5H 2 0. (b) Determine the heat of solution of CuS0 4 . Then (b - a) = heat of hydration. Heat of Dilution By heat of dilution is meant the quantity of heat liberated or absorbed when a solution is further diluted by the solvent. The method here again is similar to the determination of heats of neutralization. The result is expressed as the amount of heat change resulting from a given increase of solvent. Both the initial and final concentrations must be stated in the result. It is equal to the difference between the heats of solution for the two respective volumes of solvent. Experiment to Determine the Heats of Dilution of a 3 per Cent. Solution of Potassium Nitrate Dissolve 12 grams of nitrate in 400 grams of water, and determine the heat evolved on adding 100 grams of water. Heat of Precipitation The heat of precipitation is the quantity of heat evolved when a gram molecule of substance separates out from a solution. It is the converse of heat of solution, and is numerically equal to it. Experiment to Determine the Heat of Precipitation of Silver Chloride Dissolve 1 gram of sodium chloride in 500 c.c. of water, and place it in a calorimeter fitted up as before. Prepare 15 c.c. of normal silver nitrate at the same temperature. When the temperatures are equal, mix the solutions, and note the change in temperature. From the results calculate the heat of precipitation. Details of the experiment are the same as in the previous cases. The result is the same as the heat of solution with the opposite sign. Heat of Combustion The heat of combustion of a substance is the quantity of heat evolved in the complete combustion of 1 gram molecule of substance. 80 THERMO-CHEMJCAL MEASUREMENTS Let x be the amount of substance used in the experiment, and M the molecular weight of the substance ; also let W be ^ the weight of water in the calorimeter, and w the water equivalent of the appara- tus, T x and T 2 the initial and final temperature, then Q, the heat of combustion, will be given by The reaction is usually caused to take place in com- pressed oxygen inside a calorimetric bomb. A convenient form of bomb is as shown in Fig. 45. It is known as the Mahler- Cook bomb, and is a modifi- cation of the Berthelot- Mahler bomb. The Bomb This consists essentially of an enamel- lined steel vessel, capable of withstanding high pressures. The lower part, D, is closed by a lid, A, which is screwed on, an air-tight connection being obtained by means of a lead-washer, C. Two stout platinum wires pass through the cover, one, T, being insulated by means of a quartz plug; these wires are connected by two terminals. One of the wires is bent round in the form of a loop, so as to support a crucible, which may be of platinum, unglazed porce- lain, or silica. The substance is placed in the crucible, and the ignition is effected by means of a coil of iron wire, which joins FIG. 45 THE CALORIMETER 81 the two platinum wires, which is caused to burn by means of an electric current. Oxygen is admitted through a valve in the centre of the lid, the opening and closing of the valve being controlled by screw F. The oxygen, which is supplied from a cylinder fitted with a pressure gauge, is attached at E. The Calwimeter The calorimeter consists of a large nickel- plated vessel, A, to contain the water in which the bomb is to FIG. 46 be immersed. This is surrounded by an outer water-jacketed vessel. Both calorimeter and outer vessel are fitted with suitable stirring arrangements. The stirrer in the calori- meter may be conveniently worked with a small motor. On the downward stroke the stirrer should almost touch the bottom of the calorimeter, whilst on the upward stroke it should remain completely immersed in the water (see Fig. 46). The change in temperature is read by means of a Beckmann thermometer. The outer jacket is closed with a non-conduct- ing lid, fitted with the necessary holes for stirrer and ther- mometer. 82 THERMO-CHEMJCAL MEASUREMENTS The Water Equivalent of the whole apparatus is determined by means of a substance of known heat of combustion. The heat received by the water in the calorimeter can be calculated from the elevation in temperature on combustion, and from this value and the known heat of combustion of the substance the heat taken up by the apparatus can be obtained, and hence the water equivalent. Camphor, or naphthalene, are suitable for this purpose, and they give out 9292 and 9693 calories respectively per gram of substance. Experiment Open the bomb by unscrewing the nut B and carefully remove the cover. Place a crucible in position. Make a small tabloid of, say, camphor ; weigh it accurately (use about 1 gram), and place it in the crucible. Make a short spiral of about 15 cms. of iron wire, and weigh it, and then connect it between the two stout platinum wires. The iron spiral is then pressed down until it makes a contact with the substance ; the lid is then replaced, and the nut B screwed tightly down, the bomb being held by the bottom nut, 0, which is fitted into a hexagonal plate fitted to the bench. The bomb is then connected at E with an oxygen cylinder and pressure-gauge. The valve F is closed, and the valve on the oxygen cylinder opened slowly ; then slowly admit the gas to the bomb by opening F. When the pressure reaches 25 atmospheres with F well open, close the valve F tightly, and then shut off the oxygen cylinder and disconnect. The water-jacket of the calorimeter should be filled with water several hours before the experiment is to be done. Weigh out into the calo'rimeter about 2-5 kgs. of water (sufficient to immerse the bomb up to the nut B}. The calorimeter is then placed in position, being insulated at the bottom by a wooden block or cork. To counterbalance the loss by radiation, the water in the calorimeter should be at a slightly lower temperature than that of the room such that the temperature of the room is the mean between the initial temperature of the water in the calorimeter and the highest temperature of the experiment. The total rise is usually about 3, therefore the initial difference should be about 1'5. The bomb is now carefully lowered into the calorimeter and the terminals connected to the battery, the circuit being broken by a switch key. Insert the Beckmann thermometer and commence stirring. After about five minutes, TEMPERATURE READINGS 83 record the reading every minute for about eight minutes. At the eighth minute complete the electric circuit, thereby causing the ignition to take place. Continue to take minute readings. When the highest temperature has been reached, the readings should be continued for a further eight or ten minutes. The observations are then complete. Open valve F carefully, and then unscrew B. If any iron wire is unburnt, it must be care- fully weighed and subtracted from the original weight of iron used. The method of calculating the results will be better understood from the following example, in which the water equivalent of the apparatus is calculated by means of naph- thalene : Weight of naphthalene = 1*2966 grams. Weight of iron = 0-1568 gram. TEMPERATURE READINGS I Time in Minutes Beckmann Reading t 1-805 _ 1 1-808 0-003 2 1-813 0-005 3 1-815 0-002 4 1-818 0-003 5 1-821 0-003 6 1-823 0-002 7 1-824 o-ooi 8 1-825 o-ooi (circuit closed) Mean = 0-0025 II 8 1-825 (circuit closed) 9 3-814 10 4-536 11 4-998 12 5-514 13 5-666 14 5-700 15 5-706 16 84 THERMO-CHEMICAL MEASUREMENTS III Time in Minutes Beekmann Reading ft 16 5-706 17 5-706 18 5-705 o-ooi 19 5704 o-ooi 20 5-703 o-ooi 21 5-703 o-ooo 22 5702 o-ooi 23 5-700 0-002 24 5-697 0-003 25 5-695 0-002 26 Mean = 0-0011 During the middle period (heating period) heat will have been lost by radiation. From Series I and III the rates of 003 OOZ 001 001 002 003 jt / / v 18 2 8 3 / 8/ + 8 5 8 / / / FIG. 47 cooling can be calculated. In Series I the rate of cooling is negative, denoting the temperature is rising i.e., A/ is nega- tive and 8t positive. TEMPERATURE READINGS 85 Draw a cooling curve as shown in Fig. 47 by drawing , a straight line through points 1-8 to 0-0025, and 5-7 to 0-0011. Then correct all temperatures in Series II from this curve. Temperature Cooling in Each Minute | Total Loss Corrected Tem- perature 1-825 1 _ 1-825 3814 - 0-0007 -0-0007 3-8133 4-536 o-o -0-0007 4-5353 4-998 + 0-0004 -0-0003 4-9977 5-514 + 0-0009 + 0-0006 5-5146 5-666 +0-001 + 0-0016 5-6676 5700 +0-0011 + 0-0027 57027 5-706 +0-0011 + 0-0037 5-7097 The values in the second column are read off from the curve. The corrected temperature is therefore 5*7097 for the maximum. Hence the elevation = 5-709 7 - 1*8250 = 3'8847. The calorimeter contained 2500 grams of water. The heat of combustion of naphthalene ... =9,693 cals. per gram. The heat of combustion of iron Therefore heat evolved by naphthalene Therefore heat evolved 1,600 cals. 1 2966x9,693 = 12567-9 cals. by iron Total heat evolved = 0-1568x1600 =260-9 cals. = 12828-8 cals. Of this, 2500x3-8847 = 9711-9 cals. were taken up by the water. .-. 12828-8 cals. -9711-9 cals. = 3116-9 cals. Therefore 3116*9 cals. were taken up by the apparatus in rising 3-8847. 3116'9 . -. Water equivalent = 3.3047 = 802-3 grams. The water equivalent of apparatus = 802 -3 grams. 86 THERMO-CHEMICAL MEASUREMENTS In accurate work it is necessary to estimate the oxides of nitrogen which will have been formed during the combustion, and the heat of formation allowed for. In the above example the water equivalent of the calori- meter was the unknown factor, the heat of combustion being known. In determining the heat of combustion the value found above will be used, leaving the heat of combustion as the only unknown. CHAPTER XIII DETERMINATION OF TRANSPORT NUMBERS WHEN a current is passed through an electrolyte the numbers of positive and negative ions discharged at the respective electrodes in a given time are equal. It must not, however, be assumed that the velocities of the ions are equal, because this is not the case. The speed of the anion may be very different from that of the cation, and, in fact, this is almost invariably so. The result is, the con- centration of the faster ion round the electrode towards which it travels increases. This being the case, Hittorf showed how, by experiment, the relative speeds of the ions could be deduced from the changes in concentration round the electrodes after electrolysis. The speed of the cation is usually represented by w, and that of the anion by v. The total amount of electricity passed through the solution is proportional to the sum of the ionic velocities i.e., u + v. Of this let n be the fraction carried by the anion, then 1 n will be the fraction carried by the cation, and from this it follows that n = and 1 - n u+v u+v The value of n is termed the transport number of the anion, and 1 - n the transport number of the cation. The transport number can therefore be found by deter- mining the total amount of electricity which passes through the solution and the amount of one of the ions which have passed from the solution in the -immediate neighbourhood of one of the electrodes i.e., determine the change of concentra- tion of one of the ions round one of the electrodes. Hence, in order to investigate the changes of concentration, it is only 87 DETERMINATION OF TRANSPORT NUMBERS necessary to analyze a portion of the solution round one of the electrodes. The above will only be correct if the liquid which is not in the immediate neighbourhood of the electrodes does not alter. This can be approximated too, if the time during which the current passes is not too long. The time should also be as short as possible so as to minimize the effect due to diffusion. Hittorf showed that the transport numbers are practically independent of the electromotive force between the electrodes. They are, however, influenced by temperature to some extent, and in the case of mono- atomic univalent ions approach 0*5 as the temperature rises. Experiment to Determine the Trans- port Numbers of the Silver Ion and the Nitrate Ion in a Solution of Silver Nitrate The apparatus which is best suited for this purpose is Ost- wald's modification of Hittorf's ap- paratus (see Fig. 48) : two glass tubes, usually of unequal length, connected near the upper end. The lower end of the shorter limb is closed, while the longer limb is pro- vided with a stop-cock. Into the tubes are fitted, by means of para- ffined corks, two electrodes. The one in the longer limb is of silver, made by fusing stout silver wire on to stout copper wire, and cement- ing the electrode into a glass tube so that only the silver is exposed. The electrode in the shortest limb may be wholly of copper, but it should be enclosed partly in a glass tube. Prior to the experiment the silver anode should be coated with finely divided silver by electrolysis (see p. 128). The shorter limb, which is the anode compartment, is filled with a concentrated copper nitrate solution to just above the exposed part of the electrode. The rest of the apparatus is then carefully filled FIG. 48 TRANSPORT NUMBERS 89 with ^r silver nitrate in such a way that a fairly sharp boundary is maintained between the copper nitrate solution. The cell is now connected in series, with variable resistance, an ammeter, a copper voltameter, and a source of current, such as an electric lighting circuit. The resistance must be so adjusted that a current of 0*01 ampere and a difference of potential of 30 to 40 volts is passed. The copper voltameter may be made up in a glass cylinder as follows : Make up a solution of 125 grams, CuS0 4 5H 2 O, 50 grams H 2 S0 4 , 50 grams of alcohol, and a litre of water. Two copper electrodes of about 2 cms. square are cut from sheet copper. The cathode must be cleaned and weighed at the commencement, and then at the end of the experiment it is washed first with distilled water, and then with alcohol, dried, and again weighed. C0 2 should be passed through the volt- ameter during the experiment. When the apparatus has been fitted up as indicated, the current is passed for about two to three hours. At the end of this time the cathode of the voltameter is removed, and weighed according to previous directions. Then run off a measured volume of about three-quarters of the anode solution, weigh it, and determine the amount of silver present by titration with thiocyariate or electrolytic deposition. The remainder of the silver nitrate solution is then run off, and on analysis should have as near as possible the original composition. If not, the experiment must be repeated for a shorter period. From the weight of copper deposit on the voltameter cathode and the change in silver concentration at the anode the transport numbers can be calculated as follows : Calculation Before the experiment : 15 '06 grams of solution contained 0*127 gram of silver nitrate, which equals 0*000747 gram equivalents of silver for 15*06 grams of solution. After the experiment: 20*28 grams of anode solution con- tained 0*2113 gram of silver nitrate, which equal 0*00124 gram equivalents of silver for 20-28 grams of anode solution. Hence, before the experiment 14*933 grams of water con- tained 0*000747 gram equivalents of silver, after the experi- ment 20-0687 grams of water contained 0*00124 gram equivalents, ** 90 DETERMINATION OF TRANSPORT NUMBERS If there had been no change in composition, 20-0687 grams of water would have contained equivalents of silver . So the increase was 0-00124- 0-001004 = 0-000236 gram equivalents of silver. The weight of copper deposited in the copper voltameter was 0*0145 gram, or 0*0004602 gram, equivalents of copper. Hence the amount of silver liberated at the anode due to the discharge of N0 3 ions was 0-0004602 gram equivalents of silver, therefore the concentration ought to have increased by this amount if no silver had migrated to the cathode. The amount which must have migrated equals 0-0004602-0-000236 = 0-0002242 gram equivalents. Now, the values 0-000236 and 0-0002242 must be pro- portional to the velocities of anion and cation respectively. Hence the transport number for silver ion equals 0-0002242 M 1 -^Q-QQQ4602 = 0487> and for N0 8 ion 0-000236 n = 0-0004602 - CHAPTER XIV ELECTRICAL CONDUCTIVITY ELECTRICITY may be conveyed in two ways : (1) By con- ductors in which there is no transference of matter, as in the case of metallic conductors ; (2) by conductors which undergo simultaneous decomposition, as in the case of fused salts and solutions. In the present case we are only concerned with the second type of conductor. Ohm's Law, which holds for conductivity in general, may be stated somewhat as follows : The strength of an electric current passing through a conductor is proportional to the difference of potential between the two ends of the conductor, and inversely pro- portional to the resistance of the latter i.e., difference of potential volts -- ' resstance This is usually expressed symbolically thus : P E = K' The standard of resistance is 1 ohm, and is defined as the resistance of a column of mercury 106-3 cms. long, and weighing 14*4521 grams, and the resistance measured at 0. An ampere is that strength of current which will deposit 0*001118 gram of silver from a solution of silver nitrate, under definite conditions, in one second. The quantity of electricity which passes in one second with current strength of 1 ampere is known as a coulomb. When a current of 1 ampere passes along a conductor whose resistance is 1 ohm, then the difference of potential between the two ends of the conductor is 1 volt. 91 92 ELECTRICAL CONDUCTIVITY The unit of electrical energy is 1 volt x 1 coulomb, and is equal to 10 7 ergs. The resistance of a conductor is proportional to its length and inversely proportional to its cross section. Hence the resistance R is given by equation R = /o where p is a con- S stant. If I and s are each unity, then R = p. The constant p is known as the specific resistance, and may therefore be defined as the resistance in ohms offered by a cube of 1 cm. dimensions to a current of electricity. It will be seen that a conductor of low resistance will have a high conductivity. Hence specific conductivity will be the inverse of specific resistance, and therefore equal to - = *, where K is the specific conductivity. Specific conductivity is measured in reciprocal ohms, fre- quently termed " mhos." In dealing with solutions, the conductivity does not depend upon the solvent, but on the solute, and it is convenient to compare solutions containing quantities of solute proportional to the respective molecular weights. By molecular conductivity is meant the conductivity or con- ductance of a solution containing 1 gram molecule of solute when placed between electrodes of indefinite dimensions exactly 1 cm. apart, and is represented by /x. where V is the volume in cubic centimetres, which contains 1 gram molecule of solute. By equivalent conductivity is meant the conductivity of a solution which contains 1 gram equivalent of solute, when placed between two electrodes 1 cm. apart. It is usually represented by A where V is the volume, which contains 1 gram equivalent of solute. It will be seen that for such substances as KC1, which gives rise to two simple monovalent ions, //. = A. Determination of the Conductivity of Electrolytes The great difficulty in determining electrical conductivities lies in the fact that by the use of a continuous current the products of CONDUCTIVITY OF ELECTROLYTES 93 electrolysis accumulate at the two poles and set up a back electromotive force of uncertain value. This effect is known as polarization. The actual resistance measured will be therefore the sum of the resistance of the solution and the polarization at the electrodes. This difficulty was over- come by Kohlrausch, who proposed the use of an alternating current instead of a direct current. By this means the polar- ization caused by the passage of the current in one direction is removed before it has time to attain any appreciable magni- FIG. 49 tude by the reversal of the current and its passage in the opposite direction. Hence by this means the true resistance, and hence the conductivity of the electrolyte, can be deter- mined. The most suitable mode of obtaining an alternating current in the present case is by means of a small induction coil. The method usually employed to determine the resistance of an electrolyte is the Wheatstone bridge method. The arrangement of the apparatus is shown diagrammaticaily in Fig. 49. R is a known resistance, S the cell with platinum electrodes, between which the resistance of the solution is to be measured; a b is a platinum wire (may be iridium-platinum or nickelin) of uniform thickness, which is usually about a metre long, and is stretched along a scale graduated in millimetres ; 6' is a sliding contact. By means of a battery a direct current is sent through the coil L, thereby giving rise to an alternating current, 94 ELECTRICAL CONDUCTIVITY which divides into two circuits at the contact (7, one part going along the circuit C, a, d through #, and the other along C, 6, d through the cells S. The object of the experiment is to balance these two circuits. This is done by means of a sliding contact at C. Since an alternating current is used, a galvano- meter cannot be used, so a telephone T is connected to a b. The sliding contact C is moved along the wire until there is FIG. 50 no sound in the telephone. When this is the case, a balance has been made between the two circuits, hence the points a and b must be at the same potential. When such circum- stances exist, the following relationship holds E : S : : ac : cb ; i.e., S=E. ac Here R is known, as cb and ac can be measured. Hence the resistance of the cell S can be easily calculated. In actual experiment it is not usually possible to obtain complete silence in the telephone, so the point of minimum CONDUCTIVITY OF ELECTROLYTES 95 sound is taken i.e., a point such that if the con tact be moved, the least bit either to the left or to the right the intensity of the sound is increased. The coil used in these experiments should be as small as possible, so that the amount of current which passes at each pulse is as small as possible. The coil may be worked from a small accumulator or dry cell, but the current should be regulated with a sliding resistance, so that the sound of the coil can be distinctly heard, the vibration of the hammer being quite uniform. The resistance usually takes the form of the ordinary type of resistance box, the various resistances being put in circuit by the removal of brass plugs, thereby causing the current to pass through a wire of definite resistance ; the value of each resistance being indicated on the box. Various types of electrolytic cell are used. Fig. 50 indicates two types. A is a type used for solutions of small conductivity while B is used for solutions of high conductivity. The elec- trodes are circular platinum plates fitted with platinum wires, which are sealed into glass tubes. These tubes are held in position by being fixed into the ebonite cover which closes the cell. The electrical contact is made by placing mercury in the tubes. The open ends of the glass tubes attached to the electrodes should be closed by rubber plugs when the apparatus is not in use. The bridge, which is represented by TS 1 1 FIG. 51 ab in Fig. 49, is seen in detail in Fig. 51. The ends of the wire are frequently held in position by the brass plates, and to each of these brass plates two terminals are fixed. C in- dicates the platinum contact, which also carries a connecting terminal. It will be seen that the actual length of wire necessary in Tt bridge form will depend upon the ratio ^ - The nearer this is to unity, the nearer to the centre of the scale will be the final position of C. So that if R, S are suitably arranged, the 96 ELECTRICAL CONDUCTIVITY position of C may be confined to about 40 or 50 cms. in the centre of the scale. Hence the actual bridge can be reduced in length, and the excess of wire wound round a suitable drum. In some special forms of apparatus modifications of this type are introduced, and in some cases the scale is so graduated to give directly the ratio of the two resistances (see Fig. 52). FIG. 52 It is not advisable to rely upon the accuracy of the bridge scale, as the wire is rarely absolutely uniform. The motion of the contact over the wire also changes its resistance slightly ; so it is necessary to calibrate the wire from time to time. Calibration of the Bridge Wire The difficulty of measur- ing the resistance of short lengths of the wire lies in the un- certainty of making a contact with other wires which shall be free from resistance. The method usually adopted is that devised by Strouhal and Barus, which is based on the Wheat- stone bridge principle. In this method the resistances of the contact do not interfere with the measurement. Ten approxi- mately equal resistances are required, the sum of which should be about the same resistance as that of the bridge wire. These resistances are in the form of wire coils (Fig. 53) soldered on to stout copper wire, and for protection they are mounted in glass tubes. The ends of the copper wire are thoroughly cleaned and amalgamated, and arranged along a CALIBRATION OF THE BRIDGE WIRE 97 board, as shown in Fig. 54, the ends of the copper wires dipping into cups filled with mercury, thus connecting up the series. This is then placed parallel to the bridge to be FIG. 53 FIG. 54 tested. The principle of the method is to find lengths of wires at different positions along the bridge which are of equal resistance. The source of current in this case may be either direct or alternating, the exact compensation being FIG. 55 detected by a sensitive galvanometer in the former case, and by a telephone in the latter case. The bridge is then connected to the resistance series by stout copper leads, D. The whole arrangement will be under- stood from Fig. 55. One of the resistance coils must be 7 98 ELECTRICAL CONDUCTIVITY chosen as a standard, and should carry some suitable mark of distinction. It does not matter which of the coils is chosen as the standard. The standard coil is placed in cups 1 and 2, and one of the wires from the telephone placed in cup 2 (see Fig. 55) ; then the point on the bridge wire, where a balance is noted. Now move the standard coil to position 3 without changing the telephone wire, and again determine the balance- point. The telephone wire is now placed in cup 3, and re- determine the balance. The difference between the last two readings corresponds to a length of the bridge wire, the resistance of which is the same fraction of the total resistance of the bridge wire as the standard is of the sum of the ten resistance coils. The " standard" is now brought to position 3, 4, the tele- phone wire being first in 3, and then in 4, and the balance determined in each case. This is repeated until the standard has reached position 10, 11, where only one reading is taken i.e., with the telephone wire in cup 10. By this method the bridge wire has been divided up into ten equal resistances, each of which is equal, or approximately equal, to one-tenth of the whole resistance. These ten lengths are added together, and the difference of the sum from 1000 mm. divided by 10, and each single value corrected by this amount, so that now the sum is exactly 1000 mm. i.e., the exact length of the bridge wire, which, of course, it must be equal to. If the single corrected values are now added together as follows, 1,1+2, 1+2 + 3, and so on, we obtain readings which correspond to successive tenths of the wires. This will be better understood by studying the example on p. 99, which is derived from an actual experiment. It is advisable to plot a graph from values in the sixth column of figures, so that any intermediate values may be approximately determined. Purity of the Water used for Conductivities It is abso- lutely essential that water used in conductivity experiments, owing to the sensitiveness of the method of experiment, be of a high degree of purity. Water exhibits very different degrees of conductivity, depending upon the manner of distillation and preservation ; while perfectly pure, freshly distilled water exhibits an ex- tremely low conductivity. The purest water so far obtained had a specific conductivity CALIBRATION OF THE BRIDGE WIRE Cl^HOOOO^-i^-iO I + + I + I I I I I tr 00 O OS O O I-H r i O O OiCSOOSOOOOOO \ -J o F I SO \ O t^ i i I-H OS O O O O OS OS O OSOOOSOOOOOSOS I O 2 O"i O^ O^ O5 O^ O^ O"i O^ O^ O^ 6000000000 I I I I I I I I I I I as j>- I-H i i os i i o o o as as asooasoooooios HI J3 t^* ^2 ^H ^^ C^ ^H ^^ ^^ Oi c3 O gasoooooooasg ^_^ ^H S rTS 13 ^2 ^ s as as o o o o o o o | ^ |2 S ^ ^ -M ^J^l I 100 ELECTRICAL CONDUCTIVITY of 0-04 x 10~ 6 reciprocal ohms at 18, but water with a con- ductivity up to 3 x 10" 6 reciprocal ohms can be used for experiments, in which a fair degree of accuracy is re- quired. The chief causes of conductivity are the presence of small quantities of carbon dioxide and ammonia. The ordinary laboratory distilled water is frequently sufficiently pure for ordinary purposes. It can be consider- ably improved by redistillation in as pure an atmosphere as possible, neglecting the first and last fractions. Where a high degree of purity is required, the condenser should, according to Kohlrausch, be of block tin, but fre- quently a Jena glass tube in the condenser is sufficient. The water should be preserved in a glass flask which has been used for a long time to contain distilled water. The flask should be closed with a paraffined cork fitted with siphon tube and soda-lime tube. If the water contains much carbon dioxide, it may be treated with baryta before distilla- tion. In cases where absolute accuracy is necessary, the con- ductivity of the water itself must be determined. Determination of Cell Constant The resistance of an electro- lyte must depend on the capacity of the cell. By capacity is meant the actual volume of solution which is actually between the electrodes, or, in other words, upon the product of cross section of the electrodes and the distance between them. The specific conductivity, and hence the specific resistance, could be calculated if these two factors were known, but it is more convenient to determine what is termed the cell constant, which is proportional to its capacity. This is done by using an electrolyte of known conductivity, and a -$ normal solution of potassium chloride is usually used for this purpose. As before mentioned (p. 94) Rcb = ac' Hence conductivity I ac ==== Therefore C can be determined by experiment. DETERMINATION , OF CELL .CONSTANT 101 Further, the specific conductivity' K must 'be proportional to the observed conductivity K = KG. K, K being the cell constant. Experiment to Determine the Cell Constant by Means of ^Q Potassium Chloride The type of cell used in this experi- ment should be that with the electrodes near together (Fig. 50, .4). The experiment must be carried out in a thermostat at 25. It is essential that the temperature of the thermostat should be exceedingly constant, since a change of 1 influences the result 2 per cent. The cell, thoroughly clean, is FIG. 56 supported in the thermostat and connected up by stout copper wire, of negligible resistance. The ends of the wire must be cleaned with emery paper so as to give a good contact. The ends of the wire which make a mercury contact (at the con- ductivity cell) should be amalgamated. The arrangement of the apparatus will be understood from Fig. 56. The electrodes should be coated with a uniform layer of platinum black (see note at end of chapter), and when freshly platinized they contain traces of impurity which cannot readily be washed out, and which would increase the con- ductivity. To remove this, put conductivity water into the cell to just above the electrodes and determine the resistance of the cell. 102 ELECTRICAL CONDUCTIVITY Any soluble matter entrained in the platinum black will slowly dissolve out. Pour out the water from the cell, put in fresh, and again determine the resistance. Repeat this until the resistance is constant, or only differs by 3 4 mm. on the bridge. Note this last reading, because from it we can calcu- late the conductivity of the water when we have determined the cell constant. Make up carefully a ^ solution of pure potassium chloride. Wash the electrodes once or twice with it. Then fill up the cell to just above the electrodes, and then allow the solution to come to the temperature of the bath. Then determine the resistance of the solution. The resistance put in from the box should be so arranged that the reading falls somewhere between 25 and 75 cms., because an error in the readings at either end of the bridge influences the result to a greater degree than a similar error about the middle of the wire. Having determined the position of minimum sound, change the resistance in the box and again determine the balance. Then empty the cell and fill up again with fresh solution and repeat the above proceedings. Calculate the cell constant as indicated below from each of the resistance read- ings, and take the mean value. Given for KC1 K= 2-768x10-3 at 25, = 2-399x10-3 at 18, = l-996xlO- 3 at 10, expressed in reciprocal ohms. Let R be the resistance in the box, S the resistance of the cell, x the bridge reading in centimetres, then 100 -a; S . g== R(100-s). but a _! . p X ~C R(lOO-z)' Again K = p where K = specific conductivity. .-.K = K being the cell constant. DETERMINATION OF MOLECULAR CONDUCTIVITY 103 Having obtained the cell constant, the conductivity of the conductivity water can be calculated, for the resistance of the cell containing the conductivity water has already been deter- mined when testing the electrodes. The equation in v K(100-z)R K= ~V~ K is the only unknown, and hence can be easily calculated. If any difficulty is experienced in obtaining a balance, it may be due to the fact that sufficient time has not elapsed for the cell to attain the temperature of the bath. If, however, after a reasonable interval the results are unsatisfactory, the elect- rodes should be replatinized. The current should not be allowed to pass through the cell for any considerable period, as this tends to heat up the cell. Determination of Molecular Conductivity and Degree of lonization If K is the specific conductivity of a solution of known concentration, then the molecular conductivity is given by p v = K V, V being the volume which contains 1 gram molecule of solute. If K be determined for a whole series of dilutions of the original solution, the value of ^ will finally approximate to /AOO i-V; molecular conductivity at infinite dilution. It is, however, not possible to measure the conductivity at infinite dilution with any degree of accuracy, so use is made of Kohlrausch's law, which states that the molecular con- ductivity at infinite dilution is equal to the sum of the veloci- ties of the ions where u and v are the speeds of the cation and anion respect- ively. At any given dilution V the formula will be where a represents the fraction of the molecules of the solute, which is ionized. Hence we get, by dividing the second equation by the first that is, the degree of dissociation a at any dilution is the ratio of the molecular conductivity at that dilution to the molecular con- ductivity at infinite dilution, 104 ELECTRICAL CONDUCTIVITY Consider, say, the case of a solution of acetic acid of concen- tration 1, and let a represent the fraction which split up into ions. Then the concentration of the undissociated portion i ft, , will be represented by v where V is the volume, and the concentration of each ion will be y. Hence, by the law of mass action, we get or 'fl^JV where k is the equilibrium constant. Now, substituting *- for a, we get *%oo(fJ^/*v)V' A; is known as the dissociation constant or ionization constant. The above value is usually very small, so K = 100& is usually quoted as the dissociation constant ; ^^ cannot be found directly as a rule, but has to be calculated from the ionic velocities, as before indicated. Experiment to Determine the Molecular Conductivity and Dissociation Constant of Succinic Acid The apparatus in this case is the same as in the former experiment. The cell and electrodes must be clean and dry. The electrodes may be conveniently dried by washing first with distilled water and then with pure alcohol, and then allowed to dry in a warm atmosphere free from fumes. Prepare T \ molar solution of succinic acid, and place 20 c.c. (or other convenient definite quantity according to size of cell) of this solution in the cell, in the thermostat at 25. When solution has taken the temperature of the bath, determine the resistance as in previous experiment, using three different resistances in the box. Now withdraw carefully 10 c.c. (if 20 c.c. has been used, otherwise half the original volume) of solution from the cell, and introduce 10 c.c. of conductivity water (from a stoppered flask which has been kept in the DISSOCIATION CONSTANT 105 thermostat). Mix the water and solution thoroughly, and then determine the resistance again. Repeat this process until the dilution reaches 1 gram molecule in 10 24 litres i.e. t make six dilutions. The dilutions are as follows : One gram molecule to 16, 32, 64, 128, 256,512, 1024 litres. Calculation = __ __ R (100-cc)' Since /^ = /cV, _KV x ^ R (100-z)' Hence the molecular conductivity for various values of V can be calculated. Again, substituting the values found for /^ in equation _ given also that IM X for succinic acid equal 381, k can be easily calculated, and also K = 100k, k being the dissociation constant. The value k is a very important constant, since it is a measure of the strength or affinity of acids and bases. It is therefore frequently called the affinity constant. Application of Conductivity Measurements to Determine Neutralization Points Consider the case of a dilute solution of hydrochloric acid. According to Kohlrausch's law, the conduct- ivity depends upon the sum velocities of the ions in this case the chloride ion and the hydrogen ion. Now, suppose a little caustic soda is now added, part of the acid will be neutralized. This means that some of the hydrogen ions have been replaced by sodium ions viz. : H- + 01' + NaOH = Na' + Cl' + H 2 0. Now, the velocity of the sodium ion is much less than that of the hydrogen ion. Hence the effect will be to reduce the conductivity. Further, the conductivity will decrease until the whole of the acid has been neutralized. As soon, how- ever, as the neutralization is complete, further additions of caustic soda increase the number of ions i.e., increase the 106 ELECTRICAL CONDUCTIVITY sodium ions and also introduce OH' ions, therefore the con- ductivity begins to rise again ; and since the OH' ion is very mobile, the turning-point is very decided. Experiment to Determine the Strength of a Given Solution of Hydrochloric Acid The manipulation is as in previous experi- ments. Introduce into the cell a known volume of hydro- chloric acid (dilute) and determine the resistance as before. Run in from a burette small quantities of standard caustic soda, and determine the resistance at each point. At a certain point the direction of the movement of the sliding contact will change. Then the neutralization-point has been passed. Make three or four readings after this. To deter- mine the exact neutralization-point plot the bridge readings as ordinates against the number of cubic centimetres of acid added. The point of intersection of the two curves thus obtained gives the exact point of neutralization. This method is of value when dealing with highly coloured or turbid liquids. In the case of weak acids use a strong base, and add the acid to the base to obtain a decided break in the curve. Note : Platinizing Electrodes Thoroughly clean the electrode by means of chromic acid solution. Prepare also a 3 per cent, solution of chloroplatinic acid to which 0*025 gram of lead acetate is also added. Place the electrodes in the solution, and connect up to a 4-volt accumulator. A commutator, or a reversing switch must also be in the circuit. Pass the current for about fifteen minutes, re versing it every half -minute, so that each electrode becomes cathode and anode alternately. The evolution of the gas should not be too rapid. This may be controlled by having a sliding resistance in the circuit. Owing to the horizontal position of the electrodes, the gas is very liable to collect underneath, thereby causing uneven distribution of the platinum black. This may be avoided by supporting the electrodes in an inclined position. When finished the electrodes should present a fine velvety appearance. They still contain a small amount of absorbed platinizing liquid and a small amount of chlorine. To get rid of this place the electrodes in dilute sulphuric acid, and pass the current for fifteen minutes, reversing it every minute. Then wash the electrodes several times in warm distilled water, and then conductivity water, and finally preserve them in conductivity water required for use. CHAPTER XV MEASUREMENTS OF ELECTROMOTIVE FORCE IN the present chapter we are concerned mainly with the study of the relation between chemical and electrical energy. Electrical energy, it must be remembered, involves two factors, namely, the amount of electricity and electromotive force, or fall in potential. Of these two factors the latter, namely, electromotive force, is the more important, and will be con- sidered in some detail in the succeeding pages. When a chemical reaction takes place, the energy of the reaction, or chemical affinity, may manifest itself in the form of heat. Hence heat of reaction is frequently used as a measure of affinity. Many reactions, on the other hand, give rise to electrical energy, as in galvanic cells ; in these cases a measure of chemical affinity can be obtained from a measure- ment of electromotive force. It must not be assumed from this that electromotive force is equal to the heat of reaction, or that electromotive force is a measure of the heat of reaction. In some cases they are equal, but generally they are not equal. The electromotive force is rather a measure of the diminution of free energy of a system. The relation between free or available energy and the heat of reaction in a reversible reaction given by the thermodynamical equation- A-U-Q, where A is the free energy i.e., that portion of the energy which can be transformed into work U is the diminution of the total energy of the system (diminution of internal energy), and Q is the heat of the reaction. This equation may be written as a free energy equation A TJ-T \rr 107 108 MEASUREMENTS OF ELECTROMOTIVE FORCE When, however, the chemical energy of the reaction is trans- formed into electrical energy, it is only necessary to substitute the corresponding electrical terms in the above equation to get an expression of the relationship between the chemical energy transformed and the maximum electrical energy obtainable in a reversible galvanic element. The resulting equation is or Where E is the E.M.F. of the cell, Q is the heat of reaction ; for molar quantities, expressed in electrical units, F is 96540 coulombs. T is the absolute temperature at which the cell is working, n is the valency or the number of charges carried by a molecule of substance undergoing change,-^ is the temperature coefficient of the E.M.F. Q has been substituted for U, since they are equal when no external work is done. A becomes wFE i.e., the maximum electrical energy for molar quantities dA. . ._dE -Tm becomes BSrfr, n and F being constants. The equation given above is known as Helmholtz equation. On considering the equation in the first form, it will be seen that dE (a) If ^rp is positive, then %FE > Q, hence the cell takes heat from its surroundings while working. dft (b) If, on the other hand, ^ is negative, the Q > ?iFE, hence the cell becomes heated while working. (c) If - is zero, then Q = nFE i.e., the heat of reaction is equal to the electrical energy, and hence the temperature of the cell remains unaltered. Measurement of Electromotive Force The most convenient method of measuring the E.M.F. of a cell is by what is known as Poggendorffs compensation method. The principle of the method is that the E.M.F. of the cell to be tested is MEASUREMENT OF ELECTROMOTIVE FORCE 109 just compensated by the E.M.F. of another cell in the opposite direction, the E.M.F. of the latter being adjusted so as to just balance the cell. The general arrangement of the apparatus is shown in Fig. 57. A is a source of electricity of constant E.M.F., such as, say, a lead accumulator, which is connected by two copper wires to the ends of the uniform resistance wire, B C, which may conveniently be a metre in length. The cell, E, the E.M.F. of which is required, is connected through some suitable measuring instrument, such as an electrometer or FIG. 57 galvanometer, G, and a tapping key to one end of the wire bridge at B, the other pole being connected to sliding contact D. The point of balance is found by moving the sliding contact D to a position such as that when the contact is made through the tapping key no current passes through the galvanometer i.e., there is no deflection. When such con- ditions hold, we have the following relationship : E.M.F. of accumulator : E.M.F. of cell : : length BC: length BD n T\ . - . E.M.F of cell = E.M.F. of accumulator x g_(f The E.M.F. of A, or, as it is called, the working cell, is not sufficiently constant for accurate experiments, so it is usual to do a preliminary determination with a standard cell *.., a cell of known constant E.M.F. in place of E. Suppose we 110 MEASUREMENTS OF ELECTROMOTIVE FORCE find that the standard cell balances at D', and the cell to be tested at D, then we have B D' E.M.F. of standard cell B D "unknown E.M.F. of cell E It is essential that the E.M.F. of the working cell A should be greater than that of the cell whose E.M.F. is to be deter- mined. Usually a 2-volt accumulator of large capacity, 30 to 40 ampere hours, will be found to meet the requirements. The measuring wire BC is usually the same as described for conductivity experiments (p. 95), and it should be calibrated in the same manner. If in a metre wire the difference of potential between the two ends is 2 volts, then 1 mm. on the bridge will correspond to 2 millivolts. So that it is easily possible to get a degree of accuracy of less than 1 millivolt of error with a fairly sensitive galvanometer. The Standard of Electromotive Force The standard usually employed is the Westvn, cell, the composition of which may be indicated as follows : Hg | Hg 2 S0 4 (solid), CdS0 4 (saturated solution). CdS0 4 |H 2 (solid), | Cd amalgam (13 per cent. Cd). Another well-known standard is known as the Clark cell. This cell has the following composition : Hg | Hg 2 S0 4 (solid), ZnSO 4 (saturated solution). ZnS0 4 7H 2 O (solid), | Zn amalgam (10 per cent. Zn). The Weston cell is most frequently used now; it has the advantage of being easily reproduced, and has a very low temperature coefficient. The cell itself usually consists of an H -shaped glass vessel. The vertical tubes are sealed at the bottom (see Fig 58). Into one of the limbs pour a layer of freshly distilled and thoroughly purified mercury to a depth of about 1 cm. Then prepare a paste of mercurous sulphate thus : Grind together in a mortar mercurous sulphate, a little mercury, and one or two crystals of cadmium sulphate, with a little saturated solu- tion of cadmium sulphate. Filter through a plug of cotton- wool. Then rub the paste again with a little cadmium sul- phate solution, and again filter. Repeat this process a third time. The object of this process is to completely remove any THE STANDARD OF ELECTROMOTIVE FORCE 111 traces of mercuric sulphate. Place the paste moistened with cadmium sulphate solution thus prepared to a depth of about 3 mm. over the mercury ; then add several large clear crystals of cadmium sulphate. Into the other limb place a layer of cadmium amalgam prepared as follows : Heat at 100 (say on a water-bath) 7*5 parts by weight of pure mercury and 1 part of cadmium. Stir well with a glass rod. Heat up the limb of the cell in hot water, and add the liquid amalgam to a depth of about 1 cm., then allow to cool, and the amalgam solidifies. On the top of this amalgam place about FIG. 58 3 mm. layer of finely powdered cadmium sulphate crystals, slightly moistened. Then add several large clear crystals of cadmium sulphate, and, finally, fill up the apparatus within about 1'5 cms. of the top with a saturated solution of cadmium sulphate. The cadmium sulphate crystals used in making up the above cell must have the composition CdS0 4 |H 2 0, and in preparing a saturated solution of the salt the temperature should be kept below 75, because above this temperature the monohydrate is the stable phase i.e., CdS0 4 H 2 0. The open ends of the tube must now be hermetically sealed, at the same time an air space must be left in the tubes for 112 MEASUREMENTS OF ELECTROMOTIVE FORCE expansion due to rise in temperature. A small quantity of clean paraffin wax is melted, the cell tilted a little to the left, and the paraffin wax poured carefully on to the surface of the solution in the left-hand limb to a depth of about 0*5 cm. The tube is then tilted to the right, and the right-hand tube treated in the same way. On the top of the paraffin place a layer of cork O5 cm. thick, and, finally, close the tube with the sealing wax. In the above cell the mercury is the positive pole, and the amalgam the negative pole. The E.M.F. of the Normal Weston cell is practically independent of temperature, as it only changes -0-00004 volt per degree for the range 15 to 20. THE E.M.F. AT TEMPERATURES FROM TO 30 Temperature E.M.F. in Volts 1-0189 5 1-0189 10 1-0189 15 1-0188 20 1-0186 25 1-0184 30 1-0181 Generally for a temperature t. Ee = 1 '0186 - 0-00004 (t - 20) nearly. For ordinary room temperatures we may take the E.M.F. as 1-019 volts. Care must be taken not to short circuit the cell, as this changes slightly the E.M.F., since it causes some solid Hg 2 S0 4 to go into solution, and it takes some time for the cell to recover its normal condition. It is also advisable to enclose the cell in an opaque case. The Clark cell only differs from the Weston in that zinc is substituted for cadmium in each case. The temperature coefficient of the Clark cell is higher than that of the Weston, as will be seen from the following equa- tion, which gives the value of the E.M.F. at any tempera- ture (f) : E= 1-433 -0-0012 (f -15) very nearly. In the experimental determination of E.M.F. it is found CAPILLARY ELECTROMETER 113 much more convenient to use a capillary electrometer instead of a galvanometer. Capillary Electrometer The most convenient form of electrometer for common use is what is known as the open form of capillary electrometer, a useful design of which is indicated in Fig. 59. It consists of two fairly wide-bored tubes, one having a bulb at one extremity ; these two tubes are joined together by a fine capillary tube. Pure, clean, dry mercury is poured into limb A until the mercury stands just over halfway up the fine capillary tube ; then the bulb of limb B is filled to about halfway with mercury ; the rest of the tube B is filled with dilute sulphuric acid (1 part sulphuric acid to 6 parts of water), which had been previously agitated with a little pure mercury. The sul- phuric acid should make a clean junction with the mercury in the capillary. To do this blow down tube A until a little mercury has been drawn over into B. On re- leasing the pressure, the sulphuric acid will be drawn back into the capillary. It is sometimes neces- sary to suck at tube A in order to bring the sulphuric acid back, but care must be taken not to get the sulphuric acid round the bend. A platinum wire passes down tube B, making contact with the mercury; the wire is insulated from the sulphuric acid by means of a glass tube. Contact is made in limb A by means of a piece of platinum wire. It is essential that in using the capillary electrometer the sulphuric acid limb should be connected with the positive pole, and the mercury limb with the negative pole. If they are connected in the reverse way i.e., the mercury limb made the anode the mercury would go into solution, giving rise to mercurous sulphate in the capillary, which would dirty the tube, thereby causing the mercury to stick FIG. 59 114 MEASUREMENTS OF ELECTROMOTIVE FORCE and give fallacious results. If this should happen by acci- dent, and another electrometer is not available, it should be thoroughly cleaned out with a hot solution of potassium bichromate and sulphuric acid, followed by several washings with distilled water, and finally dried with filtered air. It may then be filled as before described. Principle of the Capillary Electrometer When mercury and sulphuric acid in a capillary tube are connected in the manner mentioned above with some source of electromotive force, the area of separation between the liquids in the capillary diminishes. This is due to a change in the potential difference between the two liquids. CirCU * Elecrromerer Elecfromerer Circu^ Circuit- Circuit E lee from erer FIG. 60 A certain amount of mercury dissolves in the sulphuric acid, giving rise to mercurous sulphate. Now, the osmotic pressure of the solution of mercury salt will be greater than the solution pressure of the mercury, hence positive mercury ions from the solution will be deposited on the surface of the mercury, and this surface will, as the result of this, become positively charged with regard to the solution ; then in all probability this positively charged surface holds a correspond- ing negative layer near the surface of the acid, thus giving a sort of Helmholtz double layer. Another factor has also to be considered namely, surface tension. The effect of surface tension is to tend to make the PRINCIPLE OF CAPILLARY ELECTROMETER 115 surface area as small as possible. The attraction between the two oppositely charged layers will tend to counteract this effect ; in other words, diminishes the surface tension. In actual experiment the two poles of the electrometer must be connected so as to bring the two surfaces to the same potential difference before any measurement is made. This is achieved by means of a triple contact Morse key (Fig. 60). Now, if any increase or de- crease charge be brought about from outside sources, then the concentration of the ions in the immediate neigh- bourhood of the mercury alters by causing some mer- cury to either pass into solu- tion or else be deposited. The effect of this is to alter the potential difference, and hence the surface tension, thereby causing the mercury thread to rise or fall in the capillary tube ; therefore when, on put- ting the electrometer into circuit, no movement occurs in the capillary tube, there is no difference of potential i.e., both sides balance. This form of electrometer was devised by Lippman, and is therefore known as Lipp- irian's Electrometer. The advantages of this electrometer consists in its action being practically astatic one, no current being taken from the element operating it. In any experiment the object is, of course, to find the point at which the level of the mercury remains stationary, for then the two opposing potentials balance. If a high degree of accuracy is required, it is necessary to observe the meniscus of the mercury by means of a microscope, because, for small differences of potential, the meniscus alters only very slightly, FIG. 61 116 MEASUREMENTS OF ELECTROMOTIVE FORCE and cannot be accurately observed with the naked eye. The electrometer and microscope are mounted on a suitable stand ; the electrometer should be illuminated by a mirror or diffused light from a suitably protected electric lamp. The apparatus is usually sold complete by the makers (see Fig. 61). The eyepiece contains a graduated scale, by means of which the rise and fall of the meniscus can be measured. With the aid of a microscope, the electrometer is sufficiently accurate to detect 0-0001 of a volt. FIG. 62 Experiment Standardization of Weston Cell The Weston cell, prepared according to the directions already given, must be compared with some other known standard cell. The apparatus is fitted up as shown in Fig. 62. A is the working cell connected to the end of bridge wire B 0; E a capillary electrometer; T lt T 2 are connecting terminals ; K is a Morse tapping key ; S l is the known standard, and S 2 the standard to be tested, they are put in circuit separately, as required, by means of a two-switch, P ; D is the sliding contact on the wire bridge. It is also advisable to insert a plug, M, so that the accumulator can be easily disconnected. Make sure all connections are clean, and give a good con- tact ; then put in circuit the known standard S 1 ; allow the SINGLE POTENTIAL DIFFERENCES 117 current to flow along the bridge wire by inserting plug M\ move the sliding contact to just past the middle of the bridge ; press down the Morse key sharply, and observe through the microscope the movement of the mercury men- iscus in the electrometer. If the mercury appears to go down in the microscope i.e., in reality it moves up then move the sliding contact down a little until a point is found where the mercury begins to move in the opposite direction. The null-point of the electrometer is between these two readings. Now move the sliding contact a few millimetres at a time until the motion of the mercury meniscus is again reversed. Repeat this process until a point is found such that a slight movement of the sliding contact either one way or the other causes the meniscus to move in the opposite direction. At the point itself the meniscus should not move at all on pressing the tapping key. As a check on the above result, find two points 1 mm. apart such that they give opposite directions to the motion of the meniscus ; then measure the extent of the movement at both points by means of the scale in the eyepiece, and calculate the exact position of the balance by proportion. As the point of balance is approached, it will be necessary to keep the Morse key depressed several seconds before any movement may be detected. Now, having determined the balance-point for S v alter the two-way switch so as to put S 2 in circuit instead of S v and repeat the above process. Then, if B D be the reading for S, and B D l for S v we have E.M.F. of S l BD or E.M.F. of Measurement of Single Potential Differences When a metal is dipped into a liquid, it possesses a certain definite solu- tion pressure, so that the metal tends to dissolve ; it can, how- ever, only dissolve in the ionic form, hence it sends into solution a number of positively charged ions. The solution therefore becomes positively charged, and the metal must acquire the corresponding negative charge. An electric double layer is then found, and a state of equilibrium is ultimately 118 MEASUREMENTS OF ELECTROMOTIVE FORCE reached, when the electrostatic action of the double layer just balances the solution pressure of the metal. If, however, the liquid contains already a dissolved salt of the metal, the solu- tion will already contain positive ions of the metal, and these positively charged ions will resist, by virtue of their osmotic pressure, any increase of metallic ions by solution of the metal. In this way a potential difference is set up between the metal and the solution, which will be equal to the differ- ence between the solution pressure of the metal and the osmotic pressure of the ions in the solution. It will be clear that the relative charges on the metal and solution will depend on the relative values of the solution pressure of the metal and the osmotic pressure of the ions in solution. Let P be the solution pressure of the metal, and p the osmotic pressure of the ions in the solution. Then, if (a) P > p t the metal sends ions into the solution until a balance is obtained; the metal will then be negatively charged and the solution positively charged. (b) P

H 2 , if negative, the gaseous hydrogen becomes ionized H 2 ^2H'. An electrode of the above type is known as a hydrogen electrode. An oxygen electrode behaves similarly. Preparation of Hydrogen Electrode The glass portion of the apparatus is very similar to that used for the calomel electrode. A convenient form is as shown in Fig. 66. It consists essentially of a fairly wide glass tube, A, with a tube, suitably bent, sealed into the bottom. This is the inlet tube for the gas. The electrode consists of a piece of platinum foil 2x1-5 cms., to which is welded a piece of 132 MEASUREMENTS OF ELECTROMOTIVE FORCE platinum wire, and this in turn is sealed into a glass tube. The electrode is held in position by means of a rubber stopper. Connection with a second electrode is made by means of a side tube, (7. The gas escapes through side tube D, which is provided also with an air trap, F. The electrode must be coated with an even layer of platinum black. This is best done as described on p. 106, the electrode being previously cleaned with hot potassium bichromate and dilute sulphuric acid. For efficiency of the B FIG. FIG. 67 electrodes, the coating of platinum black should be quite uniform and fairly thick, since the amount of gas absorbed will depend upon the thickness of the coating. The occluded impurities, chiefly chlorine, may be removed by immersing the electrode in an acidified (H 2 S0 4 ) solution of a mixture of ferrous and ferric sulphate for about twenty minutes. Then thoroughly wash the electrodes with distilled water. If not required for use immediately, preserve it in distilled water. Another form of electrode is as indicated in Fig. 67. It PREPARATION OF HYDROGEN ELECTRODE 133 consists of a hard glass tube, A, sealed on to a narrow tube, B- A short piece of thin platinum wire is sealed into A at C. The tube is thoroughly cleaned, and then bulb A coated with an even layer of "liquid platinum" (see Appendix). The tube is then carefully warmed. Raise the heating slowly as the film drys and darkens, becoming almost black. Then heat the tube to dull redness, taking care not to let the tube soften. The tube should, on cooling, be coated with a fine grey metallic film of platinum. The wire C makes a contact with this film, so by means of a little mercury poured into the tube a contact can be made between the film and the rest of the apparatus. The first form of electrode has the disadvantage that it requires several hours for the gas in the electrode and solu- tion to attain equilibrium, and hence a constant potential. The second type gives a constant potential much quicker, but on the whole is not so efficient and reliable as the type in which rectangular sheets of platinum are used. Experiment : Determination of Electrode Potential of tlie Hydro- yen and Normal Hydrochloric Acid Electrode Prepare a normal solution of pure hydrochloric acid, and fill up the electrode to just about the side tube C. Fix the platinum electrode so that just over half of it is immersed. The trap F should contain a little mercury. Open tap C (which need not be lubricated with vaseline) and pass in a slow current of hydrogen, which has been made to pass through potassium permanganate solution, and then through silver nitrate solution, and finally through normal hydrochloric acid solution, before entering the elec- trode. Close exit F, thereby forcing some of the acid through C, filling the tube ; then close tap C, at the same time opening F. Now allow the hydrogen to bubble through for at least an hour (longer if possible) to completely saturate the elec- trode with hydrogen. Now complete the cell H 2 | ?*HC1 I wHCl | Hg 2 Cl 2 7iKCl | Hg. i.e., join up with a calomel electrode by means of normal hydrochloric acid. The tap C should be kept closed, since if the barrel is wetted with the solution it will be a sufficiently good conductor. The hydrogen should bubble through only very slowly. Now determine the E.M.F. of the cell by balancing it against a Weston cell, exactly as in previous 134 MEASUREMENTS OF ELECTROMOTIVE FORCE experiments. In this case it is necessary to determine the E.M.F., say, every fifteen minutes, until the consecutive read- ings practically coincide. Then, knowing the E.M.F. of the cell and the electrode potential for the calomel electrode, the electrode potential for electrode can be calculated as in previous experiments. An electrode such as the above, in which the hydrogen is at atmospheric pressure, and normal acid used, is sometimes taken as the standard of potential difference. The E.M.F. is 0-277 volt. Experiment to Determine E.M.F. of a Hydrogen Concentration Cell Prepare cell H 2 | wHCl | nHCl | HC1 | H'. Take the same precautions with each electrode as described in previous experiment for the hydrogen electrode. Deter- mine the E.M.F. every fifteen minutes, until the E.M.F. is constant. The E.M.F. in this case is small, so put the cell in series with the Weston cell. Having determined the E.M.F. of the cell, determine the degree of ionization of hydrochloric acid in normal solution, given that - =0*17 and the degree of ionization for , ~ hydrochloric acid is 0*91. Extension In a similar manner the student might deter mine the E.M.F. of H- | ?iHCl | TiHCl | nHCl | Cl' i.e., hydrogen-chlorine cell. Electrical Potentials of Oxidation and Reduction Media When an indifferent electrode, such as platinum or iridium, is placed in an oxidizing solution, it will acquire a positive charge relative to the solution ; and if placed in a reducing solution, it will acquire a negative charge. If a change from a higher to a lower state of oxidation occurs, then a positive charge is given up or negative charge OXIDATION AND REDUCTION POTENTIALS 135 taken up. Hence change of ferric ion to ferrous ion may be represented thus Fe - ( + ive charge) = Fe * ; or Fe " + (- ive charge) = Fe * '. Reducing agents act in the reverse way. When an oxidizing salt is present in aqueous solution, its affinity for a negative charge will tend to take such a charge from the hydroxyl ions, thereby liberating oxygen. For example, if cobaltic sulphate is dissolved in water and sulphuric acid added, the affinity is sufficient to cause the liberation of oxygen. Co 2 (S0 4 ) 3 + H 2 = 2CoS0 4 + H 2 S0 4 + O ; or 2Co + 20H' = 2Co + H 2 + O. Consider a cell made up of a hydrogen electrode on one side and a platinized electrode dipping in a solution of a ferrous and ferric salt on the other, connected up with some indifferent electrolyte. When these electrodes are joined together, the current goes from the hydrogen electrode to the other in the cell. Hence the hydrogen is going into solution i.e., acquir- ing a positive charge hence at the other electrode the ion is losing corresponding charge. The total change will be i.e., the ion is reduced. When the cell is reversed, Fe will be converted in Fe * * *, and hydrogen will be liberated. If, on the other hand, the platinum electrode dips into a solution of stannous chloride in potassium hydroxide, and connected with a hydrogen electrode so as to form a cell, the current passes from the solution to the hydrogen electrode in the cell i.e., hydrogen ions are discharged, and the stannous ion acquires two positive charges, becoming stannic. In the first case the solution is said to have an oxidation potential, and in the second case a reduction potential. Measurement of Oxidation Potentials : Experimental Determina- tion of Electrode Potential of Ferric-Ferrous Salt Electrode Both oxidation and reduction potentials are measured in a precisely 136 MEASUREMENTS OF ELECTROMOTIVE FORCE similar manner as that used for the measurement of single potential differences between metals and salt solutions. Prepare a solution containing 0-09 gram molecule FeCl 3 -i-0-01 gram molecule FeCl 2 per litre. Prepare also a platinized platinum electrode as directed for hydrogen electrode. Fit up an electrode similar to the metal salt solution electrode previously described i.e., platinum elec- trode immersed in the iron salt solution. Complete the cell by combining it with a normal hydrogen electrode H 2 | wKCl by means of an electrolyte such as normal KC1. The E.M.F. of this cell is then determined in exactly the same manner as in previous experiments (see Fig. 62). Then, taking the hydrogen electrode potential as 0'277 volt, the oxidation potential can be determined. The result should be about 0-43 volt. Further experiments may be done in a similar manner with the following oxidation media : 0-01 Mol FeCl 3 0-09 Mol FeCl 2 ... 0-32 volt. 0-1 normal HMn0 4 1 '18 volts HN0 3 , 6 per cent 0-67 volt HN0 3 , 35 per cent 075 HN0 3 , 90 per cent 0'82 Measurement of Reduction Potentials These measurements are carried out in precisely the same manner as in the above experiments. Experiments Measure the reduction potentials with the following media : Normal Cu 2 Cl 2 in concentrated HC1 ; SnCl 2 in 5nHCl. CHAPTER XVI VELOCITY OF CHEMICAL REACTION ALL chemical reactions require time for their accomplishment. The actual velocity of the reaction is governed mainly by Guldberg and Waage's law of mass action, according to which the velocity of reaction at any moment is proportional to the concentrations of the substances taking part in the reaction. Consider a simple reversible reaction, such as ester formation, in which a, b, c, d are the initial equivalent concentrations of the reacting substances. Let x be the amount of ester formed in the time t, the equation for the velocity of reaction at any instant will be ^ = K(a - x) (b - x) - K,(c + x) (d + x), where dx is the increase in the amount of x during the small interval of time, dt. In many cases it will happen that the reaction is reversible only to a very slight extent, and K t becomes negligible in comparison with K. When such is the case, the equation simplifies down to The simplest type of chemical reaction is that in which only one substance is undergoing change, and there is practically no back reaction. A reaction in which only one molecule of a single substance is undergoing change* is termed unimolecular reaction, or a reaction of the first order. Unimolecular Reactions In cases where the reaction is unimolecular, the equation becomes 137 138 VELOCITY OF CHEMICAL REACTION which on integration gives 2-302 j-log^-log^a *)J_ Hydrolysis of Methyl Acetate in Presence of Hydrochloric Acid When methyl acetate is acted upon by water, it is par- tially converted into methyl alcohol and acetic acid. When the amount of water is relatively large, the hydrolysis is practi- cally complete that is to say, the following equation goes from left to right CH 3 COOCH 3 + H 2 < > CH 3 COOH + CH 3 OH. The rate of hydrolysis is greatly accelerated by the presence of acids, and is, in fact, proportional to the concentration of the hydrogen ion. Experiment Prepare a standard solution baryta, approxi- M mately , and determine its actual value by titration against 20 pure succinic acid, using phenolphthalein as an indicator. Make up also a semi-normal solution of hydrochloric acid, standardizing it by means of baryta solution (the water used should be free from C0 2 ). Clean two small Erlenmeyer flasks with steam, and dry them. Fit them with corks which have been previously soaked in paraffin. It is also necessary to weight the flasks with a ring of lead, in order to make them sink to a convenient depth in the water of the thermostat. Two other Erlenmeyer flasks, about 100 c.c. capacity, fitted with corks, will be required in which to carry out the titra- tions; also three pipettes, one delivering 20 c.c. and two delivering 2 c.c., also a small stoppered bottle containing pure methyl acetate. Into one of the small Erlenmeyer flasks introduce 20 c.c. of HC1, and into the other 40 c.c. of 6 HC1. Suspend the flasks in a thermostat at 25, so that z they are immersed up to the neck, also suspend the bottle containing the methyl acetate in the thermostat. When the liquids have assumed the temperature of the bath (i.e., about fifteen minutes), introduce 2 c.c. of methyl HYDROLYSIS OF METHYL ACETATE 139 acetate into one of the flasks of acid, shake well, and at once remove 2 c.c. of the mixture. This is run into about 50 c.c. of ice-cold water, free from CO 2 , in order to arrest the reaction, it is then titrated as quickly as possible with baryta solution. The moment when the mixture was diluted must be noted. In this way the initial concentration of the acid is determined. Now introduce 2 c.c. of methyl acetate into the other flask of acid, and find the concentration of the acid in this case exactly as before, taking care to note the time when the reaction is arrested. About ten minutes after the first titration, again withdraw 2 c.c. of the mixture from each of the flasks, and determine, as before, the concentration of the acid, noting carefully in each case the moment when the reaction is arrested. Go through the same procedure after intervals of 20, 30, 40, 60, 120 minutes from the starting-point, and then, after forty-eight hours, carry out the final titration. Now, if the initial titration is To, and the final titration Toe, then a is proportional to Too To, anda x is proportional to T X -T H , where T H is the titration after n minutes ; hence we get K = 2-302 Thus to calculate K it is not necessary to calculate the actual amount of ester hydrolyzed, but the value of K can be obtained directly from the titration readings. The velocity constant can be calculated from any stage in the reaction. For example, if T x and T tJ are the titrations at the times t x and t tj , then we have K= 2-302 The above experiment should now be repeated, using semi- normal H 2 S0 4 . Assuming that the velocity constants are directly propor- tional to the degree of ionization of the respective acids, calcu- late the degree of ionization of H 2 S0 4 in semi-normal solution given The value of a for ^ H. 2 S0 4 is 0-53. 140 VELOCITY OF CHEMICAL REACTION Exercise Plot the values of x against the corresponding values of time, and draw a smooth curve. Velocity of Inversion of Cane Sugar Another very interest- ing reaction of the first order is the hydrolysis of cane sugar into dextrose and laevulose. This is represented by the equation C 12 H 2a O n + H 2 = C 6 H 12 6 + C 6 H 12 6 . As the acid which accelerates the hydrolysis remains un- altered at the end of the reaction, it does not occur in the equation. The reaction can be conveniently followed by measuring the change in the rotation of the plane of polarized light. Whereas cane sugar is dextro-rotary, invert sugar is laevo-rotary, so that the result of inversion is that the sign of rotation changes from right to left. As both sugar and water take part in the reaction, the velocity equation, according to the law of mass action, is dx dt -T7=K.C,sugar -C Water- Since, however, the water is present in great excess, its con- centration, and therefore its active mass, remain practically constant throughout the reaction, and the equation therefore reduces to one of the first order. The amount of cane sugar present at any time is propor- tional to the difference between the angle of rotation at that time and the angle of rotation at the end of the reaction. If A represents the initial angle, and Aoo the final angle of rotation after complete inversion has occurred, and A n the angle of rotation after time t n , then the initial amount of cane sugar will be proportional to A -Aoo i.e., total change in rotation and A n A^ the amount of cane sugar present after time tn i.e. & = A AOO and (a x) = A n AC*. .-. K = 2-302 If K is calculated for any two readings, say t x t y , the equa- tion becomes K = o. 30 o -^00)- log )"] J VELOCITY OF INVERSION OF CANE SUGAR 141 The values of the angles must be given their correct sign, rotations to the right being + , and those to the left - . Experiment Prepare a solution of cane sugar by dissolving 20 grams of pure cane sugar in water, and making the volume up to 100 c.c. If the solution is not clear, filter and add a crystal of camphor as a preservative. Prepare also a normal solution of hydrochloric acid. Place 30 c.c. of the sugar solution and 30 c.c. of HC1 solu- tion in separate flasks, which have been thoroughly cleaned and dried, and suspend the flasks in a thermostat at 25 C. Set up a polarimeter, and place a clean, jacketed, observation tube in the polarimeter. Circulate water at 25 C. between the jacket and the observation tube (see Fig. 36), and deter- mine the zero (see Polarimeter Measurements). Mix the acid and sugar solutions thoroughly, and, as soon as possible, fill the observation tube with the mixture, and determine the angle of rotation. Note the time at which the reading is made. The angle of rotation changes rather rapidly at first, so take five or six readings in succession, and note the time for the first and last of these readings. The mean value of the angles should be taken as A at the time, halfway between the first and last reading being taken as the starting-point of the reaction. Take subsequent readings after 10, 20, 40, 60, 120 minutes, and a final reading after forty-eight hours, the tube being kept during this latter period in a thermostat. Calculate the value of K from the equation given. The value for a 20 per cent, sugar solution, with equal volume of normal HQ at 25, is 0*00472. The experiment should be repeated with normal H 2 SO 4 . Note The value of zero should be redetermined at the end of the experiment, in order to see that it has been constant during the experiment. Bimolecular Reactions When two substances react and both alter in concentration, the reaction is said to be bimolec- ular or of the second order. If the initial molecular concentra- tion of one substance is a, that of the other b, and x the amount transformed in the time t, the velocity equation is ~ = K(a-x)(b-x). 142 VELOCITY OF CHEMICAL REACTION When the substances are present in equivalent quantities, the equation becomes which on integration gives K l x JV = - r - v. t a(a - x) When the reacting substances are not present in equivalent proportions, the calculation is somewhat more complicated on integrating dX IT-/ v ,7 x -^ = K(a-x)(b-x) we get (a-b)t' 2-302 ^ g (a -ft)/ l (&-) Experiment: Saponification of Ethyl Acetate with Sodium Hydroxide In this case the velocity of saponification is approximately proportional to the concentration of OH' ions CH 3 COOC 2 H 5 + OH' = CH 3 COO' + C 2 H 5 OH. This reaction differs from the hydrolysis by acids, where the concentration of H ion remains unchanged ; in this case the concentration of the OH' ion changes throughout the experiment. 7? Make up - - solution of ethyl acetate. Place 50 c.c. in an Erlenmeyer flask (100 c.c.), fitted with a paraffin cork, and suspend in a thermostat at 25. Into a similar flask intro- N duce 50 c.c. of -- NaOH (free from carbonate), and suspend this also in the thermostat. When these two solutions have acquired the temperature of the thermostat, pour the alkali into the ester, and shake the mixture well. The initial alkali concentration is calculated from the amount of alkali added, after correcting for the amount of alkali which has remained on the sides of the flask; the latter is found by titration. BIMOLECULAR REACTIONS 143 After intervals of 3, 5, 10, 20, 30, 60, 90 minutes, 5 c.c. of the mixiure is withdrawn and run into a known volume of ^r HC1. The excess of acid is found by titration with baryta. The mean point of the time taken to introduce the 5 c.c. mix- ture into the acid is taken as time at which the reaction was stopped. The final titration should be taken after twenty- four hours. K can then be calculated from the following equation K = T?J P g 10 Te + loglo(T " Too) ~ log loT ' log lo(Tf " T * )]) where TO, T,, T^ are the numbers of cubic centimetres of acid required to neutralize the amount of alkali in the mixture at the beginning of the reaction, after the interval of time, t, and at the end of the reaction respectively. The actual value of K obtained depends on the normality of the solutions when it is calculated in the manner indicated above, but the value which would be obtained with normal solutions can be calcu- Y lated by multipling the above expression by ^., where V is the number of cubic centimetres removed for each titration, and N the normality of the standard acid ; in this case 5 and ^ respectively. Determination of the Order of a Reaction Velocity measure- ments are made with definite concentrations of the reacting substances, and with double and treble those concentrations, determining in each case the times taken to complete a definite fraction (say one-third) of the total change. Then, according to Ostwald, the order of reaction can be determined as follows : 1. For a reaction of the first order, the time taken to com- plete a certain fraction of the reaction is independent of the initial concentration. 2. For a reaction of the second order, the time taken to complete a definite fraction of the reaction is inversely propor- tional to the initial concentration i.e., if the concentration is doubled, the time is halved to complete the same fraction of the reaction. 3. Generally speaking, for a reaction of the wth order, the times taken to complete a certain fraction of the reaction are inversely proportional to the (n 1) power of the initial concentration. CHAPTER XVII QUANTITATIVE ELECTROLYTIC ESTIMATIONS Quantitative Electrochemical Analysis. Electrolytic Deter- mination of Metals There are many advantages in favour of electrolytic methods, where available, over the usual gravimetric method. The latter are frequently very laborious, and at the same time the chances of error are not by any means small. The electrolytic methods, on the other hand, are usually very much simpler, quicker, and determination can be made with a very high degree of accuracy, hence electrolytic methods are coming more and more into use, particularly in the commercial world. The metals are usually estimated in the form of the pure metal or in the form of a metallic oxide. In order to make a successful determination it is essential that the metal should be obtained as a very fine deposit firmly adhered to the cathode, and as smooth as possible, so that it can be well washed without any marked loss. If, on the other hand, the deposit is coarse or granular, it is very liable to be lost in the washing of the deposit, and at the same time is liable to be impure. In order to obtain a successful deposit the potential difference, temperature, and current density must be carefully controlled. Apparatus The most suitable form of apparatus is as shown in Fig. 68. A light platinum dish, A, serves as the cathode, and is supported on a suitable stand by means of a metal ring. The anode B is usually of the form of a flat spiral of platinum, or in some cases a flat perforated platinum plate welded to a platinum wire, the object of the perforations being to allow the escape of gas which would otherwise collect under the plate. The other connections are as shown in Fig. 67. The current and voltage are noted by means of an ammeter, M, and voltmeter, V, respectively, the voltmeter being placed between 144 ELECTROLYTIC DETERMINATION OF METALS 145 the anode and cathode. Another simpler form of apparatus is as shown in Fig. 69, the hollow platinum cylinder being used instead of a platinum dish, and the apparatus being placed in a beaker. In all experiments it is necessary to know the cut-rent density at the electrodes. In the case of metallic depositions the current density at the cathode only is required. The current density is usually expressed in amperes per square centi- metres, or amperes per 100 square cms. Hence the surface of the electrode used must be calculated. This may be done once for all for a given volume of liquid in the basin. FIG. 68 FIG. 69 Experiment : Electrolytic Determination of Copper Weigh out accurately 1 gram of CuSO 4 5H 2 and dissolve in a little water (distilled) ; transfer to the platinum basin, adding the washings, and make up to a suitable volume, then add 3 per cent, by volume of nitric acid. Heat the solution to about 50 to 60 C., and keep the temperature approximately constant by placing a small flame under the basin. Pass a current of E.M.F. 2'2 to 2'5 volts and a current density 0'5 to 2*5 am- peres per 100 square cms. The nitric acid becomes gradually weaker during electrolysis, so from time to time a few more drops should be added. The dish should be covered with a 10 146 QUANTITATIVE ELECTROLYTIC ESTIMATIONS clock-glass, which has a hole in the centre for the anode wire to pass through. To test whether the copper has been com- pletely deposited, add a few cubic centimetres of distilled water, thereby raising the level of the liquid in the basin, and note whether any copper is deposited on the fresh surface. The solution is tested finally by removing a drop of the liquid by means of a glass rod, and touching a drop of ammonia solution on a white tile. If the deposition is incom- plete, a blue colour will result. When the whole of the copper has been deposited it is essential to remove the liquid before the current is stopped, otherwise the nitric acid will redissolve some of the copper. First dilute the solution with distilled water, then syphon off the liquid by first filling a bent glass tube with water, closing one end with the finger, and then putting the other end of the tube below the surface of the liquid in the basin, then, on removing the finger, the liquid will siphon over. As the liquid is removed from the basin the distilled water must be added so as to keep the electrodes wholly immersed. This is done until the acid is too dilute to affect the copper. The current is stopped, the basin removed, and the deposit washed once or twice with distilled water and then with alcohol, and finally dried in an air oven at 80. The basin + deposit is then weighed, and then, by subtracting the weight of the basin, the amount of copper can be estimated. Note the deposit should be perfectly smooth and uniform. Technical Application of the Above Method A solution con- taining copper and metals of the iron group can be analyzed quantitatively for copper by the above method, since the iron group metals remain dissolved in the nitric acid. Commercial copper and many copper ores frequently contain as impurity arsenic and antimony ; on electrolysis some of the arsenic and antimony are deposited also, giving a brownish colour to the copper. In this case the deposit is dried and weighed as before, and then ignited over a bunsen flame. The arsenic and antimony volatilize, leaving the copper as copper oxide. This is dissolved in dilute nitric acid, and the copper once more deposited, washed, dried, and weighed as before. The difference in the last two weighings gives the amount of arsenic and antimony which had been deposited. The above method is frequently used to estimate copper, in simple commercial alloys such as copper-aluminium, etc. ELECTROLYTIC DETERMINATION OF METALS 147 Electrolytic Estimation of Lead In this case the lead is not estimated as metallic lead, but in the form of peroxide. The deposit is formed at the anode, so in this experiment the basin is made the anode. If possible, a basin with an unpolished surface is preferable, as the deposit is not as fine as in the case of copper, and the rough surface assists the adherence of the deposit. Experiment Weigh out into the basin about 1 gram of, say, lead nitrate, dissolve in distilled water, add nitric acid until the solution contains 10 per cent, of free nitric acid. Keep the liquid at a temperature of about 55, and electrolyze with a current of E.M.F. 2-3 to 2-7 volts and current density of 1 to 2 amperes per 100 sq. cms. Test the end-point first by raising the level of the liquid in the basin, and finally by removing a drop on a watch-glass and adding ammonia and ammonium sulphide. Siphon off the liquid as before. Then carefully wash the hydrated oxide deposit with dis- tilled water, and dry at 185 in an air oven until the weight is constant. From the weight of peroxide calculate the amount of lead. The estimation usually requires one and a half hours. To clean the anode add hot dilute nitric acid and a few crystals of oxalic acid. Electrolytic Estimation of Nickel In this case the basin will be the cathode. Dissolve 1*5 grams of nickel ammonium sulphate and 4 grams of ammonium oxalate in water (120 c.c.). Electrolyze with a current density of 1 ampere per 100 sq. cms. and E.M.F 2-5 to 3-5 volts. Other details as for copper. Theoretical Explanation of Electrolytic Depositions We have already seen that the potential between a metal and its salt is given by the equation Q.Q5g p E- log,.-, where P is the solution pressure of the metal, and p is the osmotic pressure of the metallic ions in the solution. Now, the potential difference between a metal and its ions may be considered as a sort of affinity of the metal for a certain charge either positive or negative, hence to convert metallic ions into free metal we have only to apply a contrary E.M.F. slightly higher than the potential difference. In this case it is termed the decomposition potential, and its value is given by the equation- 148 QUANTITATIVE ELECTROLYTIC ESTIMATIONS The value of E will, however, be slowly changed as the metal is deposited, since the value of p is changing ; but even if the concentration be diminished 10000 times, the change in the decomposition is only 4 x 0'058 = - 232 volt for a mono- valent element, and half this for a divalent element, which is comparatively small. Suppose, then, we have a solution of two metals whose decomposition potentials are not too near the same value, then it is possible to separate the metals by carefully adjusting the potential difference applied to the solution. Example Experiment : Determination of Silver and Copper in an Alloy of the Two Metals Dissolve 0-5 gram of the alloy, 2 c.c. of nitric acid (1:3) diluted with water ; make up to 150 c.c. Add 5 c.c. of absolute alcohol, and raise the temperature to 55 C. The alcohol and the temperature prevent the formation of silver peroxide at the anode. Electrolyze the solution with a current of E.M.F. 1'360'1 volt and current density 0*5 to 1 '5 amperes per 100 sq. cms. Great care must be taken to keep the voltage constant. When the electrolysis is complete, quickly decant off the solution into a beaker, wash the silver with a little water, add washings to solution, wash with alcohol, and dry at 80, and weigh. Clean the basin and completely transfer the solution into it, and determine the copper under the con- ditions for copper i.e., increase the potential to 2'2 to 2'5 volts. Quantitative Estimation of Nitric Acid (or Nitrates) by Electrolytic Reduction to Ammonia Nitric acid or nitrates in the presence of sulphuric acid is reduced at the cathode during electrolysis. The product of reduction depends on the nature of the metal at the electrode. If platinum is used, no ammonia is evolved ; but if a little copper salt is added, copper is deposited on the cathode, reduction at once com- mences, and the greater portion of the nitrate is transformed in ammonium salt. The ionic equation is K0 8 ' + 8H- = NH 3 + OH' + 2H 2 O. Under ordinary conditions a certain amount of hydroxylamine is always formed. N(y + 6H- - NH a OH + OH' + H 2 0. The relative proportions of ammonia and hydroxylamine ESTIMATION OF NITRATES 149 depend on the physical nature of the electrode. For example, according to Tafel, if a smooth copper electrode is used, 11-5 parts of hydroxylamine to 76 -8 parts of ammonia are formed, whereas if the electrode is coated with electro-deposited copper, 1 part of hydroxylamine to 92 '3 parts of ammonia results. The problem is to reduce the production of hydroxylamine to a negligible amount. A small amount of hydroxylamine is counter-balanced by solution of a small amount of copper from the electrode in the sulphuric acid. Ulsch has succeeded in obtaining conditions under which nitrates can be estimated to within O'l per cent. Apparatus Prepare a copper cathode. By winding about 2 metres of copper wire 1*4 mm. diameter round a glass tube, 15 mm. diameter, so as to give about forty rounds, are formed. About 15 cms. of wire are left over and bent so as to lie along the axis of the spiral cylinder. Remove the glass tube and draw out the spiral so that each turn is just separated from the next, the total length of the spiral being about 70 mm. Make an anode of thin platinum wire, sup- porting it on a glass tube ; this passes down the centre of the copper spiral (see Fig. 70). The liquid to be electrolyzed is contained in a test-tube-like tube, 2 cms. diameter, cms. long, the two electrodes being held in position by means of a cork, which must be fitted with ^ IG - ? an outlet for the gases evolved during electrolysis. Prepare the copper electrode by coating it with spongy copper in a copper voltameter (see p. 122), using current density of about 3 amperes per 100 sq. cms. Experiment : Determine the Amount of Nitrate in a Sample of Potassium Nitrate Dissolve 0'5 of a gram of potassium nitrate in a little water, and add exactly 50 c.c. of normal sulphuric acid. Make up to 100 c.c. with water. Take 20 c.c. of this solution and transfer it to the glass cell and fit the electrodes in position (they should go right to the bottom). If the spiral is not covered, add a little water. Now electrolyze the solu- tion, using an E.M.F. of 4 volts and a current density of 2 '5 to 3 amperes per 100 sq. cms. The current density should not be above this, otherwise the amount of hydroxylamine 150 QUANTITATIVE ELECTROLYTIC ESTIMATIONS becomes appreciable. No gas will be evolved at first, since reduction is taking place ; but when the reduction is nearing completion, hydrogen is evolved quite freely. When this occurs, continue the electrolysis for a further period of fifteen minutes, to be sure of complete reduction. Remove the elec- trode carefully before breaking the current ; wash then with distilled water, and keep the washing in a beaker. Then transfer the contents of the tube to the beaker containing the washings, and wash out the tube. Then titrate the unused acid with standard alkali. The equation for the reaction is 2KN0 3 + 2H 2 S0 4 + 8H 2 = K 2 S0 4 + (NH 4 ) 2 S0 4 + 6H 2 i.e., two equivalents of acid for one equivalent of nitrate. From the amount of acid used (in this case 50 c.c. normal acid) the amount of nitrate can be calculated. With careful manipula- tion not more than 0-1 to O2 per cent, error should be allowed. CHAPTER XVIII ELECTROLYTIC PREPARATIONS Reduction of Aromatic Nitre-Compounds The final pro- duct in the reduction of aromatic nitre-compounds is the amine, but it is possible to obtain a large number of inter- mediate products, corresponding to the various stages of reduction, by carefully controlling the conditions of the re- action. The whole process is usually a combination of electro- chemical reductions and purely chemical reactions. As an example we will consider nitrobenzene. The following diagram represents all the important changes in the reduction of nitrobenzene : C 6 H 5 N0 2 i /o\ j *C 6 H 5 C 6 H 5 X-NC 6 H* C.HLNHOH - NHC 6 H 5 64 OH (1) ^NH 2 (4) Reduction in Moderately Acid Solutions The following series of products are formed in which the last is the principal final product : ( 1) C 6 H 5 N0 2 + H 2 = H 2 + C 6 H 5 NO. (2) C fi H 5 NO>H 2 = C 6 H 5 NHOH. (3) C 6 H 5 NHOH + H 2 = C 6 H 5 NH 2 + H 2 0. Reductions in Strongly Acid Solutions In this case the reduction stops at the end of equation (2) above i.e., the principal reduction product being C 6 H 5 NHOH. 151 152 ELECTROLYTIC PREPARATIONS Under the influence of the strong acid the phenyl-hydroxy- lamine is converted into the isomeric para-amido phenol NH 2 Reduction in Alkaline Solution In this case the equations (1) and (2) are fulfilled, and these combine as follows : /o\ (4) C 6 H 6 NHOH + C 6 H 5 NO = C 6 H 6 N - NC 6 H 5 + H 2 0. /0\ (5) C 6 H 6 N - NC 6 H 5 + 2H 2 = C 6 H 5 NH - NHC 6 H 5 + H 2 0. /\ 3C 6 H 5 NH - NHC 6 H 5 + 2C 6 H 5 N0 2 = C 6 H 5 N - NC 6 H 5 + (6) Hence azo-benzene is the principal final product. The re- duction of hydrazo-benzene to aniline only takes place to a slight extent. Preparation of Aniline from Nitrobenzene Take a tall beaker and place inside a porous pot to serve as the anode chamber, the cathode chamber being the space between the porous pot and the walls of the beaker. The anode consists of strips of sheet lead (about 2 to 3 mm. thick), the cathode is also of sheet lead, but it should be perforated. The cathode is bent in the form of a cylinder so as to encircle the porous pot. Introduce into the anode chamber dilute sulphuric acid of specific gravity ri. For the cathode liquor make a mixture of 20 grams of nitrobenzene, 150 c.c. of alcohol, and 125 c.c. of dilute sulphuric acid, specific gravity 1*2. Electrolyze the solution with a current of density 4 to 8 amperes per 100 sq. cms. at the cathode, and voltage about 5 volts. After the passage of about 26 ampere hours, remove a little of the cathode liquid and titrate with sodium nitrite. If the result indicates about 85 to 89 per cent, of the theoretical quantity of aniline, remove the cathode liquid, distil off the alcohol, cool, and about 20 grams of aniline sulphate should crystallize out. The crystals may be decomposed with caustic soda, and the mixture steam distilled. The o.m.p. toluidines can be similarly prepared, but in the PREPARATION OF AZOBENZENE 153 case of the reduction of ^-nitrotoluene the percentage is lower. Preparation of Azobenzene from Nitrobenzene In this case nickel electrodes are used, otherwise the apparatus is as before. The anode liquid is a cold saturated solution of sodium carbonate, and is contained in the porous cell. The cathode liquid consists of 20 grams of nitrobenzene, 5 grams of crystallized sodium acetate dissolved in 200 c.c. of 70 per cent, alcohol. The cathode density should be 6 to 9 amperes. The electrolysis is carried out at boiling-point, and almost immediately after the theoretical amount of current has been passed (17*5 ampere hours), a considerable amount of hydrogen begins to come off; at this point lower the current density and pass 1 to 2 ampere hours' more current. The contents of the cathode are now free from nitrobenzene, but contains a small amount of hydrazobenzene and azoxybenzene. The bulk of the azobenzene crystallize out almost chemically pure, and may be filtered off on a Buchner funnel. The re- mainder is precipitated by the addition of water or distilled off in steam, and purified by re-crystallization from alcohol or ether. The current efficiency is over 80 per cent., and the yield is over 90 per cent, of the theoretical amount. Preparation of lodofonn When free iodine is warmed with water and an aqueous alkaline solution of alcohol, iodoform is formed according to the following equation : CH 3 CH 2 OH + 10I 2 + H 2 = CHI 3 + C0 2 + 7HI. The hydriodic acid then reacts with the alkali to form iodide. Iodoform is prepared electrolytically by electrolyzing a solu- tion containing potassium iodide, sodium carbonate, and ethyl alcohol. Free iodine is liberated at the anode, which reacts with the alcohol yielding iodoform. The purely chemical method only gives a yield of about 40 per cent., whereas the electrolytic method gives as much as 98 per cent, yield. The anode consists of a large sheet of platinum (or wire gauze), the cathode, which is relatively small, is made of nickel or platinum foil wrapped in parchment. The anode liquid consists of a solution of 20 grams of anhydrous sodium carbonate, 20 grams of potassium iodide, 200 c.c. of water, and 50 c.c. of alcohol (96 per cent.). This solution is poured into the porous cell ; the cathode liquor is a solution of sodium carbonate. The 154 ELECTROLYTIC PREPARATIONS experiment is carried out at 50 to 70, with a current density at the anode of 1 to 3 amperes per 100 sq. cms., and a cathode current density of 4 to 8 amperes per 100 sq. cms. During electrolysis the solution tends to become alkaline, so a slow stream of carbon dioxide must be bubbled through the cathode liquid so as to neutralize the caustic soda formed. The solution should be from light to dark yellow ; if it becomes brown, interrupt the current of carbon dioxide for a short time. The electrolysis should be allowed to continue for about three hours in order to get a fair quantity of iodoform. Then on cooling the iodoform separates out, and is filtered off, washed with water, and dried at room temperature. The filtrate, after the addition of fresh quantities of potassium iodide and alcohol, may be used over again, until it contains large quantities of potassium iodate and carbonate. The cur- rent efficiency is 80 per cent. The equation given above represents the formation of iodoform, neglecting the inter- mediate products and secondary reactions. The hydriodic acid reacts with the sodium carbonate to give sodium iodide and carbonic acid. The sodium iodide is continually decom- posed by the current, thereby making fresh quantities of iodine available at the anode. The iodine produced at the anode, coming in contact with free alkali or alkali carbonate from the cathode, forms hypoiodite, both as alkali salt and as free acid ; this reacts with the alcohol by simultaneous oxida- tion and iodizing, to produce iodoform and carbonic acid. The chief by-product is alkali iodate, which is produced from that portion of the iodide which does not immediately react with the alcohol. (1) 2HI + Na 2 C0 3 =2NaI (2) 2NaI + 2H 2 = 2NaO (3) I 2 + 2NaOH = NaI + NaIO + H 2 O. (4) M alO + ILO^ r> NaOH + HIO. (5) 5HIO + C 2 H 5 OH = C0 2 + CHL + 2HI + 4H 2 0. (6) 3HIO=2HI + HI0 3 . (7) It is not possible to prepare the corresponding bromoform and chloroform by a similar method, as aldehydes and other products of oxydation of alcohol are given on electrolysis. This is due to the fact that the decomposition potential of PREPARATION OF AMMONIUM PERSULPHATE 155 iodine from potassium iodide and soda solution is only 1*12 (normal hydrogen electrode as zero), whilst oxygen is liberated at 1-7. With potassium bromide alcohol and sodium car- bonate, bromide separates at T75 volts ; with potassium chloride chlorine at 2-1 volts. Preparation of Ammonium Persulphate from Ammonium Sulphate A porous pot of capacity 100 to 150 c.c. serves as the anode chamber. This is surrounded by a lead spiral, through which cold water can be circulated. A piece of copper connecting wire is soldered on to the lead spiral which forms the cathode. The anode is platinum wire spiral, having a surface of 1 to 2 sq. cms. Fill the anode chamber with a cold saturated solution of ammonium sulphate, the space between the porous pot and the containing beaker i.e., cathode chamber being filled with a mixture of 1 part con- centrated sulphuric acid and 1 part of water, by volume. The temperature of the anode chamber should be kept between 10 and 20 by circulating iced water through the lead cathode spiral. The anode liquid is kept saturated with ammonium sulphate by suspending in the anode chamber a test-tube, with one or more holes at the bottom, containing solid ammonium sulphate. Pass a current having density of 500 to 1000 amperes per 100 square centimetres at the anode, and a current density as low as possible at the cathode, thereby saving the voltage, and excessive evolution of heat. The electrode in the anode chamber should dip only half-way into the liquid. After about four hours stop the electrolysis and filter the liquid in the porous pot. The crystals thus obtained are dried on a porous plate. The filtrate is then re- saturated with ammonium sulphate, returned to the porous pot, and the electrolysis recommenced. The liquid in the cathode gradually becomes neutralized owing to the migration of the sulphuric acid anions out of it and the ammonium ions into it. Hence from time to time the acid must be replaced. The anode liquid becomes poorer in ammonia, and accumulates free acid. Hence after every two operations ammonia should be added to the anode liquid (gradually to prevent heating) until the acid is almost neutralized. At the first operation the separation of persulphate is small, since the solution has first to become saturated in respect to persulphate. In later operations the deposit commences almost immediately, and a good yield results. The current efficiency is 70 per cent., and 156 ELECTROLYTIC PREPARATIONS the yield 60 per cent. It is essential that the anode should be washed with water and heated to glowing before each experi- ment. The raw product contains about 5 per cent, ammonium sulphate. A pure specimen can be obtained (with considerable loss) by making quickly a saturated solution of the crude salt with water at 50 C., and then cooled slowly to a low tempera- ture. Ammonium persulphate is only stable when perfectly dry. The purity of the sample may be tested by pouring a solution (freshly made up) into a strongly acid solution of ferrous ammonium sulphate and titra- ting the excess of ferrous salt with potassium permanganate. It must be remembered that the oxidation by persulphate takes several minutes to accomplish completely. In the pre- paration of persulphates, hydrogen peroxide and its derivatives are also formed in the anode chamber; these can be determined directly by perman- ganate. Hence, to follow the course of electrolysis, take a sample of the anode liquid titrate with permanganate, then add excess of acid ferrous am- monium sulphate. The first titration gives the peroxide content, and the second the persulphate content. Potassium persulphate may be similarly prepared, but the method is not quite satisfactory. In small quantity potassium persulphate can be easily prepared by the apparatus indicated in Fig. 71. A wide boiling-tube, P, contains a saturated solution of potassium sulphate in sulphuric acid, of specific gravity 1-2 to 1-3. The anode, A, consists of a platinum wire, a large portion of which is surrounded by a glass tube, into which the platinum is sealed. The wire (which must be ignited before use) passes almost to the bottom of the boiling-tube. A wider tube, R, surrounds the anode to carry away the oxygen liberated at the anode, without stirring up the liquid, which would prevent concentration at the anode. The cathode consists of a plati- num loop, (7, which passes outside to the tube R. The contents of the tube are kept cool by immersing the whole apparatus in a large beaker of cold water use a current density of FIG-. 71 PREPARATION OF AMMONIUM PERSULPHATE 157 100 amperes per 100 sq. cms. at the anode, utilizing a current of 1 to 2 amperes. A thick deposit of potassium persulphate will form at the bottom of the vessel after ten minutes. The formation of persulphates at the anode is explained by the fact that in concentrated solutions of sulphates, such as, say, ammonium sulphate, there are present HS0 4 anions as well as S0 4 anions, and the greater the concentration arid current density the greater the extent to which they are discharged. The discharged anions may react in two ways /ONH 4 X)NH 4 (1) 2S0 2 < + H 2 = 20 2 S/ +0. X) X)H ONH 4 X)NH 4 NHXX o _ =0 2 S/ o Q >0, High current density favours the second reaction, hence high current densities are necessary for the formation of persul- phates. The above graphic formula agrees with its properties i.e., the persulphates behave as derivatives of hydrogen per- oxide. Upon warming an aqueous solution of the acid, or its salts, oxygen is evolved. X ONH 4 NH 4 V /ONH 4 2 S< >S0 2 = 2S0 2 < +0. X A low temperature is therefore necessary for their prep- ation. aration CHAPTER XIX PREPARATION OF COLLOIDS A LARGE number of substances are capable of apparently dissolving in water to form what may be termed pseudo- solutions. Such pseudo-solutions are characterized by an ex- tremely low diffusive power, a low osmotic pressure, and an inability to undergo dialysis; in these respects they differ from true solutions of crystalloids, and are therefore termed colloidal solutions. Such colloidal solutions are distinguished,, according to the nature of the solvent, as hydrosols for water as a solvent, and alcosols when alcohol is the solvent. If the pseudo-dissolved substance is separated from the solvent, it is often found not to have lost the power of again passing into colloidal solution ; such are termed reversible colloids. On the other hand, many substances, mainly inorganic, when separated from the solution do not possess the power of re- dissolving again except by some special process, such are termed irreversible colloids. Solutions of irreversible colloids can be obtained by Bredig's method, by disintegrating the substance in an electric arc under water, by double decomposi- tion in aqueous solution, preventing precipitation by suitable means, or by previously imparting to the solid the ability to dissolve by treatment with small quantities of acid or alkali. This latter method is known as peptization, and has been employed to bring metallic oxides, etc., into a plastic con- dition for the formation of the so-called colloidal electric lamp filaments. Many irreversible colloids separate out from their solutions as voluminous precipitates, containing a large amount of water ; such are known as hydrogels, such are ferric oxide, aluminium oxide, etc. They contain far more water than is required for their hydrates, and are therefore frequently termed oxide hydrogels. 158 COLLOIDS 159 The change from the hydrosol state to that of the hydrogel can be very easily brought about by the addition of an electrolyte. Many colloidal solutions are exceedingly sensi- tive to electrolytes, hence an essential condition for their preparation is the entire absence of an electrolyte. A very characteristic property of colloids is their power of adsorption. Hence different dissolved colloids can combine together to form adsorption compounds. A gold hydrosol is exceedingly sensitive to electrolytes, but if a non-sensitive colloid, such as gelatine, is added, the gold solution remains stable towards small amounts of electrolyte. This would seem to indicate that some kind of combination had taken place between the two dissolved colloids. Such substances, which act like gelatine, are known as protective colloids. On the other hand, certain colloids have the property of precipitating one another out of solution. Thus arsenic sulphide hydrosol and iron oxide hydrosol, when mixed in the correct proportions, are precipitated as a common adsorption compound. This is due to the fact that colloids carry a charge, and in this case the charges on the respective hydrosols are of opposite sign, hence they neutralize, and precipitation results. It is a rule that two such colloids, in order to precipitate each other, must have charges of opposite sign when referred to a common solvent. The fact that colloids possess a charge explains why they are precipitated by electrolytes. The electrolyte dissociates, giving ions of opposite charges, and that which is opposite in sign to that of the pseudo-dissolved substance is adsorbed, and precipitation results. The passage of a colloidal solution through a narrow glass tube causes the precipitation of the colloid, simply because the charge is given up to the walls of the tube. When a colloidal solution is subjected to an electrical potential, the colloid " wanders " either to the anode or the cathode, according to its charge. Undoubtedly, then, the particles do carry charges, but the charges are small and the motion slow, and the number of moving particles small in comparison with an ordinary electrolyte. It is also uncertain whether the particles are discharged at the poles. Preparation of Colloidal Platinum by Bredig's Method Take two pieces of platinum wire, about 1 mm. diameter and 10 to 15 cms. long, and insulate them by sealing them 160 PREPARATION OF COLLOIDS into a glass tube so that about 3 cms. project. Then connect the other ends of the wire with 110-volt lighting circuit by means of binding screws, these junctions being insulated by " insulating tape," or, better, by a wider glass tube (see Fig. 72). Insert an ammeter and a resistance in the circuit. Take about 150 c.c. of distilled water in a glass dish, arid clamp one electrode so that it dips below the surface of the water. Take the other in the hand and touch the first one, and then remove it a short distance, so as to maintain a small arc under water. A current of 6 to 10 amperes should be used, this being regulated by the resistance. Of course, care must be taken to see that the wiring will take such a current. It is not usually possible to maintain an arc for any length of time, so that when the arc breaks FIG. 72 it must be restarted by bringing the electrodes into con- tact again. This process is repeated until the solution becomes almost opaque or very hot. The solution thus obtained contains a considerable amount of coarse platinum powder. This is removed by filtering the solution. The filtrate then contains colloidal platinum. Test the colloidal solution as follows : 1. Take a few cubic centimetres in a test-tube, and add a drop or two of an electrolyte (say KC1 solution) ; after a time the colloid metal separates out. 2. To a few cubic centimetres of a dilute solution of hydro- gen-peroxide add a few drops of the colloidal solution. Oxygen is evolved, due to the catalytic action of the platinum. Preparation of Colloidal Antimony Sulphide Prepare 100 c.c. of a 1 per cent, solution of tartar emetic, and place COLLOIDAL ANTIMONY SULPHIDE . 161 it in a dropping funnel, and allow it to drop, drop by drop, into 100 c.c. hydrogen sulphide water, through which a moderately rapid stream of hydrogen sulphide is passing. Under these conditions no precipitate of antimony sulphide should be formed, but the antimony sulphide should remain in colloidal suspension as a deep orange-coloured pseudo- solution, which is perfectly clear when seen by transmitted light. The excess of hydrogen sulphide must now be removed by passing through the solution of pure hydrogen. The solution thus obtained is now dialyzed. This may be conveniently done by stretching a sheet of parchment over a wooden hoop, thus forming a sort of tambourine, and floating this in a basin of water (see Fig. 73). The solution is placed inside the drum, and the salts present in solu- tion gradually diffuse through the orange-coloured material remaining on the parchment. Fresh quantities of distilled water are added to the colloid in the drum every three or four hours the first day, and later every twelve hours for four days, after which the colloidal solution FIG. 73 will be free from foreign salts. The orange solution may then be transferred to a clean beaker. Experiments with Colloidal Antimony Sulphide Prepare approximately normal solutions of potassium chloride, barium chloride, and aluminium chloride. Take three separate portions of 10 c.c. each of the colloidal solution, and to each portion add one of the above standard solutions from a burette, and determine the amount of each of the above electrolytes, which will just completely precipitate the anti- mony from the solution. This should be done roughly at firs't, allowing the precipitate to settle after each addition, and noting the effect of the next addition in the supernatant liquid, which should gradually become colourless. The largest amount of electrolyte required will be in case of potassium chloride, and the smallest in the case of aluminium chloride. The precipitating power depending for this class of colloid on the valency of the cation i.e., on its electrical charge. 11 162 PREPARATION OF COLLOIDS Preparation of Colloidal Gold Solution by Donau's Method Dissolve 0-25 gram of crystallized HAuCl^SHgO in 500 c.c. of distilled water. Pass through this solution a slow stream of carbon monoxide, prepared from oxalic acid and strong sulphuric acid, passing the gas first through a solution of potassium hydroxide to remove the carbon dioxide. There is produced first a violet, then a reddish-violet, followed by a deep red coloration. Stop the reaction at this point. Pre- serve the solution for later experiments. Preparation of Colloidal Stannic Oxide To 5 c.c. of tin tetra chloride add 150 c.c. of distilled water, thus hydro- lyzing it. Add this solution to 500 c.c. of distilled water, to which a few drops of ammonia have been added. Dialyze this solution for five days, changing the outside water, about three times a day until it shows no test for chlorides. It is quite probable that the hydrogel may to some extent result. The contents of the dialyzer are transferred to a beaker, and the gel. peptised by the addition of three or four drops of ammonia. After a time the jelly will completely dissappear, leaving a perfectly clear hydrosol. A pseudo-solution of zircon oxide may be similarly pre- pared by dialyzing for five days a 15 per cent, solution of zircon nitrate. The ferric oxide hydrosol may be prepared from dilute ferric chloride similarly. Experiments (1) To 2 c.c. of the colloidal gold solution add 2 c.c. of the stannic oxide hydrosol ; no change occurs. Now add a little ammonium chloride solution ; a beautiful deep reddish purple precipitate is formed, which has the characteristic property of being soluble in ammonia. In this experiment we have synthesized the Purple of Cassius. (2) Take 75 c.c. of a boiling colloidal gold solution and add 15 c.c. of boiling zircon hydrosol solution ; a zircon- gold-purple precipitate results in this case without the addi- tion of an electrolyte. The precipitation takes place slowly in the cold. (3) Take 10 c.c. of the colloidal gold solution and add a few drops of hydrochloric acid ; a blue coloration first results, followed by a deposit of the metal. Take a further 10 c.c. of the gold hydrosol solution and add 1 drop of a 2 per cent, solution of gelatine, and again add a little hydrochloric acid. In this case there is neither change of colour nor a deposit of the metal. Here we have an example of a protective colloid. APPENDIX TABLE OF RELIABLE MELTING AND BOILING- POINTS Liquid Hydrogen ............... _ 253 Liquid Oxygen ... ... ... ... 182 Freezing Mercury ... ... ... _ 390 Melting Ice ... ... ... Boiling-point of Aniline at 760 mm. pressure ... 184 11 ,, Naphthalene ............ 220 ,, Diphenylamine ......... 302 ,i Sulphur ............ 445 Melting-point of Tin ............... 232 ,, Zinc ............... 419 >, Antimony ............ 632 Aluminium ... ... ... ... 657 i) Sodium Chloride ......... 800 Silver (in air) ......... 955 ii ,> Silver (in reducing atmosphere) ... 962 Gold ... ......... 1064 ,, Copper (in air) ......... 1062 Potassium Sulphate.. ...... 1070 ii Copper (in reducing atmosphere) ... 1084 Nickel ............ 1427 >, Pure Iron ............ 1503 ,, Palladium ........... 1545 Platinum ............ 1750 Boiling-point at 760 mm. pressure of Magnesium ... 1120 i ,, Antimony ... 1440 n 5 > Lead ...... 1525 j> ,, Aluminium ... 1800 > Manganese ... 1900 ... Silver 1955 Chromium ... 2200 Tin 2270 Copper ... 2310 Iron 2450 163 164 APPENDIX DENSITY OF WATER Temperature Density Temperature Density 0-99987 21 0-99802 1 0-99993 22 0-99779 2 0-99997 23 0-99756 3 0-99999 24 0-99732 4 1-00000 25 0-99707 5 99999 26 0-99681 6 0-99996 27 0-99654 7 0-99993 28 0-99626 8 0-99988 29 0-99597 9 0-99981 30 0-99567 10 0-99973 31 0-99537 11 0-99963 32 0-99505 l'2 0-99953 33 0-99473 13 099940 34 0-99440 14 0-99927 35 0-99406 15 0-99913 40 0-99224 16 0-99897 50 98807 17 0-99880 60 0-98324 18 0-99862 70 0-97781 19 0-99843 80 97183 20 0-99823 90 0-96534 VAPOUR PRESSURES OF WATER Temperature Vapour Pressures Temperature Vapour Pressures Mm. Mm. 4 6-1 19 16-5 5 6-5 20 17-5 6 7-0 21 18-7 7 7-5 22 19 8 8 8-0 23 21-1 9 8-6 24 22-4 10 9-2 25 23-8 11 9-8 26 25-2 12 105 27 26-7 13 11-2 28 28-4 14 12-0 29 30-1 15 12-8 30 31-8 16 136 31 33-7 17 14-5 32 35-7 18 15-5 33 37-7 APPENDIX 165 VISCOSITY AND SURFACE TENSION OF WATER Tempera- ture Viscosity Surface Tension Tempera- ture Viscosity Surface Tension 10 74-05 35 0-00724 15 73-26 35 7029 15 0-01142 40 69-54 20 72-53 40 0-00657 20 0-01006 45 68-6 25 0-008926 45 0-00600 25 71-78 50 67-8 30 71-03 50 0-005500 30 0-00800 1 PHYSICAL DATA FOR BENZENE Temperature Density Viscosity Surface Tension 0-9006 11-4 28-83 14-8 0007038 20 0-8790 30-8 0-005522 31-2 26-68 40 0-8576 46-9 0-004435 55-1 2353 60 0-8357 68-5 21-70 70 0-8247 78-3 20-51 78-8 ~ 0-003177 ^~" DENSITY OF PURE ALCOHOL Temperature Density Temperature Density 10 20 30 0-7979 0-7894 0-7810 40 50 0-7722 0-7633 16(5 APPENDIX DEGREES OF IONIZATION OF SOME ELECTROLYTES AT 18 Electrolytes N n 10 Electrolytes N n To CuS0 4 0-21 0-38 KI 0-79 0-86 AgNO s 0-58 0-81 KN0 3 063 0-83 ZnS0 4 0-23 0-39 NaCl 0-68 0-84 KC1 076 0-86 HC1 071 0-92 KBr 0-86 EQUIVALENT CONDUCTIVITY OF INFINITE DILUTION Tempera- tures Electrolytes Conduc- tivity Tempera- tures Electrolytes Conduc- tivity 18 NaOl 108-99 18 KCNS 121-30 18 NaNO, 105-33 18 KC10, 11970 18 KC1 130-10 18 AgNOg 115-80 18 KBr 1 132-30 25 Acetic Acid 389 18 oro a 126-50 25 Benzoic Acid 381 DISCHARGE VOLTAGES OF DIFFERENT IONS FROM AQUEOUS SOLUTIONS On reversing the signs, the values represent the solution tendency. (a) Cation discharge points. Cation Volts Cation Volts K' -2-92+* (0-058 log 10 C) Ni" + 0-06 + -(0-058 log , C) Na' --2-52 + , Pb" + 0-16 +, Mg" -1-27 + , Sn" + 0-18 +, Zn" -0-48 + , H' + 0-277+, Fe" -0-15 + , Cu" -f-0-62 + , Cd" -0-12 + , Ag' + 1-08 +, Tl' -0-04 + , Hg" + 1-14 +, CO" -0-01+, Au' + 1*78 +, APPENDIX (b) Anion discharge points. 167 40H'( X> 2 +2H S 0) Br' Cl' -0-28 + ^(0-058 log 10 C) 0-69 + 0-82 + 1-36 + 1-63 + 2-18 + C = Ionic concentration at 25. n = Valency. SPECIFIC HEATS AND ELECTRICAL RESISTANCES AT Specific Heat Specific Resistance Aluminium Iron . . . Copper Nickel Platinum Silver Mercury Glass 0-22 0-11 0-093 0-11 0-032 0-056 0-0332 0*19 0-028xlO- 4 0-99 -0-15x10-* 0-Ol7xlO- 4 0-08 -0-llxlO- 4 0-108-0-11 xlO-4 0-016x10-4 0-958x10-4 1-0 xlO- 15 Graphite Retort carboi i . 0-155 0-165 14-3 xlO- 4 49-0 xlO-* LIQUID PLATINUM Moisten 0-3 gram of platinic chloride with cone. HC1, and mix with 1 c.c. of cone, boric acid solution. Dissolve in alcohol and a Id 1 c.c. of French turpentine, and 2 c.c. of oil of lavender. NERNST LIQUID RESISTANCE The Nernst liquid resistance, suitable for conductivity work, consists of 121 grams of mannite, 41 grams of boric acid and 0-06 gram KC1 in a litre of aqueous solution. K = 0-00097 at 18, and temperature coefficient is exceedingly small. TABLOID PRESS A suitable form of press for making compressed tabloids, as required for combustion experiments, etc., is as shown in Fig. 73. It consists of a mould, M, the two halves being 168 APPENDIX joined by a hinge on one side and secured by a winged nut on the other. The substance of which a tabloid is required is placed in the mould (in the case of hard substances like coal they should be finely powdered) and a plunger inserted. The mould is then placed in the screw press, as indicated in Fig. 74, FIG. 74 and the screw turned as far as possible, thus exerting great pressure on the substance. The pressure is then relieved, and then by undoing the winged nut the mould can be opened and the tabloid removed. In order to make a tabloid successfully, the groove of the mould must be perfectly clean, and kept as smooth as possible. APPENDIX 169 DETERMINATION OF MOLECULAR WEIGHTS BY THE ELEVATION OF BOILING-POINT AND DEPRES- SION OF THE FREEZING-POINTS (BECKMANN'S METHOD) 1. VALUES OF K FOR BOILING-POINT METHOD Solvent Boiling-Poiut K Ether 34-9 2110 Carbon disulphide .. 46-2 2370 Acetone 56-3 1670 Chloroform ... 61-2 3660 Ethyl acetate 74-6 2610 Ethyl alcohol 78'3 1150 Benzene 80'3 2670 Water ... 100-0 520 Acetic acid ... 118-1 2530 2. VALUES OF K FOR FREEZING POINT METHOD Solvent Freezing-Point K Water 18GO Acetic acid ... Benzene 17 5'5 3860 5000 LATENT HEATS Solvent Vaporization Fusion Water . . 535-9 79-1 Acetic acid 43-1 Benzene 92-9 30-1 Ether Acetone 90 125-3 Ethyl alcohol 215-0 170 APPENDIX VALUES OF K (LANDSBERGER'S METHOD) Solvent K Solvent K Alcohol Ether '.. Water 1560 8030 540 Acetone Chloroform Benzene 2220 2600 3280 Note The values of K in Beckmann's Method are for 1 gram of solvent, whereas those for Landsberger's Method are for 1 c.c. of solvent. In the former case the weight of the solvent is known, and the latter case the volume. VALUES OF /t w at 25 C. (SEE CONDUCTIVITY) Acid Moo K=100 * Acetic acid 389 1'8 xlO- 3 Succinic acid Benzoic acid 381 381 6-65xlO- 3 6-0 xlO- 3 Mandelic acid 378 4-17 xlO- 2 DENSITY OF ACETONE Density (15/4) = 07971 APPENDIX 171 INTERNATIONAL ATOMIC WEIGHTS, 1914 Element Symbol Atomic Weight Element Symbol Atomic Weight Aluminium ... Al 27-1 Neon ... Ne 20-2 Antimony Pb 120-2 Nickel Ni 58-68 Argon ... A 39-88 Niobium Nb 93-5 Arsenic As 74-96 Niton Nt . 224-4 Barium Ba 137-37 Nitrogen N 14-01 Beryllium Be 9-1 Osmium Os 190-9 Bismuth Bi 208-0 Oxygen 16-0 Boron ... B 11-0 Palladium Pd 106-7 Bromine Br 79-92 Phosphorus ... P 31-04 Cadmium Cd 112-40 Platinum Ft 195-2 Caesium Cs 132-81 Potassium K 39-10 Calcium Ca 40-07 Praseodymium Pr 140-6 Carbon C 12-0 Radium Ra 226-4 Cerium Ce 140-25 Rhodium Rh 102-9 Chlorine Cl 35*46 Rubidium Rb 88-45 Chromium Cr 52-0 Ruthenium Ru 101-7 Cobalt Co 58-97 Samarium Sa 150-4 Copper Cu 63-57 Scandium Sc 44-1 Dysprosium . . . Dy 162-5 Selenium Se 79-2 Erbium Er 167-7 Silicon Si 28-3 Europium Eu 152-0 Silver Ag 107-88 Fluorine F 19-0 Sodium Na 23-0 Gadolinium ... Gd 157-3 Strontium Sr 87-68 Gallium Ga 69-9 Sulphur S 32-07 Germanium . . . Ge 72-5 Tantalum Ta 181-5 Gold Au 197-2 Tellurium Te 127-5 Helium He 3-99 Terbium Tb 159-2 Holmium Ho 163-5 Thallium Tl 204-0 Hydrogen H 1-008 Thorium Th 232-4 Indium In 114-8 Thulium Tm 168-5 Iodine I 126-92 Tin Sn 119-0 Iron Fe 55-84 Titanium Ti 48-1 Krypton Kr 88-92 Tungsten W 184-0 Lanthanum . . La 139-0 Uranium U 238-5 Lead Pb 207-10 Vanadium V 51-0 Lithium Li 6-94 Xenon ... Xe 130-2 Lutecium Lu 1740 Ytterbium (Neo- Magnesium . . . Mg 24-32 ytterbium) ... Yb 172-0 Manganese ... Mn 54-93 Yttrium Y 89-0 Mercury Hg 200-6 Zinc Zn 65-37 Molybdenum , . . Mo 96-0 Zirconium Zr ' 90-6 Neodymium ... Nd 144-3 172 LOGARITHMS Num- ber 1 2 3 4 5 6 7 8 9 (I 1 2 3 456 789 10 0000 0043 0086 0128 0170 02120253 0294 0334 0374 j 4 8 12 17 21 25 29 33 37 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 4 8 11 15 19 23 26 30 34 12 0792 0828 0864 0899 0934 09691004 1038J1072 1106 3 7 10 14 17 21 24 28 31 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 3 6 10 13 16 19 23 26 29 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 369 12 15 18 21 24 27 15 1761 17901818 1847 1875 19031931 1959 1987 2014 368 11 14 17 20 22 25 16 2041 2068 2095 2122 2148 21752201 2227 2253 2279 358 11 13 1618 21 24 17 2304 2330 2355 2380 2405 2430]2455 2480 2504 2529 257 10 12 15 17 20 22 18 2553 2577|2601 2625 2648 2672 2695 2718 2742 2765 2 5 7 9 12 14 16 19 21 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 247 9 11 1316 18 20 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 246 8 11 13 15 17 19 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 246 8 10 12 14 16 18 22 3424 3444 3464 3483 3502 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17 19 15 17 20 98 9550 9572 9594 9616 638 9661 9683 7059727 9750 2 4 7 9 11 13 16 18 20 99 9772 9795 ! 9817 9840 86398869908 931|9944 9977 2 5 7- 9 11 14 16 18 20 1 2 3 4 5 6 7 8 9 123 456789 INDEX ABNORMAL molecular weight, 33 Affinity constant, 105 Alcohol, density of, 165 Ammonium persulphate, prepara- tion of, 155 Aniline, preparation of, from nitro- benzene, 152 Antimony sulphide, colloidal, 161 Association factor for liquids, 19, 34 Azobenzene, preparation of, from nitrobenzene, 153 Balance, ix determination of zero, ix of sensibility, x Beckmann thermometer, 23 Benzene, physical data for, 165 Bimolecular reactions, 141 Boiling-point determination, 24 Beckmann's apparatus, 26 electrical apparatus, 28 Landsberger's method, 29 Boiling-points, standard, 163 Bomb calorimeter, 80, 81 Cadmium cell, 110 Callibration of bridge wire, 96 Calomel electrode, 119 Calorimeter, 74 Cane sugar, specific rotation of, 58 purity of a sample of, 59 Capillarity, 18 Capillary electrometer, 113 Cell constant, 100 Cells, concentration, 126 gas, 131 Colloids, preparation of, 158 Combustion, heat of, 79-86 Conductivity, equivalent, 92, 166 molecular, 92, 103 of electrolytes, 92 Conductivity of KC1 solutions 101 of water 98 specific, 92 vessel, 94 Copper voltameter, 122 electrolytic estimation of, 145 Cryoscopic method for determina- tion of molecular weight, 31 Decomposition, potential of electro- lytes, 147 Density of gases and vapours, 6-10 of liquids, 10-12 of water, 10, 164 Deposition of metals, 147 Depression of the freezing-point, 31 Dialysis, 161 Dilatometer, 37 Dilatometric method for the deter- mination of transition-points, 38 Dissociation constant of acids, 104 Distribution coefficient, 71 of a substance between two non-miscible solvents, 72 Electro analysis, 144 Electrode calomel, 119 hydrogen, 131 potential measurement, 124, 133 potentials, 117 Electrodes of platinum on glass, 133 preparation of, 106, 122 testing uniformity of, 123 Electrolytic preparations, 151 Electrometer, capillary, 113 Electromotive force, 107 influence of concentration on, 126 measurement of, 108 176 INDEX 177 Electromotive force, standard of, 110 Elevation of the boiling-point, 24 Freezing-point apparatus, 31 method for determining molec- ular weight, 32 Gas cells, 131 Geisler tube, 68 Gold, colloidal, 162 Heat of combustion, 79 86 of dilution, 79 of hydration, 78 of neutralization, 74 of precipitation, 79 of solution, 78 Hess's law, 74 Hydrochloric acid, strength of solu- tion by conductivity measure- ment, 106 Hydrogen spectrum, 68 Hydrolysis of esters by acids, 138 by alkali, 142 Inversion of cane sugar, velocity of, 140 lodoform, preparation of, 153 lonization constant, 104 degree of, 103, 166 Key, Morse, 114 tapping, 114 Landberger- Walker apparatus, 29 Lead, electrolytic estimation of, 147 Liquid platinum, 167 Logarithms, 172 Mapping of spectra, 66 Measuring-bridge, 95 calibration of, 96 Mercury pipette, 4 Molecular volume, 12 Molecular weight, abnormal, 33 Molecular weight, determination of : by boiling-point method, 24-30 by distribution method, 73 by freezing-point method, 31 by vapour density method, 10 12 Nernst liquid resistance, 197 Neutralization - point, determina- tion of, by conductivity method, 106 Nickel, electrolytic estimation of, 147 Nitrates, electrolytic estimation of, 148 Nitric acid, electrolytic estimation of, 148 Observation tube for polarimeter, 59 Ohm's law, 91 Order of reaction, 143 Osmotic pressure, 41, 44 measurement, 43 Oxidation and reduction cells, 134 potential, measurement of, 135 Partition coefficient, 71 Persulphates. 157 preparation of, 155 Pipette, mercury, 4 Platinizing electrodes, 1^6 Platinum, colloidal, 159 solution, 167 Polarimeter, 56, 61 adjustment, 57 measurements, 58 Potassium persulphate, preparation of, 156 Potential, electrode, measurements 124, 133 Pyknometer, 10 Reaction of first order, 137 of second order, 141 order of a, 143 Reduction of aromatic nitro com- pounds, 151 potential, measurement of, 136 Refractive index, 46 of a liquid, measurement of, 49 Refractivity, atomic, 52 molecular, 49 of substance in solution, 53 specific, 49 Refractometer, Pulfrich's, 48, 49 Resistance, specific, 92 Rotation, specific, 55 178 PRACTICAL PHYSICAL CHEMISTRY Rotation of plane of polarization, 55 Saponification of esters by acids, 138 by alkalis, 142 Semipermeable membrane, 42 Silver, electrolytic estimation of, 148 Solubility, determination of, 21 method of determining transi- tion points, 40 Solvents, associating, 71 dissociating, 71 Spectra, mapping, 66 measurements, reduction to absolute scale, 69 Spectroscope, 64 adjustment of, 65 Spectrum analysis, 62 Standard cell, 110 Stannic oxide, colloidal, 162 Stirrers, 5 Surface energy, molecular, 19 ethyl alcohol, 20 tension, 18 Suspended transformation, 37 Tabloid press, 167 Temperature, regulation of, 1 Tensimeter, 39 Thermo-chemistry, 74 Thermometer, Beckmann's, 23 setting of, 23 Thermometric method for the deter- mination of transition -points, 36 Thermo-regulator, 1 filling of, 3 for low temperatures, 4 Thermostats, 1 Transition -points, determination of, 35 Transport numbers, 87 Unimolecular reactions, 137 Vapour density, determination of, 6-10 pressure of water, 164 method determination of transition-points, 39 Velocity of reactions, 137 Viscosity, 15 coefficient of, 15, 17 influence of temperature on, 1 7 of benzene, 17 relative, 18 Voltameter, copper, 122 Water, density of, 164 vapour pressure of, 164 viscosity and surface tension of, 165 Wave lengths, determination of, 70 Weighing, x Weights, calibration of, xi Weston's cell, 110 E.M.F. of, 116 preparation of, 111 BILLING AND SONS, LTD., PRINTERS, GUILDFORD, ENGLAND 16790 fff UNIVERSITY OF CALIFORNIA LIBRARY