UC-NRLF B M D73 7Si FREEZING-POINT BOILING-POINT AND CONDUCTIVITY METHODS JONES MEMCAL tSCMOOL LUISmAllSY Digitized by tine Internet Archive in 2007 witin funding from IVIicrosoft Corporation littp://www.arcliive.org/details/freezingpointOOjonericli THE FREEZINC-POINT, BOILING-POINT AND CONDUCTIVITY METHODS. ...™™..,,.^«^™ m The Chemical Publishing Company | EASTON, PA. 1 Publishers of Scientific Books g 1 Rngineering ; Chemistry Portland Cement m ^ Agricultural Chemistry Qualitative Analysis g g Household Chemistry Chemists' Pocket Manual ^ Metallurgy, Etc. ^ ^S^^^gS^HSS^S^S^SS^^^S^^S^^^S^SS^S^^^ES^S-S^^^ THE Freezing-Point, Boiling-Point AND Conductivity Methods Second Edition, Completely Revised BY HARRY C. JONES Professor of Physical Chemistry in The Johns Hopkins University EASTON. PA. THE CHEMICAL PUBLISHING CO. 1912 {All rightt^reserved) Copyright, 1912, by Edward Hart t r * s / « • •■ Q 1^ crv? PREFACE I have been impressed, in teaching the physical chem- ical methods in the laboratory, with the fact that there is no readily accessible place in which they are treated satisfactorily from both the standpoint of theory and of practice. In the text-books, the theoretical side is de- veloped, and usually without sufficient attention to the details of manipulation to enable them to be applied successfully in the laboratory. In the laboratory man- uals, on the other hand, these methods are often treated largely from the mechanical side, and their theoretical bearing thus lost sight of. The physical chemical methods, which find most fre- quent application in the laboratory, are probably those based upon the lowering of the freezing-point and the rise in the boiling-point of a solvent produced by a dis- solved substance, and the electrolytic conductivity of solutions of electrolytes. It is my chief object in preparing this little work to give an account of the operations involved in carrying out these methods in the laboratory. But since the mere mechanical applica- tion of any scientific method is a matter of comparatively little significance, I have aimed to give, also, enough of the theoretical ground on which each of them rests, to enable the student to work with them intelligently, and to see clearly their scientific significance and use. Harry C. Jones. PREFACE TO SECOND EDITION The demand for a second edition shows that this little laboratory manual, which was first published in the very early days of Physical Chemistry in America, has met a want. The methods herein discussed are those most frequently used in the physical chemical laboratory. In revising this booklet for a second edition the aim has been to bring it up to date. A number of minor corrections have been introduced, larger tables of freezing-point and boiling- point constants have been inserted, and the boiling-point method applied to the measurement of electrolytic dis- sociation in nonaqueous solvents. The conductivity method has been described more near- ly as carried out to-day and, it is hoped, with sufficient detail to enable the method to be used successfully in the laboratory. The drawings for figures lo and 12 have been made by my assistant. Dr. E. P. Wightman. H. C. J. CONTENTS PART I THE FREEZING-POINT METHOD PA&B Theoretical Discussion i Early History i Work of Raoult i, 2 Molecular Lowering for Different Solvents 3 Molecular Lowering in Aqueous Solutions 4 Theory of Electrolytic Dissociation 5 Calculation of the Molecular Lowering 6, 7 Experimental Verification 8 Calculation of Molecular Weights from Lowering of Freezing- Point 8, 9 The Application of the Freezing-Point Method to the Determina- tion of Molecular Weights in Solution 10 The Apparatus of Beckmann 10-13 Carrying out a Determination 13-15 Correction for the Separation of Ice 15, 16 The Application of the Freezing-Point Method to the Measure- ment of Electrolytic Dissociation 16 The Method of Calculating Dissociation from Lowering of Freezing-Point 16, 17 The Method of Work 18 The Apparatus of Jones 19-22 Comparison of the Results with the Dissociation from Con- ductivity Measurements 23 VI CONTENTS PART II THE BOILING-POINT METHOD PAGE Theoretical Discussion 25 Historical 25, 26 Work of Raoult 26, 27 The Relative Lowering of the Vapor-Tension 28 Calculation of Molecular Weights from Lowering of the Va- por-Tension 29 Beckmann's Work on Rise in Boiling-Point 29, 30 Calculation of Molecular Weights from Rise in the Boiling- Point of Solvents 30 Values of the Constants for Solvents 31 Relations between Boiling-Point and Freezing-Point Meth- ods 31, 32 The Application of the Boiling-Point Method to the Determina- tion of Molecular Weights in Solution 32 The Apparatus of Beckmann 33-35 The Apparatus of Hite 35-37 The Apparatus of Jones 36-39 Carrying Out a Determination 3942 Correction for Separation of Vapor 42 Results of Measurements 43, 44 RESULTS FOR A FEW SUBSTANCES The Application of the Boiling-Point Method to the Measure- ment of Electrolytic Dissociation 44 Measurements of Electrolytic Dissociation 45, 46 Calculation of the Dissociation 46-48 PART III THE CONDUCTIVITY METHOD Two Classes of Conductors 49 Electrolytes and Non-Electrolytes 49 Specific Conductivity 50, 51 Molecular Conductivity 51 Dissociation Measured by Conductivity Method 52, 53 Determination of /*„ 53-57 CONTENTS Vll PAGB The Application of the Conductivity Method to the Measurement of Electrolytic Dissociation 57 The Apparatus Employed 57-59 Calculation of the Molecular Conductivity 59, 60 Wheatstone Bridge 61 Temperature Coefficient of Conductivity 62 Thermoregulator 63 Calibrating the Wire 65-67 Carrying Out a Conductivity Measurement 67 Determination of the Cell Constant 68 Precautions 69 Correction for the Conductivity of Water 70, 71 The Purification of Water 71-73 Substances to be Used 73 Results for a Few Substances 73-75 PART I THE FREEZING-POINT METHOD THEORETICAL It has long been known that when a solid is dissolved in a liquid, the freezing-point of the solution is lower than that of the solvent. The first quantitative relation we owe to Blagden, who pointed out that the lowering of the freezing-point of water, produced by different amounts of the same substance, was proportional to the amount of substance present. This same fact was rediscovered much later by Riidorff.^ A marked ad- vance was made by Coppet,^ who dealt with comparable, rather than with equal amounts of different substances. He used quantities of different substances which bore to one another the same relation as their molecular weights, and found that such quantities of substances which are chemically allied, produce very nearly the same lower- ing of the freezing-point of any given solvent. In a word, the lowering of the freezing-point of a solvent by a dissolved substance, is proportional to the number of parts of the substance present. This is about what was known when the problem was taken up by Raoult, and it is to him more than to anyone else that we owe the present development of the freez- ing-point method. He investigated aqueous solutions of organic compounds, and found that the lowering pro- duced by molecular quantities was very nearly a con- 1 Phil. Trans., 78, 277. 2 Pogg. Ann., 114, 63 (1861), 145, 599 (1872). 8 Ann. Chim. Phys., [4], 33, 366 (1871). 2 THE FREEZING-POINT METHOD stant. He used other solvents, such as benzene, and found that comparable quantities of dissolved substances produced the same lowering of its freezing-point. His investigations included nitrobenzene, ethylene bromide, formic and acetic acids, and in each solvent a large number of substances was dissolved. He was thus in a position not only to compare the lowerings produced by different substances in the same solvent, but the low- erings in different solvents. As the result of this work, Raoult announced the fol- lowing generalization. One molecule of any complex substance dissolved in one hundred molecules of a liquid, lowers the freezing- point of the liquid by nearly a constant amount, which is 0.62°. This has been shown not to hold rigidly. When a gram-molecular weight of any substance is dissolved in say 100 grams of a solvent, the lowering of the freezing-point of the solvent is a constant, regardless of the nature of the substance, provided that there is no aggregation of the molecules of the substance, and no dissociation. This was shown by Raoult^ to hold ap- proximately for a large number of substances, and for several solvents. The molecular lowering, which is the lowering produced by a gram-molecular weight of the substance in 100 grams of the solvent, was calculated by him thus : If g grams of the substance are dissolved in 100 grams of the solvent, if w is the molecular weight of the sub- stance, and A the lowering of the freezing-point of the solvent produced by the presence of g grams of the sub- 1 Ann. Chim. Phys., [6], 3, 66 (1884). THE FREEZING-POINT METHOD 3 stance, then the molecular lowering is calculated from the formula: , Molecular lowering = . g A few results will show the values of the molecular lowering for different solvents. SoiyVENT, AcKTic Acid. Molecular IrfOwering. Methyl iodide 38.8 Aldehyde 38,4 Acetone 38. i Benzoic acid 43.0 Ethyl alcohol 36.4 Acetamide 36. i Stannic chloride 41.3 Carbon disulphide 35.6 Sulphuric acid 18.6 Hydrochloric acid 17.2 SoivVENT, Benzene. Methyl iodide 50.4 Anthracene 51.2 Ether 49.7 Acetone 49. 3 Chloral 50.3 Stannic chloride 48.8 Methyl alcohol 25.3 Ethyl alcohol 28.2 Benzoic acid 25.4 S01.VENT, Water. Methyl alcohol 17.3 Cane-sugar 18.5 Acetamide 17.8 Chloral hydrate 18.9 Milk-sugar 18. r Acetone 1 7. i Hydrochloric acid 39. i Nitric acid 35.8 Sulphuric acid 38. 2 Sodium hydroxide 36. 2 Potassium chloride 33.6 4 THE FREEZING-POINT METHOD A careful study of these results will bring out some interesting facts. The value of the molecular lowering of acetic acid and of benzene is very nearly a constant for each solvent. This is true for a large number of substances of the general type of most of those given above, i. e., non-electrolytes. There are, however, ex- ceptions for these solvents. In the case of acetic acid, there are a few substances known which, like sulphuric acid, give a molecular lowering of only one-half that produced by the non-electrolytes. In benzene there are also a few exceptions, but in this case the substances which give only half the normal molecular lowering, are either non-electrolytes like the alcohols, or weakly dis- sociated acids like acetic, benzoic, etc. The probable sig- nificance of the small molecular lowering produced by some substances is, that they are in a state of molecular association in the particular solvent. When the molecu- lar lowering, in the case of two undissociated com- pounds dissolved in a given solvent, is twice as great for one as for the other, it means that twice as many molecules of the second are aggregated into a unit as of the first. If the molecules of the one exist singly in solu- tion, those of the second are combined in twos. This will be seen at once, if we remember that the lowering of the freezing-point of a solvent depends only on the relative number of parts of the solvent and of the dissolved sub- stance. When we come to the results with water as a solvent we have to deal with an entirely new set of phenomena. The results given above are a • few taken from a large number. Compounds like the non-electrolytes, give a molecular lowering for water which is very nearly a THE FREEZING-POINT METHOD 5 constant, and which is approximately 18.6. This is true for such a large number^ of substances that have been investigated, that there is no reason for regarding them as being exceptions. On the other hand, all the strong electrolytes, including the strong acids, strong bases, and salts of strong acids with strong bases, weak acids with strong bases, and weak bases with strong acids, give molecular lowerings which are greater than the value 18.6. The explanation that has been offered by Arrhenius,^ to account for this and related facts is that the molecules of the electrolytes do not exist as such in aqueous solution. They are dissociated into parts called ions, and the amount of such dissociation depends, for a given substance, chiefly on the dilution of the solu- tion. In a very dilute solution of a strongly dissociated electrolyte, we have practically no molecules present, only ions. If the molecule is binary, each yields two ions, and since an ion lowers the freezing-point of the solvent as much as a molecule, the molecular lowering for such sub- stances, at high dilution, is twice as great as where there is no dissociation. If the molecule dissociates into three ions, and the dilution is such that the dissociation is com- plete, the lowering of the freezing-point will be three times as great as where there is no dissociation, as is the case with the non-electrolytes. It is stated above that in aqueous solutions the mole- cules break down into parts called ions. It is so easy to confuse ions with atoms, and this is so frequently done, that a word of caution here is not out of place. An ion is not an atom, but is an atom or group of atoms charged with electricity. The resemblance between the 1 Ann, Chim. Phys. [5], 28, 137 (1883). 2 Ztschr. phys. Chem,, i, 631 (1887). 2 6 the; i^REJDZING-POINT METHOD two is far less close than might be imagined. The prop- erties of many of the atoms with the exception of their mass, could not be foretold from the corresponding prop- erties of the ions, with any degree of probability. An atom of potassium has properties so different from an ion of potassium, that one is more impressed by their dif- ference than by their resemblance. In some cases, as with the non-electrolytes, we have then to deal only with molecules in solution in water, while with the electrolytes we have both molecules and ions, or only ions, depending on the dilution of the solu- tion. That the true value of the molecular lowering for water, when there is neither molecular aggregation nor electrolytic dissociation, is 18.6, has been shown theo- retically by van't Hoff,^ and more clearly presented by Oswald,^ thus : Given a solution that contains n gram-molecules of the dissolved substance in N gram-molecules of the sol- vent. Let T be the temperature of solidification of the solvent and A the lowering of its freezing-point produced by the dissolved substance. Let enough of the solvent solidify to dissolve a molecule of the substance, JV (— \ n molecules ) . Let A. be the molecular heat of fusion n / of one gram of the solvent, the amount of heat set free in the above process = — A. If the ice is now separated from the solution, warmed to the temperature T, fused, and finally allowed to mix with the solution which has also been warmed to the same temperature, by pass- 1 Ztschr. phys. Chem., i, 481 (1887). 2 I^ehrbuch allg. Chem., i, 760. THE FREEZING-POINT METHOD / ing through a semi-permeable membrane, an osmotic pressure p will be exerted. If the volume of the solvent N which solidifies is v, the work equals /z', the heat — X, It pvn A* But pv = RT and R = 2 cal. Substituting we have: Let M be the molecular weight of the solvent, and placing JV = —rry we have: A = .--— (i) 100 A ^ C In the Raoult formula w = — j , »« is the molecular A weight of the dissolved substance, A is the specific low- ering of the freezing-point, which equals — , in which/ is the percentage composition of the solution, and C is a constant, w, the number of molecules of the dis- solved substance in 100 grams of the solvent = ~ . tft A=:C« (2) From (i) and (2) we have : C=— — 100 * \ If L is the heat of fusion of one gram of the solvent, A =: LM, and * Work done is to the heat set free as the difference in temperature is to the absolute temperature ; pv : —X : : A : T. n THE^ FREEZING-POINT METHOD 2 7' C = looZ^* The absolute temperature T of the freezing-point of water is 273°, and L, the heat of fusion of one gram of water, was taken by van't Hoff as 79*^.^ When th.ese values are inserted in the above expression, C = 18.9. The value of L is probably more nearly 79.7 when C becomes 18.8. I have shown experimentally^ that the value of C for water, as determined with solutions of urea, ethyl and propyl alcohols, is respectively: 18.18 18.76 18.77' The formula of van't Hoff applies to the calculation of the freezing-point constant of any solvent. The freezing-point method has thus two distinct ap- plications : To determine the molecular weight in solu- tion of compounds which are not dissociated by the solvent; and to measure the amount of the dissociation of electrolytes in solutions of different concentrations. The applicability of the freezing-point method to the determination of the molecular weights of substances in solution, was pointed out by Raoult.* If we represent the unknown molecular weight of a substance by m, the molecular lowering or constant of the solvent by C, and the lowering of the freezing-point produced by a one per cent, solution of the dissolved substance by S, we have C 1 Ztschr. phys. Chem. i, 497 (1887). s Ibid, la, 653 (1885). » The most recent work indicates that the freezing-point constant for water is 1.86. *Compt. Rend., loi, 1056 (1885). the; freezing-point method 9 If the weight of the solvent used is W, that of the dis- solved substance w, and the observed lowering of the freezing-point A, lOOW ' Substituting this value of 5* in the above expression, we have loo Cw If the constant C is multiplied by loo and termed C the expression becomes Cw The values of C for a number of the solvents common- ly used with the freezing-point method are Melting-point Constant Acetic Acid 17.0 39.0 Acetoxime 59.4 56.0 Aniline —5-96 58.7 Benzene 4.97 49.0 Benzoic Acid 123,0 78.5 Bromoform 8.0 144.0 Dimethylaniline 1.96 58.0 Dinitrobenzene (w) 91.0 106.0 Diphenylmethane 26.3 67.0 Triphenyl methane 93.0 124.5 Ethylenebromide 8.0 118. o Formic Acid 8.0 28.0 Naphthalene 80. i 68.0 Nitrobenzene 5.3 70.5 Phenanthrene 96.25 120.0 Phenol 38.5 74.0 Phosphorus 44.0 390.0 Resorcine i lo.o 65.0 Thymol 48.2 80.0 Water 0.0 18.6 10 TH^ IfREEZING-POiNT METHOD The Application of the Freezing-Point Method to the Determination of Molecular Weights in Solution Beckmann^ has devised a form of apparatus that is both simple and efficient. C (Fig. i) is a small glass Fig. I. battery- jar covered with some poorly conductirig sub- stance, and which is filled with the freezing material. A mixture of finely powdered ice and salt is convenient, care being taken to use the smallest amount of salt that 1 Ztschr, phys. Chem., 3, 638 (1888), the; Freezing-point method ii will freeze the solution. B is a thick-walled glass tube, into which tube A, containing the solution, is inserted. A side tube attached to tube A, is thought to be useful in introducing the substance whose molecular weight is to be ascertained, but can be readily dispensed with. The thermometer, of the Beckmann differential type, is fitted into the tube A, by means of a cork, which can be easily removed. The stirrer S passes through the same cork, and must be of such form and dimensions as to move freely up and down between the inner walls of the tube and the bulb of the thermometer. A small glass rod, bent at the bottom in the form of a ring, which will easily enter the glass tube A, is quite efficient. A short piece of glass tubing, through which this rod will move freely, is forced through a hole in the cork at the top of tube A, and serves both to hold the stirrer in place, and to allow smoother movement through the cork. The apparatus of the following di- mensions has been found in this laboratory to be con- venient. Tube A is 20 cm. in length and 3 cm. in width. B is about 15 cm. long and 5, cm. wide. The glass tube used in constructing the stirrer should be about 2.5 mm. in thickness. A thermometer with a short, thick bulb, such as is usually furnished on the market, is not as desirable as one with a bulb that is longer and of smaller diam- eter; since it requires a longer time to register the tem- perature of the liquid. In case the solvent used is hydroscopic, some precau- tion must be taken to protect it from the moisture in the air. An apparatus satisfying this requirement has been constructed also by Beckmann,^ by forcing the air 1 Ztschr. phys. Chem., 7, 324 (1891). 12 THE FREEZING-POINT METHOD which enters the apparatus to pass over some drying agent, like sulphuric acid. The device is shown in Fig. 2. The handle of the stirrer E passes through a glass tube, into which the side tube F, containing a few drops of sulphuric acid, is fused. The air enters through this side tube, is dried, and passes out through the tube Fig. 2. receiving the handle of the stirrer. The remainder of the apparatus is of exactly the same form as that shown in Fig. I, except that it is provided with a glass siphon H, for removing the melted freezing-mixture. This is really superfluous, since a piece of rubber tubing answers the purpose equally well. TH^ ]?RKEZING-POINT ME^THOD I3 Forms of apparatus capable of yielding far more accu- rate results than those just described, have been devised and used ; ,but since such extra refinement is desirable rather to measure dissociation than to determine molecu- lar weights, reference will be made to it under the second application of the freezing-point method. Carrying Out a Determination The thermometer must first be so adjusted that the freezing-point of water falls near the top of the scale. To accomplish this, water is poured into the tube A until the bulb of the thermometer, when placed in posi- tion, is covered. Tube A is placed directly in the freez- ing-mixture in C, and the water allowed to freeze. As soon as fine particles of ice separate, tube A is remov- ed from the freezing-mixture, placed in tube B, and the whole then introduced again into the freezing-mixture. The thermometer is then raised out of the water contain- ing ice particles, allowed to remain in contact with the warmer air a moment, and then given a sudden jar. The mercury falls from the top to the bottom of the upper cup, and leaves the column of mercury free at its upper end. The thermometer is then placed again in the ice-cold water, and if the end of the mercury column does not come to rest on the upper half of the scale, the process just described is repeated. A few trials generally suffice to bring the reading on the thermometer approxi- mately where desired.- The thermometer being adjusted, tube A is carefully dried, closed at the top and side with stoppers, and weighed. Enough pure water is poured into the tube to cover the bulb of the thermometer when in position, and the tube is again weighed. The weight of the sol- 14 THE FRDEZING-POINT METHOD vent employed is thus determined. The stopper is then removed from the top of the tube and the thermometer and stirrer placed in position. Tube A is inserted into tube B, and the whole system into the freezing-mixture. During the cooling of the solvent the stirrer should be raised and lowered frequently. The water will cool down below its freezing-temperature often a degree or more, before ice will begin to separate. When the un- dercooling of the solvent or of a solution is very much more than a degree, a small fragment of pure ice should be thrown into the undercooled liquid. This will start the separation of ice, which will continue until the true freezing-temperature is reached. When the ice begins to separate the mercury column will rise, rapidly at first, then slower, until it reaches the point of equilibrium. While the thermometer is rising, and especially when near the point of rest, it must be tapped gently to prevent the mercury from lag- ging behind in the capillary, due to friction against its walls. A lead pencil is convenient to use in jarring the thermometer. The freezing-point of the water is then noted on the thermometer. The reading on the ordi- nary Beckmann instrument can easily be made to o.ooi° by means of a small pocket lens. The tube containing the solvent, with the thermometer and stirrer in position, is removed from the freezing- mixture and the ice melted by seizing the tube for a few moments with the hand. The freezing-point of the water is then redetermined exactly as described above. The two determinations should not differ more than two- or three-thousandths of a degree. The substance whose molecular weight is to be deter- TH^ :^rEe:zing-point me^thod 15 mined is weighed in a weighing tube, poured into the solvent and brought completely into solution. If cane- sugar is use,d, that quantity is taken which will give a solution about one-tenth normal. If urea, or any of the alcohols is used, a more concentrated solution may be employed. A solution of cane-sugar, dextrose, etc., more concentrated than one-tenth normal, gives abnormally large depressions of the freezing-point of water. The reason for this was not entirely clear. The solution is then placed in the freezing-mixture and its freezing-point determined, and redetermined, exactly as described for the solvent. All the necessary data for calculating the molecular weight of the substance from the expression already given are thus made available. Correction for the Separation of Ice A certain amount of the solvent separates in the solid form in all such determinations, and the solution be- comes concentrated by just this amount. The freezing- point of the solution, as read on the thermometer, is there- fore always lower than would correspond to a solution of the concentration originally used. A correction for the change in concentration, due to the separation of the solid solvent, must be introduced. The amount of the solvent which separates in the solid phase can easily be determined, knowing the amount to which the solution is undercooled before the ice begins to separate, the heat of fusion of a unit quantity of the solvent, and the specific heat of the liquid. The fraction of the sol- vent which separates is calculated thus, as was pointed out by the present writer :^ If we represent by u the amount of the undercooling 1 Ztschr. phys. Chem., 12, 624 (1893). i6 the; fre:i:zing-point method of the solution in degrees centigrade, by w the heat of fusion of unit weight of the solvent, by s the specific heat of the liquid, and by T the fraction that will solidify, we have w When water is used as a solvent ^ = i and w = 80. The fraction of this solvent that will separate as a solid, for every degree of undercooling, is therefore ^/so, ^^^ the concentration of the original solution is increased by just so much. Instead of applying the correction to the concentration, it is simpler to apply it directly to the freezing-point lowering itself. The Application of the Freezing-Point Method to the Measurement of Electrolytic Dissociation An ion lowers the freezing-point of a given quantity of a solvent just as much as a molecule. If a molecule dis- sociates into two ions these will lower the freezing-point of a given amount of a solvent, just twice as much as if the molecule is not dissociated. The lowering of the freezing-point of a given solvent by a partially dissociated electrolyte, depends upon the relation between the num- ber of molecules of the solvent, and the sum of the molecules plus the ions of the dissolved substance. Thus, it is possible at any given dilution, to determine the amount to which an electrolyte is dissociated. The cal- culation of the dissociation from the freezing-point low- ering is simple. The molecular lowering of the freez- ing-point of any solvent by any substance was defined by Arrhenius^ as the lowering produced by a gram-molecu- 1 Ztschr. phys. Chem., a, 494 (1888). THE FREEZING-POINT METHOD 1 7 lar weight of the substance in a liter of solution. This can be taken as approximately one-tenth of the molecu- lar lowering as defined by Raoult. For our present purpose we accept the definition of Arrhenius, and find that the molecular lowering of the freezing-point of wa- ter produced by a gram-molecular weight of a non- electrolyte, like urea, the alcohols, etc., in a liter of so- lution, is the constant i.86°. If the substance used is dissociated, the molecular lowering is always greater than 1.86°. The first step is to calculate the molecular low- ering for the solution in question, which is done by di- viding the lowering found by the concentration in deci- mal part of normal. If there were only molecules pres- ent the molecular lowering would be i.86°. The molecu- lar lowering found must therefore be divided by i.86°, which gives the value of the van't Hoff coefficient i, for the solution.^ Molecular Lowering . 1^86 "~ ^" If the molecule breaks down into two ions, the percent- age dissociation^ a (Arrhenius activity coefficient), is expressed thus a ^ i — I . If the molecule breaks down into three ions. t a = - If into n ions, 1 Ztschr, phys. Chem., i, 501 (iS *Ibtd, 11,535(1893). i8 the: frdezing-point method The Method of Work Exactly the same apparatus may be used as was em- ployed in the determination of molecular weights. The method of preparing the solutions is, however, some- what different. The solvent is poured into the innermost vessel in quantity large enough to cover the bulb of the thermom- eter, and its freezing-point upon the thermometer ascer- tained, as in a molecular weight determination. The solvent is then completely removed from the vessel and the solution of known concentration, prepared in a meas- uring flask, introduced. Its freezing-point is then de- termined exactly as previously described, including the rapid stirring, the tapping of the thermometer, the intro- duction of a fragment of the solid solvent when neces- sary, and the correction for the change in concentration due to the separation of the solid solvent. The dilution of the solution is then increased one and a half, two, three, four, etc., times, and the dissociation determined for each dilution. It will be found that the value of i, and therefore of a, always increases with increase in dilu- tion. In this work any of the common chlorides, nitrates, bromides, or in general any readily soluble electrolyte may be used. It is convenient to use a solution of pure sodium or potassium chloride of concentration about 0.5 normal, and then to increase the dilution of this solution in several steps, as indicated above. The chlorides and nitrates break down into two ions each, the sulphates into three. The values of a from the freezing-point method should be preserved and compared with the values THE FREKZING-POINT METHOD I9 of a for the same solutions, as obtained by the conduc- tivity method. Far more accurate experimental methods have been devised and' used for measuring the freezing-point lower- ings, by Loomis,^ Nernst and Abegg,^ Ponsot,* myself,* and others. A form of apparatus, which was found by the writer to give excellent results, is sketched in Fig. 3. A is a large metallic vessel, 25 cm. high and 35 cm. wide. This is surrounded by a mantle of non-conducting material to protect it from the warmer air. B is a galvanized iron vessel, 21 cm. high and 15 cm. wide, which rests upon a tripod to diminish the surface of con- tact with the outer vessel. This is provided with a lid. The vessel B is completely surrounded, except above, with a freezing-mixture of ice and a little salt. The space between A and B, filled with the freezing-mixture, was covered with a ring of asbestos, aa, to protect the freezing-mixture from the air. C is a glass vessel, 18 cm. high, 10 cm. wide, and of about 1200 cc. capacity. This rests on a thick felt bottom, which protects it from the metal vessel beneath. The space between B and C is filled with air and covered above with a ring of felt, bb, which rests on a metallic shelf fastened on to the inner side of the vessel B. The air-chamber between B and C is thus closed and remains at nearly the same temperature during a determination. The glass ves- sel was covered with a glass lid. D is a thermometer whose bulb is 14 cm. in length and 1.5 cm. in width. The fine capillary was carefully calibrated. The entire scale, 1 Ber.d. chera. Ges., a6, 797, (1893); Wied. Ann., 51, 500. 2 Ztschr. phys. Chem., 15, 681 (1894). ' Compt. Rend., 12a, 668 (1896). * ztschr. phys. Chem., 11, no, 529 (1863). 20 THE I^REKZING-POINT METHOD which was 22 cm. in length, corresponded to only 0.6°. It was divided into tenths, hundredths, and thousandths of a degree. The finest divisions could be estimated to tenths, by means of a telescope, so that the scale could be read to 0.000 1 of a degree. The thermometer was of Fig. 3. the Beckmann type, and the freezing-point of the sol- vent could be adjusted wherever desired upon the scale. It was fastened firmly into the cork c, and passed loosely through g, being suspended in the liquid in C. E is a stirrer, which was constructed as follows: A circular piece of sheet-silver was cut slightly smaller than the glass vessel, and plated electrolytically with THE FREEZING-POINT METHOD 21 gold. This was cut along the circular lines shown in Fig. 4, and also horizontally, as indicated. The ends Fig. 4. marked o were bent upwards, those marked u down- wards. S is a small hole which received the handle. P is a large hole in the center, through which the bulb of the thermometer passes. In Fig. 5 is given a section -fl5 Fig. 5- across one of the openings, to show how the ends are cut and bent. This section corresponds to the dotted line a, h, in Fig. 4. A stirrer of this form has the advantage that at every movement up and down the liquid is moved horizontally and vertically, and any currents set up during the stroke in one direction are completely reversed by the opposite stroke. The advantage claimed for this method of work is that by using a large volume of the solution the temperature 3 22 the: freezing-point METHOD can be much better regulated. The comparatively thick layer of air at constant temperature around the inner- most vessel, makes it far less susceptible to the influ- ence of changes in the temperature of surrounding ob- jects. The large volume of the liquid exposes rela- tively less surface to the cooling mixture, and the rate of cooling is comparatively slow. This makes it possible to determine more accurately the temperature of the liquid in which the ice separates. Since the rate of cooling is slow, the ice that separates during the time required for the thermometer to become constant, is relatively small. A liter of pure water is placed in the vessel C, and its freezing-point determined on the thermometer. A cer- tain volume of this is then removed, and an equal vol- ume of a solution of known concentration, added. Thus the volume of the solution in the vessel always remains a liter, which facilitates the calculation of the results. The same process is repeated in making successive di- lutions. By this method of work the first solution of a series is the most dilute, and the solutions become more and more concentrated to the end of the series. Such accuracy as is obtainable with this apparatus is not necessary for laboratory practice, but is very desir- able where the problem of the measurement of electro- lytic dissociation presents itself. The applicability of the method to the problem of elec- trolytic dissociation will be seen by comparing the values of the dissociation of a number of acids, bases, and salts, as obtained by it,^ with the dissociation as determined by the conductivity method of Kohlrausch.^ » Ztschr. phys. Chem., la, 639 (1893). 2 Wied. Ann., 26, 161 (1885). THE IPREEZING-POINT METHOD 23 Dissociation Dissociation from from lowering of Concentration conductivity, freezing-point. Substance. normal. Percent. Percent. NaCl -r o.ooi 98.0 98.4 o.oio 93.5 907 o.ioo 84.1 83.5 K2SO4 0.002 92.2 94.1 O.OIO 85.8 88.2 O.IOO 70.1 72.0 BaCl2 0.002 93.9 941 O.OIO 87.9 88.4 O.IOO 75.3 76.8 HCl 0.002 loo.o 98.4 O.OIO 98.9 95.8 O.IOO 93.9 88.6 HjSO^ 0.003 89.8 86.0 0.005 85.4 83.8 0.050 62.3 60.7 HNO3 <^oo2 loo.o 98.4 O.OIO 98.5 96.8 O.IOO 93.5 87.8 H3PO4 0.002 87.8 85.2 O.OIO 63.5 68.8 KOH 0.002 loo.o 98.4 O.OIO 99.2 93.7 O.IOO 92.8 83.1 NaOH 0.002 98.9 98.4 O.OIO 99.5 93-7 0.050 90.4 88.4 An absolute agreement between the dissociation values obtained by the conductivity method and by the freezing- point method, is not to be expected, since the former method was used at 18° or 25°, while the latter was 24 THie FlueEZING-POINT METHOD applied at about o° ; and further, the hydration of the dissolved substance produces a greater effect upon the results of the freezing-point, than upon the results of the conductivity method, as has been shown by Jones and Pearce.^ 1 Amer. Chem. Journ., 38, 683 (1907). PART IL THE BOILING-POINT METHOD THEORETICAL The presence of a foreign, non-volatile substance diminishes the vapor pressure of the solvent in which it is dissolved. Since the boiling-point of a solvent, or of a solution, is the temperature at which the vapor-pres- sure just overcomes the pressure of the atmosphere, it follows that the solution having a lower vapor-pressure than the solvent, will have a higher boiling-point. There are thus two quantities, either of which we may- measure : The depression of the vapor-tension of the sol- vent, caused by the presence of the dissolved substance; or the rise in the boiling-point of the solvent, due to the same cause. Passing over the work of Faraday, Griffiths, Legrand, and others, along this line, since it all failed to give any very important generalization, we come to that of von Babo,^ who found that the relation between the amount of salt present and the diminution of the vapor-pressure, was independent of the temperature. The work of Wiillner^ w^as of greater significance. He measured the depression of the vapor-pressure of water especially by salts, and arrived at the conclusion that the diminution of the vapor-pressure of water, pro- duced by dissolved, non-volatile substances, was pro- portional to the amount of substance present. 1 Jahrb. Chem., 1848-49, 93 ; 1857, 72. « Fogg. Ann., 103, 529, (1858); 105, 85 (1858). 26 THE BOIUNG-POINT METHOD While this is true only in certain cases, or indeed only for certain classes of compounds, yet it is strictly analo- gous to the earliest generalization reached in connection with the study of the depression of the freezing-point of a solvent by a foreign substance. It will be remembered that Blagden stated that the depression of the freezing- point of a solvent by a dissolved substance was propor- tional to the amount of substance present. When depressions of the freezing-point were measured with a fair degree of accuracy, it was shown that the generalization of Blagden held only approximately, and ill some cases. So also, the relation pointed out by Wiillner was shown by the work of Pauchon,^ Tam- mann^ and Emden^, to be only an approximation under certain conditions. It is to Raoult more than to any other investigator that we owe the theoretical development of the subject in hand. He employed the first of the two quantities men- tioned, and measured the depression of the vapor-tension of a solvent by foreign substances. A number of rela- tions were brought out by him from a study of solutions in solvents other than water, which would not have been discovered in aqueous solutions, since these are often dis- sociated, and to a different amount for different dilutions. Raoult* confirmed the generalization of von Babo, that the relation between the depression of the vapor- pressure and the vapor-pressure of the solvent, was in- dependent of the temperature between o° and 20°. Also that of Wiillner, that the depression of the vapor-pres- 1 Compt. Rend., 89, 752 (1879). « Wied. Ann., 24, 523 (1885). 87*1^,31,145(1887). * Compt. Rend., 103, 1125 (1886). THE EOIUNG-POINT METHOD 27 sure was proportional to the concentration (when there was no dissociation). If we represent the vapor-pressure of the pure solvent by p, and that of the solution by />', P-P' P is independent of the temperature and proportional to the concentration. The nature of the substance used was then investi- gated to determine whether the chemical composition of the molecule had any effect on its power to depress the vapor-tension. Solutions containing the same number of molecules of different substances in solution in the same number of molecules of a given solvent, must be compared as to their vapor-pressures. This would be difficult to carry out directly. Convenient concentrations of different substances were used, the vapor-pressures of the solu- tions determined, and the molecular depression of the vapor-pressure calculated for each substance from the expression — P-P\ , ^ p g in which m is the molecular weight of the substance, and g the number of grams in 100 grams of the solvent. He found that the molecular depression of the vapor- pressure of a solvent is a constant for a given solvent, independent of the nature of the substance which is dis- solved in it. This holds, as we now know, only when the dissolved substances are undissociated by the solvent. Raoult^ investigated also the relative diminution of 1 Compt. Rend., 104, 1430 (1887). 28 THE BOII, />' and a, we can directly calculate m. As a practical method for determining molecular weights this is not used, since such measurements are not easily carried out and are not very accurate. It has been found to be simpler and more accurate to determine the temperature at which the vapor-pressure of the solution is equal to that of the solvent. Since the boiling-point of a liquid is the temperature at which its vapor-pressure just overcomes the pressure of the atmo- sphere, the boiling-points of a solvent and of a solution in that solvent are the temperatures of equal vapor-pres- 1 Ztschr. phys. Chem., 2, 371 (1888). 30 the; boiung-point method sures. The object is then to determine the rise in the boiling-point of a solvent produced by the substance dis- solved in it. The experimental method for carrying out such de- terminations we owe to Beckmann. The forms of appara- tus which seem best adapted to this work, and the details of an experiment will be considered in the second part of this chapter. The rise in the boiling-point is directly proportional to the lowering of the vapor-pressure, and depends upon the relative number of molecules of the solvent and of the dissolved substance. The probability of calculating molecular weights directly from the rise in the boiling-point of solvents produced by substances dissolved in them, is at once ap- parent. The expression by which the molecular weights are calculated, is analogous to that already given for calcu- lating molecular weights from lowerings of the freezing- point of solvents by dissolved substances. If we repre- sent the unknown molecular weight by w, the weight of the substance taken by s, the weight of the solvent used by ►S', and the rise produced in the boiling-point of the solvent by R, we have — C s in which C is a constant of different value for each sol- vent. The analogy between the lowering of the freezing- point and the rise in the boiling-point holds still further, in that the value of C can be calculated from the same formula : — THE BOII.ING-POINT METHOD 3 1 100 L When applied to calculating the constant for the boil- ing-point method of determining molecular weights, T is the absolute temperature at which the pure solvent boils and L the heat of vaporization of the solvent. The values of C /or a number of the solvents more commonly used, are given below. Boiling-point Constant Acetic acid 118.0 25,3 Acetone 56.3 16.7 Ammonia — 33.7 3.2 Amylalcohol (/56>) 131. 5 25.75 Aniline 184.0 32.2 Anizol 155.0 44.3 Benzene 80.3 26.7 Benzonitrile 191. o 36.5 Bromine 63.0 52.0 Chloroform 61.2 36.6 Carbon disulphide 46.2 23.7 Carbon tetrachloride • . 78.5 48.0 Ethyl acetate 75.5 27.9 Ethyl alcohol 78.8 11. 5 Ethyl bromide 37.7 25.3 Ethylene bromide 130.0 64.3 Ethyl ether 35.0 21. i Formic acid 100.6 34.0 Isobutyl alcohol 104.6 19,4 Mercury 357.0 130.0 Methyl acetate 56.5 20.6 Methyl alcohol 67.0 8.4 Methyl formate 32.3 15.05 Methyl iodide 41.3 41.9 Nitrobenzene 205.0 50.1 Paraldehyde 123.0 41.8 Phenol 183.0 30.4 Propyl alcohol 94.8 15.8 Pyridine 115. o 30.1 Water loo.o 5.2 32 THE BOIUNG-POINT METHOD Some of the relations between the boiling-point and the freezing-point methods have been mentioned, but others, however, exist. It will be remembered that the freezing-point method can be used to determine the molecular weights of only a limited number of sub- stances — ^the non-electrolytes. The boiling-point method is subject to the same limitation. Those substances that give abnormally great depressions of the freezing- point, due to electrolytic dissociation, give abnormally great depressions of the vapor-tension, or rise in the boiling-point. It was pointed out that in such cases the freezing-point method could be used to measure the amount of dissociation in the solutions. The boiling- point method may be used for the same purpose, but is not capable of the same degree of accuracy as the freezing-point method. Some recent work,^ however, has shown that it can be applied to the problem of electrolytic dissociation in solution, and when all the indicated precautions are taken, it is capable of giving fairly satisfactory results. The Application of the Boiling-Point Method to the Determination of Molecular Weights in Solution The precautions that are necessary in making such measurements will be understood best by pointing out the more prominent sources of error to which the boiling- point method is subject. The method as such, is not capable of that refine- ment to which the freezing-point method lends itself. It is sensitive to barometric changes, which seriously af- fect the boiling-points of liquids. In this method the 1 Jones and King : Amer. Chem. Journ., 19, 581 (1897). THE EOIUNG-POINT METHOD 33 vapor escapes quickly from the solution in which its presence is necessary to establish the equilibrium tem- perature. The difference in temperature between the liquid and surrounding objects is generally much greater in this method than in the freezing-point method, so that more precautions are necessary to protect the solution and thermometer from changes in the temperature of external objects. In this method a part of the com- paratively pure solvent is constantly separating from the solution as vapor, and is returned as a liquid, at a tem- perature lower than that of the boiling solution. The amount of this liquid cannot, for given conditions, be determined with the same degree of accuracy as was possible in ascertaining the amount of ice that separated in the freezing liquid. The large Beckmann thermom- eters are more liable to undergo change at the compara- tively high temperatures to which they are subjected in this method, than in the freezing-point method, where the temperature of the thermometer is at no time widely re- moved from the ordinary. The boiling-point method has this advantage that more solvents can be employed, since comparatively few solvents freeze within the ordinary range of temperatures ; and further, the solubility of sub- stances is generally increased at the higher temperatures. It is, on the other hand, a misfortune for the boiling- point method that aqueous solutions cannot be used satis- factorily, partly because of the very small constant for water. A number of forms of apparatus for determining the boiling-points of solvents and solutions have been de- vised by Beckmann,^ to whom we are as much indebted for the experimental development of the subject as we 1 Ztschr. phys. Chem., 4, 544 (18S9); 8, 224 (1891); 15, 663, (1894); ai, 246 (1856). 34 THE BOILING-POINT METHOD are to Raoult for its theoretical. That one, which judged by the results/ seems to be, on the whole, the most satisfactorily, is seen in Fig. 6. The inner glass Fig. 6. vessel A, provided with a return condenser K, receives the liquid whose boiling-point is to be determined. The bottom of this vessel is filled to a depth of a few 1 Ztschr. phys. Chem., 8, 224 (1891). TH]^ BOIWNG-POINT METHOD 35 centimeters with glass beads or small garnets, so that the boiling may take place simultaneously from a number of points and proceed more smoothly. The bulb of the Beckmann thermometer is placed well below the surface of the liquid. Tube A is surrounded on the sides with a double- walled glass jacket B, into which some of the same solvent placed in A is introduced. The object is to surround the boiling liquid with a liquid as nearly at its own temperature as possible. This jacket is provided with a return condenser K2. The whole is supported on a box of asbestos C, which is open beneath. Heat is ap- plied as shown in the drawing. The results obtained by Beckmann^ with the use of this apparatus were very good. It is, however, not free from objections. It is certain that the eiffect of radia- tion from the bulb of the thermometer outward upon the colder objects, was not entirely cut off by the form of jacket employed. Beckmann^ used in a later form a porcelain jacket, having abandoned a metallic one, which doubtless cuts off the radiation more effectively than the one of glass. But an objection which applies to every form of apparatus devised by Beckmann, is that the cold solvent from the condenser is returned directly into the hot liquid into which the thermometer is immers- ed. That the thermometer is affected by this, in that it tends to lag behind the true boiling-temperature of the liquid, is certain. A form of apparatus which largely eliminates this latter source of error, was devised by Hite,^ and is shown in Fig. 7. The distinctive advance made by » Ztschr. phys. Chem,, 8, 226 (iigi). 2 /*lrf, 15,662(1894). 3 Amer. Chem. Journ., 17, 514 (1895). 36 THE EOIUNG-POINT MEiTHOD Hite is the introduction of an inner glass tube, which prevents the condensed solvent from coming in contact with the thermometer before it is reheated to the boil- ing-point. The cooled liquid must pass through a layer of the boiling liquid between the walls of the inner and outer vessel, some centimeters deep, before it can enter the inner tube which receives the thermometer. The inner vessel is closed at the bottom by means of a glass stopper. Grooves are filed into the edge of the stop- per to allow the vapor to stream through into the inner vessel in fine bubbles, and stir the liquid around the thermometer. I am inclined to lay rather less stress upon the importance of this device, than upon the separation of the condensed solvent from the liquid in which the thermometer is placed, until it has been re- heated to the boiling-point. The apparatus gave ad- mirable results with low-boiling solvents, but could not be used for solvents which boil over ioo°. The present writer^ has devised a form of apparatus which aims both at reducing to a minimum the error from radiation, and at preventing the condensed solvent from coming in contact with the thermometer until it is reheated to the boiling-point. It is also one of the sim- plest of the efficient forms thus far devised. It is shown in section in Fig. 8. A is a glass tube i8 cm. high and 4 cm. in diameter, drawn out at the top to a diameter of about 2^ cm. and ground to receive a ground-glass stop- per. This tube is filled to a depth of from 3 to 4 cm. with glass beads. P is a cylinder of platinum, 8 cm. high and 23^ cm. in width, made by rolling up a piece of platinum foil, and fastening it in position by wrapping it near the top and bottom with platinum wire. Into the 1 Amer. Chem. Journ.,19, 581 (1897). p Fig. 7. Fig. 8. 38 THE BOIUNG-POINT METHOD cylinder P, some pieces of platinum foil are thrown. These are made by cutting foil into pieces about ^ cm. square, bending the corners alternately up and down, to prevent them from lying too closely upon one another, and serrating the edges with scissors, to give a greater number of points from which the boiling can take place. The bulb of the thermometer is thus entirely surrounded except directly above by metal at very nearly its own temperature. A condenser C, about 40 cm. in length, is attached to the tube Aj, which is 2 or 2>4 cm. in di- ameter, by means of a cork. When it is desired to pro- tect the solvent from the moisture in the air, the top of the condenser tube should be provided with a tube con- taining calcium chloride or phosphorus pentoxide. Dur- ing an experiment, the vessel A is closed above by a cork, through which the Beckmann boiling-point thermometer T passes. M is a jacket of asbestos, 12 cm. high and i^ cm. thick, over the top of which the rate of boiling can be satisfactorily observed. It is constructed by bending a thin board of asbestos tightly around the tube A, and fixing it in place by means of a copper wire. Thick asbestos paper is then wound around this until the desired thickness is reached. The apparatus is supported on a small iron tripod S, 8 cm. in diameter, on which rests an asbestos ring R, about 9 cm. in exter- nal diameter. A circular hole is cut in the center of this ring, about 35^ cm. in diameter, and over this is placed a piece of fine copper gauze. The source of heat is a Bunsen burner B, surrounded by an ordinary metal- lic cone I, to protect the small flame from air-currents. The glass vessel A is shoved down until it comes in contact with the wire gauze. Under these conditions a THE BOILING-POINT METHOD 39 very small flame suffices when low-boiling solvents are employed, and not a large flame is required when a sol- vent like aniline is used, A number of other forms of apparatus have been con- structed for determining the boiling-points of liquids, but these cither do not sufficiently eliminate sources of error for accurate work, or are so complex that they can scarcely hope to find general application in the labora- tory for the purpose of determining molecular weights. Carrying Out a Determination The thermometer must first be so adjusted that the top of the mercury thread comes to rest on the lower half of the scale, when the bulb is immersed in the boil- ing solvent. This is accomplished by placing some glass beads in cylinder A, and adding the pure solvent until the bulb of the thermometer will be covered when inserted in place. The solvent is then boiled, and as much mercury as possible is driven out of the lower bulb into the upper cup. The thermometer is then removed from the liquid, inverted for a few moments, when still more of the mercury in the bulb will run down into the cup. The thermometer is then quickly brought into normal position and given a sudden tap, when the mer- cury will fall from the top to the bottom of the cup and leave the column free. The bulb is again placed in the boiling solvent, and if the thread comes to rest where de- sired, the apparatus is ready for a determination. If not, the process must be repeated until the desired result is reached, which, however, does not usually require any considerable expenditure of time. When the thermometer is adjusted, it must be re- 40 THE EOII.ING-POINT METHOD moved, and the apparatus and beads entirely freed from the liquid. The glass beads are then poured into the glass cylinder, the platinum cylinder inserted, and pressed down into the beads to a distance of from >4 to i cm. The platinum plates are then introduced into the platinum cylinder, the end of the tube A, closed with a cork, and the ground-glass stopper inserted into A. The apparatus is then set into a small beaker glass and weighed, the solvent introduced, and the whole re- weighed. Great care must be taken that not enough of the solvent is employed to boil over from the inside of the platinum cylinder to the outside. In case a labora- tory is not provided with a balance capable of weighing accurately 200 or 300 grams, the solvent must be weighed directly and poured into the apparatus. This method of procedure, for low-boiling solvents, is necessarily less ac- curate, due to loss by evaporation. After the solvent is weighed the glass stopper is re- moved, and the thermometer, fitted tightly into a cork, is placed in position, as shown in the drawing. The appa- ratus is then placed upon the stand in the mantle of asbes- tos, the cork removed from A, and the condenser at- tached. Heat is then applied and the solvent boiled. The size of the flame must be so regulated by means of a screw pinch-cock, that the boiling is quite vigorous, but not so violent as to be of an irregular or explosive character. A quiet but very active boiling is absolutely essential to the success of the experiment. The time required to establish the true temperature of equilibrium between the pure liquid solvent and its vapor, is much greater than in the case of a solution. This is strictly analogous to what is observed with the freezing- THIS BOIUNG-POINT METHOD 4I point method. Here the time necessary to establish the temperature of equilibrium between the solid and liquid phases of the pure solvent, is always much greater than for a solution. Before taking a reading on the Beckmann thermometer, it is always necessary to give it a few sharp taps with a lead pencil, and indeed this should be done occasionally while the mercury is rising, and especially when it is near the point of equilibrium. The use of an electric hammer to accomplish this object is an unnecessary complication. A small hand-lens, magnifying a half dozen times, is quite sufficient to use in making the readings. It is always best to redetermine the boiling-point of the solvent. After this point has been ascertained, a tube containing the substance pressed into pellets, whose molecular weight it is desired to determine, is weighed, and a convenient number of these poured into the solvent, either through the condenser or directly through the tube A when the solvent is not too volatile and has ceased to boil. The tube is then reweighed, and the amount of substance introduced, thus ascertained. The boiling-point of the solution is then determined. The carrying out of a determination with a low-boil- ing solvent is a much easier process than with one boil- ing at a considerably higher temperature. Thus; when anisol or aniline is employed, much care and some experience are necessary to determine the rate of boiling which must be adopted. If the boiling is too slow, the thermometer will never reach the temperature of equilibrium ; if so rapid that it is irregular and explo- sive, the thermometer may rise above the true point, and then suddenly drop below it at the moment when a large amount of the vapor is set free. In a word, for high- 42 THE BOILING-POINT METHOD boiling solvents the rate of boiling must be as vigorous as possible, in order to proceed with perfect regularity. In all such determinations the barometer must be care- fully observed; but after the boiling-point of the sol- vent has been determined, that of the solution can be as- certained so quickly that the changes in the barometer during this short interval are usually so slight that they are negligible. Whenever they are of appreciable value, a correction must be accordingly introduced. The cor- rection for methyl and ethyl alcohols is 0.004° for o.i mm. change in the barometer. A portion of the nearly pure solvents is constantly evap- orating from the solution, and condensing on the walls of the apparatus itself and in the condenser. The solu- tion is thus more concentrated than would be calculated from the amount of substance and of solvent used. A correction must be introduced for the amount of the sol- vent which separates from the solution, as was neces- sary in the freezing-point method. Unfortunately, we cannot determine the amount in the boiling-point method with even the same degree of accuracy as in the freez- ing-point method. The amount of the solvent which exists under ordinary conditions, as vapor and condensed liquid, is given by Ostwald^ as 0.2 gram, and 0.35 gram of water. But this evidently must be taken, as only a rough approxima- tion. Thus all the data are at hand for calculating the molecu- lar weight of the substance in the solvent used, from the formula already given (page 30) : 1 Hand und Hilfsbuch zur Ausfuhrung Physiko-Chemischer Messungen, p. 224. THE BOIUNG-POINT ME^THOD 43 Cw "' = -rW Below are given a few of the results obtained with my apparatus for solvents boiling from 34.9° to 182.5°. Soi,vKNT, Ether : ^^ = 2110 ; Boiwng-Point, 34.9° at 760 mm. Naphthalene, 128. FIRST SERIES. Ether. Naphthalene Rise in Molecular Grams. Grams. boiling-point. weight. 1 57.573 1-2365 0.357° 126.9 2 57.573 2.5155 0.716° 128.8 3 57.573 3.8733 i.iio** 127.9 Mean, 127.9 Soi,vENT, Benzene: /& = 267o; Boiwng-Point, 80.36° at 760 mm. Naphthalene, 128. Benzene. Naphthlene. Rise in Molecular Grams. Grams. boiling-point. weight. 1 70.560 0.7594 0.215° 133.7 2 70..560 2.0548 0.574° 135.4 3 70-560 3.0780 0.850° 137.0 4 70.560 4.4790 1.234° 137.4 Mean, 135.9 Soi^VENT, AN11.INE : ^=3220 ; Boii^iNG-PoiNT, 182.5° AT 738 mm. 7 fiphenylmethane, 244. FIRST SERIES. Aniline. Triphenylmethane. Rise in Molecular Grams. Grams. boiling-point. weight. 1 60.126 0.8017 0.180° 238.6 2 60.126 1.6052 0.353° 243.5 3 60.126 2.2914 0.496° 247.4 4 60.126 2.9213 0.654° 239.2 Mean, 242.2 44 THE) BOII.ING-POINT METHOD Dipheny laming, i6g. Aniline. Triphenylmethane. Rise in Molecular Grams. Grams. boiling-point. vyeight. 1 64.220 0.7780 0.224° I74-I 2 64.220 1.3326 0.391° 170.9 3 64.220 1.7832 0.535° 167.1 Mean, 170.7 For practice in the laboratory it is far better to use solvents with low boiling-points, such as ether or ben- zene. Ethyl alcohol can be employed, but the results are liable to be less accurate, since its constant is com- paratively small. Naphthalene is easily obtained pure, and may be used in both ether and benzene. In alcohol: benzoic acid, urea, or acetamide may be conveniently used; while tri- phenylmethane, diphenylamine or benzanilide, give good results with aniline as a solvent. The Application of the Boiling-Point Method to the Measurement of Electrolytic Dissociation The importance of being able to apply the boiling- point method to measure the dissociation of electrolytes in nonaqueous solvents will be seen from the following: Take methyl and ethyl alcohols ; next to water they are probably the most important solvents in all chemistry. Until quite recently there was no method available for measuring the dissociation of even the most strongly dissociated electrolyte in these solvents. The conductivity method could not be used, since with the forms of cells then in use it was impossible to determine the values of fio. in these solvents. The dilution at which complete dissociation in these solvents was reached was so great, that it was impossible to apply the conductivity method THE EOIUNG-POINT MI^THOD 45 to these dilutions with any reasonable degree of ac- curacy. These solvents are so frequently used, and the prob- lem of the dissociation of electrolytes dissolved in them so fundamental to our scientific knowledge of alcoholic solutions, that we must have some method of measuring their dissociating power. The freezing-point method obviously cannot be used with these solvents because they freeze at temperatures that are far too low to measure accurately. Until the conductivity method was recently improved in this lab- oratory, we were practically limited to the boiling-point method to solve this problem. The solvents named above, and many others of great importance for the science of chemistry, boil at temperatures not so very widely re- moved from the ordinary, and their boiling-points can, therefore, be accurately determined. Before the boiling-point method could, however, be used to measure electrolytic dissociation, it must be im- proved so as to eliminate many errors that were inher- ent in the method as Beckmann left it. Indeed, it was this objection especially that led me to introduce the improvements in the boiling-point method already re- ferred to. Measurement of Electrolytic Dissociation The carrying out oi an experiment for the purpose of measuring electrolytic dissociation is the same in all es- sential details as in the determination of the molecular weight of a dissolved substance. The thermometer is so adjusted as to bring the boiling-point of the alcohol near the bottom of the scale. A weighed quantity of the al- 46 THE BOII.ING-POINT METHOD cohol is then introduced into the tube and its boiHng-point determined at least twice upon the scale, care being taken not to introduce enough alcohol to boil over from the outside into the inside of the cylinder. In determining the boiling-point of the solvent all of the precautions pre- viously referred to must be observed. The boiling must be vigorous but not explosive, the thermometer must be tapped to prevent any sticking of the mercury, and the barometer must be carefully read. The substance whose dissociation is to be measured is weighed in a ground-glass stoppered weighing tube, and introduced into the solvent after it has cooled sufficiently. The boiling-point of the solution is then determined in the same manner as that of the solvent. The proper cor- rection for any change in the barometer is applied to the rise in the boiling-point of the solvent produced by the dissolved substance, to get the true rise in the boiling- point; this correction for methyl and ethyl alcohols and solutions in these solvents is, as already stated 0.004° for a barometric change of o.i mm. of mercury. Calculation of the Dissociation The method of calculating the dissociation of electro- lytes from the rise in the boiling-point of the solvent produced by them, is strictly analogous to that employed for calculating the dissociation of electrolytes from the lowering of the freezing-point of the solvents in which they are dissolved. From the rise in the boiling-point observed on the ther- mometer, the molecular rise is calculated by dividing the observed rise by the concentration of the solution ex- pressed decimally. The concentration is calculated on the the: boiung-point method 47 basis of a gram-molecular weight of the substance in one thousand grams of the solvent. When the observed rise is divided by the concentration we obtain the molecu- lar rise in the boiling-point of the solvent produced by the substance at the dilution in question. From the molecular rise the dissociation is calculated very simply. If there were no dissociation the molecular rise would be the boiling-point constant of the solvent. If the binary electrolyte were completely dissociated the molecu- lar rise produced would be twice the boiling-point con- stant of the solvent, etc. If we divide the molecular rise in question by the boiling-point constant^ of the solvent we obtain the van't Hoff coefficient i. If the electrolyte is binary, i. e., dissociated into two ions, the dissociation a = t — I If the electrolyte is ternary, i. e., each molecule disso- ciated into three ions, the dissociation If each molecule of the electrolyte yields v ions, the dissociation 1 — I To make the above perfectly clear a few experimental results^ are given. 1 This is really the molecular rise of the boiling-point of a solvent produced by a completely undissociated, unpolymerized, unsolvated substance. 2 Jones: Ztschr. phys. Chem., 31, 129 (1899). 48 THE BOIUNG-POINT METHOD Potassium Bromide in Methyi, Alcohoi, (C = 8.4). Grams Grams Concentration Rise in Molecular Disso- CH4O KBr. molec. norm. B.p. rise ciation 56.648 o.64cx> 0.00949 0.119° 12.54 49.3 56.915 0.7987 0.01178 0.149° 12.65 50.6 54.698 0.8765 0.01345 0.170° 12.64 50.5 58.510 0.8595 0.01233 0.156° 12.65 50.6 56.970 0.9141 0.01347 0.170° 12.62 50.2 Potassium Iodide in Ethyi, Ai^cohoi, (C — 11.5) . Grams Grams Concentration Rise in Molecular Disso- CaHeO KI molec. norm. B.p. rise ciation 57.084 0.9035 0.00954 0.139° 1457 26.7 55.647 I.I170 0.01209 0.176° 14.56 26.6 55.789 1.2990 0.01403 0.203° 14.47 25.8 58.070 1.2846 0.01333 0.193° 14.55 26.5 58.750 0.9415 0.00965 0.140° 14.50 26.1 PART III THE CONDUCTIVITY METHOD Conductors of electricity may, for the sake of conven- ience, be divided into two classes, those that conduct without undergoing any decom|x>sition, such as the metals, carbon, etc., and those which, during the passage of the current, undergo a decomposition or electrolysis at the poles, such as solutions of acids, bases and salts. It is not at all certain that there is any fundamental dif- ference between the two classes, and at present, it seems that a very close relation between the two modes of conduction is becoming clearly recognized. It is by no means true that solutions of all substances conduct. Thus, aqueous soultions of the so-called neu- tral organic compounds, such as the alcohols, carbohy- drates, urea, and a large number of such substances, do not conduct the current. This furnishes ground for a division of substances into those whose solutions con- duct the current and are called electrolytes; and those which, in solution, do not conduct and are called non- electrolytes. The application of the conductivity method in phys- ical chemistry is limited to conductors of the so-called second class, i e., to solutions of electrolytes, which are chiefly solutions of acids, bases, and salts. The conductivity of any conductor of electricity is the reciprocal of its resistance. The resistance r is, from Ohm's law, expressed thus: r =■ — r t 50 THE CONDUCTIVITY METHOD IT is the difference in potential at the two ends of the conductor, and i is the strength of the current. The con- ductivity c is the reciprocal of r. i c = — . TT The unit of resistance, called the ohm, is that of a col- umn of pure mercury 106.3 cm. long and i square mm. in section, at 0° C. The Siemens or mercury unit is the resistance of a column of mercury 100 cm. in length and with a cross section of one square mm. The two units bear the rela- tion to another of 106.3 • lO^- Specific and Molecular Conductivities The resistance of conductors depends upon their form as well as upon their chemical nature. In order that the resistances of different conductors should be meas- ured in comparable quantities, their dimensions must be taken into account. The dimensions usually chosen are a cylinder i meter in length and i square mm. in cross section. The resistance of such forms of conductors is known as their specific resistance. The reciprocal of this is their specific conductivity. The conductors of the so-called second class are solu- tions of some electrolyte in some solvent, and their con- ductivity depends chiefly or wholly upon the presence of the electrolytic substance. That the resistances of such solutions should be comparable, it is clear that we must deal with comparable quantities of the dissolved substances. The most convenient quantities are gram- molecular weights. Given a normal solution that contains a gram-molecu- the: conductivity method 51 lar weight of the electrolyte in a liter. If this liter of solution be placed between two electrodes that are i cm. apart, the cross section would be 1,000 square centi- meters. This will have o.ooi of the resistance, or 1,000 times the conductivity of a cube of the same solution whose edge was i cm. in length. If we represent by v the number of cubic centimeters of any solution which contains a gram-molecular weight of the dissolved sub- stance, and by s the specific conductivity of a cube of the solution whose edge is i cm. in length, the molecu- lar conductivity /* is the product of these quantities : \k •=■ vs. But if we represent by s the specific conductivity of a cylinder of the solution i meter in length and i square mm. in cross section: fi = 10,000 vs. A general expression, where g gram-molecular weights are contained in a liter of the solution, is : s X 10' when s, the specific conductivity, is referred to a cube of the solution, or : s X 10' when s is referred to a cylinder of the solution, one meter in length and a square mm, in cross section. The molecular conductivities of solutions are, then, the conductivities of comparable quantities of different sub- stances, and when the same dilutions are used the molecular conductivities are directly comparable with one another. 52 THE CONDUCTIVITY METHOD Different substances behave very differently with re- spect to their power to carry the current when in solu- tion in a given solvent. The fundamental distinction between substances that conduct, and those that do not conduct at all, has been already mentioned. But among conductors very marked differences exist. Some reach a maximum of conductivity at moderate dilution, while others attain this only at extreme dilution. Take the case of a strong acid Hke hydrochloric or nitric; the molecular conductivity increases with the di- lution to about one one-thousandth normal, when it be- comes constant. While, on the other hand, the molecu- lar conductivity of a weak acid like acetic, will increase with the dilution as far as the dilution can be studied by the conductivity method. The question arises, whence this difference between substances in respect to their power to carry the cur- rent? Here, again, the theory of electrolytic disso- ciation comes to our aid. Those substances that give abnormally great depressions of the freezing-point, ab- normally large elevations of the boiling-point, and which show abnormally great osmotic pressures, conduct the current; and only such substances conduct. The explanation of the abnormal results with respect to the properties just mentioned, was sought in the dis- sociation of the molecules into ions. From a large amount of evidence from many sources, we seem justi- fied in concluding that only ions conduct the current. Molecules are entirely incapable of carrying electricity through the solvent in which they are dissolved. If only ions conduct, then the conductivity of a solution is proportional to the number of ions present, provided the: conductivity method 53 that the ions move with the same average velocity, which is true of ions of the same kind. The conductivity method can then be used to meas- ure the dissociation of electrolytes in solution, and this is its most important scientific application. When the molecular conductivity attains a maximum constant value, it means that the dissociation is complete, and this value of the molecular conductivity is termed /aoo. The molecular conductivity at any dilution is written //y. in which v is the volume of the solution, i. e., the number of liters that contain a gram-molecular weight of the electrolyte. The percentage of dissociation at any dilu- tion, a, is the ratio between the molecular conductivity at that dilution, and the molecular conductivity when the dissociation is complete: /W,oo In order to determine the dissociation of an electrolyte at any given dilution by means of the conductivity method, it is necessary to determine the molecular con- ductivity, \y.v at that dilution, and the value of /aoo for the electrolyte, when the value of a can be calculated at once. Determination of /moo The value of /mu is determined directly for any electro- lyte in any solvent, by means of the conductivity method. The determination of /*«> for strongly disso- ciated electrolytes is comparatively simple. The value of /Au is determined at a given dilution, the dilution in- creased, the molecular conductivity determined at the new dilution, and this icontinued until a dilution is 5 54 rut CONDUCTIVITY METHOD reached which is so great, that when further increased the value of fiv remains the same. It has then attained a constant maximum value, which is the value of ^loo. The value of ftoo for strong acids and bases, and for salts, is usually attained at a dilution between v = 500 and V = 5000. This will be seen from the following ex- amples : Hydrochloric Acid. Potassium Hydroxide. Potassium Chloride. V. tJiv ^8°- V. flv 18°. V. flv ^8°. 2 301 2 184. 1 2 95.8 32 335 20 204.5 20 108.3 128 341 100 212.4 100 1 14. 7 1000 346 500 214.0 1000 1 19-3 1667 344 1000 211. 1 5000 120.9 A large number of substances, such as the organic acids and bases, which are only weakly dissociated at any ordinary dilution, present a new problem when it is desired to determine their maximum molecular con- ductivity. That this is not reached at dilutions to which the conductivity method can be applied, is seen from the following examples: Acetic Acid. Ammonia .1 V. fly ^8°. V. f^v 18°. 2 1.9 2 1.2 20 6.2 20 4-3 TOO 13.2 100 9.2 1000 38.0 1000 26.0 5000 79.6 5000 50.0 lOOOO 99-5 lOOOO 61.0 It is evident from these results that the value of [xm for such substances cannot be determined by the method given for strongly dissociated compounds. The dilution at which complete dissociation would take place lies far beyond the possibility of applying the conductivity method directly. 1 Ammonia is taken, since work on the substituted ammonias has not gen- erally been carried to very great dilutions. the: conductivity method 55 The method of determining the value of /too for such substances is as follows: While the weak organic acids are only slightly dissociated, salts of these acids are completely dissociated at moderate dilutions. So also with respect to the weak bases, which, at ordinary dilu- tions are only slightly dissociated; their salts are com- pletely dissociated at dilutions which lie well within the range of the conductivity method. Take an organic acid. Its sodium salt is prepared and the value of fioo for this salt is determined ; or taking an organic base, the nitrate of the base is used and the value of /a^ for the nitrate determined. It remains to see what relation exists between the value of /xoo for the sodium salt of an acid and the acid itself, or between the nitrate of a base and the base. Kohlrausch* has shown that the value of fi^ for any compound is the sum of two constants, the one depend- ing upon the cation, the other upon the anion. The value of fxoo for sodium acetate is the sum of two con- stants, the one for the cation, sodium, and the other for the anion, CH3COO. If the constant for sodium be subtracted, the remainder is the constant for the anion of acetic acid. If to this constant the constant for hy- drogen be added, we have the value of /*« for acetic acid itself. Exactly the same line of reasoning applies to the nitrate of the base. The constant for NO3 is substracted from ft* for the nitrate, and the remainder is the constant for the cation of the base. To this the constant for hydroxyl is added, and the sum is the value of /a» for the base. The value of the constant for sodium is 49.2 at 25°, and of hydrogen, 325 at 25°. If we add 275.8 to the 1 Wied. Ann., 6, 167 (1879). 56 the: conductivity method value of /Moo for the sodium salt of an acid, we have the value af />t» for the acid. The value of the constant for NO3, at the same temperature, is 65.1, and for (OH), 170. We must, therefore, add 105 to /*« for the nitrate of a base, in order to ascertain /xoo for the base itself. It is thus possible to determine fxoo for compounds that are only slightly dissociated at ordinary dilutions. Since /x» can always be determined for any electrolyte, we are able to measure the dissociation of compounds, which, even in water, are only slightly dissociated. The application of the conductivity method to meas- ure the exact dissociation in solvents other than water is not usually successful. Water exercises the strong- est dissociating action of any known solvent. The ion- izing power of many solvents is so weak, that it is impos- sible to determine the value of /xoo for electrolytes dis- solved in them by the direct application of the con- ductivity method. In such cases, it is possible to deter- mine the dissociation only approximately. The general applicability of any method of measuring electrolytic dissociation is of wide-reaching significance. This will appear, when we consider that most chemical reactions take place between ions, molecules as such not coming into play. The chemical activity of solutions is then a function of the dissociation, and since conduc- tivity is a measure of dissociation, there is a close rela- tion between the conductivity of solutions, and their power to react chemically. Indeed, the former has often been used to measure the latter. In this connection is to be mentioned, especially, the work of Ostwald^ on the conductivity of organic acids, from which he calculated their dissociation constants. * Ztschr. phys. Chem., 3, 170, 241, 369 (1889). THE CONDUCTIVITY METHOD 57 Knowing the dissociation constant, the chemical activity of the acid is known. The work of Bredig^ on the con- ductivity of organic bases is strictly analogous to that just cited, Ostwald^ has also shown that it is possible to deter- mine the basicity of acids by determining the conduc- tivities of their sodium salts. The conductivity method has also been extensively applied to determine what we have already called the constants for the ions, or the relative velocities with which the ions move through the solutions. A large number of applications of the conductivity method to special problems in dissociation have been made in the last few years, so that it may be said to be one of the most important of all the physical chemical methods. The Application of the Conductivity Method to the Measurement of Electrolytic Dissociation When a continuous current is passed through a solu- tion of an electrolyte the electrodes become quickly covered with gas, or, as we say, become polarized. This increases the resistance to the passage of the current, and interferes with the measurement of the resistance of the solution. Several devices have been proposed for over- coming the effect of polarization,^ but none has proved as simple as the use of the alternating current. The effect of polarization, tending to retard the flow of the current in one direction, is practically counterbalanced by the action in the opposite direction, where the polarization 1 Ibid, 13, 289 (1894). 2 Ztschr. phys. Cheni , 1, 105 (1887); 2, 902 (1888). 3 Stroud aud Henderson : Phil. Mag., 43, 19 (1897). 58 the; conductivity method current adds itself to the original. This method of measuring the conductivity of solutions we owe to Kohl- rausch. The apparatus employed is sketched diagrammatically in Fig. 9. J is a small induction coil, with only one or two layers of wire. A larger coil must not be used, since it does not give a sharp tone minimum in the tele- phone. The coil, tuned to a very high pitch, should be inclosed in a box surrounded by a poor conductor of sound, and placed at some distance from the bridge where the reading is to be made. The coil is driven by a storage cell of medium size. A platinum wire, or bet- ter one of manganese alloy which has a small tempera- ture coefficient of resistance, is tightly stretched over the meter stick AB which is carefully divided into millime- ters. A rheostat W, whose total resistance amounts to 11,110 ohms, is convenient. The resistance vessel R, containing the solution and electrodes, is shown enlarged in Fig. 10. The electrodes are cut from thick sheet platinum, and into each plate a stout platinum wire, about an inch in length, is welded. Glass tubes are sealed on to the platinum wires and electrode plates, by means of sealing glass, as shown in the drawing. These the; conductivity method 59 tubes pass tightly through a ground-glass stopper, which fits into the glass vessel. They are filled to a convenient height with mercury, and electrical connection established by means of copper wires, which dip into the mercury. One arm of the telephone T is thrown into the circuit Fig. 10, between the rheostat and the resistance, and the other arm is connected with the bridge wire, by means of a slider. This is moved along the wire until that point is found at which the hum of the induction coil ceases to be heard in the telephone. Let this be some point c, and 60 rut CONDUCTIVITY METHOD let us represent Ac by a, and Be by b, the resistance of the solution in the vessel R by r, and the resistance in ohms in the rheostat by w; then, from the principle of the bridge, we have: ra =■ wb. wb a But the conductivity of a solution c is the reciprocal of the resistance r; therefore, a wb The conductivity of solutions, determined by this ex- pression, would not, in any sense, be comparable with one another, since there is nothing in the expression that takes into account the concentration of the solu- tion. It is most convenient to refer all concentrations to gram-molecular normal, containing a gram-molecular weight of the electrolyte in a liter. If we represent by V the number of liters that contain a gram-molecular weight of the dissolved substance, the preceding expres- sion becomes — va wb Instead of the conductivity c, we write for the molecu- lar conductivity, /x, and to indicate the concentration at which the /a is determined, we write /a-,,, in which v has the significance indicated above. va wb But even this expression does not take into account the dimensions of the cell used. A cell-constant C must be TH^ CONDUCTIVITY METHOD 6i introduced and determined for each cell, before the cell can be employed for conductivity measurements. The complete expression for the molecular conductivity is then — fJi-v = C Va wb Wheatstone Bridge Instead of the straight wire bridge sketched diagram- matically in figure 9, it is far better to use the form indi- This form is furnished by Leeds cated in figure II. Fig. II. and Northrup, of Philadelphia, from whose catalogue the above sketch was taken. The manganine wire is wrapped around a marble cyl- inder which is about 15 cm. in diameter. Instead of one 62 the: conductivity method meter a wire about five meters in length is used, and thus the error in reading is reduced about five times. This form of bridge occupies much less space than the straight form, is much more convenient to handle, and, as stated, is far more accurate. Temperature Coefficient of Conductivity The conductivity of solutions of electrolytes increases rapidly with rise in temperature. The molecular conduc- tivity of a quarter-normal solution of hydrochloric acid, which is 223.3 a-t 10°, rises to 397.9 at 35°. This is even more marked in the case of sodium sulphate; a quarter- normal solution having a conductivity of 68.5, at 0° has a conductivity of 156.1 at 35°. From this it is evident, that a definite, constant tem- perature must be carefully maintained in all conductivity work. This is accomplished by placing the vessel con- taining the solution in a large volume of water which is maintained at a constant, known temperature. A con- venient form of thermostat (Fig. 12) for such work is used in the laboratory. A double-walled metallic vessel, holding from 15 to 20 liters of water, is stirred by pad- dles driven by a hot-air motor, which is kept in motion by means of a small gas jet placed beneath it. The space be- tween the two walls is filled with asbestos cement. A large glass tube placed near the bottom of the vessel is filled with a 10 per cent, solution of calcium chloride. The change in volume of this solution with temperature, can be used to regulate the temperature of the water-bath. The Ostwald regulator (Fig. 13) can be easily ad- justed, so that the temperature of the water-bath will re- main constant to within one-tenth of a degree for a day. TH]^ CONDUCTIVITY ME:TH0D 63 Tube A is connected with the gas supply. The glass tube C, which opens just above the mercury meniscus, contains a 'fine perforation in the side, so as to supply Fig. 12. gas enough to keep the flame alive, when the lower end of the tube is closed by the mercury. Tube B connects with the burner, and D with the large tube containing the 64 THE CONDUCTIVITY METHOD calcium chloride solution, resting on the bottom of the water-bath. Pig. 13. When it is desired to adjust the regulator for a defi- nite temperature, the stop-cock is opened, the flame lighted, and a thermometer divided into tenths of a de- gree, suspended in the bath. The end of tube C is raised above the mercury surface, and the stirrer is set in motion by means of the hot-air motor. When the thermometer registers the desired temperature the stop- cock is closed, and the end of tube C is pushed down until it just touches the mercury surface. The apparatus will then control the temperature automatically. A very efficient electrically controlled regulator has recently been described by Reid,^ and a part of this is shown in Fig. 12. A very convenient temperature to use for routine work with the conductivity method is zero degrees. Fur- thermore, this is an easy temperature to realize and to maintain. Take a battery jar and fill it with finely crushed ice. Then add just enough distilled water to moisten 1 Amer. Chem. Journ., 41, 148 (1909). the; conductivity method 65 the ice. If more water is added the temperature always remains somewhat above zero. Place the, battery jar in question in a larger vessel and fill the space between the two vessels with ice and water. Place the conductivity cell containing the solu- tion in the innermost vessel, and within an hour or so the solution if stirred will be within a few hundredths of a degree of zero. Calibrating the Wire A stout platinum wire can be used in constructing the Wheatstone bridge, but, as already stated, it is better to use one of an alloy of manganese (manganine). This wire is usually of very nearly uniform resistance, but this can never be taken for granted without testing it. A convenient method for calibrating such a wire has been described by Strouhal and Barus.^ A piece of German-silver wire about a meter and a half in length, is cut into ten pieces (Fig. 14), which are, as nearly as Fig. 14. possible, of the same length. The insulation is removed from the ends of these wires, and they are soldered on to thick copper wires about an inch in length. Nine holes are made in a board, which is about a meter in length, at equal distances apart. These are partly filled with mercury, and receive the ends of the copper wires which 1 Wied. Ann., lo, 326 (1880). 66 THE CONDUCTIVITY METHOD have been previously amalgamated. The board, with wires in position, is placed along by the side of the bridge wire, and the two end loops attached to the ex- tremities of the bridge. The current from the small in- ductorium is passed through the bridge, and also through the series of loops. One of the loops is chosen as the standard and is suitably marked so as to dis- tinguish it from the others. One end of this standard is attached to one end of the bridge, and the other placed in the first mercury cup. One arm of the tele- phone is placed in the same mercury cup, and the other attached to the pointer, which moves along the bridge wire. The point of silence on the bridge is ascertained. This is the first reading for point i. The telephone, and all other connections remaining unchanged, the stand- ard measuring wire which was at position i, is moved to position 2, and wire 2 is placed in position i. A reading is again made in the telephone which is the second reading for position i. The arm of the telephone, which was in cup i, is then removed to cup 2, and the point of silence ascertained. This is the first reading for cup 2. The standard wire which is now in position 2, is moved to position 3, wire 3 is taken back to 2, and all other connections are unchanged. The point of equilibrium is again ascertained at 2, which gives the second reading for this position. The standard wire is thus interchanged in position with each of the loops, and two readings obtained on the bridge for each position except the last, for which only one reading is available. It must be observed that in all such work in which the telephone is used it is not advisable to try to ascertain directly the exact point on the wire at which the coil the: conductivity ME:TH0D (i'J cannot be heard, or at which the tone is a minimum; but to find a point on each side of the true zero, at which the intensity of the tone is the same. These two readings should, at most, be not more than a centimeter apart. The true zero is then just half-way between these points. The bridge wire is thus divided into ten lengths. The application of the calibration correction is simple. The ten values are added together, and their sum subtracted from I, GOO mm. The difference is divided into lo parts and each length is corrected by this amount, so that the sum is I, GOO mm. By adding the parts thus, i, 1+2, etc., we obtain the points which correspond to tenths of the wire. The difference between these and 10, 20, etc., gives the correction to be applied. Carrying Out a Conductivity Measurement After the wire is calibrated, the next step is to deter- m.ine the value of the constant (C) for the cell which is to be used. The preparation of the cell is a matter of some care. In the first place, the electrodes must be placed at a convenient distance apart, by shoving the glass tubes through the stopper, and these must then be fastened firmly in the stopper, so that no further movement is possible. If a fairly concentrated solution is to be studied, the plates must be as much as 2, or 3 cm. apart. If a very dilute solution is to be used, a distance of 0.5 cm. is sufficient. The ordinary white platinum plates, such as are furnished by the manu- facturers, cannot be used directly since they would not give a sharp tone-minimum in the telephone. They must be carefully cleansed by washing in chromic acid, 68 the: conductivity me:thod and then in water. A few drops of a solution of pla- tinic chloride are poured into the conductivity cell, (Fig. lo) and the cell filled with pure water until the elec- trodes are covered. A current from a storage battery is then passed through the solution until the electrodes become more and more deeply blackened. The direction of the current should be frequently reversed, so that both electrodes may become coated, and in order that the de- posit may be as nearly uniform as possible. After the plates are completely covered with a layer of platinum black, the platinic chloride is removed from the cell, a little sodium hydroxide added and the current is passed through this solution. The object of the alkali is to remove any chlorine which may have been retained by the platinum black as it was being deposited. The sodium hydroxide is then removed by hydrochloric acid, and the acid by repeated washing with pure redistilled water. In order to determine the value of C, in the expression, for any cell, it is necessary to use some solution for which the value fiv is known. Since potassium chlo- ride can generally be obtained in a high degree of purity, by five or six crystallizations, it is convenient to use in standardizing the cell. A one-fiftieth normal solution of potassium chloride has a molecular conductivity (/au) of 129.7 at 25° C. and 70.8 at 0°. The solution is poured into the cell until the electrodes are covered, and brought to exactly 25° C. or 0° in the thermostat. The bubbles of ail which usually separate on the electrodes with rise in temperature, having been removed, a resistance is thrown into the circuit by means of the rheostat, which will TH^ CONDUCTIVITY METHOD 69 bring the point of tone-minimum not very distant from the center of the bridge. Thus, all the quantities in the above expression except C, are known, and the equation can therefore be solved at once for the value of C. The constant for any given cell being determined, it is a matter of fundamental importance that its value should not be changed. This would be done if the electrodes were moved with respect to one another, or their sur- faces in any wise altered. It is therefore necessary that the electrodes should never be placed upon a hard surface, but always upon clean, thick, filter-paper, and the plates must never be touched with any hard object. Knowing the constant for the cell, the measurement of the conductivity of a solution involves exactly the same procedure as that just described. The difference is in the calculation. C is known and it is desired to find the value of /a^ for a given solution. The solution is placed in the cell, brought to 25° C. or 0°, the resistance introduced in the rheostat and the bal- ance effected on the bridge. All the values in the above expression are known except n-v, which is calculated directly. If the solution used is more concentrated than 2^^^ normal, it is better to use the cell with electrodes far apart. If more dilute, the electrodes whose distance from one another is not more than 0.5 cm. should be employed. Precautions are necessary at every turn. The wire after calibration, must never be touched with the hand on account of grease, and the point of contact with the wire must be moved over its surface very carefully. The current must not be allowed to flow through the resist- 7 70 THE CONDUCTIVITY MEiTHOD ance coils for any considerable length of time, or the tem- perature, and therefore the resistance of the coils will change. The inductorium should be allowed to run only during the actual measurement of the resistance. Es- pecial care should be taken that every connection is clean and well made, otherwise resistance will be introduced at the junctions. Correction for the Conductivity of Water Since water is the most general solvent known, and solutions in this solvent have the greatest conductivity, one is called upon most frequently to measure the conduc- tivity of aqueous solutions. In all such cases the quan- tity actually measured is the sum of the conductivities of the water and of the dissolved electrolyte. The con- ductivity of the vv-ater alone, must, in every case, be de- termined, in order that the conducting power of the electrolyte may be ascertained. It would, at first sight, appear to be possible to use water of only a fair degree of purity, to determine its conductivity, and then to sub- tract this from the conductivity of the solution. Whether this could be done, would depend upon the nature of the impurities. They might easily be of such a character as to react chemically with the dissolved electrolyte, and thus seri- ously affect the nature of the solution. Thus, ammonia, which would neutralize any acid forming a salt, would materially change the nature of the ions present, and therefore the conductivity. Carbon dioxide would, in like manner, afifect the conductivity of any strong base. It is therefore necessary, in all work involving the use of the conductivity method, to prepare water in as pure con- the; conductivity method 71 dition as is practicable, and then to introduce a correc- tion for its conductivity when this is larger than the necessary experimental error. Kohlrausch^ has prepared the purest water thus far obtained, by distilling the purest water obtainable by other methods in a vacuum. He determined its con- ductivity without exposure to the air, and found it to be 0.04 X lO"*'. To prepare water of this degree of purity is not practicable, and indeed is not necessary for con- ductivity work. Nernst^ has suggested fractional crystallization as a means of purifying water for conductivity purposes, but equally efficient and far more rapid methods have been subsequently devised. Hulett^ has obtained water of a high degree of purity, by distilling it first from potassium bichromate and sul- phuric acid, and then redistilling from a solution of barium hydroxide. The water purified in this way had a conductivity of from 07 to 0.8 X io~**. More recently, Jones and Mackay* have used an appa- ratus in which the water is distilled first from acid potas- sium bichromate, which decomposes any organic matter present and retains the ammonia, and second from barium hydroxide which retains any carbon dioxide. The apparatus is shown in Fig. 15. Ordinary distilled water with a little sulphuric acid and potassium bichromate, are distilled from a Jena glass balloon flask and condensed in a tube of block tin. It is then boiled in A from barium hydroxide, the vapor passing into B, which contains distilled water, and a little barium hydrox- 1 Ztschr. phys. Chetn., 14, 317 (1894). ^ Ibid, 8, 120 (1891). ^ Ibid, ai, 297(1896), < Araer. Chem. Journ., 19, 91 (1897); Ztschr. phys. Cheni., 23, 237 (i?97). 72 THE CONDUCTIVITY ME^THOD ide. A small flame is sufficient to keep the liquid in B at the boiling temperature. The vapor passes from B along the long neck of the retort, into the tin condenser, and is received in the flask E. Certain precautions must be taken in fitting up and using the apparatus. Vessels A and B are connected with a tube of block tin H. When- ever the apparatus is cleaned and refilled, which should be done about once a month when in constant use, the dis- tillate collected at first must be discarded. The carbon dioxide not absorbed in A, is absorbed by the alkali in B. Fig. 15. The process is thus perfectly continuous for a least a month, or it can be interrupted at any time by removing the burner. Eight to ten liters of water can be obtained daily with the use of this apparatus. The water purified by this method gave a conductivity at 25°, varying from i to 1.5 X io~^ in mercury units. The correction which must be applied to the values of fiv, for the conductivity of the water employed in pre- paring the solutions, is calculated by multiplying the specific conductivity of the water w5 by the volume of the solution in liters. This quantity for water properly THE CONDUCTIVITY ME;TH0D 73 purified, is negligible for concentrated solutions, and attains an appreciable value only in dilute solutions. In case the 'substance under investigation reacts chemically with the impurities in the water, such a correction would be so uncertain that it is better not to attempt to apply it except at very high dilutions. Substances to be Used In practice", it is well to use some of the same sub- stances whose freezing-point lowerings have been meas- ured, so that the dissociation as determined by conductiv- ity may be compared with that calculated from the de- pression of the freezing-point. Prepare say, a tenth-, normal solution of the substance chosen, determine the value of ft^ for this dilution, increase the dilution to i^^-, sUf ttjVt7> and -^^Vo-* normal, determining in each case the value of /jl^. At about TTAyiF> f^v will become con- stant for most of the strong binary electrolytes, and will show no further increase with increase in the dilution. This is the value of fioo. To find the per- centage of dissociation, a, at any dilution, divide the value of /x^ at that dilution by the value of /w-oo for the substance in question. a = . floo Results for a Few Substances Some results for the conductivity and dissociation of a few typical electrolytes will give an idea of the order of magnitude of these values, and the way in which they change with temperature and dilution. The molecu- lar conductivities are represented by /u,^, the dissociation by a and the volume of the solution by v. 74 THK CONDUCTIVITY MliTHOD Hydrocht.oric Acid.* xoo /A7/25° a250 /X^35° a 35^ 4 223.3 93-5 348.2 91.8 397.9 91.8 8 227.0 95.1 357.0 94.1 407.1 93.9 i6 231-8 97.1 365.2 96-3 415.5 95.9 32 235.0 98.4 370.7 97-7 423.4 97.7 128 238.8 lOO.O 379-3 lOO.O 433-3 lOO.O Sui^PHURic Acid.' V. /^.o° aoo /Az.25° aaso /A. 35° a 35° 4 292.9 65.2 419.3 59.1 457.2 56.1 8 303.9 67.7 431.5 60.8 471-7 57.9 i6 323.6 72.0 456.6 64.3 498.0 61.2 32 347.2 77.3 491.4 69.2 533.6 65.5 128 403.6 89.8 589-4 83.0 646.2 79-3 512 442.7 98.6 675.2 95.1 753.0 92.5 2048 449.2 lOO.O 709.9 lOO.O 814.4 lOO.O Potassium Chi^oridk.' I/. 1^.0- aoo A*^25° a 25° /A^50° a 50° 2 62.96 83.8 109.5 79.9 161. 9 76.3 8 66.47 88.5 II8.6 86.6 179.I 84.4 32 68.40 93.5 122.9 92.6 192.8 90.9 128 70.27 97.2 126.8 96.6 204.3 96.3 512 73.00 98.8 132.4 98.9 209.1 98.6 1024 74-24 lOO.O 135.5 lOO.O 211. 6 99.8 2048 75.14 137.0 212. 1 loo.o Potassium SuIvPhate.* V. /^.o° aoo l^., 25° a 25° /A^50° 2 87.19 60.1 152.6 56-9 224.8 8 101.9 70.3 183.6 68.5 276.7 32 117.9 81.3 214.4 80.0 329.2 128 131.9 91.0 242.1 90.3 376.0 512 142.7 98.4 263.5 98.3 406.7 1024 145.0 lOO.O 268.0 lOO.O 419.6 1 Jones and West: Amer. Chem. Journ., 34, 412 (1905). « Jones and West: Ibid 34, 415 (1905). 3 Jones and West: Ibid., 34, 381 (1905); Jones and Clover, Ibid., 43, 202 (1910). < Jones and West: Ibid, 34, 387 (1905). 6 Jones and Clover: 43, 203 (1910). THE CONDUCTIVITY METHOD 75 The conductivity of sulphuric acid is greater than that of hydrochloric, since the molecule of hydrochloric acid dissociates into two ions, while the molecule of sulphuric acid dissociates into three. The same applies to potas- sium chloride as compared with potassium sulphate. The conductivity of a strong acid is greater than that of its salts, because the hydrogen ion has a much greater velocity than that of any other cation. It should be noted that the dissociation decreases slightly with rise in temperature. This is a general phenomenon among electrolytes. The dissociation increases with the dilution until com- plete dissociation is reached. SCIENTIFIC BOOKS PUBLISHED BY THE CHEMICAL PUBLISHING CO. EASTON, PA. BENEDICT— Elementary Organic Analysis. Small 8vo. Pages VI + 82. 15 Illustrations $1.00 BERGEY— Handbook of Practical Hygiene. Small Svo. Pages 164 ... . $1.50 BILTZ — The Practical Methods of Determining Molecular Weights. (Translated by Jones). 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