Electrochemical Investigation of Liquid Amalgams of Thallium, Indium, Tin, Zinc, Cadmium, Lead, Copper, and Lithium. BY THEODORE WILLIAM RICHARDS WITH THE COLLABORATION OF J. HUNT WILSON AND R. N. GARROD-THOMAS. PUBLISHED BY THE CARNEGIE INSTITUTION OF WASHINGTON 1909 CARNEGIE INSTITUTION OF WASHINGTON PUBLICATION No. 118 CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE JSorb BALTIMORE, MD., U. S. A. CONTENTS. I. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS OF THALLIUM, INDIUM, AND TIN. BY T. W. RICHARDS AND J. H. WILSON. PAGE Introduction I Values of Constants 3 Preparation of the Amalgams 8 Densities of the Amalgams 12 The Cell 15 The Potentiometer 17 Electromotive Force between Thallium Amalgams 20 Electromotive Force between Indium Amalgams 25 Electromotive Force between Tin Amalgams 27 Temperature Coefficient of the Amalgam Cells 30 Application of the Equation of Cady 31 Application of the Equation of Helmholtz 33 Summary 37 II. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM. BY T. W. RICHARDS AND R. N. GARROD-THOMAS. Introduction 39 Zinc Amalgams 39 Electromotive Force between Zinc Amalgams 41 Determination of the Temperature Coefficients of Cells containing Zinc Amalgams 43 Lead Amalgams 47 Copper Amalgam 5° Iron Amalgam 54 Lithium Amalgams 55 Application of the Equation of Cady 57 Equation of Helmholtz 64 Comparison of Deviations from Concentration Law 68 Summary 71 in ^(LIBRARY aol I. Electrochemical Investigation of Liquid Amalgams of Thallium, Indium, and Tin. BY THEODORE W. RICHARDS AND J. HUNT WILSON. INTRODUCTION. The change in free energy during a chemical reaction may be regarded as composed of at least two separate quantities, one which may be said to be due to the affinities involved in the reaction, the other depending upon the relative concentration of initial substances and products. The calcula- tion of the magnitudes of these quantities is a matter of prime importance, for free energy is the driving agency of all earthly things. Unfortunately the actual determination of changes of free energy is only possible in the case of easily reversible reactions, and these form a comparatively small part of many examples of chemical change. Of great theoretical importance in this connection are the reversible galvanic cells, which involve in their action simply the dilution of liquid amalgams, and consequently suffer no appreciable change of heat capacity. The study of such cells can furnish much light upon the second of the two independent quantities which together constitute the total free energy of a reaction, namely, concentration effect. Von Turin pointed out the analogy between such cells and the concentration elements first investi- gated by Helmholtz and offered the first consistent theory of amalgam cells. G. Meyer measured cells of this type, but much more accurate data have been obtained at Harvard University. The object of this recent work, which concerned itself with cells containing zinc and cadmium amalgams over a considerable range of concentration, was to test the application of the gas law to solutions of this type, as well as to apply the equations of Helmholtz and of Cady to the data. Great accuracy was sought. Since the two metals presented widely different phenomena, and since both of these metals are bivalent, it seemed desirable to extend the work by meas- uring similar cells, employing a wide variety of other metals with other valencies. In this way a more complete survey of the possibilities would certainly be obtained. V 2 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS This monograph embodies the results of the further investigation of amalgam cells, containing not only the two metals already mentioned, but also thallium, indium, tin, lead, copper, and lithium. The first section of the monograph deals with thallium, indium, and tin. These metals are especially interesting because they are respectively univalent, trivalent, and (under some conditions) quadrivalent. Thallium is, moreover, inter- esting in its chemical behavior, having in common with the alkali-metals a soluble hydroxide, carbonate, and sulphate, while on the other hand resembling lead in the possession of an insoluble chromate and sulphide, and a slightly soluble chloride. Indium is the only trivalent metal that forms satisfactory amalgams for the present purpose.1 The effort was made to attain precision sufficient to afford an adequate basis for the desired theoretical considerations. No attempt was made to attain the greatest conceivable precision, because such an attempt would have defeated the object of the investigation, by so limiting the variety of results obtainable in the limited time as to have restricted their gen- eralization. 1 An almost complete historical review may be found in the monograph of Rich- ards and Forbes (Publication of Carnegie Institution of Washington, No. 56; Zeitschrift fur phys. Chem., 58, 683 [1907]). A paper by J. Regnauld (Compt. Rend,, 53, 533 [1861]) on the heat of amalgamation of the metals was overlooked in this review, and the date of Helmholtz's publication (Monatsbericht d. kgl. pr. Akad., Berlin, 1877, p. 713) was accidentally given as 1882 instead of 1877. The reference to Lindeck's work is Wied. Ann., 35, 311, 1888. Mention should be made of a mathematical paper by Trevor on the " Electromotive Force of Concentration Cells" (Zeitschr. Elektrochem., 11, 681 [1905]). While this paper contains inter- esting features, experimental verification of the equation deduced therein is not possible at present. In a recent paper published after most of the work embodied in this monograph had been completed, Carhart discusses the Helmholtz equation, as applied to amalgam cells. (Phys. Rev., March, 1908). In a yet more recent paper by Hulett and De Lury, published after the conclusion of the present work, the work of Richards and Forbes is in part repeated and extended to more dilute solutions. In so far as the two investigations overlap, they confirm one another (J. Am. Chem. Soc., 30, 1812 [1908]). Another theoretical paper, by van Laar (Arch. Neerl. d. Sci. ex. et nat. [n] vm, 296), should perhaps be mentioned. OF THALLIUM, INDIUM, AND TIN 3 VALUES OF CONSTANTS. In the discussion which follows, all the experimental work is viewed in the light of three mathematical expressions : T r J_ (0 '=::£-/» 7 (2) In these expressions, TT = electromotive force. c± = concentration of more concen- F= Faraday's equivalent — 96,530 trated amalgam. coulombs. c2 = concentration of less concen- R = the gas constant. trated amalgam. T=the absolute temperature. U = the change of total energy in- v = valence. volved in the dilution of the In — natural logarithm to the base e. amalgam. The first of the numbered equations is the well-known expression of Helmholtz (sometimes called the Gibbs-Helmholtz equation) ; the second contains the substance of the proposal of von Turin and G. Meyer ; and the third is the suggestion of Cady and Lewis. Both of the last two may be said to be the outcome of other work of Helmholtz, and to be covered by the equation of Nernst. Before defining the quantities whose symbols are given in the foregoing list, it may be well to say a word about these funda- mental equations themselves. Equation (i) needs no comment. Equation (2) has been reached in somewhat different ways by a number of thinkers ; it is based essentially upon the epoch-making discussion by Helmholtz of the concentration cell.2 The forms in which the several investigators have expressed their results appear to be different, although they express essentially the same idea; the equation, as given here, is not exactly like that of any of them. Nernst,3 who did not himself at first apply his equation to cells of the type under consideration, used the ratio of pressures instead of the ratio of concentrations, and would have expressed the result thus RTl, P P'\ J I 2 Helmholtz, Monatsberichte d. kgl. pr. Akad., Berlin, 1877, p. 713. Helmholtz's other well-known paper on the thermodynamic equation numbered (i) above was published in the Sitzungsberichte der kgl. pr. Akad., Berlin, in February, 1882, p. 22. 3 Nernst, Zeitschr. phys. Chem., 4, 129 (1889). 4 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS In this equation P and P' represent the unknown solution-pressures, whose ratio alone is to be inferred, and p the osmotic pressure of the appropriate ion in the electrolyte. The latter cancels, being common to P both electrodes, and the expression becomes ir= — -p ln~^i . ^ no other source of free energy other than osmotic effect is present, -— may be taken as equal to — and the equation reduces to ours. In this expression the Cl absence of association in the dissolved metal is assumed. Both Nernst's expression and that given above are calculated on the basis of the gram-atom. On the other hand, von Turin4 and Meyer" expressed their equations in terms of concentration, and calculated them on the basis of the electro- chemical equivalent in terms of grams per coulomb ; and both introduced the molecular weight (M or jn) of the dissolved metal — although, to be sure, von Turin seems to have accidentally omitted this quantity from his final statement.8 Their equation, reached in different ways, reads T gram-atomic -weight Bearing m mind the fact that their q meant — - — — and that vr we have made the additional assumption (based upon the measurements of many investigators) that M = gram-atomic weight, it is seen that their form is essentially identical with that given above. Our form will be called in future merely " the concentration-equation," as its ascription to any one author might under the circumstances seem invidious. Attention should be called to the fact that Helmholtz, himself, insisted that his original concentration-equation holds true only when there is no heat of dilution involved in the reaction,8 a condition reiterated by von Turin. The same limitation applies, of course, to the equation in its present simplified form ; but this limitation does not necessarily apply to the equation of Nernst, involving solution-pressures instead of concentrations. The term solution-pressure must be interpreted as including combined effect of all the tendencies affecting the escape of the dissolved metal from 4 von Turin, Zeitschr. phys. Chem., 5, 340 (1890) ; 7, 221 (1891). BG. Meyer, Zeitschr. phys. Chem., 7, 447 (1891). 6 See von Turin on the bottom of page 221, Zeitschrift fur physikalische Chemie, 7 (1891). T By a coincidence of misprints, of which there are many in the papers of both von Turin and Meyer, the decimal point of the factor 19.1 has been misplaced in each case and reads 1.91. This mistake was inadvertently copied in reporting the history of their work in Publication 56 of the Carnegie Institution of Washington. 8 Helmholtz, Berliner Monatsbericht, November, page 713 (1877). OF THALLIUM, INDIUM, AND TIN 5 the amalgam, except the osmotic pressure of the ion dissolved in the electrolyte. Thus P and P' include the effect of the chemical free p energy change connected with dilution ; and if such exists —7 can not be equal to — . This explanation appears to be necessary, because of the C-i misconception of Carhart concerning the significance of the Nernst equation.9 The equation of Cady 10 and of Lewis " is an attempt to take account of the heat of dilution, thus resolving the tendencies P and P' into their most important components. This equation may only be supposed to hold true when there is no change of heat capacity during the reaction. Further explanation may be deferred until the present research has been described, when a still more recent suggestion of Lewis, concerning the application of the law of Raoult [— £ = — - — ] to osmotic work, will also be con- \p N+nJ sidered. Before beginning a description of our experimental work it will be well to consider the accuracy with which the various quantities in the equations are defined. In a previous contribution from this laboratory" the results of Ray- leigh,13 F. and W. Kohlrausch,14 Kahle,15 and Patterson and Guthe,1' con- cerning the value of Faraday's equivalent F, have been compared ; and the conclusion was reached that 96,580 coulombs are associated with 107.93 grams of silver, if the silver is weighed in a form free from mother-liquor, after having been deposited in a manner avoiding anode complications. The more recent work of Smith, Mather and Lowry, and others, has not changed our opinion on this point." Since Richards, Collins and Heim- rod,18 and Richards and Stull 19 have established the universality of Fara- day's law on a firmer basis than ever, the same value can be used for a gram equivalent of thallium or indium with reasonable accuracy. If the atomic weight of silver is taken as 107.88, a value probably nearer the 8H. S. Carhart, Phys. Rev., 26, 216 (1908). 10 Cady, Journ. Phys. Chem. 2, 551 (1898). 11 Lewis, Proc. Am. Acad. 35, 34 (1899). 12 Proc. Amer. Acad., 37, 415 (1902). "Phil. Trans., 175, 411 (1884). 14Wied. Ann., 27, I (1886). "Wied. Ann., 67, I (1889). 16 Phys. Rev., 7, 257 (1898). 17 Smith, Mather and Lowry, Phil. Trans. Roy. Soc. London, Series A, 207, 545 (1908) ; also see especially T. W. Richards, Proc. Am. Acad., 44, 91 (1908). The Report of the International Conference on Electrical Units and Standards, " Science," 28 (1908), recommends F = 96,540 for the same atomic weight without these pre- cautions. This probably amounts to about the same thing. 18 Zeit. phys. Chem., 32, 301 (1900). 19 Proc. Amer. Acad., 35, 123 (1899). 6 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS truth, the value F must be diminished by 0.05 per cent, and becomes 96,530 coulombs per gram equivalent. This latter value is used in the work which follows, and all atomic weights also are referred to this standard. The symbol v represents the valency of the metallic ion in the electrolyte of the cell. Since thallous sulphate and indium sulphate were used as electrolytes in the cells of thallium and indium amalgams, it is difficult to conceive how the valency of the ions of thallium and indium could be other than i and 3 respectively. The valency of tin will receive especial consideration when that metal is discussed; in our experiments it was undoubtedly 2, not 4. The work of Daniel Berthelot 20 probably affords the most accurate value of R, which we may express conveniently in mayers. A mayer is the heat capacity which is warmed I degree centigrade by i joule. According to Berthelot's work, the space occupied by a gram-molecule of a perfect gas at 760 mm. pressure, 45° latitude at the sea-level, may be taken as 22.412 liters (the atomic weight oxygen being 16.000), and the absolute zero at — 273.08° C. These values are probably accurate at least to within 0.05 per cent. The value of R on this basis will be R= 76.00x13.596x980.6x22,412 =g 6 s< 273.08 xio7 T, by which R is multiplied in the formula, is the temperature of the cell referred to the hydrogen scale. This was fixed in our experiments by means of four exactly known thermometers. Over the range of tempera- ture employed in the following measurements these readings are closely comparable with the corresponding thermodynamic temperatures. More- over, the experimental determination of the temperature to within 0.01° T" would fix the value of -f-1 within one part in 30,000, a degree of accuracy Jo far greater than can be attained with the rest of the data used in calculat- ing the electromotive forces. It appears, then, that the values of v, R, T, and F are known with considerable accuracy, and it now remains to consider the concentration ratio -£L. An error of o.i per cent in this ratio would cause an error of Ct o.ooooi volt in the electromotive force, and it is clear that the early investi- gators have not determined this ratio with sufficient accuracy. If a weight w of amalgam of concentration c^ is mixed with a weight nw of mercury to form a new amalgam of concentration cz, it is not permissible in accurate work to write ""Tray. et Mem. du Bureau internat. des poids et mesures, 13, 113 (1903). OF THALLIUM, INDIUM, AND TIN 7 as seems to have been the custom of previous workers in this field. Richards and Forbes have shown the necessity of applying a correction for the difference in density of the two amalgams being compared. For example, let w be the weight of an amalgam of concentration ct diluted with wHg grams mercury to form a new amalgam c2. Now, if Z)x and D2 are the densities of the amalgams, we have wl C\___V* ___ Dt _ Z^l + c2 vl ~ w± wv t D, Careful determinations were made of the densities of the several amal- gams at various concentrations ; and corresponding corrections were applied to the calculated values of the concentration ratio. These determi- nations will be considered later in their proper place. The densities were all measured at 20° ; their relative values undoubtedly change slightly with the temperature, but not enough to affect appreciably the calculation in question. In calculating the thermochemical results, one 18° calorie was taken as equal to 4.181 joules.*1 A number of typical cadmium standard cells, containing crystals of cadmium sulphate, prepared from different pure materials at different times, were used as the standard of electromotive force. As these all agreed within the tenth of a millivolt, their value was taken as 1.0184 — 0.00004 (t° — 20°) international volts and this value was used as the standard of electromotive force.22 21 Callendar and Barnes, Phil. Trans., A, 199, 149 (1902). 22 See Report of International Conference on Electrical Units and Standards, 1908 — published in many places, for example, "Science," 28, 743 (1908). 8 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS PREPARATION OF THE AMALGAMS. The thallous sulphate used in preparing the thallium amalgams was a sample which had been many times recrystallized, both as acid sulphate and as sulphate. The original preparation had been of a high grade of purity. The indium amalgams were prepared from a sample of very pure indium, which, through the kindness of Professor L. M. Dennis, of Cornell University, was available for this work.23 The sample in question had been carefully purified for use in the determinations of the atomic weight of indium, although it was not the purest specimen used for this purpose, and was finally fused in a current of hydrogen. It contained no impurity, except a trace of iron. Metallic tin was obtained by the electrolysis of an acid solution of pure stannous chloride, using a pure carbon anode. The fine needles of tin were washed with distilled water and alcohol and dried in a desiccator over sulphuric acid. Pure mercury was obtained as follows : Crude mercury was shaken first with sulphuric acid to remove the major part of the metallic impuri- ties and then for some time with dilute nitric acid and mercurous nitrate. The sample was now wholly free from contamination with the more electropositive metals. It was then distilled under a pressure of 20 mm. of hydrogen in an apparatus somewhat similar to that described by Hulett.24 The hydrogen was passed through three towers, containing solid potash, in order to purify and dry it. The entire apparatus, as far as the connection to the pump, was wholly fused together in order to avoid rubber connections or glass joints. The pipettes in which the mercury was kept were themselves used as the receivers of this still, and the mercury was sealed in them without for an instant coming in contact with the air. The stopcock, regulating the supply of gas bubbling through the mercury, was lubricated with sirupy phosphoric acid. The mercury thus obtained must have been very pure. Distillation in air, recommended by Hulett, affords an excellent means of oxidizing other metals present; but our experience leads us to fear that the product contains a trace of dissolved oxygen. Accordingly, we used hydrogen instead of air. The water used in making up the solutions was distilled twice, first from an alkaline permanganate solution, and then from very dilute sulphuric acid. Since amalgams of all the metals studied are very susceptible to oxida- tion, they were made and introduced into the measuring apparatus wholly out of contact with the atmosphere, and the mercury from which they were made was never allowed to come into contact with the air after its distillation in rarified hydrogen. 23 For details of purification of this indium see Jour. Amer. Chem. Soc., 29 (1907). 24 Zeit. phys. Chem., 33, 611 (1900). OF THALLIUM, INDIUM, AND TIN 9 It was found that the thallium amalgams could be most conveniently prepared by the electrolysis of a solution of thallous sulphate, using a mercury cathode. Addition of ammonium oxalate prevented the formation of peroxide on the anode. The complete apparatus used in preparing and transferring the amalgam is shown in fig. i. Hydrogen Fig. 1. Apparatus for Making and Preserving Amalgams. The amalgams were prepared by electrolysis in the flask H. Connection was made to the mercury cathode by means of glass tube passing through the stopper carrying the wire K. The anode / terminated in a spiral of platinum wire. The anode was inclosed in a small linen bag (not shown in the figure), in order to prevent any peroxide which might be formed from falling on the cathode. The amount of thallium deposited was measured by a silver coulometer included in the circuit. The coulometer was of the form used by Richards and Heimrod. The porous cup was cleaned with concentrated nitric acid and then boiled with many portions of water before use. The anode was a bar of pure silver which had been prepared for use in an atomic weight research. Care was taken to keep the level of the liquid within the porous cup lower than that outside in order to prevent outward filtration. An amperemeter, also in the circuit, served for an approximate measurement of the current strength. IO ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS A weighed amount of pure mercury was run into the flask H, which was then nearly filled with a saturated solution of thallous sulphate con- taining about ten grams of ammonium oxalate. The stopper was inserted, care being taken that the cathode and the tube T leading to the flask C were immersed in the mercury. The current was now allowed to run until the desired quantity of thallium had been deposited. The time neces- sary for this could be calculated approximately from the readings on the amperemeter. On breaking the circuit, the amalgam was immediately sucked up into C by cautiously opening the stopcock S4. The platinum crucible containing the deposited silver was washed with water, dried at 200°, and weighed. From the weight of the silver deposited, the concen- tration of the amalgam could be calculated. The arrangement employed in transferring the amalgams was essentially similar to that used by Richards and Forbes. Hydrogen, prepared from pure hydrochloric acid and zinc, and purified by passing through four towers containing concentrated potassium hydroxide solution and dry fused potash, was supplied through the tube G. The pipette B communi- cated through A with either the hydrogen supply or the vacuum-pump. The outlet tube of B, terminating in a thick capillary, passed through a tightly fitting rubber stopper into the flask C. (The rubber stopper had been boiled with alkali, thoroughly washed with water and finally covered with soft paraffin.) The flask C was supplied with two side necks. The tube F communicated with the vacuum-pump, while T was bent down and passed to the bottom of the flask H. The whole apparatus being thoroughly clean and dry, it was manipu- lated as follows: First ^4, 5\, and S5 were closed and S2 and S3 were opened; the pressure in B and C was reduced to 15 mm. of mercury, and 56 was closed. The manometer, R, proved that the apparatus was free from leakage. By cautiously opening 5"5 the system was now filled with hydrogen ; and the exhaustion and filling with hydrogen were repeated three or four times. Care was taken to expel the air in the capillary also by a stream of hydrogen. In order to force the hydrogen through the shallow layer of mercury in the bottom of H, the pressure in H was slightly diminished by suction through S7. After the amalgam had been drawn up into C, a rapid stream of dry hydrogen was bubbled through it by opening S5 and ^3, at the same time maintaining a low pressure in C. This served to dry the amalgam and to mix it thoroughly. After 10 or 15 minutes S2 was closed and the system was allowed to fill with hydrogen. 5\ was then opened and B exhausted. By opening S3 the amalgam could be drawn up into B. S5 was finally opened and normal pressure restored in B, which was then sealed off at A by using a small blast flame. F was cut with a file and the flask C detached. The capillary tip of the pipette- OF THALLIUM, INDIUM, AND TIN II like tube of B was immediately sealed with wax to protect it from air. The pipettes were kept in a rack, shown in fig. 2. Precisely the same mode of procedure was followed in preparing and protecting the electrolyte used in the cell. The stream of hydrogen was allowed to bubble through C for some time to remove the last traces of air from the solution. It was then drawn up into the pipette and sealed off as before. When the solution was wanted its weight was, of course, not sufficient to draw it out; accordingly the following method was used to follow it up with hydrogen : A clean rubber tube, delivering a stream of pure hydrogen, was slipped over the drawn-out portion, and the tube was then broken ; in opening the stopcock, the solution readily flowed out. Fig. 2. Rack with Pipettes containing Amalgams. The amalgams of indium and tin were prepared in the same apparatus. It was found more convenient to prepare the latter amalgams by adding the metals directly to the mercury in the atmosphere of carbon dioxide in the flask H, for they are far less readily oxidized than the others ; but afterwards the amalgam was treated just as the others. 12 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS DENSITIES OF THE AMALGAMS. It has been pointed out K that a knowledge of the densities of the various amalgams is essential in order to fix accurately the value of the concen- tration-ratio in calculating the theoretical potentials of the cells. More- over, such data make possible the calculation of the contraction or expan- sion occurring on the amalgamation of the various metals. For these reasons numerous determinations were made of the densities of the amal- gams of thallium, indium, and tin. The pycnometer used was of the Sprengel type, as modified by Ostwald ; its capacity was about 3 cc. and its tubes I mm. in diameter. Before use it was thoroughly cleaned with appropriate reagents, and, after washing with water, dried by suction. The weight of the pycnometer filled with mercury at 20° was then carefully determined. Since in filling the pycnometer with the amalgams, it was sometimes difficult to adjust the contents exactly to the marks, the weight of a centimeter length of mercury in the capillary was determined, and a suitable correction was applied. The length of any excess in the column of amalgam was accurately determined with dividers. Since the correction was small, never amounting to more than 0.15 gram, the difference in density between mercury and the amalgam would cause no appreciable error. All the densities were determined at 20°. The amalgams used in these determinations were prepared in the manner already described. When all was ready, a sufficient quantity of the amalgam was run out into a small weighing bottle, filled with carbon dioxide, and hastily drawn up into the pycnometer. By working in this fashion, no serious oxidation occurred. The thread of mercury was adjusted only after the pycnometer had been in a thermostat at 20.0° for some time. The data of a typical determination are as follows : Weight of pycnometer and mercury 53.228 Weight of pycnometer alone.... 18.134 Weight of mercury 3S-OQ4 Weight of pycnometer and amal- gam 53.121 Weight of pycnometer alone.... 18.134 Weight of amalgam 34.987 The density of mercury at 20° is 13.545, therefore the density of the amalgam is 3_4j9__Z x 13.545 = I3-5°4 35-094 This amalgam contained 1.845 Per cent thallium. Table I contains the results with amalgams of thallium, indium, and tin. There are given also imaginary values which the densities would have shown if no contraction or expansion had taken place on amalgamation. 25 Richards and Forbes, Publication of Carnegie Institution of Washington, No. 56, II (1906). Also, pp. 6 and 7 of the present monograph. OF THALLIUM, INDIUM, AND TIN The values of the densities of the pure metals used for this calculation are given in the first column of the table. The value for the density of pure indium is the mean of two closely agreeing determinations made by us with Professor Dennis's pure sample of the metal, because the values previously obtained, 7.421 by Winkler and 7.12 by Thiel, are in very poor agreement. Our data are as follows : First Determination : Weight of pycnometer : Grams. With air-free water (20.0° ) 10.1338 Alone 7.0012 With indium alone 10.2568 With indium and water 12.9420 Result : Density 7.277 Second Determination: Weight of pycnometer : With indium alone 10.0045 With indium and water 12.7525 Result : Density 7.291 The mean value is 7.284. Corrected to vacuum the true density of indium is found to be 7.277. TABLE i.— Densities of Amalgams. Metal. Per cent of solid metal in amalgam. Correct weight of liquid needed to fill pyc- nometer. Actual density of liquid. Calculated imaginary density of amalgam. Thallium (density n .85) 1.854 34.987 1 1 . 504 13.509 Indium (density 7.28) I .410 0-793 I .920 35-017 35-049 34 • 548 13.515 13.527 13.334 13.520 13.530 13.324 Tin (density 7.29) 1-430 I .OQO 0.928 0.770 0.468 0.45 34-703 34.784 34.835 34-867 34-949 35.012 13-394 13.426 13.446 13.457 13.489 13.513 13.380 13.419 13-439 13-455 13.490 13.493 Mercury, pure (density 13.545) 0.30 0.21 0 35-027 35-053 35-095 13.519 13.529 13-545 13.510 13.519 13-545 The density curves for the thallium, indium, and tin amalgams are shown in fig, 3. The dotted lines give the imaginary values that would be obtained if neither expansion nor contraction took place on mixing. Indium and tin contract on amalgamation, while in the case of thallium there is a slight expansion. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS 13.34 13.36 13.38 13.40 13.42 13.44 13/46 (3.48 13.50 13.53 13.54 13.55 In /A Tl 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 a.o Fig. 3. Densities of Thallium, Indium, and Tin Amalgams. Densities are plotted as ordinates, per cents by weight of solute in amalgam as ab- scissae. The continuous lines represent actual densities, the dotted lines the averaged densities of the components, that is, the density which the amalgam would have possessed if there had been no change of volume on mixing. The dotted line for tin coincides essentially with that for indium. OF THALLIUM, INDIUM, AND TIN 15 THE CELL. The multiple cell used in all the measurements of electromotive force is shown in fig. 4. This apparatus, devised by Richards and Forbes, must be very carefully annealed, for even at the best the glass receptacle is very fragile. The body of the vessel is used to hold the electrolyte ; the four cups contain the amalgams to be measured. The advantage of the four cups is obvious: six different measurements may be made at one filling, and at the same time important checks can be secured on the accuracy of the readings. Fig. 4. Amalgams in Cell ready for Potential Measurement. The glass receptacle was carefully cleaned and dried, and fused at A to the delivery tube of an apparatus supplying pure hydrogen. A vacuum pump was now attached at S2 and the whole cell exhausted as far back as the stopcock 6\. The tops of the tubes, B, C, D, and E were closed with small pieces of rubber tubing and glass rod. When the pressure had been reduced to about 20 mm., the stopcock S2 was closed and the cell allowed to fill with hydrogen through S^. This was repeated four times. The glass rod was now removed from one of the tubes and the fine tip of a pipette, containing the proposed electrolyte, inserted. The issuing stream of hydrogen prevented the diffusion of air into the cell. When the vessel was about half full of the aqueous solution, the pipette was withdrawn and the stopper was replaced. In the same manner suitable amounts of the 1 6 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS various amalgams and mercury were introduced into the four cups. Finally, the electrodes, sealed into narrow glass tubes, were introduced — care being taken that the platinum points did not touch the glass. S: was now closed, the coil broken off from the hydrogen supply, and the vacuum connection removed from S2. After gentle shaking for several minutes, the completed cell was transferred to the thermostat, and the measure- ments soon begun. Amalgams prepared thus remained bright as long as was necessary and showed no signs of oxidation. It is evident that Hulett and De Lury did not fully read the somewhat similar description by Richards and Forbes, or they would not have suggested that the method contained faults which existed only in the preliminary work, not in the procedure finally adopted.28 The manner of adjusting the wires connecting the potentiometer to the cell should be mentioned. In the first trials long platinum wires dipping in the various amalgams were connected with the copper wires by means of mercury cups. The junctions of unlike metals were thus outside of the thermostat — an objectionable feature. Accordingly, in the final measurements only a short length of platinum wire was fused in the bottom of each tube dipping into the cell, and above this was placed, inside the tube, a drop of mercury. The copper wires were now pushed down the narrow tubes until connection was made with this drop. The contact of unlike metals was now deep in the cell and, being at constant temperature, could cause no disturbance. Most of the potentials were measured at 30° and o°, and many of the thallium cells were also measured at 15°. The temperature of the 30° bath was kept constant by means of a sensitive electrical regulator. A large heating coil was used in place of an incandescent lamp as the source of heat, since it avoids any disturbing effect due to radiant energy when the heater is in frequent operation. The temperature of this bath was always constant within 0.01°. The 15° bath was exactly similar except that it was equipped with a cold-water coil in order to compensate for the higher temperatures of the surroundings. For the zero bath a metal trough was filled with clean, finely crushed ice, covered with distilled water. This trough was placed in a larger one, the space between being filled with ice, and the box in turn was tightly packed in sawdust. This arrangement gave a very constant temperature. The temperatures of all the thermostats were determined with small Beckmann thermometers, capable of being read to within 0.005° 5 tne.v were standardized by com- parison with a very accurate Reichsanstalt thermometer, taking all the precautions necessary for ascertaining the temperature to within o.oi.° M Compare Hulett and De Lury, Journ. Am. Chem. Soc., 30, 1809 (1908) with Richards and Forbes, Publication of Carnegie Institution of Washington, No. 56, page 40 (1906). OF THALLIUM, INDIUM, AND TIN THE POTENTIOMETER. Considerable time was spent in the elaboration of a suitable potentiom- eter for use in this work. The arrangement used by Richards and Forbes, while probably accurate to 0.000005 of a volt, was complicated and involved troublesome calibrations. Moreover, it seemed desirable to dispense with the one-volt element and compare the drop of potential directly with a standard Weston cell. The arrangement finally adopted is shown in fig. 5. It was elaborated with the help of R. N. Garrod-Thomas, and was used also for his work, to be described later. H roo o o ] IP O O O I IG Q O O i E o ° ° - o o o A o o 0 o o 0 T o V- V X Fig. 5. The Potentiometer. A large Daniel cell F was used as the source of the fall of potential. When in use, it was found best to keep it short-circuited through a resist- ance of about 300 ohms in the box E. The rough box D was so adjusted that the fall of potential between the points U and V was equal to 1.0184 volts, as measured against the normal cell H. C was a constant resistance of 9000 ohms. A and B were resistance boxes of mi ohms each, and MN was a manganin wire of 1.063 ohms resistance. At the commence- l8 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS ment of a measurement, the plugs were all placed in the box A and all removed from B. The resistance between U and V under these conditions was 10,112.06 ohms, embracing a drop of potential of 1.0184 volts, as given above. By removing plugs from A to the corresponding place in B, in order to keep the drop of potential constant, and manipulating the slider X, it was easy to compensate the potential of the unknown cell by opposing potential tapped from the box A and the slide-wire bridge, since the poten- tials measured never amounted to as much as o.i volt. Suppose the total reading of the box A and the slide wire to be a ohms. Then the potential of the cell measured would be - x 1.0184 volts. 10,112.06 The factor — - — ?-, being a constant value, its logarithm was found once 10,112.06 for all, and entered into all calculations. In following this mode of procedure, the only portion of the resistance which needs very accurate calibration is the box A. The wire MN was 65 cm. in length, and was divided by a scale into divisions 6.10 mm. long, each of these corresponding to the millionth of a volt. Since the total fall of potential in the wire was only about o.oooi volt and preliminary calibra- tion showed it to be very uniform in resistance, no correction was deemed necessary for the readings of this scale under the wire. PQ was a three- way switch. When thrown towards P, the standard cell H was balanced against the fall of potential between U and V. When thrown toward Q, the potential was ready to be balanced against a portion of the bridge MN and box A. The galvanometer G of the d'Arsonval variety was manu- factured by the Leeds and Northrup Company, of Philadelphia, and is designated by them as Type H. It was read with a telescope and scale at a distance of 60 cm. 6" was a double-rocker switch, the base of which was a thick plate of ebonite. It was so arranged that the galvanometer was either in the circuit or short-circuited itself. The galvanometer was extremely sensitive, and when short-circuited it returned to zero without any oscillations whatever. The whole potentiometer with the exception of the galvanometer was placed inside of a large glass case with a swing- ing door in order to avoid disturbing effects from changes of temperature and impurities in the atmosphere. The apparatus, as described above, was used in the measurements on thallium amalgam cells and was easily accurate to within three or four millionths of a volt. Since thallium under the conditions of the measure- ments was univalent, and consequently gave comparatively large poten- tials, the above accuracy was fully sufficient; but in the case of trivalent indium, which for equal concentrations gives potentials only one-third as large as those of a univalent metal, even greater accuracy was desirable. OF THALLIUM, INDIUM, AND TIN IQ As has been previously mentioned, the portion of the bridge wire MN corresponding to one ohm was divided into 100 parts, giving direct read- ings to o.oooooi volt for each 6 mm. of wire. The graduation of the instrument was therefore adequate ; improvement was to be attained only by eliminating all irregularities ; and prominent among these, as every one knows, are thermoelectric effects due to junctions of dissimilar metals. Two ways of suppressing thermoelectric effects are available: one, to use only one metal ; the other, to keep the temperature the same through- out. The latter method was in the present case the more convenient. It was at first found that the temperature at the two ends of the glass case containing the potentiometer differed by as much as 0.5°. Part of this difference was traced to the proximity of an incandescent light, which was removed ; but there still remained a considerable variation. This was finally overcome by the use of a small revolving fan which was attached to an axle run through one of the corners of the case and driven at high speed by a motor. Thus the air was stirred and kept at the same tempera- ture throughout. Contact of the operator's hand with the bridge slide was obviated by the use of two cords attached to opposite sides of X and passed through small holes in the ends of the case; and the final adjust- ment was made on the bridge with the case closed. In this way another frequent source of irregularity was avoided and the readings were im- proved. The room in which all the apparatus was placed was kept as constant in temperature as possible. In seeking for the causes of the yet remaining fluctuations, it was found that the galvanometer was influenced by the proximity of the observer, and even more so by heat-effects due to the operation of the rocker switch 5" with the hand. Therefore, the galvanometer was removed some dis- tance from the apparatus and screwed against a very firm wall, the con- nections being made by insulated copper wires incased in glass tubes. The case of the galvanometer was packed in felt and covered with a sheath of copper, a small hole permitting a view of the mirror ; and the instru- ment was read by a telescope and scale placed at a distance of about 130 cm. The rocker switch 5 was placed inside the case and operated from outside by means of a long cord, the observer being seated at the telescope some distance away. The resistance box A was standardized by substitution. A sensitive Wheatstone bridge was used and the corrections on the various resistances were determined and tabulated exactly as if they were weights.27 Only two of the corrections thus found were as much as o.oi ohm, and since each o.oi ohm corresponds to very nearly o.oooooi volt, it is easily seen that all others were negligible. The two in error were the 300 and " Richards, Proc. Am. Chem. Soc., 22, 144 (1900). 2O ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS 400 ohm coils ; and the deviation of these amounted to only 0.000002 and o.oooooi volt respectively. The boxes B and C were of the same quality as A and a preliminary standardization showed them to be fully as accu- rate. Since the resistances in B and C need be known only one-tenth as accurately as those in A, any corrections on these boxes would be super- erogatory. The one important point, that 1000 ohms in A should be exactly one-ninth of the 9000 ohms in B, within o.oi per cent, was demon- strated. The standard Weston cells were made up from pure material as recom- mended by Hulett. These cells were compared with one another and also with three similar cells kindly loaned by Dr. H. L. Frevert. They all furnished the same value to within o.oooi volt at 20°, and for their value the electromotive force 1.0184 was accordingly assumed. The improved potentiometer described above appeared to be accurate to within a microvolt (o.oooooi volt) — a high degree of precision. ELECTROMOTIVE FORCE BETWEEN THALLIUM AMALGAMS. With the apparatus and materials which have been described, measure- ments upon a variety of amalgams were executed. The description of a preliminary experiment will be given in detail, in order that the method may be more thoroughly understood. Amalgam I was prepared in the closed apparatus by depositing into 180.557 grams of mercury the amount of thallium equivalent to 0.9473 grams of silver (deposited in a coulometer in the same circuit), that is to say, 1.7915 grams of thallium, if silver and thallium are assumed to have the atomic weights of 107.88 and 204.03 respectively. Hence the amalgam contained 0.9822 per cent of thallium by weight. One portion of this amalgam was introduced into one cup of the multiple cell, and another weighed portion was introduced out of contact with air into another cup, being diluted by the addition of a weighed amount of the pure mercury, which had been preserved in hydrogen as previously described. The second cup contained 36.513 grams of mercury, and received 25.721 grams of amalgam. It is easy to calculate that the dilute amalgam must have contained 0.4059 per cent of thallium. In order to mix thoroughly the amalgams and mercury in the second cup, the cell was gently shaken for some time, great care being taken to avoid any splashing from one cup to another. The cell was then introduced into the 30° ther- mostat and, after it had acquired the temperature of the bath the readings were begun. Two measurements of the cell gave values of 25.235 and 25.238 millivolts respectively, in mean 25.237. The potential remained very constant over a considerable interval of time. Two entirely separate measurements taken with the same cell 48 OF THALLIUM, INDIUM, AND TIN 21 hours later gave the values 25.231 and 25.243, in mean 25.237, exactly the same as before. In subsequent work the agreements were of this order of accuracy ; usually average values alone will be given. It is worthy of remark in this connection that the electrolyte was not found to be the least alkaline to phenolphthalein after thus standing for 48 hours over a thallium amalgam. This fact is very satisfactory, not only with regard to thallium, but also in its implication concerning the probable integrity of amalgams of less easily oxidized metals, whose oxides are less easily detected. It is interesting to compare the result with the ideal value calculated from the gas law. The theoretical potential, calculated according to the formula v = 8.3i6x (273.09°) X2.3026 j c* 96,530 Cn is 23.064 millivolts. This is 2.183 millivolts, or nearly 10 per cent, less than the observed value 25.237. Having thus cleared the way by this preliminary work, four series of more accurate measurements were made. Four multiple cells containing thallium amalgam, designated A, B, C, and D, were prepared. In each case an amalgam prepared electrolytically was placed in cup I ; and cups 2, 3, and 4 were filled with the same amalgam diluted (in an atmosphere of hydrogen) with weighed amounts of mercury. The " parent amalgam " in cups Ai and Bi was made by depositing in 197.33 grams of mercury the amount of thallium equivalent to 0.4290 gram of silver. This amalgam was diluted as follows: grams of amalgam. grams of mercury. 13-272 + 82.933 in A2 IS-679 4I-938 A3 23.710 32.791 B2 6.838 97.483 63 11.736 83.642 64 The " parent amalgam " in cup Ci was made by depositing in 168.361 grams of mercury the amount of thallium equivalent to 1.6738 grams of silver. This amalgam was diluted as follows : grams of amalgam. grams of mercury. 12.487 + 31.420 in C2 10.710 75-495 C3 10.448 112.095 €4 Finally the " parent amalgam " in cup Di was made by depositing in 213.65 grams of mercury the amount of thallium equivalent to 0.2289 grams of silver. This amalgam was diluted as follows : grams of amalgam. grams of mercury. 14.967 + 29.589 in D2 8.851 75-453 D3 9.461 122.984 D4 22 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS The electrical measurements made with these amalgams are summarized in table 2, together with the theoretical values calculated upon the assump- tion that the gas law applies with exactness, according to the concen- tration equation: RT , cm T — —^ in - F Cn TABLE 2. — Electrical Measurements of Thallium Amalgams. Designation of cup containing amalgam. Approxi- mate per cent of thallium in amalgams. Exact value of log^ Cn Electromotive force between each pair of cups, in millivolts. o°c. 15°C. 30°C. Observed. Theo- retical. Observed. Theo- retical. Observed. Theo- retical. Al 0.410 , O.III C 0.0565' 0.410 -. 0.172 1 0.0512^ o . 0269 ' I.8456-. 0.5249:* 0.2294| 0-1575 0.220 , 0.074 I 0.0231 j 0.0157^ 0.56502 0.29498 0.37694 0.53272 0.27338 0.54518 0-35943 0.16340 0.47203 0.50556 0.16729 31-543 16.360 30 . 608 15.980 33.166 17.238 32 . 290 16.858 34.810 18.110 23-523 32.408 16.531 37-134 22.610 10.090 28.964 30.592 10.114 33-971 17-735 22.664 32 . 026 16.436 32.775 21 .6lO 9.824 28.379 30.455 10.058 A2 A3 . Bi B2 83 . 64. 33.897 20.485 9.II8 29.533 19.471 8.852 35-511 21.530 9.601 3I-I55 20.541 9.338 Ci €2 C3 . €4 . Di D2 D3., 04., The measurements with cell B at the lower temperatures were unsatisfactory, and were rejected; cell D was measured only at 30°. Each observed figure is the mean of at least three measurements. For example, the Di-D2 was found to have a potential of 28.969 millivolts by direct measurement. Di-D3 was found to be 59.551, and D2-D3, 30.596. Subtracting, we find again Di-D2 = 28.955. In the same way, by subtracting the observed value for D2-D4 from that for Di-D4, the value 28.969 is found. The mean value 28.964 is given ; the same practice was adopted in all cases. OF THALLIUM, INDIUM, AND TIN 23 The difference between the observed and the ideal values is usually great; in the case of the concentrated cell, Ci-C2, it amounts to 13 per cent. Further study of the figures shows that as the dilution is increased, this difference between the observed and calculated potentials diminishes, becoming only about 0.6 per cent in the case of the very dilute cell 03-04. Deviations from the theoretical are always positive ; the cell always gives a potential higher than the value computed simply from its concentrations. Cells of thallium amalgams thus appear to behave in a fashion similar to those of cadmium with increasing dilution, although in the case of the thallium cells the deviations are larger. Zinc varies in the opposite direction. The results of these measurements and calculations are plotted graphi- cally below according to the method employed by Richards and Forbes, which affords a convenient method of noting the departure of the cells from the gas law. In fig. 6 there are plotted as abscissae the logarithms of the volumes occupied by a given weight of amalgamated thallium, taking the volume of the most concentrated amalgam in cup Ci as unity. The progress of the curve in the direction of ordinates between the points corresponding to any two volumes indicates the extent of the deviation from the theory of the electromotive force of the cell made from the two indicated amalgams. The curve is built up by plotting first the results with cell C, then those with cells A and B, and finally those with cell D. In each case as the drawing progressed the " parent amalgam " was started at its proper concentration on the curve already drawn ; and this proceeding of necessity fixed the other points obtained from that particular cell. If into each cell a two-phase amalgam, having a constant potential, had been introduced, according to the excellent suggestion of Hulett and De Lury, the construction of this curve would have been somewhat facili- tated ; but the final result would have been identical. In this case greater care about perfect constancy of temperature would have been necessary. The regularity of the curve affords strong evidence of the accuracy of the measurements. The curve for the thallium amalgams, like those for both zinc and cadmium, shows that as dilution is increased the potential of any cell approaches nearer and nearer to the requirement of the simple concentra- tion law ; that is to say, the slant of the curve becomes less and less. Com- plete horizontality would indicate complete fulfilment of the gas law. The regular form of the curve indicates the absence of oxidation in the more dilute amalgams, one of the most insidious sources of error in this sort of work. Thallium amalgams are extremely sensitive to oxidation and its elimination in these measurements is a source of gratification. The results depicted by this curve will be discussed later in connection with the results for the other metals. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS + 7 -1-5 + 4 •f 3 + 2 log 2 Iog8 log 16 log 64 log 128 log 256 Fig. 6. The Deviations of the Electromotive Force of Thallium Amalgams. 7? f r Deviations from the expression w =: ~p ln ^ are plotted in millivolts as ordinates, the logarithms of the concentration ratios as abscissae. The most concen- trated amalgam contained 1.85 per cent by weight of thallium and 98.15 per_ cent by weight of mercury. A horizontal line on the diagram would indicate complete fulfilment of the concentration law. This curve is almost if not quite independent of temperature, at least between o'and 30". OF THALLIUM, INDIUM, AND TIN ELECTROMOTIVE FORCE BETWEEN INDIUM AMALGAMS. Amalgams of indium were now studied in the same manner. They had been prepared in the fashion described on page 9, and all the dilutions were made inside the cell in an atmosphere of hydrogen with the same precautions as in the case of thallium. Density corrections were applied in the calculation of the concentration ratio. Three parent amalgams, Ei, Fi, and Gi, were prepared. The first, Ei, contained 3.0014 grams of indium dissolved in 152.783 grams of mercury; the second, Fi, 23.276 grams of this amalgam with 116.472 grams more of mercury, and the third, Gi, contained 40.812 grams of Fi with 72.926 grams more of mercury. These " parent " amalgams were diluted as follows : grams of amalgam. 10.368 El 9732 El 8.074 El 11.727 Fi grams of mercury. + 41.883 -f- 68.490 + 123.133 + 36.564 in £2 E3 E4 F2 grams of amalgam. 8.498 Fi 8-543 Fi 8.177 Gi 9.328 Gi grams of mercury. + 71.897 + 118.680 + 58.144 + 102.808 in F3 F4 G2 G3 The measurements of electromotive force, and the theoretical values calculated from the concentration law, are given in table 3. TABLE 3. — Electrical Measurements of Indium Amalgams. Designation of cup containing amalgam. Approxi- mate percent of indium in amalgams. Exact value of log^7? Cn Electromotive force between each pair of cups, in millivolts. o°c. 30°C. Observed. Theo- retical. Differ- ence. Observed. Theo- retical. Differ- ence. El 1.92 , o.384[ 0.242 | 0.120 ' 0.319 j 0.078J 0.034 [ 0.021 ' 0.016 j o . 008 | 0.00 ' 0.69705 0. 201 1 1 0.30466 O.6l38l 0.36079 0.19750 0.31887 o. 16941 14-455 3.823 5.692 11.387 6.588 3.666? 5-775 3-035 12.587 3.631 5-501 I I . 083 6.515 3.566 5.758 3-003 1.868 0.192 O.I9I 0.304 0.073 0.100? 0.017 0.032 15.786 4.231 6.287 12.616 7-3II 3-989 6.411 3-430 I3-967 4.030 6.106 12.301 7.231 3.958 6-390 3-390 I.8I9 0.201 O.lSl 0.315 0.080 0.031 0.021 0.040 E2 £3 . E4. Fi F2 F3 . F4 . Gi G2 G3 . 26 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS Comparison of the observed and calculated potentials of the indium amalgam cells shows the behavior of these cells to be similar to those of thallium, but in a less degree. The cells with concentrated amalgams show considerable deviation from the theoretical value, not so much, however, as with thallium amalgams of the same concentration. On the other hand, at great dilutions the agreement between the observed and calculated values is exceedingly close. The cell Gi-G2 differs by only 0.000019 volt or 0.3 per cent from the theoretical potential. The significance of the results of these measurements can best be illus- trated by the same sort of curve as was employed in the case of thallium amalgams. The curve for indium amalgams is shown in fig. 7. As before, the common logarithms of the concentration ratios are plotted as abscissae and the value of the deviations from the simple concentration law as ordinates. The sign of curvature is the same as with thallium, since both deviate in the same direction from theory. The significance of this curve also will be discussed later. •H log a |0g4 logS log 16 log 33 Iog64 log!23 log 256 Fig. 7. The Deviations of the Electromotive Force of Indium Amalgams. J? T c Deviations from the expression ir = *~ In -\ are plotted in millivolts as ordinates, 3^ ci the logarithms of the concentration ratios as abscissae. The most concen- trated amalgam contained 1.92 per cent by weight of indium and 98.08 per cent by weight of mercury. A horizontal line on the diagram would indicate complete fulfilment of the concentration law. This curve is almost if not qxiite independent of temperature, at least between o* and 30°. OF THALLIUM, INDIUM, AND TIN ELECTROMOTIVE FORCE BETWEEN TIN AMALGAMS. The tin amalgams were prepared in a manner similar to that employed with indium. The electrolyte used in the cells was a solution of stannous chloride, about half normal. Before use it was allowed to stand over pure tin and was then preserved under hydrogen. Great care was taken to insure the absence of stannic compounds. Since concentrated tin amalgams deposit a solid phase on cooling to o°, the first series of measurements were performed by the dilution of an amalgam containing 0.66 per cent by weight of tin — less than half of the higher concentration used by Cady. As even this was found to separate a solid at o°, another series was made beginning with an amalgam con- taining only 0.21 per cent of tin. The data concerning the preparation and dilution of these amalgams were as follows: 1.0766 grams of metallic tin were dissolved in 161.161 grams of mercury to make amalgam Hi. This was diluted as follows : grams of amalgam. 17.351 13.279 10.391 grams of mercury. + 39-593 + 99-824 + 147-265 in H2 H3 H4 The more diluted series was made from a " parent " amalgam obtained by dissolving 0.3116 grams of tin in 149.021 grams of mercury. From this were prepared : grams of amalgam. 18-537 16.436 9.919 grams of mercury. + 44.845 + II3.3I2 + 117-947 in J2 J3 J4 TABLE 4. — Electrical Measurement of Tin Amalgams. Designa- tion of cup con- taining Approxi- mate per cent of tin in Exact value of log — Electromotive force between each pair of cups, in millivolts. 0°C. 30°C. amalgam. amalgams. Observed. Theo- retical. Difference. Observed. Theo- retical. Difference. Hi.... 0.66 N 0.51495 7.632 13-949 -6.317 I3.I82 15.480 — 2.298 H2.... 0.20 0.4I40I I0.6I4 11.213 -0.599 I I . 820 12.447 — 0.627 H3 0.077' Ji. O.2IO j 0.53655 I3.6I2 14.532 — 0.920 15.156 16.128 -0.972 T2.. 0.061 ] 0.36025 9.548 9.758 — 0.210 10.622 10.829 — 0.207 13.. 0 . 027 \ 0.21345 5.715 5.781 — 0.066 6.371 6.416 -0.045 J4- 0.016 ' 28 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS Examination of these results shows that the observed potentials of the amalgam cells of tin, like those of all the other metals thus far studied, approach the theoretical requirements more and more closely as the dilu- tion is increased. The results are depicted graphically by the curve in fig. 8. It should be noted that the sign of curvature is exactly the reverse of that of the otherwise similar curves obtained with cadmium, thallium, and indium amalgams, since tin amalgams deviate in the opposite direction from theory. In this respect tin is similar to zinc. -I logZ log 16 log3Z log 64 Fig. 8. The Deviations of the Electromotive Force of Tin Amalgams. r> *j* Deviations from the expression ir = - - - in — are plotted in millivolts as 1r C% ordinates, the logarithms of the concentration ratios as abscissae. The most concentrated amalgam contained 0.66 per cent by weight of tin and 99.34 per cent by weight of mercury. A horizontal line on the diagram would indicate complete fulfilment of the concentration law. This curve is for 30°. The most concentrated amalgam separates solid at o°. In the case of the tin amalgam cells complete exclusion of oxygen is necessary, not only on account of the amalgams, but also in order to insure the stability of the electrolyte, since stannous chloride when exposed to the air quickly becomes basic according to the equation : When the solution is in contact with tin amalgam in the air this reaction proceeds very rapidly, perhaps because the stannic chloride is reduced by the amalgam. The formation of stannic chloride would be expected to lower the potential, and the constancy observed in the values of the various cells proves the complete elimination of any such disturbing effect. OF THALLIUM, INDIUM, AND TIN 29 With the idea of testing the effect of stannic chloride, but without much hope of obtaining results fully corresponding to a quadrivalent ion, a further attempt was made to measure a tin amalgam concentration cell, using an electrolyte containing at first pure stannic chloride. Pure tin was dissolved in aqua regia and the nitric acid was removed by boiling repeatedly with fresh portions of hydrochloric acid. The solution was then diluted with water, most of the free acid was neutralized with sodium hydroxide, and the solution containing all its tin in the state of highest oxidation was placed in the cell. No constant readings could be obtained with any of the tin amalgams under these conditions. Evidence was obtained, however, that this electro- lyte tended to give lower potentials than those obtained with stannous chloride. For example, with a cell whose calculated potential would be 0.01605, if the tin were quadrivalent, and 0.0321, if bivalent, a value of 0.0262 was obtained. Clearly, as we had expected, ionized quadrivalent tin is not in a state of electrochemical equilibrium with tin amalgam. Cady28 supposed that he attained this equilibrium by using potassium stannate as an electrolyte, but in our opinion it is extremely doubtful if in a solution of a stannate, the quadrivalent tin ion is in reversible equilibrium with a tin amalgam. Our practical experience confirms this conclusion. We attempted to measure a cell with a solution of sodium stannate as its electrolyte, but were unable to obtain anything approaching constant potentials. We regret to state that another fact also points to the conclusion that Cady's work with tin was questionable. Roozeboom and van Heteren have shown that at 25° tin amalgams containing from 1.2 to 99 "atom per cent " of tin give the same potential, there being present two phases of invariable composition — a liquid phase containing 1.2 "atom per cent" tin and a solid phase of 99 per cent tin. But Cady supposed he had made a tin amalgam of 1.73 per cent by weight or nearly 3 atom per cent, when he used potassium stannate as electrolyte in the attempt to obtain the potential of a cell in which tin behaved as quadrivalent. He calculated the concentration ratio on the basis of his supposed percentage.29 In the light of the work of Roozeboom and Van Heteren this work is evidently faulty, since the strongest liquid amalgam in the cell could not have exceeded 0.8 per cent by weight of tin, and the more dilute amalgam might have been affected by crystals of tin dissolved on dilution. Clearly Cady's work on tin is without significance. 28 Jour. Phys. Chem., 2, 551 (1898). Attention should be called to another serious error in Cady's paper, of which due acknowledgment was made. (Ibid., 3, 107 [1899]). All this work of Cady's was done under the direction of W. D. Bancroft. 29 Professor Cady has kindly looked up his data in his original note-books, and finds that the mistake was not an error of proof-reading, but arose from lack of knowledge of the solubility of tin in mercury. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS THE TEMPERATURE COEFFICIENT OF THE AMALGAM CELLS. Since all the potentials have been measured at two or three tempera tures, interest next centers in the computation of the temperature coeffi- cients of the various cells. The temperature coefficient — ^ over a finite Ay range of temperature is conveniently divided by the potential at o°, in order to compare the values obtained from the various amalgams with the same range. The values of the quantity thus obtained, ATT for the thallium, indium, and tin amalgams are given in the following table as calculated from the electromotive forces already recorded. The change of electromotive force between o° and 15° was almost always essentially identical with that between 15° and 30°. On account of the comparatively small change of electromotive force, 15° is rather a small range for this purpose ; therefore the whole range of 30° is given below as the basis for computing the temperature coefficient. The values given in table 5 are arranged in the order of the concen- tration of the most concentrated amalgam in each cell. Thus the effect of concentration upon the temperature coefficient is to be ascertained at a glance. TABLE 5. — Temperature Coefficients of Electromotive Force. Thallium amalgams. Indium amalgams. Tin amalgams. Per cent Per cent Per cent of of of thallium ATT indium in ATT tin in ATT Designa- of most Designa- the more Designa- the more rr* _, A T* tion of concen- ^"o * tion of concen- TTflA J tion of concen- ^"o -* cell. trated cell. trated cell. trated amalgam 0° to 30°C. amalgam 0°to 30°C. amalgam 0°to 30°C. in each in each in each cell. cell. cell. CI-C2 1.85 0.00319 Ei-Ea 1.92 o . 00309 JI-J2 0.21 0.00378 C2-C3 0.52 0.00350- E2-E4* 0.38 0.00350 H2-H3 0.20 o . 00380 Ai-A2 0.41 0.00346 Fi-F2 0.32 o . 00360 J2-J4 0.06 O.00378 C3-C4 0.23 0.00355 F2-F4* 0.08 0.00354 A2-A3 O.II 0.00357 Gi-G2 0.015 o . 00364 * The cells E2-E3 and F2-F3 had such small electromotive forces that the accu- rate measurement of the temperature coefficients was beyond the range of the apparatus. Therefore those cells were combined with cells E3-E4 and F3-F4 re- spectively, for the present purpose. It should be pointed out that the error involved in calculating the temperature of the indium cells is rather large, since the poten- tials are small, the metal being trivalent. Although these results are not perfectly regular, and show evidence of experimental imperfection, their general tendency is clear. OF THALLIUM, INDIUM, AND TIN 3! The temperature coefficients of the thallium and indium amalgams exhibit very similar behavior. The concentrated amalgams give a value much lower than 0.00366 (the coefficient of expansion of the unit volume of perfect gas), but as the dilution is increased, the coefficient approaches nearer and nearer to the ideal value. The most dilute indium cell measured gave a value 0.00364, very nearly the theoretical coefficient. This same cell gave a potential only 0.4 per cent different from that demanded by the formula of von Turin ; thus, as the electromotive force approaches the requirement of the gas law, the temperature coefficient does likewise. APPLICATION OF THE EQUATION OF CADY. The equation of Cady claims that the deviations from the simple equa- tion of von Turin are due to the heat of dilution of the amalgams.80 On comparing this equation with the equation of Helmholtz it is apparent that if the former really held true, the last terms of the equations would be identical. This was pointed out by Cady. Placing the second members equal to one another and dividing through by T we obtain the expression R Cm UTT I \ —T? In -- = ,~ (4) v-r cn dT That is to say, the temperature coefficient should depend upon the relation of the concentrations, not upon the electromotive force which they hap- pen to exert. This consequence is readily tested by the data in hand. Take for example the cell Ci-C2. Here — =3.516, and its natural logarithm is Cn 1.2574. Hence the first member of the above equation (4) becomes 8.316x1.2574 ^.ooo^ 1x96,530 and the second member becomes 00371347^233887 = 0m000ld&1 30.0° The agreement is so striking that other cases should be studied. ^Journ. phys. Chem., 2, 551 (1898). 32 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS Take for example 62-63. Here ' =3.4104, and its natural logarithm cn is 1.2268. Hence the first member of the equation becomes 8316x1,2268 =a 1x96,530 and the second member becomes 0.032408 — 0.029303 —2- ^o_o =0.0001035 30.0° Here the agreement is not so good ; but, on the other hand, it might be worse. Another thallium amalgam cell, Ai-A3, taken at random, shows essentially the same relation, the terms being as follows : 8.316x1.3808 =aoooi700 52.920-47.903 =0.000,670 - 96,530 30.0° In the case of indium, a somewhat less percentage accuracy in fulfilling the requirements of the Cady equation is shown. For the cell Ei-E2 the terms are these: 8.316x1.6082 15.786—14.455 — 2- =0.0000461 -2-*- n =O.OOOO444 3X96,530 30.0° With tin, about the same order of agreement is to be found. For example, in the cell, Ji-j2, the first member of equation (4) becomes 8.3i6x 1.2365 — ^- .. £ J =0.0000532 2 X 96,580 and the second member becomes 15.156-13.612 =0.0000515 a difference of about 3 per cent, or about like that found in the case of indium. One conclusion drawn from these partial agreements is the same as that drawn from the case of cadmium studied by Richards and Forbes, namely, that the equation of Cady does not contain an exact representation of all the influences producing electromotive force. On the other hand, the new results strongly reinforce the hope expressed in the earlier paper that this equation, although not wholly exact, is really a step in the right direction. For it is inconceivable that all these cells, possessing very different temperature coefficients, one as much as 13 per cent different from the requirement of the gas law, should all come within 3 per cent of the fulfilment of equation (4), if the equation were without meaning. Expressed in other words, the meaning of the results and mathematical considerations just detailed may be stated as follows : The reason for the deviation of the actual electromotive forces of amalgam cells from the values calculated from the concentrations is found to be primarily in the free energy of the change of chemical affinity involved in the dilution of OF THALLIUM, INDIUM, AND TIN 33 the amalgams. The electromotive force may be looked upon as being due to at least two entirely different phenomena superposed : one, the " chemi- cal free energy," which manifests itself as heat on dilution, and the other the " osmotic energy," due to the difference of concentration of the two different amalgams. In these cells all the free energy of the essentially chemical part of the change may be supposed to appear as heat, because the heat capacity of the system is essentially unchanged during the reac- tion ; hence the system is peculiarly well adapted for tracing the mechanism of the chemical production of electromotive force.31 This was indeed the reason why the whole investigation was undertaken. The probable reasons for the lack of exactness in the application of the equation of Cady will be discussed in the second half of the monograph, when other results have been presented. APPLICATION OF THE EQUATION OF HELMHOLTZ. The importance of the heat of dilution in the case of amalgam cells leads one to inquire concerning its exact values under the conditions of the present experiments. These values are most readily calculated from the well-known equation of Helmholtz, whose verity is undoubted. The only difficulty in the present case lies in the fact that the temperature coefficients were perforce determined over a rather large range of tem- perature — 30° — on account of their otherwise too insignificant magni- tudes. Moreover, even then their determination carries with it by far the largest percentage error of any part of the work. Fortunately the nearly if not quite linear nature of the coefficients with these metallic cells prevents the introduction of any considerable error from the large range needed. In 1882, Helmholtz, in a paper already referred to, evolved the equation (5) an expression already given in a somewhat different arrangement as equation(i). According to this expression the sum of the heat of reaction and the product of the absolute temperature and the temperature coeffi- cient of the change of free energy should equal the change of free energy itself. The experimental work already described furnishes sufficient data for applying this equation to the amalgam cells of thallium, indium, and tin. Take, for example, the thallium cell Ci-C2. Here 71-0 = 0.033897, ATT = 0.003237, AT = 30.00°, 7 = 273.09, v = i, and F = 96,530. 81 Richards, Proc. Am. Acad., 38, 293 (1902) "The relation of changing heat capacity to change of free energy, etc." This theorem has been recently expanded mathematically by Nernst, with the help of an interesting assumption concerning the extrapolation to the absolute zero. 34 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS Then nnvF = 3272.1 joules ATT Fv T - = 2844.4 joules Difference U = + 427.7 joules Thus upon the dilution with mercury of an amalgam containing nearly two per cent (1.846 per cent) by weight of thallium to about treble its volume (more exactly, 3.5 fold) we should obtain 428 joules or 102 small calories for every 204 grams of thallium. Again, in cell C2-C3, ^ = 0.020485, A?r = 0.002 125, AT = 30.00°, 7 = 273.09, v— i, and F = 96,530. Then tr0vF = 1978 joules FvT KT ~ J^9 Joules Difference U = 109 joules Turning now to the indium amalgams, we may consider for example the cell Ei-E2, in which TTO = 0.014455, A?r = °-OOi33i, AT = 30.00°, 7=273.09, v = 3, ^ = 96,530. Then ;r vF= 4186 joules vFT = 3509 joules Difference U — 677 This difference, the heat of dilution, is here much larger even than in the concentrated thallium cell, because the electrochemical equivalent of indium is only about one-sixth as great as that of thallium. In the case of a cell with very dilute amalgams, on the other hand, the heat of dilution is almost negligible, as is shown by the following calculation of cell Gi-G2, about a hundred times as dilute as the previous example. There = 1858 joules = 1862 joules Difference U = — 4 joules The agreement here is very satisfactory, being about 0.25 per cent. The minus sign can hardly be significant, as the probable error of the measurements is as great as 4 joules. There now remains to be considered only the tin amalgam cells. For example, we have in one cell, H2-H3 : 7r0 = o.oio6i4, A7r = o.ooi2o6, Ar=3O.oo°, 7=273.09°, v = 2, ^ = 96,530. Then TT vF = 2284 joules ATT joules Difference £/=— 69 joules OF THALLIUM, INDIUM, AND TIN 35 Thus the dilution of the tin amalgams gives a small cooling effect — a conclusion wholly in accord with the deviation of its potential from the equation of von Turin and Meyer. If more concentrated amalgam could have been used, the result would undoubtedly have been greater. If possible, it would be well to verify these values of heats of dilution by actual experiment. Unfortunately, however, an accurate determination of the heat of dilution is only possible with the more concentrated amal- gams, and even in these cases it is difficult. Five millionths of a volt in the potential of a concentration cell corresponds to the development of one joule during the transport of an univalent gram-atom. A mass of amalgam containing a gram-atom of thallium dissolved in 99 times its weight of mercury, when diluted with an equal volume of mercury would involve a heat capacity not far from 6000 mayers ; hence one joule would produce a temperature change of less than 0.0002°. On account of the high inertia of mercury, the liquids do not mix easily ; and for the same reason the plentiful stirring evolves much heat. The exact evaluation of the stirring correction is very difficult. Moreover, the dilution must be carried out in an indifferent gas in order to avoid oxidation with its attending heat effect. Nevertheless, in spite of these difficulties the attempt was made to determine the heat of dilution in the cases of the more concentrated amal- gams of thallium and indium. 1226 grams of a I per cent thallium amal- gam were diluted with an equal bulk of mercury and found to cause a rise of 0.015° in a calorimetric system having a heat capacity of 431 mayers. On further diluting by an equal bulk of mercury the mixture resulting from this first experiment, the increased system (having now a heat capacity of 762 mayers) was raised through only 0.002°. These effects were in the expected direction, but not of the expected magnitude. The experiments were conducted in the apparatus of Richards and Forbes, in which the mixing was conducted by a clock-work stirrer. Lack of time had prevented the proposers of this apparatus from testing it thoroughly. Our present experience indicates that the clock-work stirring was inadequate, and hence that an inadequate change of temperature must have been observed in all cases. Nevertheless, in spite of the quantitative inadequacy of these results, they are qualitatively of value ; for they afford experimental evidence that the conclusions drawn from the equation of Helmholtz are at least in the right direction, and therefore that the data upon which the conclusions are based are not seriously in error. In the case of indium, 150 grams of an amalgam containing 1.92 per cent of indium was diluted with 600 grams of mercury in a small calo- rimeter, the total heat capacity being 157 mayers. Here, in this smaller apparatus, the stirring was more effective, and the temperature rose 0.048°, 36 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS a result more nearly in accord with the expected value, but still below its full magnitude. The computation of the result is not worth while, as there can be no doubt that this experiment, like the others, has no more than qualitative value. The small per cent of tin in a tin amalgam which remained wholly liquid at o° corresponds to a heat of dilution which would cause a change of only 0.002° in the calorimeter — an amount too small to be determined within 50 per cent by means of our thermometers. Hence an attempt to carry out this experiment was without object. In view of all these circumstances, we are inclined to agree with Carhart in thinking that the electrical method of determining the heats of dilution of amalgams is to be preferred to the thermochemical method. It is worthy of note, in this connection, that the Helmholtz equation shows at once why the temperature coefficient of the electromotive force divided by the electromotive force approaches the coefficient of expansion of a perfect gas as the dilution of the amalgam proceeds. To illustrate this relation, the equation may be cast into a somewhat less familiar form. The normal form, transposed, is thus: Dividing through by vF-n-T, we obtain ATT _i_ U ~ T Evidently, because U, the heat of dilution, diminishes as the dilution pro- ceeds, the last term will become smaller and smaller. Finally, when the heat of dilution becomes negligible at great dilution, the equation will become simply —^_, = ?rA 1 j Simultaneously, the equation of Cady RT . cm U ' ~- loses its last term, and becomes the simple concentration equation. It is equally clear that a positive heat of dilution ( + U) will cause the potential to be high and the temperature coefficient to be low. In the case of thallium and indium, this was found actually to be the case. On the other hand, with a negative heat of dilution ( — U) the potential will be low and the temperature coefficient high. This was found to be the case with tin, and by Richards and Forbes with zinc. Thus the theory of these cells seems to be complete, except for the quantitative understanding of the minor deviations from the equation of Cady. These deviations, which are probably to be traced primarily to the inaccuracy of the simple concentration ratio — as an index of the precise Cn OF THALLIUM, INDIUM, AND TIN 37 osmotic work to be obtained from the dilution of an amalgam, may best be discussed in the light of the further data presented in the next paper. Hence they will be deferred to the conclusion of the monograph. In conclusion, it is a pleasure to express our indebtedness to the Carnegie Institution of Washington for the apparatus and materials used in this work. SUMMARY. The main points of the present research may be summarized as follows : 1 i ) The potentials between various liquid amalgams of thallium, indium, and tin were investigated at 30° and o°. Many precautions were taken against experimental errors. The potentials of the thallium cells are thought to be reliable within o.ooooi volt; those of the indium and tin cells within 0.000005 volt. (2) Thallium and indium amalgams gave potentials higher than those calculated from the simple concentration law ; and tin amalgams gave potentials lower than those calculated from the simple concentration law. (3) The temperature coefficients of the various cells have been calcu- lated and found to approach the ideal value 0.00366 for a unit potential as infinite dilution is approached. (4) The equation of Cady was applied to the results, and found to afford a fairly accurate explanation of the deviations from the concentra- tion law in all three cases. (5) The equation of Helmholtz was used for the calculation of the heats of dilution, and was found to account for the changes in the tempera- ture coefficients. (6) It was found impossible to obtain satisfactory results with an elec- trolyte containing tin in a quadrivalent condition, either as stannic chlo- ride or as sodic stannate. In this connection it was pointed out that Cady must have had a two-phase amalgam in his tin cell, and that his results with tin were illusory. (7) The density of pure indium was determined and found to be 7.28. (8) The densities of various liquid amalgams of thallium, indium, and tin were carefully measured and compared with the calculated values. SEPTEMBER 1907 TO JANUARY 1909. II. Electrochemical Investigation of Liquid Amalgams of Zinc, Cadmium, Lead, Copper, and Lithium. BY THEODORE W. RICHARDS AND R. N. GARROD-THOMAS. INTRODUCTION. Simultaneously with the work described in the foregoing paper a similar investigation upon other metals was begun in the laboratory. The parallel progress of these two investigations was an assistance to each, for not only were the potentiometer and other apparatus used in common, thus economizing time for each investigator, but also the experience gained in the one was immediately helpful in the other. The object of the work to be described was, of course, similar to that of the work just chronicled, namely, to extend as far as possible the study of liquid amalgams in their relation to thermodynamical theory and to the essential nature of solu- tions and the galvanic cell. The present paper contains, as its title indi- cates, an experimental study of the liquid amalgams of zinc, lead, copper, and lithium. It will be seen that the theoretical discussion of these results together with those concerning cadmium, thallium, indium, and tin, already described, furnishes much light upon these general questions and the out- come will be seen to have justified the time and trouble spent upon the somewhat exacting investigation. ZINC AMALGAMS. The energy changes involved in the dilution of zinc amalgams have recently been studied in this laboratory by Richards and Forbes.82 Zinc amalgams of different concentrations, ranging from 0.9 per cent to about 0.015 per cent of zinc, were connected by means of an electrolyte consist- ing of zinc sulphate in water ; and the potentials of the resulting concen- tration cells were measured, and were compared with the theoretical poten- tial deduced from an equation derived from that of von Turin : M RT . c, IT— j-. In - vr c.2 "Carnegie Institution of Washington, Publication No. 56, p. 36 (1906). 83 Zeit. phys. Chem., 5, 340 (1890). 39 4O ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS An attempt was made also to determine the heat which the amalgam of concentration c± would evolve or absorb on dilution to concentration c2 in the case of one cell. In this trial a 0.9 per cent zinc amalgam on dilu- tion by its own weight of mercury absorbed 52 joules per gram-atom of zinc. It seemed very desirable that this thermochemical result should be verified by the application of the equation of Helmholtz: through the determination of the temperature coefficient of the electro- motive force. Lack of time prevented this in the earlier work ; accord- ingly the present investigation was undertaken. The problem obviously involved simply the extension of the work of Richards and Forbes to two different temperatures, but the execution of the work was less easy than had been expected. Since the value of ATT which would be expected in the case of the above cell is very small, it was found necessary to make AT somewhat large. Measurements were at first made at 30°, 15°, and o°, but the interval of only 15° is too small to allow of an accurate measurement of the temperature coefficient, and so in the final experiments measurements were made at 30° and o° C. only. Most of this investigation was carried out in identically the same way as the earlier work, and the densities of the amalgams were taken from those results. The methods of purification of the zinc, zinc sulphate, and mercury, the methods of preparing the amalgams, of sealing them in hydrogen, and of introducing them into the cell, and diluting them with mercury, which had been distilled and sealed in hydrogen, were identically the same in every respect. The potentiometer used was, however, considerably modified. If in a cell of a bivalent metal where—1 = 2, it is desired to distinguish between 2 a temperature coefficient of 0.00366 and 0.00367, the potential of the cell at 30° and o° must be measured with an error of not more than 0.000002 volt. Hence it was clear that a potentiometer more sensitive than that employed by Richards and Forbes would have to be used. Accordingly, much time was spent, with the help of J. Hunt Wilson, in elaborating a suitable potentiometer. As this instrument is described in detail in the foregoing paper,34 any further account of it is unnecessary here. The thermostats, also, were the same as those described there ; they could be relied upon to keep at a temperature constant within 0.01°. The thermometers were accurately standardized by means of instruments bear- ing the certificate of the Reichsanstalt. 4 This monograph, pp. 17 to 20. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM ELECTROMOTIVE FORCE BETWEEN ZINC AMALGAMS. The first series of results with zinc amalgams, although not of sufficient accuracy to yield trustworthy temperature coefficients, are worth recording as a corroboration of the results obtained during the previous investigation of Richards and Forbes. In the first case the most concentrated amalgam contained 0.90 per cent of zinc. It was placed undiluted in the first cup of the multiple cell described in the foregoing paper,35 was diluted with mercury in the third and fourth cups, and finally the parent amalgam was again put undiluted in the remaining second cup, in order to be sure that no change had taken place in the amalgam during the filling of the cell, and also that the amalgam had been in the first place thoroughly mixed. This precaution was usually taken in the subsequent work also, but only in one case, mentioned later, was a difference greater than 0.000002 volt ever found between the first and the last portions of amalgam. As is shown below, the maximum difference in the present case was only one millionth of one volt. In addition to this series of measurements, another was made upon three more dilute amalgams, in order to show the increasingly near approach of the potential to the gas law. Table 6 gives both series of measure- ments at 30°. The details of dilution, etc., need not be given as regards these preliminary results. The theoretical potential given below is calcu- lated according to the simple concentration equation. TABLE 6. — Preliminary Electrical Measurement of Zinc Amalgams. Designation of cup containing amalgam. Approximate per cent of zinc in amalgams. Exact value of \og — Cn Electromotive force, in millivolts, be- tween each pair of cups. 30°C. Observed. Theoretical. Difference. Kl O.QOO , O.QOO 0.384| ' 0.234' 0.100 . 0.036 1 0.020 ' 0 . 0000 0.37045 0.21459 0.44404 0.26303 0.001 10.175 6.123 13.262 7.828 0.000 11.129 6.446 13.341 7.903 O.OOI 0-954 0.323 0.079 0.075 K2 K3. K4. Li L2 L3 . This monograph, p. 15. 42 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS These results confirm wholly the work of Richards and Forbes, carried out at 23°, showing that cells of zinc amalgams give a much lower electro- motive force than that required by the concentration law. The quantita- tive agreement of the two series of results is shown in the accompanying diagram (fig. 9), where the points surrounded by single circles are the points found by the earlier work, and those surrounded by double circles the present data. This curve is drawn on the same scale as that used in the other similar curves in this monograph. The cells were measured also at 15° and o°. In no case did the poten- tial between cups I and 2 exceed o.oooooi volt. At 30° the other measure- ments also were sufficiently concordant and convincing. At o° the more dilute amalgams gave less consistent results, and evidently were not so log 2 Iog4 Iog8 log 16 log3Z log 64- lo£)28 log 256 Fig. 9. The Deviations of the Electromotive Force of Zinc Amalgams. r> '•p _ Deviations from the expression ir = - - in -1 are plotted in millivolts as ordinates, 2/< C2 the logarithms of the concentration ratios as abscissae. The most concen- trated amalgam contained 0.9 per cent by weight of zinc and 99.1 per cent by weight of mercury. A horizontal line on the diagram would indicate complete fulfilment of the concentration law. This curve is almost if not quite independent of temperature, at least between o° and 30°. Single circles depict points found by Richards and Forbes; double circles depict points found by the present investigation. trustworthy. As the technique and accordingly the consistency of the results were both greatly improved later, these early measurements need not be given in detail. It is enough to say that there was undoubted evidence of the truth of the prediction of Richards and Forbes that the temperature coefficient is greater than 0.00366, demanded by the gas law. Moreover, it was clear that the value approached more and more nearly that required by the gas law as the dilution became greater. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 43 DETERMINATION OF THE TEMPERATURE COEFFICIENTS OF CELLS CONTAINING ZINC AMALGAMS. The previously described measurements had all been made with the potentiometer in its original less complete condition. For further more accurate experiments, the potentiometer was modified with a view of eliminating all thermoelectric currents, as has been already described." The air in the case containing the potentiometer was stirred by means of a fan, worked by an electric motor outside the case, so that the tempera- ture inside was sensibly uniform. It was also arranged that all final adjustments on the potentiometer could be made from outside the case, thus avoiding all danger of thermal effects due to heating by the warmth of the operator. Moreover, the connections with the cell were made so as to avoid thermoelectric effects ; contact was made between copper and mercury well under the surface of the thermostat and inside the cell, so that all unequal heating of junctions of dissimilar metals was avoided. A series of test experiments with this improved potentiometer showed that although thermal currents had been completely eliminated, so that the potentials could be read to even less than o.oooooi volt, nevertheless, the amalgam cells themselves were not constant to this same degree. It was thought that the irregularities might be due to the formation of a basic salt by the action between the amalgam and water. To test this, in one case the electrolyte was made slightly acid (about 0.02 N. with H2SO4) , but no effect was observable, and hence in the final experiments neutral electrolyte was again used. In all the measurements thus far recorded the potential at 29.96° was first measured, and then the potential at o°, and finally the readings repeated at 29.96° and at o° again. It was always found that the reading at 29.96° remained throughout constant to about 0.000005 volt, while the value at o° showed much greater change, sometimes even as much as 0.000030 volt. If the cell at 29.96° was shaken, the values were only temporarily altered, while at o° this treatment caused a more permanent change, which did not completely vanish even if the cell was heated to 29.96°, and cooled to o° again. Being unable to eliminate the difficulty, we sought to arrange the experi- ments in such a way as to minimize its influence. In the final set of read- ings to be recorded, the amalgams and electrolyte were cooled before using, and were put into the cell as cold as possible. The readings at o° were first taken and then the readings at the higher temperature. Finally the cell was cooled to o° and measured again. The first readings at o° and the readings at 30° were constant, even if the cell was shaken, but the second series at o° showed after a time the former irregularities. 38 This monograph, pp. 17-20. 44 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS In order to make these results as definite as possible, it was decided to carry out two sets of experiments simultaneously, the two cells containing the same amalgams. To effect this, the usual method of diluting a " parent " amalgam in the cell was, of course, impracticable, and four separate amalgams had to be made and sealed in the pipettes. The con- centration of these amalgams was known to within about 0.5 per cent — a degree of accuracy, which, although not sufficient to admit of the theo- retical potentials being calculated with the utmost precision, was ample for finding the temperature coefficients with great exactness. The cells were filled as in table 7. TABLE 7. Cup. Per cent of zinc. Cell M. Cell N. I 2 3 0.913 0.296 0.0998 0.913 0.303 0.0998 4 0.0302 0.0302 The cells were then put into the o° bath, and their potentials measured at two intervals of about an hour, the cell being shaken between. The greatest change in potential during this treatment was 0.000004 volt. Cell N was then put in the 30° bath, and each pair of amalgams was put in opposite to the similar pair in cell M at o°, and hence a direct measure- ment of the temperature change was obtained. Cell M was then put in the 30° bath, and the potential of both cell M and cell N determined at 30° ; finally, N was once more packed in ice, but after two readings had been taken, the familiar irregularities at o° became too great for further accurate work. A slight mischance prevented the complete fulfilment of the program, but although this mischance complicated affairs, it did not interfere with the significance of the results for the present purpose. Probably because of insufficient mixing in the bulb before the stem was filled, the amalgam in cup M2 was found to be slightly less concentrated than in N2. This prevented the direct comparison of these two cups, but did not affect the results from each separately. The concentrations of the amalgams in these two cups, as given above, were calculated from their potentials in con- nection with the others, by the method given at the very end of this paper. All the other cups were perfectly comparable, as was shown by the precise equality of each pair, both at o° and at 30°. All the figures in table 8, except the last two columns, represent the actual readings of the potentiometer. The last two columns are obtained by difference from the appropriate preceding columns. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 45 TABLE 8. Cell. M at 0°. N at 0°. N3o-M0. M at 30°. N at 30°. M^No. Mjo-Mo. NM-NO. 1-2 II 8l3 1 1 . 5 30 I3.2II 12.807 1.398 i 367 1-3 1-4 2-7 24.236 38.196 12 427 24.241 38.196 12.714 2.791 4-327 27.033 42.527 13.831 27.029 42.525 14. 1 38 2.795 4-330 2-793 4-333 1 .404 2.788 4-329 i 424 2-4 26. 393 26 . 669 29. 311 29.637 2.938 2.968 3-4 13.962 13.960 1-544 15.507 15.506 1-543 1-545 1-544 Thus for cups 1-3 there are four results for A?r to be taken directly from the table, and three more by subtracting the values for the cups 3-4 from those for the cups 1-4. There are also four values for the value of TT for 1-3 at o° — two given in the table, and two obtained by subtracting the values for 3-4 from those for 1-4. These are recorded below in table 9, in order to give some idea of the accuracy of the work. TABLE 9. [Cell Mi-M3 (or Ni-N3)]. TTO in millivolts. ATT (0° to 29.96°), in millivolts. 24.236 24.241 24.234 24.236 2.791 2-795 2.793 2.788 > Tft? Average.. 24.237 2.7O3 2.788 2.785 Average 2 799 "Probable error".. 0.0008 "Probable error". .. o.ooi Thus this cell with its amalgams containing about 0.0913 and o.ioo per cent of zinc, respectively, gave a potential of 0.024237 volt ±0.0000008 at o°, and changed its potential by 0.002799 vo^ ±0.000001 on being raised to 29.96°. The value for ATT is therefore 0.003855 instead of the value 0.00366 shown by the increase in pressure of a nearly perfect gas — the standard upon which our temperature scale rests. In the same way, seven results for cell 1-4 give on the average ATT= 0.004332 volt ±0.000001 ; and for cell 3-4, seven similar results give A7r=o.ooi54i volt ±0.000001. From these results, as well as from the figures given in the table for the other combinations, the corresponding values for the temperature coefficients may be readily computed, it being borne in mind that wherever cup 2 is concerned, the cells M and N must 46 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS be calculated separately. When thus treated the final results from tht two are essentially identical, and may be averaged together. As the details may be worked out from the data, by anyone wishing to verify the results, further space need not be wasted by their minute presentation. It is enough to present the final table of values for the function * Cup 1-2 0.00397 i-3 0.003855 1-4 0.003794 Cup 2-3 0.00375 2-4 0.003715 3-4 0.003685 Thus it is clear that in the case of zinc amalgams, as in all other cases thus far studied, the temperature coefficient of the electromotive cell becomes nearer and nearer the limiting value as the dilution proceeds. In the most dilute cell measured, whose two amalgams contained respec- tively about o.io and 0.03 per cent of zinc, the value of the temperature coefficient had come within 0.7 per cent of the requirement of the gas law. The significance of these results as regards the theory of the galvanic cell will be discussed in a later section, after the facts concerning other cells have been presented. It will be observed that the first value given for the temperature coeffi- cient exceeds the ideal value by as much as 8.5 per cent. This high value for the temperature coefficient, which appears wherever the most con- centrated amalgam was concerned, might possibly be due to the crystal- lization of zinc at o°. That this, however, was not the case seems almost certain from the regularity of the results obtained, and from the fact that the temperature coefficient between 15° and o°, and between 30° and o° for even a stronger amalgam than was here used, were nearly the same. The point was, however, also experimentally investigated in the fol- lowing manner. Both the limbs of an H tube were filled with a 0.91 per cent zinc amalgam, and the potential between them at o° was measured and found to be almost zero. Then a small quantity of pasty zinc amalgam was added to one limb, and a large and permanent potential was produced in the direction indicated by theory. In another similar cell, one of the limbs was very slightly diluted with mercury and again a permanent poten- tial, in the direction foretold by theory, was observed. These facts could not be explained if the parent amalgam had crystallized out at o°, but are precisely what would be expected from an unsaturated amalgam. Control experiments were made in which an amalgam known to be more than saturated replaced the 0.91 per cent amalgam in the above experi- ments. On the dilution and on the concentration of one of the sides of the cell no permanent potential greater than o.ooooi volt was obtained, showing in this case that the presence of the solid phase caused the effec- tive concentration of the amalgam to become constant. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 47 LEAD AMALGAMS. In order to generalize concerning facts of any kind, it is desirable to obtain as wide a variety of data as possible. Hence it was decided to investigate lead amalgams in the same manner. Previous work on the subject had been done by G. Meyer,37 and by Spencer,38 but no data of sufficient accuracy had been published. The investigation was carried out in a manner exactly similar to the above-described work, hence details of manipulation will not be described again. Commercial " C. P." lead acetate was found to contain traces of iron, but after one recrystallization with centrifugal filtration this impurity was eliminated, and after two more such crystallizations the lead acetate was considered sufficiently pure to be used as the source of the metal, as well as for the electrolyte. The metallic lead used was prepared by the electrolysis of the acetate solution. The crystals of the metal thus obtained were carefully washed, and were then fused in porcelain boats in an atmosphere of hydrogen, and the lead thus obtained was used to make the amalgams. The electrolyte was prepared by taking a solution of the acetate, saturated at o°, and diluting with about one-tenth its volume of half normal " chemically pure " acetic acid. In this way the formation of basic salts was prevented, and a perfectly clear electrolyte was obtained. This solution was, as usual, boiled in a partial vacuum in an atmosphere of hydrogen, and sealed in a pipette, also in hydrogen. The amalgams were made by adding a weighed amount of lead to a weighed amount of hydrogen-distilled mercury, a little very dilute acetic acid being present to cover the metals and prevent oxidation ; for the amalgam oxidizes very rapidly in air. The acetic acid was then analyzed, and was found to contain neither lead, nor iron from the steel knife used to cut the lead. The amalgams were then sealed in hydrogen in the before-described apparatus. TABLE 10. Concentration of amalgam (per cent). Weight of pycnometer full of— Density at 20°C. Amalgam. Mercury. 1.02 0.684 0-397 0 48.9587 35-073 35-079 48 . 9922 35.092 35.092 35.092 13.536 13-539 13.541 13-545 ' Zeit. phys. Chem., 7, 477. 'Zeitschr. f. Electrochem., 11, 681. 48 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS A series of density experiments of lead amalgams was carried out at 20°, and is recorded in table 10, but the necessary correction is insignifi- cant in this case, because the density of lead is so nearly that of mercury. The densities were determined by the use of an ordinary Ostwald pyc- nometer ; the only unusual precaution taken was to displace the air in the pycnometer by carbon dioxide. On this account very little oxidation took place when the amalgams were drawn into the tube. These results are plotted in fig. 10. The imaginary density, supposing no contraction to have happened, is given by the dotted line. For a i per cent amalgam this is 13.524 instead of the actually observed value 13.536. Thus as a matter of fact a slight contraction occurs on amalgamation. 13.52 13.53 13.54 13.55 0.2 0.4- 0.6 0.8 Fig. 10. Densities of Lead Amalgams at 20°. 1.0 percent Densities are plotted as ordinates, per cents by weight of lead in amalgams as abscissae. The dotted line indicates the imaginary theoretical values. The electrical measurement of similar amalgams was now undertaken. The most concentrated amalgam of lead used for the purpose contained, as before, 1.02 per cent of this metal by weight. Some of this was placed in the cup labeled Pi. Into cups P2. P3, and ?4 were placed respectively 12.684, ! 2-603, and 10.946 grams of this amalgam, diluted with 19.358, 58.96, and 108.86 grams of mercury respectively. The second series began about where this left off, with a freshly prepared amalgam contain- ing 0.0994 per cent of lead. Cup Qi contained this alone, while cup Q2 contained 14.308 grams of it diluted with 74.628 grams of mercury. The least concentrated amalgam of all, that contained in Q3, was made by diluting 8.429 grams of material like that in Qi with 115.72 grams of mercury. The electrical measurement with these two series of cells is given in table II. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 49 TABLE n. — Electrical Measurement of Lead Amalgams. Designation of cup containing amalgam. Approxi- mate per cent of lead in amalgams. Exact value of log^ Cn Electromotive force between each pair of cups, in millivolts. o°c. 29.96°C. Observed. Theo- retical. Differ- ence. Observed. Theo- retical. Differ- ence. Pi ,0, 0.404 I 0.180 j 0.0932 ' 0.0994 J 0.0160 j 0.0068 ' 0.4023 0.3517 0.2850 0-7935 0-3747 8.960 8.839 7.422 21.303 10.077 10.895 9.525 7.719 21.489 10.149 1-935 0.686 0.297 0.186 0.072 10.135 9.841 8.270 23.680 II.I86 12.092 10.569 8.564 23.848 I I . 262 1-957 0.728 0.294 0.168 0.076 P2 P3 . P4 . Qi. 02.. 0.3. . The last column in table n shows the great deviation of the strongest amalgams from the simple equation RT , cm TT= FT In ~ vF Cn and indicates, as usual, that this deviation approaches zero as the dilution proceeds in the usual fashion. The fact becomes yet clearer when the results are plotted as the other metals have been. Fig. 1 1 gives this curve, drawn on the same scale as those previously given. -I -2 logE Iog4- Iog8 log 16 lo£3Z log 64 Iogl28 Iog,a56 Fig. 1 1 . The Deviations of the Electromotive Force of Lead Amalgams. Deviations from the expression tt = -^p- In ~ are plotted in millivolts as ordinates, the logarithms of the concentration ratios as abscissae. The most concentrated amalgam contained 1.02 per cent by weight of lead and 98.98 per cent by weight of mercury. A horizontal line on the diagram would indicate com- plete fulfilment of the concentration law. This curve is almost if not quite independent of temperature, at least between o° and 30°. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS The temperature-coefficient functions ATT AT 7T, of these cells, calculated in the usual way from the figures given in table n, are as follows: Cell Pi-P2 0.00437 P2-P3 o . 003805 P3-P4 0.00381 Cell Qi-Q2 0.00376 Q2-Q3 0.003677 The first value is much higher even than that for zinc. Here again as usual, the figures rapidly approach the limiting value 0.00366 as the dilution proceeds, although the coefficient for cell Pi-P2 containing the most concentrated amalgams is 16 per cent in excess of this figure. The theoretical significance of these results will be considered later, in connection with all the other results. The possibility that the high tem- perature coefficient of the most concentrated amalgam cell might be due to the crystallization of the most concentrated amalgam at the lower temperature was considered, and wras experimentally investigated in an exactly similar manner to that used in the case of the zinc amalgams. An amalgam containing 1.03 per cent of lead was placed in an H cell and one side was in one case diluted and in the other concentrated, and in both cases a permanent potential, in the direction indicated by theory, was obtained, the measurements of course being made at o° C. Control experiments, using a saturated amalgam with excess of lead, showed no potential on adding either mercury or lead to one side of the cell. These results seem to show clearly that the most concentrated amalgam used, i. e., 1.02 per cent, is less than saturated at o°. At this point the potentiometer was recalibrated, but no change as great as o.oi ohm was found in any of the resistance, and hence, as before, cor- rections wrere unnecessary. COPPER AMALGAM. Seeking all the light available upon this type of cell, the investigators next turned to the metal copper. Copper amalgams have been examined in this connection by Meyer and by Spencer. Meyer made an amalgam, by electrolysis, intended to contain 0.217 per cent of copper. This amal- gam he dried by filter-paper and standing in a desiccator, and then diluted portions of it. Table 12 gives his results, the concentration being ex- TABLE 12. — Potentials of Copper Amalgams measured by Meyer. Electromotive t. Ci. CI. force (millivolts). Mol. wt., calc. 17.3 20.8 0.03874 o . 04472 0.009587 0.016645 18.15 I2.4 63.3 63.7 OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 51 pressed in percentage, and not in parts per unit of mercury, as it is in the original paper.39 The results obtained by Spencer were not so consistent with theory, but, as will be seen, are more like our own experience. He found great difficulty in getting constant readings of potential. His results are given in table 13 ; it will be observed that he used far more dilute amalgams. TABLE 13. — Potentials of Copper Amalgams measured by Spencer. Per cent of copper. Electromotive force. No. of cell. ft. Ci. Observed. Theoretical. I. 0.0003193 O.OOI938 26.8 2O.9 II. 0.001938 0.005399 6.4 10. 1 III. 0.005399 0.007205 5-i 8.8 It will be noticed that at first the actual potential is larger than theory, and afterwards smaller. The reason will soon become clear. The next step of the present research was to repeat these experiments in order to discover the difficulty. Commercial " C. P." copper sulphate was carefully recrystallized three times with centrifugal filtration, and the resulting copper salt was used in the experiments. A copper amalgam was then made by electrolysis, using mercury as the cathode, the amount of copper deposited being estimated by means of a silver coulometer in series. The amalgam was found to contain 0.2311 per cent of copper. On drawing this amalgam into the pipette, preparatory to its being sealed in hydrogen, a pasty residue was left which would not enter the fine tip of the pipette. Hence it was clear that the above amalgam was not a solu- tion, but rather a suspension of copper or of some copper-mercury com- pound in mercury. The amalgam which had been drawn into the pipette was used to fill a cell in the ordinary manner. This cell proved two important points : first that neutral copper sulphate could not be used as electrolyte, because the amalgam acted on it, giving Cu2O ; and secondly, that a very dilute amalgam, made by diluting the original sixteen times, gave only an exceedingly small potential with the original amalgam. Thus it appeared that the diluted amalgam was still saturated and there could be no doubt that crystals of the solid had not all been left behind in the pasty mass mentioned above. It then became necessary to find the solubility of copper in mercury. Saturated solutions of copper in mercury were made either by allowing amalgamated copper wire to stand in mercury for a week, or by carefully filtering a partially solid amalgam, prepared electrolytically, several times through leather. Zeit. phys. Chem., 7, 477. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS The saturated amalgam was then weighed, and the mercury driven off, at first by distillation in hydrogen, and the last traces by heating to a red heat in a crucible. The cupric oxide left was then either directly weighed, or it was dissolved in nitric acid, neutralized with ammonia and the con- centration of the solution approximately estimated by colorimetric com- parison with the color of a standard solution of ammoniacal cupric nitrate. The results are given in table 14. TABLE 14. — Solubility of Copper in Mercury at 20°. Method of preparation. Weight of amalgam (grams). Method of analysis. Weight of copper (rag-)- Solubility (percent). Copper + mercury 41. 1 Colorimetric 0.08 o . 0024 Do 88.5 Direct weighing 2.OO o . 0023 Electrolysis + filtration •30.0 Colorimetric O.60 0 . 0020 Do mo o Direct weighing 4. 05 0.0027 0.00235 Thus the solubility of copper in mercury at room temperature seems to be very small indeed, about 0.0024 per cent, or about I milligram in 40 grams of mercury. This agrees well with the observations of Sir W. Ramsay,40 but is somewhat higher than a result of Gouy.*1 It was then decided to measure electrically a series in which the start- ing point should be undoubtedly a real solution. An amalgam containing about i per cent of copper was made electrolytically. It was then filtered three times through leather, the last filtration leaving no solid residue. 153 grams of this amalgam were then diluted with 26 grams of mercury in order to make quite certain that no solid was present. This amalgam was bottled in the usual way. It was estimated to contain about 0.0020 per cent of copper. TABLE 15. Cell. Electromotive force, in millivolts. Observed. Theoretical. After i hour. 24 hours. 48 hours. 72 hours. 1-2 1-3 1-4 15.20 31.6 43-8 14.70 32.0 40.7 9.1 17-5 21 .6 5-4 10.8 13-8 11-53 27.38 34.83 40 Journ. Chem. Soc., 1889, Trans, n, 532. tt Gouy, Ann. der Phys. Beiblatter, 19, 758. He found o.ooi per cent of copper, 1.8 per cent of zinc, and 1.3 of lead in their respective liquid amalgams. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 53 The cell was then filled, using this amalgam in cup I, diluting it in the three other cups of the multiple cell, and using a solution of copper sul- phate in 0.0125 normal sulphuric acid as electrolyte. As table 15 shows, no constant results could be obtained. At first the potentials were all higher than the theoretical and later they all became lower. Evidently the copper reacts with the electrolyte, form- ing cuprous salt, and this reaction proceeded further in proportion in the case of the more concentrated amalgam, because of its lesser volume and larger proportion of exposed surface.42 Another series of readings was then tried, with additional precautions. The original amalgam was, in this case, made by standing amalgamated copper wire in mercury, in an atmosphere of hydrogen, for several days — the mercury being frequently shaken. It was drawn into the pipettes in the usual way, wholly out of contact with the air. The electrolyte, again slightly acid, was also allowed to stand in an atmosphere of hydrogen over a copper amalgam for several days. In spite of these precautions no more constant results were obtained, as table 16 shows. TABLE 16. Cell. Electromotive force, in millivolts. Observed. Theoretical. As soon as possible. i hour. 6 hours. 24 hours. 48 hours. 1-2 i-3 1-4 10. 60 26.2 2Q-5 II. 9 28.5 29.6 ii. 3 26.7 29.9 II. I 21.9 24-5 6.4 10. I 12.5 9.58 21 .91 30.66 Evidently the electrolyte was not saturated with cuprous salt, in spite of its week's contact with the amalgam. Considering the small concentra- tion in the amalgam and the fact that it can act upon the electrolyte only at the surface in mercury, this is perhaps not surprising. In the light of these experiments, let us turn back for a moment to the results of Meyer and Spencer. The latter's are wholly comprehensible. His first cell alone was dilute enough to be beyond the limit of saturation, and that gave a result like ours. The other more concentrated amalgams must have contained traces of solid, and if he had waited until they reached equilibrium, his cell III must have reached zero potential. His figures are just what one would have expected. Meyer's figures are harder to explain. How he could have attained his results from amalgams containing a large excess of solid phase will a See for example, Richards, Collins, and Heimrod, Proc. Am. Acad., 35, 125 (1899); Zeit. phys. Chem., 32, 324 (1900). 54 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS always remain a mystery. Perhaps the compensating effects of rate of solution and degree of saturation may have combined to give the results he observed, or perhaps his potentials came not from copper at all, but rather from some impurity. It would have been particularly interesting to have obtained good results in the case of this amalgam, for the electrolytic solution pressure of copper is of the same order of magnitude as that of mercury, and it might be expected that a balanced action would be established between the passage of mercury into the electrolyte and of copper into the amal- gam. This idea, which has been followed up by Hulett and De Lury in another way since the beginning of our work, was one of the secondary objects of the present research. A balanced action, indeed, may be in part the cause of the lack of constancy of the potentials observed, as one would be led to expect from this cause a gradual fall in potential. It is possible that if the electrolyte were wholly saturated with cuprous sul- phate, satisfactory measurements might be obtained, and one of us hopes to return to the problem in the future. IRON AMALGAM. J. P. Joule * seems to have been the first person to study iron amalgams. He records that an amalgam containing i per cent of iron is fluid, and 3 per cent is semi-fluid. An amalgam containing I per cent of iron was therefore made, by elec- trolysis. This amalgam on filtration through soft leather proved to be a suspension. The amalgam was filtered twice more, and finally the mercury in a weighed amount of the amalgam was evaporated, and the remaining ferric oxide was weighed. The same process was repeated with a fresh amalgam similarly prepared. In the first instance, 65.0 grams of amalgam gave 0.0013 gram of Fe2O4 ; solubility 0.00135 per cent. In the second, 143.0 grams gave 0.0027 grams of Fe2O3 ; solubility 0.00133 per cent. Thus the solubility of iron in mercury can not greatly exceed I milli- gram in loo grams. There is no proof that even this small trace might not have percolated in the solid state through the leather. As the solu- bility is so small, the investigation of the potential of iron amalgams was not pursued further. 43 Journ. Chem. Soc., 16, 378 (1863). OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 55 LITHIUM AMALGAMS. Up to the beginning- of last year but little accurate work had been done on the amalgams of the alkali-metals from the standpoint of potential measurements. The very recent discovery by Lewis and Kraus of a satisfactory method of measuring these metals against an aqueous solution of their hydroxides was not known to us at the time of our work, hence its assistance was not available.44 The first step in the present quest was obviously a repetition of the earlier work in the hope of discovering its validity. If this promised well, more accurate determinations were to be attempted. Meyer and Cady, in their publications already cited, have furnished the chief figures concerning the electrochemistry of the amalgams of the alkali-metals. Meyer recorded the results on sodium amalgam, but, as he spoke of using an aqueous electrolyte apparently without suitable pre- cautions, his data have little significance. Cady, working under Bancroft's direction, made measurements upon amalgams of the three most plentiful alkali-metals, using pyridine as the solvent for the electrolyte. This work shows the effects of great haste ; the figures in his tables are not wholly consistent with themselves and are evidently vitiated by serious errors, both of experiment and of proof-reading. Therefore it was thought advisable to repeat his work. We employed at first as the electrolyte a solution of lithium chloride in pyridine. The specimen of salt employed was a very pure sample which was being used for work on atomic weights in this laboratory. We are greatly indebted to Mr. H. H. Willard for his kindness in providing it. As a solvent the best pyridine, supplied by Kahl- baum, was redistilled with a fractionating column, giving as boiling-point 115.2° ±0.1° at 760° mm. It was always protected from moisture during distillation, and was subsequently kept in a potash desiccator. The con- ductivity of lithium chloride 45 in pyridine is very small, hence the electro- lyte was made very nearly saturated. The amalgams were made by placing mercury and lithium in the lower of the two bulbs in the usual apparatus shown in fig. i, page 9, sealing everything into its place, and finally melting the lithium after the whole apparatus had been filled with hydrogen. After cooling, the amalgam was driven by the pressure of hydrogen into the upper pipette, from which a sample was taken for alkalimetric analysis by means of digestion with a standard acid solution. Two amalgams made in this way, which were expected to give concentrations of about o.i and 0.5 per cent, were found to contain 0.037 Per cent and 0.036 per cent respectively ; and in both "This method has not yet been published. In the near future it will be applied either by Lewis and Kraus or at the Harvard Laboratory to a series of measure- ments like those discussed in the present paper. 45 Lasezynski and Gorski, Zeitschr. f. Electrochem., 4, 290. 56 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS cases solid amalgams could be seen floating on the liquid amalgam in the pipettes. Hence it was evident that the solubility of lithium in mercury is about 0.036 per cent. This agrees well with the observation of Kerp and Bottger," who obtained a solid amalgam containing 0.69 per cent to 0.72 per cent (having approximately the formula LiHg5) from a mother-liquor containing 0.04 per cent of lithium. In view of these facts it is evident that Cady was much in error in his supposition that his amalgam contained 1.8 per cent of lithium — far more than corresponds even to the solid amalgam. In answer to our personal enquiry, Professor Cady states that the cause of this error was a defective method of analysis, which multiplied by 50 the absolute amount of lithium in each amalgam, but did not affect the ratio of the two concentrations. The saturated liquid amalgam, whose preparation is described above, we diluted to form two less concentrated amalgams, and these were driven into the pipettes under hydrogen in the usual manner. Analysis showed them to contain 0.0255 per cent and 0.0144 per cent of lithium respectively. With these amalgams a cell was set up, two cups being filled with each. No constant readings could be obtained, but the value 0.0169 w^tn a Pos~ sible error of 0.0002 volt was indicated. The electromotive force deduced from the simple concentration law equation is 0.0159; hence it appears that, as had been expected, lithium ranks with lead, thallium, and indium rather than with zinc and tin. It is pleasant to note that this result agrees qualitatively with the outcome of Cady's experiments, in spite of their inconsistency of detail. The cell on standing rapidly changed in potential, and in a few hours a number of small crystals were observed in the electrolyte, which itself had assumed a dark -brown color. Hoping to establish a constant con- dition in a fresh portion of the electrolyte, in order to obtain better results upon refilling the cell, we allowed the solution of the chloride in pyridine to stand over metallic lithium. In a few days the pyridine had become of a dark -blue hue, which upon opening the bottle disappeared in a very few moments. In a similar bottle containing pyridine and lithium, but no lithium chloride, no blue color was formed, but nevertheless the lithium attacked the solvent in another way, and a brown powder was deposited. It thus appears that dry lithium attacks dry pyridine, and the hope of obtaining really satisfactory results in this way was dispelled. Several other series of potential measurements were tried, in some of which lithium sulphate took the place of the chloride in the electrolyte; but the series recorded above was the most satisfactory. More dilute amalgams gave more erratic potentials. In some cases a potential of over one volt was observed for several minutes, in the case of a cell where about 0.02 volt was the value which theoretical considerations would give. "Zeit. anorg. Chem., 25, i (1900). OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 57 In view of these highly unsatisfactory results, and the rapidly approach- ing conclusion of the academic year, it was decided to abandon for the present the attempt to obtain accurate data concerning the alkali-metals, and confine the theoretical treatment to the six metals which had given unimpeachable results, namely, cadmium, zinc, thallium, indium, tin, and lead. The theoretical discussion of these more satisfactory data follows. APPLICATION OF THE EQUATION OF CADY. It has already been pointed out in the preceding paper" that if the electromotive force of a cell as depicted by the equation of Helmholtz is made equal to that demanded by the equation of Cady, the term involving the heat of reaction is eliminated, and we obtain the expression : VF cn dT This equation was found as a matter of fact to hold approximately true as regards thallium, indium, and tin, and it becomes a matter of interest as applied also to zinc and lead. The average values for the zinc cells Mi-M3 and Ni-N3 are given on p. 45. The value of ^ was ^^c =0.15 Cn Thus R cm __ 8.316x2.214 ..nnnnne. ~~r^ In ~ - — ~ - ~T- — " — 0.0009 S4 VF1 Cn 2X96,530 and 2. -± =0.000934 29.96 Difference = 0.000020 This small difference, not much exceeding 2 per cent, seems at first sight inconsistent with the wide discrepancy found by the earlier investi- gation as regards cells containing zinc amalgams. There are two causes for this difference of verdict: the first and most important is not a real inconsistency, but appears only because of the different mode of presenta- tion ; the second subordinate cause of difference is due to the doubtful character of the result for the heat of dilution previously employed — a datum wholly eliminated from the present calculation. This latter circum- stance will be considered in the subsequent heading concerning the equa- tion of Helmholtz ; the former is worthy of a further word of explanation here. In the paper by Richards and Forbes, the equation of Cady was trans- posed thus : RT . Cl U it- ~^n~ In - ~c~ vr c-2 vr " This monograph, p. 31. 58 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS and the two members were calculated separately and compared. Thus all the errors, both of theory and observation, were heaped upon the smallest term involved f-^r] and naturally formed a much larger per- \vr I centage of this smallest term than they would when applied, as in the RT c present paper, to the much larger term —^- /# - L . Cady's equation thus V 1 C% failed as applied to the calculation by difference of the smallest term ; but the present method of presentation shows that the equation may be of use in calculating approximately the temperature coefficient of an amalgam cell. As the amalgams become more dilute, the fulfilment of the equation of course becomes more exact, because the concentration ratio gives more and more nearly an exact measure of the osmotic work, and all the other irregularities probably decrease. Thus for the cell M3-M4 (or N3-N/).), (pages 45 and 46), where 7^ = 0.01395 volt, ATT for 29. 96° =0.001541 volt, and the ratio of the concentrations is 3.305: I, the following results are calculated : Temperature coefficient calculated from concentrations.. 0.0000515 Actually observed temperature coefficient ............... 0.0000514 The difference is only 0.2 per cent, an amount distinctly less than the experimental error. Similar calculations for lead give similar results ; for example, let us take the cell Pi-P2, having a concentration ratio equal to 2.53. Then 8.316 — 0.9282 2X96,530 °= 0.0000392 Difference = 0.0000008 In the more dilute cell Qi-Q2 where the concentration ratio = 6.21, we have Temperature coefficient calculated from concentrations = 0.0000786 Temperature coefficient actually observed ............. =0.0000793 With this more dilute amalgam the difference is less than I per cent instead of being 2 per cent as in the case of the more concentrated lead cell. Turning back, now, to cadmium, investigated by Richards and Forbes, we find that the results recorded there give somewhat similar indications, when compared according to the present method. Thus the cell 1-5 a, the Raoult law will give a lower theo- retical value than the concentration law; and when A a 8 28 8 W Pure mercury. .. i i .y 14.8 * These values are calculated from the densities of amalgams on page 13. On comparing the last two columns, the differences are seen to be small, and with more dilute amalgams they are yet smaller. It will be observed that in cases of this kind both of these equations give results very different indeed from the mode of calculation which 64 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS takes account only of the space occupied by the solvent, where R T AT TT= —. - In ~. The latter method will evidently, as has been found by vr AI Richards and Forbes, give a much higher value. For the cadmium cell this was found to be 8.56 millivolts at o° C., instead of about 8.3 given by the equations above, the actually observed value being 8.67 at o°.55 In any case, it is clear that the new method of calculating the results from the equation of Raoult throws no light upon the major deviations of the cells from the equation of Cady, for these deviations are far too great to be explained by such insignificant alterations in the numbers predicted by theory, and some of the changes are in the wrong direction. On this account, it was thought unnecessary to recalculate the new theo- retical values for each case. As an outcome of these considerations, one may say that while the equation of Cady in one or other of its forms affords a fairly satisfactory means of calculating the temperature coefficient of an amalgam cell (and probably also of other cells in which there is but little change of heat capacity), and the best available means of finding the potential without electrical measurement, it does not afford a good method of determining the heat of dilution. This latter quantity is to be much more accurately found with the help of the equation of Helmholtz, to which the reader's attention is now directed. EQUATION OF HELMHOLTZ. In the first part of this monograph the temperature coefficients of the cells consisting of amalgams of thallium, indium, and tin were used for computing the heat of dilution, according to the equation of Helmholtz. The same calculation may now be applied to zinc, cadmium, and lead. Turning first to the case of zinc, we may take the cell Mi-M3 where 71-0 = 24.237 millivolts and ATT between o° and 29.96° C. = 2.799 millivolts." Because the temperature coefficient has been shown to be very nearly if not quite independent of the temperature, the value given may be used at o°. Then ir0vp ...................................... 4679.2 joules ATT ................................... 4926.0 j oules U .................................. —246.8 joules This value for the heat of dilution, —246.8 joules, or —59.0 calories, is considerably greater than the value —52 joules found by actual ther- mochemical experiments. The difference is due in part to the fact that 55 Richards and Forbes, Carnegie Institution of Washington, Publication 56, p. 62 (1906). The values there given are for 23°. 68 This paper, p. 45. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 65 the cell in the present calculation involved much further dilution than that corresponding- to the thermochemical experiment. In the present case one amalgam was about nine times as dilute as the other, while in the thermochemical experiment the dilution was only to double the bulk. Nevertheless, even allowing for the heat which would be absorbed by the further dilution of the amalgams, it is clear that the electrochemical estimate of the cooling effect exceeds the actual thermochemical measure- ment. This lack of coincidence was to have been expected from the results already chronicled in the preceding section of the monograph, concerning thallium, indium, and tin ; in each of these cases also the ther- mochemical effect appeared to be too small, and in the case of lead, soon to be discussed, the same discrepancy was observed. The lack of agree- ment is undoubtedly due not to fault in the Helmholtz equation, but rather to the inadequacy of the clockwork stirrer used in the thermo- chemical work. Liquid amalgams, because of their great inertia, are hard to mix ; but their ready conductivity quickly establishes a nearly equable temperature throughout, even when they are not thoroughly mixed. Hence it is easy to be deceived concerning the results. In spite of the lack of exact agreement, the thermochemical result of Richards and Forbes is nevertheless of value, for it shows that liquid zinc amalgams really produce a large cooling effect upon dilution, and it thus confirms, both as to sign and as to order of magnitude, the results of the electrical measurements. Turning to cadmium we find that the work of Richards and Forbes has quantitative as well as qualitative significance. By reference to the origi- nal data,67 it is seen that at o° TT:= 30.826 millivolts and — ~ =0.003655, therefore , ---- 5951 joules ATT vFT'Kr ................................... 59S7 J oules U .................................. = — 6 joules This difference is no larger than the possible error of experiment, and its sign is therefore somewhat uncertain ; but nevertheless it is supported by the very small cooling effect which was at that time actually found. In this case, the inadequacy of the mixing in the thermochemical experiment would have very little significance, because the effect to be observed formed so trifling a part of the whole phenomenon. In this connection it may be noted that Carhart M assumes on the basis of his theory, without any published experimental justification, that the "Carnegie Institution of Washington, Publication No. 56, pp. 50 and 57 (1906). 68Phys. Rev., 26, p. 216 (1908). 66 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS heat of dilution of cadmium amalgams is positive, not negative. In our experience, this assumption is contrary to fact. With the help of Dr. H. L. Frevert one of us has found that solid cadmium amalgams produce a large cooling effect on dissolving in more mercury, and there is every reason to believe that the dilution of liquid cadmium amalgams is like- wise an endothermic reaction, although its thermal effect is so small as to make accurate measurement difficult. The dilution of a 3 per cent cadmium amalgam with an equal bulk of mercury would evolve over 30 joules of heat if Carhart's theory were correct, and this would have raised the temperature of the calorimetric system by 0.02°. So large a thermal effect could not have escaped detection. This example remains the most precise verification of the Helmholtz equation which has ever been offered, coming within the experimental error of about o.i per cent. The interesting measurements of C'arhart " show an average deviation of nearly 2 per cent. Turning now to lead, we find results very like those of zinc and tin. Let us take the cell Pi-P2, of which TTO = 0.008960 and ATT for 29.96° C. = 0.001175. Then rr0vp ....................................... 1730 joules ATT vFT -- .................................... 2068 joules U .................................... - 338 joules The attempt was made to verify this value by actual thermochemical experiment, using the same apparatus as in the other cases already men- tioned in the previous papers. The apparatus was not suited for exact quantitative work, but the test was enough to show a very decided cooling effect (of 0.018° C.) in the apparatus, and to confirm in sign and in order of magnitude the figure calculated from the electrical measurements. Calculated in the same way from the electrical measurements of the other lead cells, the values for the heat of dilution are found to decrease as the dilution increases. Figures for three lead cells are given in table 21 to serve as typical examples of this phenomenon, which of course appears in the measurements with other metals also, in so far as their degrees of accuracy permit. It is interesting to note that the maximum cooling effect of dilution has not been wholly reached in a solution contain- ing only o.i per cent of lead (or I gram-atom in 15 liters) ; for an amal- gam of this considerable dilution is still found to absorb 20 calories more upon dilution to fourteen times its volume. This last exceedingly attenu- ated material would probably absorb very little more on further dilution ; hence the limiting value is probably not far off. According to these results, 58 Carhart, Phys. Rev., March, 1908. OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 67 then, a gram-atom of lead dissolved in a hundred gram-atoms of mercury must absorb about 540 joules or 130 calories on infinite dilution; and of this amount about two-thirds is absorbed when the amalgam is diluted with twice its bulk of mercury. With these figures are repeated also, in conveniently accessible form, the other results obtained in this monograph by the application of the equation of Helmholtz. TABLE 21. — Heat of Dilution of Amalgams Calculated from the Electrical Measurements. Metal. Designation Range of dilution Heat of dilution of solid per gram-atom metal . Joules. Gram calories. Thallium Cl-C2 i . 84 to o . 53 + 427 + 102.3 Do C2-C3 o . 53 o . 23 + IO9 + 26.1 Indium .... Ei-E2 1.92 0.38 + 677 + l6l.9 Do .... Gi-G2 0.016 0.008 — 4 — I . Tin Ji-j2 0.21 0.061 - 69 - 16.5 Zinc MI-MS 0.91 o.io — 247 - 59-0 Cadmium. . R&Fi-s 2.45 0.2Q - 6 — 1.4 Lead PI-P2 I . 02 0 . 40 -338 - 80.8 Do P2-P4 0.40 0.093 — 117 - 28.0 Do Qi-Q3 o.io 0.007 — 77 - 20.3 Because the heat capacity of the reacting system is essentially constant, these values are independent of the temperature, as far as our measure- ments were concerned. Their chief uncertainty depends upon the diffi- culty of measuring exactly the temperature coefficients of small electro- motive forces : but they are accurate enough to serve as a fairly close guide to the behavior of the respective amalgams. They are hardly close enough to serve as the basis for a search after an exact mathematical law governing the change of thermal effect with increasing dilution, although such a search would be an interesting aspect of yet more precise measure- ments. 'Cv 68 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS COMPARISON OF DEVIATIONS FROM CONCENTRATION LAW. As in the case of the previous paper, it is interesting to compare the deviations of the potentials given by various amalgamated metals from the requirement of the simple concentration law. In order to make the understanding of this matter more vivid, there are given together in the following diagram the several curves showing the deviations of the various potentials from the concentration equation. These lines are all drawn upon the same scale and are arranged so that for any ordinate the atomic concentration is identical. If the equation of Cady represented a complete correction, it would reduce all the lines to the horizontal straight line marked O. As a matter of fact only about three-quarters of the devia- tions, on the average, are to be explained in this way ; and only thallium and lead are brought nearer to the horizontal line than the uncorrected curve for cadmium. These curves, therefore, not only give an excellent collective picture of the behavior of these amalgams, but they enable anyone with a compara- tively small expenditure of time to compute the potential which would actually exist between two amalgams of the same metal between these limits of concentration. The divisions in the direction of abscissae mean in each case the doubling of the volume. Suppose one wished to deter- mine the potential between an amalgam of a given concentration and that of one-fourth its concentration. The place of the more concentrated amalgam is found upon the proper curve and the second one will be just two divisions to the right. The difference between the ordinates corre- sponding to these two points will give the deviation from the exact gas law for that particular combination. Accordingly the potential is to be computed according to the following equation : ,r=^(/w4) ±Arr in which ATT designates the difference between the ordinates just men- tioned. If any dilution other than 2, 4, 8, 16 is desired the appropriate point may easily be found from these and a table of logarithms, it being borne in mind that each large division in the direction of abscissa; signi- fies 0.30103 for Briggs's logarithms or 0.6932 for natural logarithms. The scale of the curves here depicted is rather small for an accurate determi- nation. Obviously the potential could hardly be found more nearly than perhaps within the fiftieth of a millivolt, because the large divisions in the direction of ordinates represent millivolts ; but this same principle might be employed on a larger scale and with more accurate data to within any degree of precision desired. It will be noticed that all the curves approach horizontally as the deviation proceeds. It is clear that long before infinite dilution is reached OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM the values will accord, within a limit of error of measurement, with either the equation of von Tiirin or of Cady. This seemed to us so clear that further prolongation of the curves to the right seemed to us hardly worth + 6 + 5 + 4- + 3 + 2 -f I -I -2 Zn \ \ 7 Sn log 2 log 4 Iog8 log 16 log 32 log 64- log 128 log 256 log 512 log 1 024 Fig. 12. The Approach of the Potentials of all the Amalgams to the Concentration Law. Deviations, both positive and negative, are plotted in millivolts as ordinates; logarithms of concentration ratios are plotted as abscissa. Thallium, indium, and cadmium give potentials greater than those corresponding n rrt to the equation it — — -^r /« — — • zinc, lead, and tin give potentials less than the actual values thus computed. The origin of abscissae _ corre- sponds to 4.00 gram-atoms of dissolved metal per liter, and the diagram extends to amalgams 1024 times as dilute as this (i. e., i gram-atom per 256 liters). The dotted lines are extrapolated. The curves are almost if not quite independent of temperature, at least between o" and 30", excepting in the case of tin, which is only very slightly soluble at o°. 7O ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS the labor involved, especially as the chance of error increases greatly as the amalgams become more dilute. The possible appearance of a balanced reaction at great dilution we attempted to detect by using, not greater dilutions, but rather metals with the least possible solution-tensions. The interesting work of Hulett and De Lury, published after ours was com- pleted, supplements our work by carrying the curve of one of the metals, cadmium, much further to the right than we have done. Neither of our curves shows any certain indication of the balanced reaction for which Hulett and De Lury were independently seeking, although several of the metals are distinctly less electropositive than cadmium. In conclusion, we take pleasure in expressing our obligation to the Carnegie Institution, of Washington, for generous pecuniary assistance. ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS 71 SUMMARY. The results obtained in the foregoing papers may be summarized as follows : (1) The electromotive forces of various cells, containing amalgams of thallium, indium, tin, zinc, lead, copper, and lithium, have been measured at o° and 30°, with many precautions against experimental errors. (2) The temperature coefficients of cells containing zinc amalgams were also obtained by actually opposing cells at o° against cells at 30°. (3) It is shown that in every case the more concentrated amalgams deviate by appreciable amounts from the theoretical values calculated from the simple concentration law, thallium and indium resembling cad- mium in giving potentials higher than those demanded by the concentra- tion law ; whereas lead and tin resemble zinc in giving potentials lower than those demanded by the concentration law. Thallium showed the greatest positive deviation, and tin and lead the greatest negative deviation. (4) It is shown further that on the average about three quarters of each of these deviations are to be explained by the heat of dilution of the amalgam, according to the equation of Cady. (5) The other quarter of the deviation, not explained by the equation of Cady, must be ascribed either to experimental error or more probably to the inexactness of the concentration law. Such inexactness would be caused either by polymerization or by the formation of hydrargyrates, according as the computed potential is greater or less respectively than the observed potential. (6) It is shown that the equation of Cady requires that the temperature coefficient of a cell of this type should be equal to the total concentration effect divided by the absolute temperature, and should be independent of the temperature. The verification of these conclusions is shown to hold approximately in all the cases studied, by comparison with the actual values. This fact affords a simple method of computing with moderate accuracy the temperature coefficient of the electromotive force of cell of this type, without having recourse to electrical measurement. (7) It is shown that the equation of Cady is not well adapted for com- puting the heat of dilution, for in this case all the errors and deviations accumulate upon the smallest term of the equation. (8) The heats of dilution of these various amalgams are computed with the help of the equation of Helmholtz ; and it is shown, as was to be expected, that the heat of dilution decreases very rapidly as the dilution progresses. (9) The difficulties of actual thermochemical measurement of the heat of dilution of amalgams are emphasized. 72 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS (10) It was found impossible to obtain satisfactory results with an electrolyte containing tin in a quadrivalent condition, either as stannic chloride or as sodium stannate. In this connection it was pointed out that Cady must have had a two-phase amalgam in his tin cell, and that his results with tin were illusory. ( 1 1 ) The solubility of copper in mercury was found to be only 0.0024 per cent, and of iron 0.00134 per cent by weight, amounts too small to give satisfactory electrochemical results. The results of Meyer upon copper are shown to be without significance, because he imagined that he used a much more concentrated solution, which must have been a mere suspension of copper in mercury. (12) It is shown that since lithium is only soluble to the extent of 0.036 per cent by weight in mercury, the results of Cady upon lithium are likewise questionable ; but more dilute solutions of lithium are shown to behave in a general way as Cady's equation requires. No exact deter- minations were made, because of the difficulty of finding a suitable electro- lyte. (13) All the deviations from the simple concentration law were found to decrease as dilution increases, so that upon reaching a concentration of o.oi gram-atom per liter all the amalgams investigated behaved prac- tically as ideal solutions. (14) The density of pure indium at 20° was found to be 7.28. (15) The densities of various liquid amalgams of thallium, indium, tin, and lead were determined. Electrochemical Investigation of Liquid Amalgams of Thallium, Indium, Tin, Zinc, Cadmium, Lead, Copper, and Lithium. BY THEODORE WILLIAM RICHARDS WITH THE COLLABORATION OF J. HUNT WILSON AND R. N. GARROD-THOMAS. PUBLISHED BY THE CARNEGIE INSTITUTION OF WASHINGTON 1909 MBL WHOI LIBRARY LJH IfllV L