T H E POTEETIAL O F T H E CADMIUM ELECTRODE BY
FREDERICK H. GETMAN
I n a recent study of the copper electrode’ it was pointed out that a single crystal of pure copper functions as a constant and reproducible electrode when immersed in solutions of copper sulphate. Shortly after the paper embodying the results of our experiments on the copper electrode was written, Anderson? published an account of his investigation of the electromotive behavior of single crystals of zinc. He measured air-free cells of the type Zn, ZnClz(aq), HgZCl2,Hg, and employed fifteen crystals prepared by three different methods. He shows conclusively that a single crystal of pure zinc behaves as a “reversible electrode capable of yielding potentials constant to a few hundredthsof amillivolt and reproducible over dissimilarly prepared crystals to one or two-tenths of a millivolt.” While Anderson’s measurements were made with especial reference to the constancy and reproducibility of the potentialof the primary cleavage, or (0001)face, of the zinc crystal, he also showed that “a cylindrical section of a crystal parallel to its major axis, containing along with the (0001) face, sharp edges and orientations other than the (0001)face, gives the same equilibrium potential as the isolated basal planes.” More recently, Straumanis3 in a study of the electrochemical behavior of single crystals of zinc has found that the cleavage planes of a single crystal when immersed in a neutral solution of zinc sulphate always give rise to the same average difference of potential, and that the latter is in agreement with the difference of potential developed by immersing a polycrystalline electrode of pure zinc in the same solution. I n view of the foregoing results it seemed of interest to study in a somewhat similar manner the electromotive behavior of single crystals of cadmium. The measurements of Horsch4 on the cell Cd (amalgam), CdClz(aq), AgCl (electrolytic), Ag, undoubtedly afford the most accurate available data upon which to base calculations involving the potential of the cadmium electrode. Measurements of the cell Cd, CdClz(aq), Hg2C12, Hg. recently made by the writerJ5while substantially in agreement with the data ‘Getman: 6. Phys. Chem., 34, 1454 (1930). *Anderson: J. Am. Chem. Soc., 52, 1000(1930). Straumanis: 2.physik. Chem., 147, 161 (1930). Horsch: J. Am. Chem. Soc., 41, 1787 (1919). j Getman: J. Phys. Chem., 32, 91 (1928).
THE POTENTIAL OF THE CADMIUM ELECTRODE
589
of Horsch, are inadequate for the calculation of the electrode potential of cadmium because of the fact that the values of the electromotive force in the more dilute solutions were manifestly too low.
Experimental ,$fateriaZs. Cadmium chloride of a high degree of purity was subjected to recrystallization before making up the mother solution. dl1 of the mercurous chloride used in the cells was prepared according to the electrolytic method of Hu1ett.l Redistilled mercury was further purified by distillation in a current of air as recommended by Hu1etL2 The single crystals of cadmium were prepared for the writer by Mr. J. H. Dillon of the University of U‘isconsin according to the method recently developed by him for the preparation of single crystals of metals of low fusibility.3 The purity of the metal from which these crystals were prepared is indicated by the following analysis: Cd 99.944%, As o.oor%, Fe o.ooj%, P b 0.0j o y c . The polycrystalline electrodes were made either from cadmium especially purified for use in standard cells, or from so-called “spectroscopic” cadmium, kindly furnished us by Mr. H. M. Cyr of the Research Laboratory of the Kew Jersey Zinc Co. and guaranteed to contain not more than o.oo17~of impurity. The spark spectra of the cadmium from these three different sources when compared by means of a Hilger quartz spectrograph, failed to reveal the presence of more than a trace of foreign metals. All of the water used in making up the solutions was prepared by redistilling ordinary distilled water with chromic acid and condensing in a block tin condenser. The water was stored in tightly stoppered bottles of Jena glass. The nitrogen which was used to displace air from the electrolyte in the cells was obtained in cylinders and was purified before entering the cells by passing through aqueous solutions of potassium permanganate, alkaline pyrogallol, water and cadmium chloride of the same concentration as that in the cells. Apparatus. The apparatus employed was the same as that used in our previous study of the copper electrode4 and the same experimental procedure was followed both in setting up the cells and measuring their electromotive force. Preparation of Electrolyte. A stock solution of cadmium chloride was prepared by dissolving a mass of the recrystallized salt in conductivity water sufficient to make a solution of approximately molal concentration. To this was added a small amount of pure cadmium hydroxide, after which the solution was shaken a t frequent intervals over a period of several days. After standing until the excess of hydroxide had settled, the chlorine content of the Hulett: Phys. Rev., (2) 32, 32 (1900). Hulett: Phys. Rev., (2) 33, 307 (1901). 3 Dillon: Rev. Sei. Inst., 1, 36 (1930). 4 LOC.cit. 1
1
590
FREDERICK H. GETXAX
solution was determined gravimetrically as silver chloride. A simultaneous determination of the density of the solution with an Ostwald pyknometer supplied the necessary data for the calculation of its molality. This was found to be 0.99472 M. The solutions of smaller concentration were prepared by dilution in calibrated volumetric apparatus. Electromotive Force Measurements Immediately after setting up, the cells were immersed in the thermostat bath and their electromotive forces were measured, after allowing sufficient time for the establishment of thermal equilibrium. The measurements were continued at frequent intervals over a period of six hours. During this time the cells maintained a satisfactory constancy of electromotive force, except in the case of those in which the electrolyte was dilute. With the latter there was an increasing tendency toward a slight but steady drift 0 O a0 e 5 1 in the electromotive force. The electrodes prepared from the highly purified “spectroscopic” cadmium were prone to exhibit erratic fluctuations of potential over a range of several tenths of a millivolt. The single crystal electrodes, however, did not show this tendency to fluctuation and proved to be almost as steady as cadmium amalgams. The experimental data given in Table I1 represent the mean of ten a 75 or more measurements of the electroFIG.I motive force a t each concentration. The electromotive force of six cells containing electrodes of either “spectroscopic” or “standard cell” cadmium is denoted by E l while that of two cells containing single crystals of cadmium as electrodes is denoted by E?. I n view of the statements of both Anderson and Straumanis, i t was not deemed necessary to split the single crystals along their cleavage planes in order to expose only a single definite surface to the electrolyte. Because of the relative instability of cells in which the electrolyte is dilute, no attempt was made to measure electromotive forces in solutions having a concentration less than o.orM. It is apparent that the numerical value of the potential of the single crystal electrode is uniformly greater than that of the polycrystalline electrode. This result is similar to that obtained in our study of the copper electrode. The foregoing values, believed to be accurate to within 0.3 millivolt, are represented graphically in Fig. I . By means of a large scale plot, similar to Fig. I , the values of the electromotive force a t even concentrations were read from the curves and tabulated in Table 11.
L-
THE POTENTIAL O F THE CADMIUM ELECTRODE
591
TABLE I Measurements of the E.M.F. of the Cell Cd, CdClz(m), Hg2Cl2, Hg a t 25' m
mols CdCL/Iooo g.HtO o ,00966 0.04805
0.09986 0.2002
7
0,28766 0.49084 0,99472
El
El
o ,84652
0.8502 I
0.81165
0.81258
0,79542 0.78208 0.77628 0.76625 0.75554
0.79758 0.78390 0.77641 0.76636 0.75646
TABLE I1 Smoothed Values of the E.M.F. of the Cell Cd, CdCln(m), Hg2C12, Hg a t 25' m mols CdClz/rooo g. HzO 0 .OI 0.02
0.05 0.1 0 . 2
0.5 I.
E,
E2
0.8435 0.8290 0.8097 0,7953 0.7820 0.7660 0,7553
0,8515 0.8340 0.8120 0,7973 0.7835 0.7675 0'7563
AE 0.0080 0.0050
0.0023 0.0020 0.0015 0.0015
0,0010
Calculation of Results I n order to calculate the normal electrode potential of cadmium, Eo,from the data of Table 11, it is necessary to have recourse to the extremely accurate data obtained by Horsch with cells in which the electrolyte was very dilute. I n his calculations, Horsch made use of the best available conductivity data and assumed that in extremely dilute solutions of cadmium chloride the values of the conductivity ratios are equal to the corresponding values of the activity coefficients. Quite recently, Randall' has developed a convenient method of extrapolation for the determination of normal electrode potentials from electromotive force data. Employing this method, we have recalculated the normal electrode potential of cadmium from Horsch's data. Having thus computed the value of E,, the activity coefficients of cadmium chloride at different concentrations can readily be calculated and from these in turn, the potential, E,, corresponding to the single cadmium crystal electrode can be evaluated. The electromotive force of the cell Cd, CdClz(m), AgCI, ilg, studied by Horsch, can be computed by means of the equation RT E = E,' - -1n (4 m3 y3) nF Randall: Trans. Faraday SOC.,23, 505 (1927).
FREDERICK H. GETMAN
592
I n this equation E is the measured electromot,ive force of the cell, Eo’th normal potential of the cell, m the concentration in mols per 1000 grams o solvent and y is the activity coefficient. The symbols R, T, n and F have their usual significance. Simplifying and transforming to common logarithms, equation ( I ) takes the form E = E,’ - 0.08873 log (1.588 m y ) . (2) Following the method of Randall, equation
(2)
log y - Ea’,’o.08873 = - (E/o.o8873
may be transformed into
+
0.2007
+ log m)
(3)
If theright-hand side of equation (3) be plotted against the square root of the ionic strength, ,u, and the resulting curve be extrapolated to infinite dilution, the value of Eo’can readily be calculated by means of equation (3). The experimental data of Horsch are reproduced in Table I11 and a partial graphic representation is given in Fig. I .
TABLE I11 Horsch’s Measurements of the E.1I.F. of the Cell Cd, CdC12(m),AgC1, Ag a t 25’ m
o .ooo1oz9 o .oooro87 0.0001137 o.0001269 0.0001527 0 . 0 0 0 2 144 0.0003363
0 0 0 0 0 0 0
E 9594 9557 9545 9512 9460 9337 9178
E 0.9148 0.9050 0.8830 0.8491 0,8398 0.8165
m o 0003659 0 000479 0 000924 o 002581 0 003519 0 0074 0 0995
0.7530
The data of Table I11 were plotted on a large-scale plot and the values to log m = 6.0, log m = x.1, log m = 3.2,etc. up to log of E corresponding m = 7.0 were read from the curve and tabulated, together with the corresponding values of p’ and (E/o.o8873 0.2007 log m) as shown in Table I\’. TABLE IV Data derived from Horsch’s Measurements E (E/o.o8873 0.2007 + log m) m rf
+
+
+
0.0001000
0 , 0 0 0 1259 0.0001585
0.0001995 0 . 0 0 0 2 512 0.0003162 o .0003981 0.000~012
o.0006310 0.0007943 0.001
0.01732 0.01943 0.02181 0.02446 0.02745 0.0308 o ,0346 0.0388
0.0435 0.0488 0.0548
0.9597 0.9523 0.9445 0.9365 0.9282 0,9199 0.9117 0.9035 0.8954 0,8876 0.8801
7.0107 7 ,0407 7 ,0407
7,0507 7.0607 7.0707 7 ,0807 7.0807 7.0907 7 . I007 7,1197
THE POTENTIAL O F THE CADMIUM ELECTRODE
5 93
+
On plotting the values of (E/o.o8873 0 . 2 0 0 7 4- log m) versus p’, as shown in Fig. 2 , the averaged straight line through the points thus obtained intersects the zero ordinate a t a point corresponding to 7.005. On substituting this value in equation (3), we find Eo’ = 0.6215 volt, the normal potential of the cell. I n order to determine the normal electrode potential of cadmium, Horsch also measured the electromotive force of the cell Hz ( I atm.), HCl(o.oIM), AgCI, Ag, and found E = 0.4665 volt. Accepting 0.93 as the value of the activity coefficient of o.orM HCI, we have 0.05915 log (0.01X 0.93) Eo = 0.4665 = 0.2283 volt, H2, Hf ( h l ) , C1- (M), AgC1, Ag; Eo = 0.2283 volt. or
+
FIG.z
Hence Horsch’s value of the normal electrode potential of cadmium is
Eo = 0.6215 - 0.2283, = 0.3932 Volt. Horsch actually obtained, as the result of his calculations based upon conductivity data, EO= 0.3992 volt. Accepting 0.3932 volt as the value of Eo,we may now proceed to calculate the values of the activity coefficients of solutions of cadmium chloride by means of equation ( 2 ) . The values of y thus obtained together, with the corresponding conductivity ratios derived by Noyes and Falkl, are given in Table V. In Table V values of y are slightly less than those calculated by Lewis and Randall2 from the experimental data of Horsch. This laok of agreement is to be traced to the fact that Lewis and Randall apparently based their calculations on Horsch’s observed values of the electromotive force of the cell Cd(4. j amalg), CdClz(m), AgC1, Ag, 1
Noyes and Falk: J. Am. Chem. SOC.,34, 475 (1912).
* Lewis and Randall: “Thermodynamics and the Free Energy of Chemical Substances”, 362.
594
FREDERICK H. GETMAN
rather than on the calculated values of the electromotive force of the cell, Cd, CdClz(m),AgC1, Ag The difference of 0.0534 volt between the electromotive forces of the two cells obviously represents the electromotive force of pure cadmium against the cadmium amalgam. When allowance is made for this difference, their values for y are in close agreement with those given in Table V. A comparison of the values of y and Q shows that Horsch was not justified in assuming the equality of these two ratios, even in dilute solutions of cadmium chloride.
TABLE V Activity Coefficients of Cadmium Chloride Solutions (2 5’) m
E
Y
a
0 .OOOI
0.9567 0.9360 0.9050 0.8810
0.969 0.898
0.975 0.960
0.802
0.690
0.005
0.8573 0.8280
0.93’ 0.891 0.830
0.01
0.8085
0.02
0,7910 0,7688
0,592 0.491 0.389
0.735 0.664 0.580
0.277 0.205
0,453 0.375 0.308
0,0002
0.0005
0.001 0.002
0.05 0.1
0.2 0.5 I
O
0,7535 0.7390 0.7209 o 7080
0.748
0 ’ I49 0.096 0.067
We are now in possession of the necessary data for the calculation of the normal electrode potential of the single crystal cadmium electrode. Thus, on substituting the values of y given in Table T’, and the corresponding values of E from Table 11, in equation ( 2 ) the value of E’o can be calculated. The data resulting from this calculation are collected in Table VI.
TABLE VI Values of Elo for the Cell Cd(sing1e cryst.), CdC12(m),Hg2ClZ,Hg 0 .OI
E 0.8515
0.02
0.8340
0.05
0.8120
m
01.
0,7973
Mean
0.491 0.389 0.277 0.205
E’, 0.664j 0,6648 0.6649 0.6654 0.6649
The mean value of El0 is thus found to be 0.6649 volt. Since, according to Gerke’ the potential of the electrode Gerke: Chem. Rev., 1, 384 (r92j).
THE POTENTIAL OF THE CADMIUhI ELECTRODE
595
Hg, HgzC12 (s), Cl-, is
-0.2700
volt, it follows that Cd(s), Cd++; Eo
0.3949 volt.
This value for the normal electrode potential, it will be observed, is nearly 3 millivolts less than the value assigned by Gerke' to this constant, vis. 0.3976 volt. Presumably, however, Gerke accepted the results of the calculations of Lewis and Randall based upon Horsch's data. If the values of E in Table I1 be substituted successively in equation (3) and the resulting values be plotted against the corresponding values of p', an approximate value of E f ocan be obtained by graphic extrapolation. Employing this method, we found E'o = 0.6645 volt, or Eo = 0.3945 volt. Since single crystals of copper, zinc and cadmium have been found to function as constant and reversible electrodes, it seems reasonable to base our calculations of normal electrode potentials upon measurements of the electromotive force of suitable galvanic combinations in which single crystals of these metals are employed as electrodes. As the result of such calculations based upon the foregoing experimental data, we are led to accept, as the value of the normal electrode potential of cadmium, EO= 0.395 volt.
SHmmnrv (I)
Measurements have been made of the electromotive force of the cell
in which the cadmium electrodes were either single crystals or massive crystalline aggregates of the pure metal. Single crystals of pure cadmium were found to function as constant (2) and reproducible electrodes. (3) The numerical value of the potential of the single crystal electrode was found to be uniformly greater than that of the polycrystalline form. (4) The measured values of the electromotive force of cells with single crystal electrodes were employed to calculate the normal electrode potential of cadmium. The value of this constant has been found to be E o = 0.395volt. Hillside Laboratory, Starnjord, Conn. 1
Gerke: Chem. Rev., 1, 381 (1925).
