T H E THERMODYNAMIC PROPERTIES O F CADMIUM SULFATE I N WATER-ETHYL ALCOHOL SOLUTIONS VICTOR K. LAMER AND ERWIN L. CARPENTER Department of Chemistry, Columbia University, New York
Received August $0, 1956 INTRODUCTION
The purpose of this research was to investigate how the partial free energy, heat content, and heat capacity of a typical bivalent electrolyte, cadmium sulfate, are affected on lowering the dielectric constant by the addition of ethyl alcohol to its aqueous solution. It can be demonstrated (7, 20) that the electric free energy of an ion can be computed from the work of reversibly charging the ion from a reference potential to its actual potential #. The latter is composed of two parts: first, a part $0 which exists in the absence of any surrounding ions and arises by virtue of its own charge; and second, a part #* which arises from the unequal distribution of the surrounding ions as interpreted by the Debye-Huckel interaction theory. The interaction effect depends upon D-3'2 as a limiting first approximation, and upon a parameter a which represents in terms of the model the distance of closest approach of the ions. The interaction effect can be eliminated exactly when the experimental results a t finite concentration permit of an unequivocal extrapolation to infinite dilution. The potential, $0, which generally is of greatermagnitude, should, according to Born (3), vary inversely with the radius of the ion and the dielectric constant. Born's equation for the solvent effect assumes the same simple model, namely, that the ions may be represented by spheres of radius ~ i and the medium by a continuous dielectric having the macroscopic value D. All chemical processes of solvation are ignored. Ono aspect of this investigation was to ascertain in how far this simple model can account for the experimental results obtained with a bi-bivalent salt, where the electric effects are of greater magnitude than with a uniunivalent salt, by comparing the radii of the ions as computed from the Born equation with the value a as given by the interaction theory. Although a number of investigators (6, 10, 11, 19, 23) have utilized galvanic cells to study medium effects in terms of the free energy of transfer of electrolytes, no systematic investigation of temperature coefficients in nonaqueous solvents has been made. Such studies are of importance since 287 FHB
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3
,
288
VICTOR K. LA MER AND ERWIX L. CARPENTER
they furnish accurate data for the calculation of changes in the heat content and heat capacity of the cell process from which the thermal properties of the electrolyte can be readily obtained. Owing to the highly reproducible behavior of cadmium amalgam and mercurous sulfate electrodes, cells containing these electrodes are most suitable for attacking this problem. Since the requisite data for aqueous cadmium sulfate are available from the studies of LaMer and Parks (17) on the amalgam cell: Cd (2 phase), CdSO4 ( M , HzO), PbSO4(S), Pb (2 phase)
Cell I
for which the cell process is : Cd (satd. Hg)
+ PbSOa(S)
= CdS04 ( M , HzO)
+ Pb (satd. Hg)
werfirst investigated this cell by replacing the water progressively with elhyl alcohol. Equilibrium, however, was attained so slowly in the presence of alcohol that cell I was abandoned in favor of the amalgam cell using mercurous sulfate instead of lead sulfate: Cd (2 phase), CdSOI (IM,a per cent ELOH), HgzS04(S), Hg Cd (satd. Hg) Hg2S04(S)= CdSO4 ( M , a per cent EtOH)
+
Cell I1 + 2Hg
The limited success which the mercurous sulfate electrode has achieved in aqueous solution is due primarily to the uncertainty arising from the relatively large corrections for its solubility, which must be applied when the concentration of the more soluble sulfate (cadmium sulfate) is less than 0.005 M . Fortunately, the solubility of mercurous sulfate is greatly reduced by the addition of alcohol. In 33.3 weight per cent ethyl alcohol, using Hulett's method (14) of precipitating the mercury as chloride by the addition of hydrochloric acid, we find S H ~ , S =O 1.8 ~X moles per liter. The same value was obtained in experiments in which the alcohol was first evaporated and the chloride precipitated from aqueous solution. The solubility product of mercurous sulfate in 33 weight per cent alcohol is consequently so small that no correction for sulfate ion is necessary in calculating the observed normal potentials E"', even for concentrations as low as 0,001 M cadmium sulfate. Furthermore, cell I1 yielded highly reproducible potentials and hence is well suited for our purpose, even though its use is limited to rather narrow ranges of concentration as a result of the decreased solubility of both cadmium sulfate and mercurous sulfate, In 15 per cent ethyl alcohol the lower limit for precise work is 0.01 M cadmium sulfate; in 33 per cent ethyl alcohol the limits are 0.001 M extending to saturation (about 0.01 M ) ; above 33 per cent ethyl alcohol the internal resistance of the cell is so high that 0.01 M is the practical lower limit; above 50 per cent alcohol cadmium sulfate becomes too insoluble for precise measurements.
THERMODYNAMIC PROPERTIES OF CADMIUM SULFATE
289
To compare the results in water using cell I with those in alcohol using cell 11, it is necessary to know the thermal properties of cell 111: Cell I11
Pb (2 phase), PbSOd(S), Hg2S04(S), Hg Pb (satd. Hg)
+ HgtSOa(S) = PbS04(S) + 2Hg
Subtracting cell I11 from cell I1 yields Cd (2 phase), CdS04 ( M , a per cent EtOH), PbS04(S), Pb (2 phase) Cell IV Cd (satd. Hg) PbS04(S) = CdS04 ( M , a per cent EtOH) P b (satd. Hg)
+
+
It will be observed that cell IV is identical with cell I except that the solvent contains a per cent ethyl alcohol. By comparing results with cell I and cell IV, the free energy of transferring cadmium sulfate from water to alcohol can be computed without involving the troublesome and uncertain solubility corrections for mercurous sulfate. Henderson and coworkers (12, 13) have measured cell I11 at 18", 25", and 30°C., but as this temperature range was not sufficient, and no precautions were reported for the removal of oxygen from the solution, we have reinvestigated cell I11 over the range 0" to 50°C. APPARATUS
The electrical apparatus described in detail previously by LaMer and Parks (17) was used. The potentiometer was recalibrated. The Eppley Cell No. 74017, calibrated by the Bureau of Standards, was checked frequently against other standard cells in the laboratory. PREPARATION OF MATERIALS
The best C.P. grades of salts were further purified by repeated crystallization as described previously, using conductivity water and Nonsol bottles for storage. The preparation and storage of the amalgams was identical with previous description. The cadmium sulfate solutions were prepared by diluting a master solution (approximately 0.1 molal) by weight, the exact concentration of which was known to 0.05 per cent by the quantitative deposition of cadmium by electrolysis. Ethyl alcohol. We have corroborated the work of Stout and Schuette (24), who showed that the method in which ethyl alcohol is distilled from aluminum and potassium hydroxide is more effective in removing the aldehydes than the more common method using silver oxide. Ten grams of potassium hydroxide was added per liter of 95 per cent alcohol. The next day 6 to 8 g. of aluminum turnings per liter of alcohol was added, the reaction mixture refluxed for one hour, and finally distilled in an atmosphere
290
VICTOR K. LA MER AND ERWIN L. CARPENTER
of nitrogen in glass apparatus having an efficient fractionating column. The middle and last fractions were found to be aldehyde-free when tested with fuchsin-sulfite reagent as described by Woodman (26). The specific gravity of the alcohol was then taken at 25°C. The weight per cent of the alcohol was determined from the density. Mercurous sulfate. Mercurous sulfate was prepared electrolytically by the Hulett method (15), in which purified mercury served as the anode and a platinum wire dipping into sulfuric acid of density 1.15 was the cathode. The product was gray, owing to the presence of finely divided mercury, which is a distinct advantage in checking any tendency of the mercurous ion to be oxidized to mercuric ion. Vosburgh and Eppley (25) have shown that samples of mercurous sulfate prepared by three different methodsthe reduction of mercuric sulfate by mercury, direct current electrolysis, and the reaction of mercu;ous nitrate and sulfuric acid-give E.M.F.'S agreeing within 0.01 mv. Akerliif (1) also obtained satisfactory results with mercurous sulfate prepared electrolytically in his study on the alkali sulfates. The mercurous sulfate was stored in the dark under 2 molal sulfuric acid in a Nonsol bottle. EXPERIMENTAL METHOD
The cell vessel used for cells I and I1 was the same as that developed by Cowperthwaite and LaMer (5) for their study of zinc sulfate. This type of cell vessel permits the entire filling operation to be carried out in an atmosphere of nitrogen, and the cell can then be sealed off under mercury. The reader should consult their paper for the diagram and details of manipulation. The type of cell vessel used by LaXer and Parks was found to be more suitable for cell 111, where two solids are involved. Their cell vessel is composed of six electrodes divided by three large bore stop-cocks into two groups of three each. On one side three similar lead-lead sulfate electrodes and on the other side three similar mercurous sulfate-mercury electrodes are set up. This type of vessel has the particular advantage thatmeasurements to check the constancy and reproducibility of each leg of the three electrodes forming the one half-cell as well as the measurements of the three total cells can be made without disturbing the contents or the vacuum. EXPERIMENT.4L DATA
To test the reproducibility and freedom from hysteresis of cell I1 in alcohol solutions, three sets of five cells each were made up on different days. The concentrations of cadmium sulfate and ethyl alcohol were respectively 0.01 iM and 33.3 per cent. The average deviation a t 25°C. was h0.0064 mv. For two of these sets, the readings were taken at, different temperatures in the order: 25", 30",20°, 15", lo", 0", lo", 20", 25",
29 1
THERMODYNAMIC PROPERTIES OF CADMIUM SULFATE
and 30°C. The combined averages of the values obtained at descending and ascending temperatures of the two skts never had an average deviation greater than f 0 . 0 2 mv.; usually much less. Cell I1 is not only reproducible but it exhibits little, if any, temperature hysteresis. Henderson and Mellon (12), using both a saturated and an unsaturated solution of sodium sulfate as the conducting medium, found that cell I11 TABLE 1 Observed E.M.F. of cell I I l
1
TEMPERATURE
t".
N O . OF CELLS MEASURED
I
E=Ea)=EO
0.96051 0.96262 0,96471 0.96680 0.96891
0.0 12.5 25.0 37.5 50.0
TABLE 2 Values of E for 0.01 M cadmium sulfate
0 .o 10.0 15.0 20.0 25.0 30.0
0.14651 0.14720 (0.14673) 0.14588 (0.14476) 0.14346
1 0.0 10.0 15.0 20.0 25.0 30.0
*(
Ea' (I) (Hz0)
1
0.03812 0.03485 (0.03239) 0,02956 (0.02645) 0.02317
1.04526 1.04780 1,04870 1.04942 1.04997 1.05032
1.02425 1.02596 1.02659 1.02707 1.02744 1.02774
0.08475 0.08561 0.08567 0.08555 0.08526 0.08477
EO' (11) (33.3 PER CENT
EO' (11) (60 P E R C E N T
EO' ( I V ) 33.3 PER CENT
ALCOHOL)
ALCOHOL)
ALCOHOL)
0.93687 0.93545 0.93436 0.93310 0,93166 0.93003
0.91586 0.91361 0.91225 0,91075 0,90913 0.90745
-0,02364 -0.02674 -0,02867 -0.03077 -0,03305 -0,03552
t
0.06374 0.06377 0.06356 0.06320 0.06273 0.06219 EO' (IV) (50 P E R CENT ALCOHOL)
-0.04465 -0.04858 -0.05078 -0,05312 -0.05558 -0.05810
) interpolated values.
gave an E.M.F. of 0.96466 a t 25°C. They also demonstrated that the E.M.F. was independent of the conducting medium by using saturated and unsaturated solutions of nickel, zinc, manganese, and cobalt sulfates in place of sodium sulfate. I n table 1 are given our results for cell I11 over a wider temperature interval, using as solvents 0.33 M sodium sulfate and 0.002 M sulfuric acid (to prevent hydrolysis in wker), and 0.01 M sodium sulfate in 33.3 per
292
VICTOR K. LA MER AND ERWIN L. CARPENTER
cent ethyl alcohol. The measurements of the two sets agreed within 1 0 . 0 2 mv. and checked Henderson and Mellon’s value a t 25°C. to 0.05 mv. In table 2 are recorded the observed values of E for the respective cells for 0.01 M cadmium sulfate in the solvents water (column 2), and 33.3 per cent and 50 per cent ethyl alcohol (columns 3 and 4) a t various temperatures. Each value represents the average of a t least five cells; the average deviation was never greater than f 0 . 0 2 mv., and in many cases only fO.01 mv. The values for the cell process IV, obtained by subtracting the temperature-interpolated values of E (111) from E (11), are given for purposes of direct comparison with cell I with which they are equivalent except for the presence of alcohol. In table 3 are given the observed values for cell I1 for different concentrations of cadmium sulfate in 33 per cent ethyl alcohol a t 25°C. Each value represents the average of a t least five cells; the average deviation was TABLE 3 E f o r cells I , 11, and IV a s f u n c t i o n of concentration of cadmium sulfate and per cent of alcohol at 86°C. 0 PER
33 PER CENT ALCOHOL
CENT ALCOHOL
.?4
0.01 0,008 0.006 0.004 0,002
0.001
I
I1
IV
0.14476 0.14877 0.15404 0,16158 0.17424 0.18840
1 ,04997
0,08526 0.08778 0.09106 0.09546 0,10215 0.10915
1 05249 1 ,05577 1.06017 1 06686 1,07386
15 per cent alcohol a t 0.01 M ; E (11) = 1.07908; E (IV) = 0.11437.
never greater than d~0.04mv. The values for cell I in water were taken from a large scale graph of LaMer and Parks’ (17) Eo’ values after they had been interpolated to 25°C. using an equation of the third degree in t . THEORETICAL
When a mole of salt is transferred from an aqueous solution of dielectric constant D2to an alcoholic solution of dielectric D,,the reversible work of transfer arises from two sources. The excess electrical free energy, which the ions possess by virtue of their unequal distribution as interpreted by the Debye-Huckel interaction theory, changes somewhat with the change in the dielectric constant. Secondly, the individual ions of radius TCpossess a greater electrical free energy in the medium of low dielectric constant by virtue of the greater amount of work which is necessary to charge reversibly these ions for such a medium. Born’s equation for this solvent medium effect is
293
THERMODYNAMIC PROPERTIES O F CADMIUM SULFATE
AFo is the free energy change a t infinite dilution, where the effects of interaction are absent.‘ The activity coefficient often is a more convenient quantity to use in the numerical treatment of experimental data than is the free energy. Any activity coefficient whose standard state of reference is taken as unity for infinite dilution in pure water will be designated by the symbol f. When the activity coefficient is referred to the standard state of infinite dilution in a particular water-alcohol medium, an asterisk will be used (f*). A subscript zero indicates that the concentration of electrolyte is zero, and when the medium is pure water, a superscript zero will be used (fa; f: = 1, etc.). All concentrations of cadmium sulfate are expressed in moles per kilogram of solvent; the concentration of alcohol in weight per cent. TABLE 4 ‘lTotal medium effect” log 5/50 for cadmium sulfate at 26°C. WEIGHT PER CENT ETHYL AJAOHOL
D
15 0 33.3 50 0 WEIGHT PER CENT
33.3
70.14 59.16 48.93
I
I
D
59.16
I
1
0.01 M
0.008 Y
0.000M
0.5138 1.0059 1.3867
1.0311
1,0647
0.004M
1.1178
1 ~
0.002M
1.2187
1
I
0.001 M
1.3398
In terms of these definitions, the total medium effect is log f/fo and is composed of two parts, the solvent effect = log = log fa, since j t = 1, plus the interaction medium effect logj*/fo. Thus
fo/ft
Owen (21) uses the terms “primary” and “secondary” medium effects, but we prefer the more descriptive terms “solvent” and “interaction.” They are obviously related to the potentials $o and #* mentioned in the introduction. The total medium effect is obtained directly from the E.M.F. of the double cell I-IV by the relation
E = E (IV) - E (I) = 0.05915f/f0
(3)
1 ZEis the charge on the ion, N is Avogadro’s number, and r+ and r- are the radii of the cation and anion.
294
VICTOR K. LA MER AND ERWIN L. CARPENTER
The results are given in table 4 for the concentrations of cadmium sulfate and alcohol studied. Calculation of the solvent medium effect and the interaction coefficient f* requires a knowledge of EO for cell I1 in alcohol. In figure 1 we have plotted the values of EO’;defined as
against the square root of the molality for 33.3 per cent ethyl alcohol. The data obviously do not approach the limiting slope of the Debye-
0.92700
0’86700
I tI
I
I
0.0
0.025
0.05
, a075
0.10
TGr-
FIG.1
Huckel theory a t concentrations as low as 0.001 M . This behavior has been observed (4, 9) previously for the solubility data of salts in methyl and ethyl alcohol-water mixtures. Fortunately, a precise value of E ois not necessary, since a comparatively large error in log f* results in only a small error in log fo,f* never being greater than 1 per cent of fo. In table 5 we give the calculation of E o using the Gronwall, LaMer, and Sandved (8) equation for the activity in equation 4 for a = 2.92 A X . , which proved to give the best fit. It will be noticed that the individual values fluctuate more from the average than they do for cadmium sulfate in water solution. This is due to the fact that the higher terms do not converge rapidly in the case of the
THERMODYNAMIC PROPBRTIES OB CADMIUM SULFATE
295
alcohol solution (D = 59.16), whereas they do converge with sufficient rapidity in the case of water (D = 78.54). LaMer and Parks obtained a constant E o when an ion size of 3.6 A.U. units was used. Whether the decrease in a from 3.6 A.U. in water to 2.92 A.U. in 33.3 per cent alcohol is real, or arises from insufficient convergence, or is due to theoretical weaknesses in the Debye-Huckel theory cannot be determined a t present. It is gratifying that the Eocalculated over the range from 0.01 M to 0.001 M , agrees within 0.16 mv. of the value obtained by the linear graphical extrapolation. We estimate that E o is known to =t0.0005 volt, which fortunately introduces an uncertainty in the calculation of the solvent medium effect of only f 0 . 5 per cent. Using the average value Eo = 0.87033, the solvent medium effect for 33.3 per cent ethyl alcohol in the absence of any interaction effects equals 1.6246. According to the Born equation, the solvent medium effect, log fo, TABLE 5 Calculation of E o by the Gronwall, LaMer, and Sandved extension; a = 2.92 A . U . CONCBNTAATION
0.01 0,008 0.006 0,004 0,002 0.001
Average.. . . . . , . . , . . . , . . , . . Graphical extrapolation.. .
I
E@
0.87075 0.86994 0.86966 0.87006 0.87095 0,87107
I
DEVIATION FROM M E A N
O.OOO44 -0.00047 -0,00075 -0.00035 0.00054 0.00065
0,87041f 0.0005 0.87025
should be proportional to the reciprocal of the dielectric constant of the solvent, a prediction which Lkerlof (2) found to hold fairly well for sodium, potassium, lithium, and hydrogen chlorides up to 80 per cent methyl alcohol in water (D = 42.3). The dotted line in figure 2 has been drawn on this assumption. The distance from any point on the solid line to the dotted line a i the same value of 1/D is equal to the interaction medium effect, which, it will be noted, rapidly becomes of greater importance as the dielectric constant decreases. From the slope of the dotted line we calculate that
2
;=
;( ): +
corresponds to a value of r = 1.24 A.U. If the ions are spherical and no forces of deformation intrude, a = 2r = 2.48 A.U. The disagreement with a = 2.92 A.U., calculated from the Gronwall, LaMer, and Sandved
296
VICTOR R. LA MER AND ERWIN L. CARPENTER
form of the interaction theory, while outside experimental error, is not serious considering the highly simplified character of the model which completely neglects any influence of solvation. I n column 2 of table 6 are given the values of f*, the interaction activity coefficient for cadmium sulfate in 33 per cent ethyl alcohol and referred to
1.1
J 4 9
1.0
u5
ao le?
O-,
156
im
166
18I x
10,
FIG.2 0.OOO M ; A, 0.001 M ; 8 , 0.002 M ; X, 0.004 M ; 0 , 0.010 M
unity a t infinite dilution in this solvent and in column 3, fa, the corresponding activity coefficients in aqueous solution. The last column gives the interaction medium effect log j*/fo. The decrease in molal heat content (- AH) and the increase in molal heat capacity (Ac,) are related to the E.M.F. of the cell process by the relations :
297
THERMODYNAMIC PROPERTIES O F CADMIUM BULFATE
It can be shown that if Eo'is plotted (17) against 1/T the slope of the curve at any point is a measure of the magnitude of (- AH) corresponding to the
I-
-O'OZ
-
0.04
+ 0.04
t/
-0.05
-
0.04
-0.06
1 3.30
3.39
3.48
357
3.66
y+ x 10) FIG.3 Scale of ordinates reading from left to right refers t o cell IV (60 per cent alcohol), cell IV (33 per cent alcohol), and cell I (water). temperature and composition of the solvent at that point. Similarly, the curvature is a measure of the value of Ac, for the cell process.
298
VICTOR K. LA MER AND ERTVIS I..
CARPENTER
If EO', T is plotted against l,'T, the slope is directly related to - A H and the curvature directly to Ac,. The values of Ea'for cells I and I V are thus plotted in figure 3, froin which it is evident that with increasing alcohol content -AH decreases and Ac, becomes less negative, Le., it increases. To facilitate the numerical computation of these quantities we have expressed E for the different cell processes a t 0.01 M cadmium sulfate as polynomials of the third degree in terms of t"C. : E =A
+ Bt + Ct* + Dt3
(7)
using the experimental values of the E.M.F. at 0", loo, 20", and 30°C. To test the reliability of the derived equation, the computed values of E for TABLE 6 Interaction activity coeficients of c a d m i u m sulfate at 86°C. 'U
f' ( 3 3
f" (Hz0)
PER CENT EtOH)
0.363 0.238 0.154 0.122 0.104 0.092
0.001
0.002 0.004 0.006 0.008 0.010
-log
/'/fa
0,285 0.406 0,507 0.560 0.594 0.619
0.698 0.606 0.496 0,443 0.408 0.382
TABLE 6a ____
Coe.ficients X 103 f o r equations 10 and 11 L
CLLL PROCLbS
I (0 per cent, '2.1 = 0.01). , . . . . . . . . . . . . . , 111 (Independent of solvent). . , . . , . . . . , , . , IV (33.3 per cent, ilf = 0.01). , . . . . . . . . . . , , IV (50 per cent, ill = 0.01). . . , . . , , , , , . , ,
,
I
B
G
I
D
14651 96051 8475 6374
the two temperatures, 15" and 2j0C., were compared with the experimental values. The calculated and experiinental values checked in all cases within ~ k 0 . 0 2mv. The empirical equation may accordingly be relied upon to give the correct derivatives within the limitsof accuracy of the data. Such a check is not obtained if a second degree equation is employed. The coefficients of equation 7 are given in table 6a. AH and Ac,, calculated by substituting the proper analytical expressions of the derivatives of equation 7 in equations 5 and 6 are given in table 7 for 15OC., for which temperature the higher derivatives should be most aac reliable. Columii 5 for 2is included to preserve consistency with the ?IT
299
THERMODYNAMIC PROPERTIES O F CADMIUM SULFATE
experimental values of E a t the various temperatures, but no claim is made for accuracy since this quantity depends upon the third derivative asE/aTs. Since Parks and LaMer (22) have measured the E.M.F. and its temperature derivatives of the cell for which the process is
V
Cd(S) = Cd (two-phase amalgam) AH and Ac, for the process
+ Hg2SOd = CdSOl ( M , a per were computed by the relation VI = I1 + V. Cd(S)
cent EtOH)
+ 2Hg
VI
TABLE 7 Summary of results for 16°C. (B88.i"K) in calories
- AH
PROCESS
I11 Pb (satd.Hg)
+ Hg,SOa(S) = PbSO, + 2Hg
IV Cd (satd.Hg)
+ PbSOa = CdS04 (0.01 M ) +
P b (satd.Hg)
1E 0.0
i
+
VI1 Cd(S) PbSOd(S) = CdS04(0.01 M ) Pb (satd.Hg)
0.
+ 50.0
amg aT
ACP
-
42,208
0
8,577
-207 -109 -69
11.4 2.3 2.2
-220
17.4 8.3 7.8
4,045
3,670 56,041 51,509 51,134
- 122
-82
0.
13,833 Same as proc9,301 ess VI 8,926
I n a similar way the same quantities for process VII, involving solid cadmium instead of the two-phase amalgam, can be computed from the relation VI1 = IV V.
+
HEAT CONTENTS AND HEAT CAPACITIES OF DILUTION
The values2for AR = Z(O.01 M , a per cent EtOH)
and A6, (0.01 M )
-
- 3 (0.01 M , H2O)
E, (0.01 M , a per cent EtOH) - C, (0.01 M , HrO)
arising from the transfer of a mole of cadmium sulfate from a 0.01 molal solution in water to a 0.01 molal solution in 33.3 and 50 per cent ethyl
* The partial molal quantities, designated by the bar, always refer to the solute. The customary subscript 2 has been omitted as unnecessary in this paper.
300
VICTOR IC. LA MER AND ERWIN L. CARPENTER
alcohol are given in table 8 for the temperatures loo, 1 5 O , and 2OOC. The values of E (0.01 M ) and C, (0.01 M ) are tabulated for the different temperatures in table 9. 5 is defined by the equation = Cp
E (0.01 M , a per cent EtOH) - H0( M = 0, HzO) = 4cp (VI) cp(Cd) Cp(HgLSO4) - 2cp(Hg)
+
+
using the values as given in the International Critical Tables for solid cadmium, mercurous sulfate, and liquid mercury. The values for i; (0.01 M ) and E, (0.01 M ) for cadmium sulfate in water (22) are also listed for comparison. Table 9 shows that c, (0.01 M ) for cadmium sulfate is very nearly a linear function of the weight per cent of alcohol.
AS = a
10.01 li,u PER CENT E t O H ) H 10.01 X , H10)
PER CENT
EtOH
~
1
10'C.
33
'
50
A& = cp (0 01 M , a PER Cp
1O'C.
20°C.
15'C.
3;,::
3931 4073
-
~
j
4906 5446
~
143 185
1
1
CENT
(0.01 34,HzO) 15°C.
I
i
1;:
EtOli) 20'C.
52 89
TABLE 9 Values of C and E , f =
a
P E R CENT
EtOH
(0.01 .VI a PER CENT EtOH) (,V = 0, H10) F O R CdSOd
-
no
1
10°C.
1 ___ 15°C. 1
1 -c p (0.01 M ,a PER CENT EtOH) FOR CdSOd
ZO'C.
10°C.
0 0 33 3
.
50 0
~
4:; 4599
~
5% 5528
~
5;;: 6198
~
1
15°C.
3; -2::~
-95
58
~
~
20°C.
-z 17
In order to obtain an estimate of the probable error in these values, 0.02 mv., which was the average deviation of the experimental results, was added to or subtracted from the measurements, and new values calculated. I n the case of the heat content, it was found that the maximum error was obtained if the 0.02 my. was alternately added to and subtracted from the measurements. This amounted to f 1 . 3 per cent ( f 6 2 cal.). In the case of the heat capacity, the maximum error was obtained if the 0.02 mv. was added to the first measurement and subtracted from the third. This amounted to &2.4 per cent ( 1 2 . 6 cal. per degree). The probable error in L may be twice as large as the error in AH of transfer, since it involves the subtraction of one 4%from another. The error in C, may also be twice as large as the error in Ac,, as it is necessary to add the change in the heat
THERMODYNAMIC PROPERTIES OF CADMIUM SULFATE
301
capacity involved in the transfer of a mole of solid cadmium from the solid state to a two-phase amalgam to Ac, from process 11. The heat capacities of the solids, cadmium and mercurous sulfates, and that of liquid mercury are accurate to about 0.1 cal. per degree. Henderson and Stegeman (13) measured the E.M.F. of cell I11 a t Bo, 25O, and 30°C. From their empirical second-degree equation one would expect that Ac, (111) = 10.5 cal. per degree. Although our measurements upon the same cell a t O", 12.5", 25", 37.5", and 50°C. yield a value of AH (111) at 18°C. which checks their value within 0.2 per cent (69 cal.), we find a2E/aT2(see table 7) to be equal to zero. Consequently, Ac, (111) should be zero. This prediction can be checked, using the calorimetric heat capacity data for the respective solids given in International Critical Tables, Vol. V, pp. 85-97. The calorimetric data require Ac,, (111) equal to 0.1 cal. This agreement furnishes further evidence that the changes in heat capacity in chemical processes may be accurately calculated from precise E.M.F. measurements, provided the data extend over a wide range of temperature and an empirical equation of sufficient power for accurate representation is employed. These data show that for 15°C. the molal heat of dilution in water of 0.01 M cadmium sulfate is 621 cal., whereas the heat effect involved in transferring one mole of cadmium sulfate a t 0.01 molal from 33 per cent alcohol to water is 4532 cal., i.e., the thermal effect of interaction in water is about 12 per cent of that of transfer, wkich is essentially a pure solvent effect. Perhaps the most striking result of this investigation is the almost linear increase (i.e., to less negative values) which the partial heat capacity of the salt undergoes on the addition of alcohol. The large negative values for E , which salts exhibit in water is ascribed by Zwicky (27) to compression of the solvent in the neighborhood of the ion and to a loss in degrees of freedom of the solvent as result of electrostriction. In a solvent of lower dipole moment such effects are less and hence a less negative value of E, is observed. SUMMARY
1. E.M.F. measurements are reported for the cell: Cd (two-phase amalgam), CdS04 ( M , a per cent EtOH), Hg2SO4(S), Hg for M = 0.01 in 33.3 and 50 per cent ethyl alcohol at O", lo", 15", 20", 25", and 30°C.; as a function of M in 33.3 per cent alcohol a t 25°C.; and for M = 0.01 in 15 per cent alcohol a t 25°C. The cell: Pb (two-phase amalgam), PbSOa(S), Hg2SOd(S), Hg has been measured a t 12.5"C.-intervals over the range 0" to 50°C. 2. The partial heat contents, and the partial heat capacities of cadmium sulfate have been calculated in the alcoholic solutions for comparison with the corresponding aqueous solutions.
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VICTOR I(. LA MER AND ERWIN L. CARPENTER
3. The total medium effect for 0.01 molal cadmium sulfate in 15, 33.3, and 50 per cent alcohol, and the solvent and interaction medium effects in 33.3 per cent alcohol, have been evaluated. The results have been considered in the light of the Born transfer equation and the extended form of the Debye-Huckel interaction theory. 4. The value of T , the mean ionic radius of the cadmium and sulfate ions as calculated from the Born equation, is in fair agreement with the value of a, the distance of closest approach of two ions, calculated by means of the extended theory of Debye and HiickeI. REFERENCES (1) LKERLOF: J. Am. Chem. SOC.48, 1160 (1926). (2) AKERLOF:J. Am. Chem. SOC.62, 2353 (1930). (3) BORN:Physik. Z. 1, 45 (1920). (4) BRBNSTED, DELBANCO, AXD VOLQUARTZ: z. physik. Chem. 162A, 128 (1932). (5) COWPERTHWAITE AND LAMER:J. Am. Chem. SOC.63, 4333 (1931). (6) DANKER:J. Am. Cheni. SOC.44, 2832 (1922). (7) DEBYE:Physik. Z. 26, 97 (1924). (8) GRONWALL, LAMER,AND SANDVED: Physik. Z. 29, 358 (1928). (9) HANSENAND WILLIAMS:J. Am. Chem. SOC.62, 2759 (1930). (10) HARDMAN AND LAPWORTH: J. Chem. Soc. 99, 2242 (1911); 101, 2249 (1912). (11) HARNED AND FLEYSHER: J. Am. Chem. SOC.47, 82 (1925). (12) HENDERSON AND MELLON:J. Am. Chem. SOC. 42, 676 (1920). (13) HEXDERSON AND STEGEMAX: J. Am. Chem. SOC.40, 84 (1918). (14) HULETT:Phys. Rev. 27,344 (1908); see also TREADWELL: Analytical Chemistry, Vol. 11, p. 174. (15) HULETT:Phys. Rev. 32, 257 (1911); 22, 337 (1906). (16) LAMER. ~ N DPARKS:J. Am. Chem. Soc. 63, 2040 (1931). (17) LAMERAND PARKS:J. Am. Chem. SOC.66, 4343 (1933). (18) LAMERAND PARKS:J. Am. Chem. SOC.66, 4350, table 7 (1933). (19) NOXHEBEL AND HARTLEY: Phil. Mag. 60, 729 (1925). (20) ONSAGER: Chem. Rev. 13, 73 (1933). (21) OWEN:J. Am. Chem. Soc. 64, 1758 (1932). (22) PARKS AND LAMER:J. Am. Chem. SOC.66, 90 (1934). (23) PEARCE AND HART:J. Am. Chem. Sac. 44, 2411 (1922). (24) STOCTAND SCHOETTE:Ind. Eng. Chem., Anal. Ed. 6 , 100 (1933). (25) VOSBURGH A N D EPPLEY:J. Am. Chem. SOC.47, 1255 (1925). (26) WOODMAN: Food Analysis, p. 523. McGraw-Hill Book Go., New York (1931). (27) ZWICKY:Physik. Z. 27, 271 (1926).
