322
CARL L
CARLSON, EARL W. MALMBERG, A N D D. J. BROWN
T H E RELATIVE PHASE POTENTIAL WITHIN A HALF-CELL CARL L . CARLSON, EARL W. MALMBERG, A N D D. J. BROWK
Avery Laboratory, University of Nebraska, Lincoln 8 , Nebraska Received March 16, 1949
Cells in different solvents may have different observed values for the electromotive force when the chemical potentials of the components are the same (1, 2). This may be interpreted as due to the effect of the interface within each half-cell. The work here reported was undertaken t o determine experimentally the relation of this potential in a second solvent to that in water when the reactants in the cell are at the same chemical potential. In any solvent when Pb(s)
+ Hg&l,(s)
=
2Hg(l)
+ PbClo(s)
represents the cell reaction, the change of free energy of the reaction is the same independent of the solvent. Since the chemical potentials of the solutes are the same in both solvents, the liquid-junction potential due to the solutes is zero. As in the calculation of “liquid-junction potentials,” the value due to diffusion of solvents is considered negligible. In a preliminary study it was found that neither lead chloride, mercurous chloride, nor potassium chloride was solvated by methyl alcohol, which was selected as the second solvent. The reagents met the A.C.S. specifications. Since the cells in water as a solvent gave sufficiently consistent results, these reagents were considered satisfactory. Since very small amounts of water may have relatively large effects on the potential of the half-cell in nonaqueous solvents (2), the methyl alcohol was treated with quicklime and distilled. The water was redistilled after treatment with alkaline permanganate. Each solvent was saturated with lead and potassium chlorides a t a slightly higher temperature and allowed to cool slowly to 25°C. After each half-cell was prepared a crystal of potassium chloride was added. In the preparation of a mercury-mercurous chloride half-cell a paste of the two was prepared, using the appropriate solution as prepared above, and placed on the mercury. In the case of the lead-lead chloride half-cell lead foil was immersed for a t least 2 days in 6 N hydrochloric acid at 25°C. The lead mas not at the “standard state,” which is an unstrained crystalline form, but the results in the water solution show that the data were reproducible within the requisite limits. The treated lead was dried a t llO”C., kept in a desiccator, and immersed in the appropriate solvent for the half-cell. h Leeds & Korthrup Type K potentiometer and Type R galvanometer were used. The reference cell was calibrated against a Bureau of Standards cell. The cells and solutions were kept in an air bath a t 25°C. The following set-up, in which E represents each half-cell and ?r the junction
323
RELATIVE PHASE POTEPI‘TIAL lh* .4 HALF-CELL
of the two solutions, was used: E1 E* Pb(s) PbClz(s),KCl(s) in H20, Hg2C12(s)1 Hg(1) ~
?r
Pb(s) 1 PbClz(s),KCl(s) in CH30H, HgzC12(s)1 Hg(1) E3 E4
h stopcock uith a 0.6 em. bore was used to make a junction of the solutions. It \vas filled with the solution which had the higher specific conductance. The solution of higher conductance was placed below. T o prevent flow within the stopcock the higher level of the second solution was “compensated” by a safety tube to the first solution filled to the appropriate level. TABLE 1 A series of potential differences for four half-cells a s indicated
mi-.
0 10 20 40 120 240 Average.
+O 5075
$0 ,5304 0.5304 0.5339 0.5365 0.5360 0.5361
1
$0.5356
0 5017 0 5036 0 5023 0 5052 0 5040
I
$0.5038
~
1
$0 0 0 0 0 0
4977 4991 5020 5027 5052 5059
+0.5040
$0 0 0 0 0 0
i
5319 5326 5339 5359 5323 5343
+0.53a
-0.0024 o.ooi0 0.0019 $0.0006 -0.0013 0,0034
1
-0.0015
-0.031i 0,0309 0.0313 0.0318 0.0300 0,0277
1
-0.0302
As recorded in the tables AE12 represents the observed electromotive force of the cell in Ivater in direct relation to the chemical equation above. AE34likewise represents observed values with methyl alcohol as the solvent. AE1,r and in each case represent the same cell, but each half-cell is in a different solvent. A E l r Sand AE2,a in each case represents the same half-cell, but each is in a different solvent. Table 1 gives an example of a series of observations using a “nest” indicated above, x i t h the calculated averages omitting the initial and the 10-min. observations. These avepages are the first series in table 2. Table 2 gives such averages for seven consecutive series and their average, asterisks being used to indicate values not included in the final averages. Let EF represent the potential of the half-cell in accord with its true free energy, and e the effect on the electromotive force due to the phase boundary b e b e e n the metal and the solution. Then when E is the observed potential, E = EF e. As previously stated, e n , the potential due to the diffusion of the solvents, may be considered zero (see table 3). The first column represents the determinations as represented in tables 1 and
+
324
CARL L. CARLSOR’, E.\RL
W , MALXIBERG, .1ND D. J. BROWN
2. The second is the relation of the potential to the possibilities. Using these, the values could not be calculated. The third column represents the equation used to calculate the relation of the effect of the phase boundary to that in water, e’. The last column gives the numerical averages from table 2. The fifth series above is anomalous. On study of the variant half-cell, E,, no reason could be found. If small amounts of water affect a nonaqueous half-cell (3), infinitesimal amounts of other substances may have a similar effect. Yo observed value including this series varied as much as 10 mv. from any final average in table 2. TABLE 2 Representative averaqes as zn table I AEm
AEt,
+O ,5356
$0,5038 0,5039 0.5041 0,5056 0.4960* 0.5039
0.5356 0.5339 0.5334 0.5344 0,5353 0,5336
+o
,5345
0,5050
+O ,5044
~
AEir,
+o
,5040
0.5040 0.5030 0.5085 0.4975* 0.5048 0.5006
+0.5042
! ~
AEW
AEir3
$0.5341 0.5334 0.5328 0.5330 0.5336 0.5330 0.5364
-0.0015 0.0020 0.0021 0,0000 0,0010 0.0017 0.0031
+0.5337
1
-0.0016
AEw
-0.0302 0 0291 0 0297 0.0275 0.0371 * 0.0291 0.0312
~
1
-0.0295
Using the value of the ‘.saturated calomel” half-cell in nater as the unit of comparison and the relative potential for the interface in methyl alcohol, the calculated value in methyl alcohol is: Hg,Cl?(s)
+ 2e = 2Hg(l) + 2Cl-(I
