TEMPERATURE EFFECTSON
THE
POTENTIAL OF THE MERCURY ELECTRODE
1891
Temperature Effects on the Potential of Zero Charge of the Mercury Electrode
by Woon-kie Paik, Terrell N. Andersen, and Henry Eyrhg Institute for the Study of Rate Processes, The University of Utah, Salt Lake City, Utah (Received November 21, 1966)
The potential of a streaming mercury electrode was measured in aqueous 0.1 and 1.0 N KI, KBr, KCl, and NaF solutions from 0 to 60'. The resulting potentials of zero charge (pzc), measured with respect to a reference electrode held at 2 5 O , increased approximately linearly with an increase in temperature, T. The increase in pzc with temperature for NaF is considered to be due to deorientation of solvent dipoles on the electrode surface with increasing temperature, while the increasing potentials of zero charge in the other solutions are due to a decrease of specific adsorption as well as to solvent deorientation. Using an adsorption isotherm, double-layer theory, and the results for NaF, calculations are made of the temperature dependence of the pzc for the C1-, Br-, and I- solutions. These results compare favorably with the experimental results.
Introduction The effects of electrolyte concentration on the potential of zero charge (pzc) are widely used to provide information regarding adsorption onto electrodes and hence regarding the double-layer structure. Studies of temperature variation of the pzc, although valuable in providing additional insight into the doublelayer structure, are sparse. Anderson and Parsons obtained electrocapillary curves of Hg in K I solutions at various temperatures and from them calculated heats and entropies of specific adsorption of I- ions onto Hg.' Koenig obtained electrocapillary curves of mercury in 1 M KNOI solutions between 9.3 and 5502 and Parry and Parsons made similar studies on aromatic sulfonate anions. Grahame4 measured the temperature coefficient of the pzc of mercury in NaF solutions from 0 to 85" by the capacity method. He also measured the pzc of a streaming mercury electrode in KC1 solutions at different temperatures.5 Similar measurements have been made on streaming Hg electrodes by Randles and Whiteley6 in 0.1 N solutions of KCl, NaOH, and K2S04in the temperature range 15-35' ; by Butler on Hg and Hg-In amalgam electrodes in 0.1 N HC104;' and by Hills and Payne on Hg in 0.1 N solutions of NaN03, NaF, Na&OI, and NaCl at 20 and 30°.* Minc and Jestrzebskag have measured the capacity minima in KF, KCl, and KBr solutions at very dilute
concentrations. All of these workers, except Grahame kept their reference electrodes at the same temperature as the test solutions. In the above zero charge potential determinations the structural aspects of the double layer were only somewhat delved into. Hills and Payne* considered changes in the concentration of adsorbed water on the electrode with variation in charge. Several of the above authors6s7 noted that the temperature coefficient of the electrode potential at zero charge is larger for solutions containing more adsorbable anions and hence concluded that the pzc increases with temperature due to a decrease in specific adsorption (for solutions where such adsorption exists). In the present work we have investigated the effect of temperature on the pzc from the standpoint of a (1) W. Anderson and R. Parsons, Proc. Intern. Congr. Surface Activity, dnd, London, 45 (1957). (2) F. Koenig, Z.Physik. Chem. (Leipzig), 157, 96 (1931). (3) J. M.Parry and R. Parsons, Trans. Faraday Soc., 59,241 (1963). (4) D. C. Grahame, J . A m . Chem. SOC.,79, 2093 (1957). (5) (a) D. C. Grahame, E. M. Coffin, J. I. Cummings, and M. A. Poth, ibid., 74, 1207 (1952); (b) D.C. Grahame, E. M. Coffin, and J. I. Cummings, Technical Report No. 2 t o the Office of Naval R e search, Aug 11, 1950. (6) J. E. B. Randles and K. S. Whiteley, Trans. Faraday SOC.,61, 326 (1965). (7) J. N. Butler, J. Phys. Chem., 7 0 , 2312 (1966). (8) G. J. Hills and R. Payne, Trans. Faraday SOC.,61, 326 (1965). (9) S. Minc and J. Jastrzebska, Electrochim. Acta, 10, 965 (1965).
Volume 71, Number 6 M a y 1967
W. PAIK,T. ANDERSEN,AND H. EYRING
1892
variation in specific adsorption and a partial reorientation of water dipoles. The former contribution is calculated and the latter is estimated based on results for NaF and on calculations. To provide an experimental test for our calculations, the pzc of a mercury electrode in various aqueous alkali halide solutions was measured in the temperature range 0-60". The reference electrode was kept at a constant temperature in order to make the comparisons of the pzc at various temperatures more consistent for our doublelayer studies and to avoid the somewhat inaccurate corrections for the entropy changes a t the reference electrode. In return, possible thermal junction potentials were introduced and these are discussed later.
I
"
.28
0
Experimental Section
20
40
60
Temperature "C
Figure la. Potential of zero charge, EO (corrected The technique of the streaming mercury e l e c t r ~ d e ~ for ~ ~liquid ~ junction potential), us. the standard was employed in measuring the pzc. The cell, presatuhydrogen electrode as a function of temperature. Fluoride and chloride solutions. rator for N, gas, and a Pyrex coil which carried the mercury to the capillaiy were immersed in a bath in which the temperature was controlled to within =k0.02". .26r I I I I 1.26 The solution was connected by means of a salt bridge of saturated KC1 solution to the reference electrode, .28 which was kept at 25". A saturated calomel electrode .30 served as the reference half-cell in most experiments, although zt few experiments were repeated using an .35 Ag-AgC1 electrode. Solutions were made from reagent grade chemicals and water bidistilled from a basic permanganate solution. The elertrolytes studied were 0.1000 and 1.000 N (at 25") solutions of NaF, KC1, KBr, KI, and 0.0100 N (at 25") NaF. The solution in the cell was flushed with purified (99.99S(r,) nitrogen at least 15 hr prior to each experiment and during the measurements to prevent air . 5 4 p 4 * , oxidation of mercury and the anions. Then mercury .56 .56 was allowed to stream through the solution for a few 0 20 40 60 minutes, before the potentiometer readings were reTemperature, "C corded, to ensure a stable p ~ t e n t i a l . ~ The potential readings were made to 0.001 mv using Figure lb. Potential of zero charge, Eo, as a function a Leeds and Sorthrup K-3 potentiometer. The standof temperature for bromide and iodide solutions. EOmeasured us. standard hydrogen electrode with ard deviations of the readings were about 0.01 mv correction made for liquid junction potential. for 0.1 and 0.Cl N solutions and a few hundredths of a millivolt, for 1 N solutions. Although the actual potential values may not be this accurate (e.g., owing Results and Discussion to limits of chemical purity), this precision justifies The experimental results are shown in Figures l a the comp:trison of small differences in temperature and 1b. The recorded potentials of zero charge, EO, coefficient of the pzc. Any set of readings that were in Figure 1 consist of the raw data with an estimated not constant with time were discarded because such a shift of potential would be an indication of contamination of the solution either by impurities in the rea(10) D. C. Grahame, R. P. Larsen, and M. A. Poth, J . Am. Chem. gents or by oxidation of the mercury or anions. SOC.,71, 2978 (1949).
,$.
The Journal of Physical Chemistry
TEMPERATURE EFFECTSON
THE
POTENTIAL OF THE MERCURY ELECTRODE
1893
Table I: Temperature Coefficient of Potential of Zero Charge, d&/dT, at 25” in Millivolt per Degree at Concentrations of 0.01, 0.1, and 1 N NaF, N Ref
0.01
0.1
1
This work Grahame Randles and Whiteley (calcd) Hills and Payne
0.593
0.528 0.47“
0.507
-
0.60b
-KCI,
N-
-KBr,
0.1
1
0.673 0.586 0.67
0.697
0.1 0.870
N-
-KI, 1
0.742
0.1
0.925
N1
0.675
0. 64b
a Independent of concentration within the limits of experimental error. Calculated from the temperature coefficient data with reference electrode at the same temperature using the thermal temperature coefficient of potential of reference electrode.
correction added for the liquid junction potential between saturated KC1 and the test solution at the cell temperature. The change of the pzc, Eo,with temperature is believed to be due to the change of inner potential difference, 40, across the double layer, because we maintained the reference electrode at constant temperature and the thermal junction potentials are believed to be negligible. There are two thermal junctions, one across the copper lead and one across the salt bridge. These can be neglected without any apparent serious error because the entropies of transfer of electrons and ions across these junctions are believed to be small. This point is supported by deBethune, Licht, and Swendeman.12 Grahame also neglected the thermal junction potentials in his w ~ r k .Randles ~ ~ ~ and Whiteley6 and Butler’ measured the pzc against reference electrodes at the same temperature as the test solutions as mentioned above. They then added the entropy changes accompanying the electrode reactions, ASIF, to their measured dEo/dT to get their temperature coefficient of the inner potential difference across the double layer. This procedure, however, is equivalent to keeping the reference electrode at constant temperature as was done in the present work. This is so because the entropy change at the reference electrode is nothing but the temperature coefficient of the potential of the reference electrode. Since there are uncertainties in the entropy values of ionic species in solution, those procedures may result in uncertain values of the temperature coefficient of the inner potential difference across the double layer. In Table I the temperature coefficients of our pzc, dt&/dT (= dEo/dT) at 25”, are listed together with other data obtained by previous workers. A positive value of the coefficient means that the mercury electrode with zero charge becomes more positive as the temperature is increased. Because specific adsorption of anions makes the potential of zero charge more negative it is usually
assumed that more specific adsorption of anions is accompanied by a larger temperature coefficient of the pzc. This is the case for 0.1 N solutions of the halide ions as seen by comparing Table I with the tendency for increasing specific adsorption, ie., F- < C1- < Br- < I-.I38l4 This is, however, found to be not always true as seen from the data of 1 N solutions. The d&/dT values for 1 N solutions of KBr and K I are smaller than their 0.1 N solutions, while there is more specific adsorption of anions from the more concentrated solutions. The value of 1 N K I is even smaller than that of 1 N KBr. The fluoride solutions of different concentrations were expected to have essentially the same temperature coefficients because F- ions are only slightly specifically adsorbed. The data from 1 and 0.1 N solutions show the expected agreement, but d40/dT for 0.01 N NaF is higher than the other two. The reason for this is unknown, but it may be due to uncertainties in the correction for the liquid junction potential.
(11) This correction was calculated using the Henderson equation. Ionic mobilities at the various temperatures could not be found for all the solutions in question. Therefore, mobilities at 25O were used for the KC1, KBr, and KL calculations. For NaF limiting ionic conductances at 25O were used. The above approximationsremoved any temperature dependence from the mobility terms in the Henderson equation. This approximation seems justified since the ionic mobilities increase proportionately with temperature for all the ions studied (cf. S. Glasstone, “Textook of Physical Chemistry,” 2nd ed, D. Van Nostrand Co., Inc., New York, N. Y., p 895). The error from this approximation would be largest in the case of the most dilute solution, &e., 0.01 N NaF. Calculated liquid junction potentials did not exceed 3.2 mv and were proportional to the absolute temperature, according to our calculation. (12) (a) A. J. deBethune, T. 9. Licht, and N. Swendeman, J . Electsochem. Soc., 106, 616 (1959); (b) A. J. deBethune and A. Swendeman, “Standard Aqueous Electrode Potentials and Temperature Coefficients at 25OC,” Clifford A. Hampel, Publishers, Skokie, Ill., 1964. (13) D. C. Grahame and B. A. Soderberg, J . Chem. Phvs., 2 2 , 449 (1954). (14) D. C. Grahame, J . A m . Chem. Soc., 80, 4202 (1958).
Volume 71, Number 6 Matt 1967
W. PAIK,T. ANDERSEN, AND H. EYRING
1894
Table 11: Numerical Values Used in the Calculations ha
Pi,
r, A
&coulombs/ oms
rcoulombs/ oms
0. I 1 0.1 1
1.81
2.3 8.3 5.87 14.4
122
0.1 1
2.16
N
CI -
Br-
I-
1.95
0.605 0.0769 0.0771 0.617
105
11.14 20.13
Reference for P i
00
86 0.646 0.0776
Averages taken from data of ref 18 and 19 13 Computed from r + and r in ref 17
}
1
l4
’9. is calculated as the amount of specific adsorption that will make a square array of ions in contact.
Table I11 : Calculated Values of
WO, dqi/dT and d\LO/dT a t 25” PKCI,
N-
Wo,kcal mole -l dqi/dT, pcoulombs/ cm2deg d$O/dT, mv deg-’
P 1
0.1
B
-2. I1 0.00946 0,058
-0.008
=
is related to the amount of specific adsorption, qi, according to the relation (cf. ref 16)
Qi+u
where y is the distance between the inner and outer Helmholtz planes and e is the dielectric constant of the compact double layer. Assuming that temperature affects qi much more than it does y/e we have dT
(3)
The effect of the temperature on specific adsorption, dqi/dT, is calculated in this section from the temperaThe Journal of Physical Chemistry
---KI,
, N---
N----
1
0.1
0.0299
0. 0304
1
-6.11
-0.0285
-0.059
0.0321 -0.080
ature dependence of the adsorption isotherm. The isotherm we have used is a modified Langmuir isotherm analogous to Frumkin’s and is given by
(%) q(g) +
e
0.0244 0.039
The portion of the metal-solution potential difference due to specifically adsorbed ions can be separated into a potential difference across the inner layer (metal to outer Helmholtz plane) qi+u and that across the diffusc layer, +O. (The notation with respect to potentials used here follows that of Grahame. 15) Therefore, the temperature coefficient of the pzc due to ionic specific adsorption, ,,(d&,/dT), is given by
Pi
r
-3.90 0.020
Temperature Effects on Specific Adsorption of Ions
Qi
K 0.1
(4)
where qi is the charge of the specifically adsorbed ions per unit area, qs is the value of qi at saturation, r is the radius of the adsorbed ions, e is the electronic charge, is the activity of the ions in the bulk of the solution, and W is the electrochemical free energy of adsorption. Besides being of a fairly simple form for calculation purposes, this isotherm finds support in the work of Parry and parson^.^ Here 2r is introduced as the volume of the layer of adsorbed ions per unit area of the electrode surface.” W can be split into electrostatic and nonelectrostatic terms
W
=
wo + zW+O
+
+A)
(5)
Here +A is the potential difference from the outer to the inner Helmholtz plane. +O, the Galvani potential of the outer Helmholtz plane with respect to the bulk (15) D. C. Grahame, 2. EEektrochem., 6 2 , 264 (1958). (16) P. Delahay, “Double Layer and Electrode Kinetics,” Interscience Publishers, Inc., New York, N. Y., 1965, Chapter 4.
(17) D. C. Grahame, Chem. Rev., 41, 441 (1947).
TEMPERATURE EFFECTS ON THE POTENTIAL OF THE MERCURY ELECTRODE
solution, is obtained from diffuse layer theory as
at the pzc. A = (~~lCTC~/27r)~'' where Cd is the dielectric constant of the diffuse double layer and Co is the bulk concentration of ions. Differentiating eq 6 with respect to T and assuming Cd to change very little with temperature, we have
From eq 4, 5, and 7 we get
(${& + + (32]-"* + g'T) [l
qs qs -
F*A qi
RT
+ 2[ 1 +
1895
Table I11 shows the d#"/dT, dqi/dT, and Wo values calculated as outlined above. The total temperature coefficients of the zero charge potential at 25", qi(d+o/ dT), as calculated from eq 1 are shown in Figure 2 aa dashed lines. This plot qualitatively shows (d+o/d T) aa a function of adsorbability. The calculated qi(d+o/ dT) values show certain aspects which are in agreement with experiment, i.e., the tendency for d&/dT for 1 N I- to be less than that for 1 N Br- or 0.1 N I-. However, there are still significant differences between the experimental (d+o/dT) and the calculated ,,(d&/ dT) values. These differences are believed to come from the temperature variation of the orientation of the adsorbed solvent dipoles.
Temperature Effects on Orientation of Dipoles The d&/dT values for 0.1 and 1 N F- solutions are considered to be due to the thermal deorientation of dipoles which cover the electrode surface with their negative end pointing preferentially toward the electrode.21 The contribution to d+o/dT from this deorien-
(32]-"a
For the calculation of dqi/dT and hence ,,(d#"/dT), values for W and #A are required. W was obtained by substituting the known values for qi, r, and a0 into eq 4; qB was calculated assuming complete coverage of the surface by $he ions in a square-packed array. Table IIBtl9lists the values for qi, qB, r, and ao. The calculated W values for 0.1 and 1.0 N values of a given salt were substituted into eq 5 to give two simultaneous equations with Wo,$* (1 N ) and #A (0.1 N ) as unknowns. It was then assumed that #A for a given type of electrolyte is proportional to qi, so that #* (0.1 N ) = #* (1 N)(qi (0.1 N)/qi (1 N ) ) . Thus, Wo (independent of the bulk salt concentration for a given ion) and the #A values were determined. With W and #A known, dqi/dT was readily calculated as was d#",/dT (cf. Table 111). For the calculation of ,,(d\(."/dT) from dqi/dT, given by eq 3, the value of ?/e is needed. These two constants are not yet accurately known. However, from the integral capacity data of the double layer, d / s cm where d is estimated to be approximately 4 X is the thickness of the inner layer.16*17 In our calculations we assumed d = 4 A, c = 10, and y = d - r, where r is the radius of the anions. These values appear to be in agreement with the comparable values assumed by other workers in the field.20 Errors in the dielectric constant should affect calculations for all ions to roughly the same extent since it is found that the inner layer dielectric constant depends on the field due to electrode charge, but not on that due to specifically adsorbed ions. 14,16
t
"E
i. .61
+
I
P
4.
0
'
I ) ! u l L u i
e
.4-
I
- B
-1
--o-
}rxp.rlmo"tol
miculond *imwt m r mMbuMm cdculo(rd wlth Yatu cQIkibvtion
CI-
.2
~
I
I
I
(18) D. C. Grahame and R. Parsons, J . Am. Chem. Soc.. 83, 1291 (1961). (19) H. Wroblowa, Z. Kovac, and J. O'M. Bockris, Trans. Faraday SOC.,61, 1523 (1965). (20) J. R. Macdonald and C. A. Barlow, Jr., Proc. Auetrdian Conf. Electrochem., l s t , Sydney, Australia, 1965, 199 (1965).
Volume 71, Number 6
Maw 1967
W. PAIR,T. ANDERSEN,AND H. EYRING
1896
where (10) (a)
(b)
(C)
Figure 3. (a) Schematic diagram of adsorbed solvent dipoles and anions showing deorientation of dipoles adjacent to ion and orientation of dipoles nonadjacent to ion. (b) Projected area of adsorbed ion with its complement of nearest water neighbors when ions are separated by two or more water molecules (left) and when ions are separated by one water molecule (right). (c) Schematic diagram of surface layer of ions and water a t which water dipole contribution to electrode potential is minimal.
tation, dx,'dT, must be added to the above calculations, q,(d&,/dT), to give the total d&/dT; dx/dT for C1-, Br-, and I- will not be exactly the experimental value of d40/dT found for fluoride, since there is a different electrode coverage by oriented dipoles for different anions. The coverage of the electrode by the oriented water dipoles will decirease with increasing qi, since the adsorbed anions replace some water molecules and deorient some neighboring dipoles. The extent to which neighboring water molecules are deoriented depends on factors such as orientation forces between ions and dipoles, those between dipoles and the electrode, and mutual repulsion between oriented dipoles about the anion. S o exact answer exists to the question of the dipole structure about an ion. However, such deorientation exists as pointed out by various w o r k e r ~ ~and ~ b ~by ~ considerations of the strength of ion-dipole interactions us. dipole-image or vs. hydrogen bond interactions. In this work we take the upper limit of such orientation of water dipoles with their negative ends pointing away from the anions and assume that a complete layer of water molecules about each anion deorients (cf. Figure 3a). The adsorbed anions at low coverage will accordingly decrease the oriented dipole coverage by the amount (ql/e)n(r 2 ~ ~ , 0where ) ~ , e is the charge of the ion and THIO is the radius of a water molecule, because T(T B T ~ C , is ~ )the ~ projected area of the anion with its deoriented neighboring water molecules around it. This linearity of decreasing of the oriented water coverage, ew, with increasing qi will not continue as the surface becomes crowded with anions because each ion does not then have an independent complement of nearest-neighbor solvent molecules (cf. Figure 3b). Therefore, in reality the 0, vs. qi relation may be a curved line as shown in Figure 4. The equation of the curve may be given by
+
+
The Journal of Physical Chemistry
The third term of eq 9 is quadratic in qi because the probability of two ions getting together with the interaction energy E, as in Figure 3b, is b'qi2 exp( -E/ RT). The constant b is chosen such as to give a minimum point of the curve (Figure 4) a t qi = qio, where qio is the amount of specific adsorption, such that there remain no water dipoles free of the direct influence of anions.24 At such a coverage the average area that is covered by an anion is taken to be the combined area of the ion and its shell of nearest water neighbors. This is assumed to approximate the area of the hexagon shown in Figure 3c. Thus, values determined for qio in this way are 30.3, 28.4, and 26.1 pcoulomb cm-2 for C1-, Br-, and I-, respectively. Then the potential due to the dipoles is
x
=
x0[1 - a
+ bo2]
(11)
xo is the dipolar potential of a full layer of water molecules and the part of the temperature coefficient that is due to the water dipoles is then
dx dT
= -[I dXO
-
a
+
dT
- xO--(l da
- 2ba) (12)
dT
where da/dT = a / e ( r
Figure 4. Fractional coverage of electrode with oriented water dipoles, e,,., us. amount of specific adsorption of anions.
(21) The field within the metal may contribute to the metal-solution potential, but should not contribute to the temperature variation of this potential difference (cf. R. J. Watts-Tobin, Phd. Mag., 6 , 133 (1961)). (22) E. Shvarts. B. B. Damaskin, and A. N. Frumkin. Russ. J . Phys. Chem., 36, 1311 (1962). (23) T. N. Andersen and J. O'M. Bockris, Electrochim. Acta, 9 , 347 (1964). (24) At coverages of ions greater than qio the water dipole contribution t o the potential can only remain unchanged or increase; the latter possibility is due t o the fact that one water molecule sandwiched between two ions is not preferentially oriented toward either and may become aligned perpendicular t o the surface.
TEMPERATURE EFFECTS ON
THE
POTENTIAL OF THE MERCURY ELECTRODE
must be equal to the d&/dT values for F - solutions since this ion does not adsorb on the electrode. The difference of d&/dT between 0.01 N F- solution and the other two (1 and 0.1 N) solutions is hard to explain at this stage as mentioned previously. The average value of 0.1 and 1.0 N NaF solutions (0.52 mv/deg) is used in our calculations for dxo/dT since the value is nearly the same for both concentrations and since the concentrations of other solutions studied in this work are 1 and 0.1N. If all water dipoles are assumed to face either toward or away from the electrode and if the energy of turning an oriented dipole to the opposite direction is w , thenz6 xo=
4rNp -e
(13)
Here N is the number of dipoles covering unit area of electrode surface, p is the dipole moment, and e is the dielectric constant. w is determined from the experimental value of dxO/dT, wherez6
Taking N = 10l6,p = 1.84 D.,and e = 10 gives w = 0.28 kcal/mole and xo = -0.163 v; a variation of e affects w but does not significantly change xo as e = 6 gives w = 0.16 kcal/mole and xo = -0.155 v while e = 1 gives w = 0.027 kcal/mole and xo = -0.160 v. Hence the positive measured temperature coefficient of the pzc of F- solutions is believed to be direct evidence that the solvent dipoles are preferentially pointed with the negative end toward the electrode. Our final result of calculations including the above dipole considerations are given by
and are shown in Figure 2 by the thin lines.
1897
Although there is a certain amount of arbitrariness in choosing some of the parameters used, it is seen that from adsorbed ion and water considerations (and using the results from F-) (1) temperature coefficients of the potential of zero charge are calculated for C1-, Br-, and I- solutions which are of the same approximate magnitude as the experimental values; (2) the decrease in d#o/dT in going from certain solutions to other ones in which more specific adsorption occurs can be explained from a consideration of dqi/dT, using an adsorption isotherm. Reasonable variations in the parameters chosen would not appear t o negate conclusions 1 and 2 above. As has been discussed, corrections to the inner layer dielectric constant would be expected to be similar for all the ions studied. It is doubtful that the average value of e would differ from the chosen value of 10 by more than 40%, which would alter ni(d&/dT) values by less than 0.3mv/deg. It was shown that the value of e used in the water dipolar contribution, xo, did not affect dx/dT. The distance from-the metal to the outer Helmholtz plane d and hence y might increase with specific adsorption16 and hence with salt concentration. This would increase qi(d+o/dT) values for 1 N solutions with respect to those for 0.1 N solutions and could also increase d&/dT for larger ions with respect to that for smaller ions.
Acknowledgment. The authors gratefully acknowledge the financial support of this work by the Atomic Energy Commission under Contract No. AT( 11-1)1144.
(25) N. F. Mott and R. J. Watts-Tobin, Electrochim. Acta, 4, 79 (1961). (26) We assume that the concentration of adsorbed water molecules does not change with temperature except through variation in ion concentration.
Volume 71 Number 6 May 1067 ~
