SOLVENT CONTRIBUTION TO THE EMFOF ION-EXCHANGE MEMBRANE CELLS
259
Solvent Contribution to the Electromotive Force of Ion-Exchange Membrane Cells Containing Water and Heavy Water Solutions1
by Jerome Greyson Atomics International Division of .Vorth American Aviation, Inc., Canoga Park, California (Receired M a y 9,1366)
An investigation of solvent influence on ion-exchange membrane cell emf values has been carried out. In an earlier work it was assumed that solvent-transport contributions to the emf of such cells containing heavy and normal water ionic solutions could be neglected and the emf values were related to the entropy of transfer of salts between the isotopic solvents. A simple theory is presented which allows an experimental evaluation of the magnitude of the solvent contribution. It is found to be nonnegligible. Values are given for the solvent effect in anion membranes separating chloride ions and cation membranes separating sodium and potassium ions. Although the emf contribution to the total cell potential is not negligible, it has negligible effect on the calculated entropy of transfer. This results because the transfer process is dominated by the enthalpy of transfer rather than the free energy.
Introduction Because of current interest in sea water desalination, renewed interest in the influence of dissolved species on the structure of water has been stimulated. Several papers have appeared recently in which the differences in properties between heavy and normal water solutions have been attributed to the influences of dissolved species on s t r ~ c t u r e . ~ This - ~ writer2 reported the results of a series of measurements of the electrical potential of ion-exchange membrane electrochemical cells of the type AglAg(:ll;\lCl(aa) I +l;\ICl(ap)IAgCllAg H20 D20
I+/
where the symbol is a cation-exchange membrane, 11 is a cation, and the subscripted a's are the salt activities in the respective cell compartments. With the assumption that the contribution to the cell potential resulting from solvent transport could be neglected, the author related the emf values to the partial molal free energy and entropy of transfer of the salts between the solvents. The resulting values of free energy and entropy indicated a spontaneous transfer of salt from D20 to H20 and an associated decrease in entropy in the transfer process. The entropy values mere in-
terpreted as evidence for support of Frank's model for the structure of water and the effect thereon by the dissolved ionic salts.* That is, since heavy water was considered to be more structured than normal water, it suffered a somewhat greater disrupting effect by structure-breaking ions. The ions then, in transferring from heavy to normal water, experienced a decrease in entropy. Since the publication of that report, the several papers which have reported comparisons of the properties of heavy water solutions with those of normal water solutions have confirmed that interpret a t i ~ n . ~ *Of~ Jparticular interest was the report by Iierwin in collaboration with Frank in which entropies obtained from solubility measurements of S a C l and KC1 in DzO were compared with those obtained from the emf measurement^.^ Although the solubility (1) Supported by the U. S. Department of the Interior, Office of Saline R a t e r , Research Division. (2) J. Greyson, J . Phys. Chem., 66, 2218 (1962). ( 3 ) R. E. Kerwin, Ph.D. Thesis, University of Pittsburgh, 1964. (4) A. Ben-Naim, J . Chem. Phys., 42, 1512 (1965). (5) R. L. Kay and D. F. Evans, J . Phys. Chem., 69, 4216 (1965). (6) G. C. Kresheck, H. Schneider, and H. A . Scharaga, ibid., 69, 3132 (1965). (7) T.C. Wu and H. L. Friedman, ibid.,70, 166 (1966). (8) H. S. Frank and E. W. Evans, J. Chem. Phys., 13, 507 (1945).
Volume '71,Number B
January 1967
J. GREYSON
260
data yielded somewhat higher values for the transfer entropy than did the emf measurements, they were in agreement with regard to the order of the values, i.e., AS KC^ > A S N ~ C Iindicating , that KC1 was the more structure-breaking salt. It would seem then that measurement of the emf values of ion-exchange membrane cells containing heavy and normal water solutions can provide a technique for investigating ionic influences on water structure. I n view of the somewhat higher entropies obtained from solubility data, however, Frankg suggested that the neglect of solvent transport in these cells might be a questionable assumption. Furthermore, Kerwin3 pointed out that the conclusions derived from the cell measurements depended upon thermodynamically nonrigorous interpretations of ionexchange membrane junction potentials. The purpose of this paper therefore is twofold. The first is to report the results of a series of measurements which place the interpretation of the cell emf values on firmer thermodynamic ground. The second is to report on an investigation of the validity of the assumption that solvent transport resulted in a negligible contribution to the cell emf. As will be shown, although transport j S not the emf contribution due to negligible, it is of such magnitude that the conclusions of the original paper remain valid.
by current flow. Since the emf of cell I1 is equal to the series connection of IIa, IIb, and IIc, it is also equal to tlie difference in emf between cells I11 and I, i e . , EII = EIII - EI. Using the same arguments one can show that EV= EI - EIIIand EIV= 0. Of course, if one neglects solvent effects then analysis of the cells in Table I, i.e., passage of an equivalent of electricity and examination of the associated free energy changes, will reveal that cell I11 should exhibit zero emf values. Thus cell I1 should yield an emf equal and opposite to that of cells V and I. With nonnegligible solvent effects, however, the relations between the various cells are not trivial. They are also independent of any processes underway within the membrane junctions themselves. Measurements of the emf values of the various cell configurations therefore provided a method of testing the thermodynamic reliability of the cell data. Table I : Ion-Exchange Membrane Cell Configurations"
AglAgCl(MCl(a0)l+I~ICl(aa)l-(~ICl(aa)l +lMCl(ao)lAgClIAg HzO HzO D20 Hz0
I1 AgjAgCl/RICl(aa)1 -1hICl(ap)jAgClIAg Hz0 DzO
Theory
TTT
111
It be convenient to consider the tions shown in Table I. It should be noted that the cells are not independent. That is, one can separate any aqueous phase in any cell into two parts and reconnect them with the electrode system AgCll Agl AgIAgC1 with no resultant change in the cell process and no net change in the emf. Therefore one could as a series of rewrite cell 11, for the three cells AglAgCllAlCl(a0)1 +llICl(aa)IAgCljAg HzO HzO IIa Ag AgC1l;\ICl(aa)l-llICl(up) IAgClIAg HzO DzO IIb AglAgCl/AICl(a,) I +lMCl(ao)IAgClIAg D20 HzO IIC Cell I I b is exactly cell I11 in Table I while in the series connection of I I a and IIc the inverse process of that which would occur in cell I of Table I will be generated The Journal of Physical Chemistry
AglAgClj~Cl(ao)l+lMCl(au)l +~?rlCl(ap)l +lRlCl(ao)lAgCllAg Hz0 HzO 1120 Hz0
1%AglAgC1lMCl(ao)l-IhICl(aa)l +I~\.ICl(ap)l-l~ICl(ao)lAgC1[Ag Hz0 HzO DzO H20 5.' a
The symbol
1-1
refers to an anion-exchange membrane and
a,, is the activity of the salt in the electrode compartments of
the three-membrane cells. The other symbols are defined in text.
Further, in the analysis which folloms and in which solvent transport is considered, it will be shown that each of these cell configurations displays an emf value which is a linear combination of terms, each of which is characteristic only of salt or solvent transfer. The values of the solvent transfer terms will in addition be shown to be experimentally accessible. The analysis is based on an analysis of ion-exchange membrane cells which was presented originally by Scatchard.lo Starting with Scatchard's equation for the (9) H. S. Frank, personal communication. (10) G. Scatchard, J . A m . Chem. Soc., 7 5 , 2883 (1953).
SOLVENT CONTRIBUTIOK TO THE EMFOF ION-EXCHANGE MEMBRANE CELLS
emf of a voltaic cell and specifying symmetric Ag/AgCl electrodes and uni-univalent salts one gets
Ef RT
-
E"f RT
+ In a c ~ --~In
The symbols R and T have their usual significance, f is the faraday, E" is the standard potential resulting from all processes underway in the cell, and ai is the activity of the species i. The transference numbers t , are mass transport numbers and include the transport of neutral species." They represent the number of moles of species i which pass through the cell in the direction of positive current when a faraday of electricity passes from left to right in the cell. The mass transport number of a negative species is therefore negative. The integral over tid In ai extends over the composition range from (Y to 0. The electrical transport number r,, the fraction of current carried by the species i, is xiti where x i is the charge on the species. The electrical transport number is therefore positive for charged species and zero for neutral species. For the cell configurations shown in Table I the integral in eq 1 can be written
tcl-d In a c l -
4- twd In aw
+ tDd In
UD)
(2)
where tD and t ~ vare the solvent-transference numbers for heavy and normal water, respectively, and the primes indicate the compositions of the extreme cell compartments. The sum of the electrical transport numbers can be written as
r M + + rCl-
= Z>f+tM+
+
Zcl-bl-
=
tM+
-1
where a M C l is the mean activity of the salt. If eq 5 , with the second term integrated, is substituted into eq 1, the result is
Pwmwd In aw
+ PDmD -d
I
In
UD]
(6)
I
For the single-membrane configurations of cells I and I11 eq 6 can be solved in the following way: since ai = yimi where yi is the activity coefficient of the species i, the last two terms in eq 6 may be written
Sa
PDd(YDmD)
and
TDI
(7)
One would expect that solvent activity coefficients and mobilities will not depend significantly upon isotopic composition. Therefore one writes @=O
pwd(ywmw) =
pwmw
I
- --tw
(8)
and
Substituting 8 and 9 into eq 6 and integrating the remaining term over the appropriate composition range one obtains
where the activities in the respective cell compartments are indicated by the superscripts. Equation 10, it should be noted, is independent of the nature of the superscript membrane but applied to cell I (as the indicates) it shows that the emf contains a contribution resulting from the difference between the transport numbers of the two solvents. For cell 111, containing an ideal anion membrane, t M + = 0. Further, no net solute-transfer process which leads to an emf contribution can occur. Thus, applying eq 10 to cell I11 results in
+
1
Thus tcl- =
261
(3)
Also, by definition one can write (4)
where pi and mi are the mobility and concentration, respectively, of the species i. Substituting eq 3 into the second term on the right-hand side of eq 2 and eq 4 into the last two terms one gets
where the superscript - indicates an anion membrane. Equation 11 predicts that cell I11 will exhibit an emf which is dependent upon solvent transport and which is independent of the concentration of salts bounding the membrane. (11) A. J. Staverman, Trans. Faraday Soc., 48, 176 (1952).
Volume 71, Number 2 Januury 1967
J. GREYSON
262
Finally, as was shown above, EII = EIII - E I and Ev = EI - EIII. That is, one can write for the triplemembrane cells containing ideal membranes
Ef RT
-[%- 21n--,
anfcl
P
-
aMCl
(tD
- tW)+
+
(tD
-
tW)-]
(12)
for cell I1 and
Ef RT
- E”f RT
aMCl
B
21n-
In y = Am”’/(l
-
aMCla
(LD - tw)+
+ ( t +~ tw)-
(13)
for cell V. One can see from these equations that, as stated earlier, the various contributions to the cell emf are additive. For = a the emf is simply the standard emf plus a term characteristic of solvent transport. Having the value of E” for the process (from solubility and activity coefficient measurements for example) one can obtain the solvent transport terms via measurements of cells I, 11, or V. Alternatively, one can obtain the solvent transport term in anion membrane cells directly via eq 11. Also one could, as a rederivation of eq 10 will verify, obtain the solvent transport contribution to the emf of cation membrane cells by using a cell I configuration and cation reversible electrodes. We have made measurements of the emf values of the five different cell configurations containing solutions of LiC1, KaC1, KCl, and (CH3)kNCl. The results of the measurements have been interpreted in the following sections according to the preceding arguments. Experimental Section
Procedure. The experimental procedure was substantially the same as that described in the original paper.2 Membranes were clamped between No. 15 “0”ring joints which in turn were sealed to vertical tubes which served as the cell compartments. Membranes were supplied by the Ionac Chemical Co. and were designated by them as MA-3475 XL anion membranes and MC-3470 XL cation membranes. A Rubicon slide wire potentiometer, wired in series with the cell and with a Leeds and Northrup high-impedance null detector, was used to measure the emf. Measurements were carried out in an air thermostat controlled at 22 f 0.50’. Solution Preparation. As in the original paper, solutions were prepared by weight to concentrations varying f10% around 0.1 aquamolal. Aquamolality is defined as moles of salt per 55.5 moles of solvent and The Journal of Physical Chemistry
places heavy and normal water solutions in thermodynamically comparable ~ t a t e s . ~ ,The ’ ~ salts were reagent grade and were used as received. Heavy water (99.88 mole %) was supplied by the Atomic Energy Commission’s Savannah River Operations Office. Its specific resistivity was 5 X lo5 ohms ern and it was used without further purification. Calculations. Solution activities were calculated from the composition with the aid of an expression for the activity coefficient y
+ m”’) + Bm
due to Guggenheim and Turgeon13and with the assumption that the tabulated “B” values given by those authors were applicable to heavy water solutions. l4 The constant A in the equation, which was evaluated for each of the solvents, is the Debye-Hiickel limiting law constant. The measured emf values were plotted us. the logarithm of the calculated activity ratios and the value of the standard emf for the cell was calculated from the intercept with the ordinate at log (aP/ a,) = 0. At least nine different concentration ratios were measured for each of the salts except (CH3)4?\’C1 for which only three were measured. For the alkali halides, a t least two different pairs of concentrated stock solutions were prepared independently and working solutions were prepared therefrom. Results and Discussion The results are displayed in Table 11. Values of the intercept, E’, and the slope of the graph of E vs. log (aP/aa)were obtained from least-square analysis of the data for the various activity ratios. The values of E” are shown with their root-mean-square deviation from the least-square line. For ideal membranes, Le., t ~ + += 1 and t ~ + -= 0, where the superscript indicates the membrane type, one should obtain a slope of 117 mv when silver chloride electrodes are used at 22’. Table I1 shows that, except for KC1 in cell 11, the least-square slopes varied no more than about 5% from ideal. For I t ~ .Since it is not likely that solution of any salt could invert the viscosity ratio of heavy and normal water, the solvent contribution to the cell I emf should always be positive. The positive emf values observed for cell 111 are confirmation of this argument. Furthermore, a positive error in the value of the standard potential will always lead to a more positive value for the apparent standard entropy. Thus the less negative values obtained from the cell I measurements compared to Kerwin’s values have physical justification.
