RICHARD W. LAITYAND ALBERTS. TENNEY
3112
Relative Cation Mobilities in Silver Bromide-Potassium Bromide Melts1
by Richard W. Laity and Albert S. Tenney School of Chemistry, Rutgers University, New Brunswick, New Jersey 08005 (Received October 24, 1969)
Direct current transference experiments have been used to compare the rates of cation migration relative to bromide at a number of temperatures and concentrations of the system AgBr-KBr. Individual cation conductance isotherms have been calculated from a combination of these data with A values for the same mixtures. Both mobilities decrease with decreasing concentration of AgBr, that of the initially more mobile silver ion falling considerably more rapidly. The resulting “crossover point” shifts toward higher concentrations of AgBr as temperature increases. Although no frits or other porous materials were employed in this work, the observed behavior is remarkably similar to that found in previous transference experiments on other binary mixtures. It is contrary, however, to the equality of cation mobilities at all concentrations implied by some emf values reported in the literature for AgBr-KBr concentration cells with transference. By dividing the potentials predicted for such cells into four “components” in such a way that contributions due to thermodynamic nonideality and to inequality of cation mobilities (“liquid junction potentials”) are evaluated separately, it is shown that the results of some new emf measurements are consistent with the transference behavior observed directly and do not support conclusions based on the earlier reports of concentration-cell emf’s.
Previous transference experiments on molten LiC1KC1 mixtures revealed a strong and unexpected dependence of relative cation mobilities on concentration.2 Subsequently, similar behavior was observed in such other systems as NaN03-KN033”)band LiN03-KN03.4 As was pointed out previouslyJ6however, emf measurements reported by Murgulescu and Marchidan6 indicate significantly different behavior : equal cation mobilities over the entire concentration range studied in a number of systems. Although most of the latter systems have not been the subject of direct transference experiments, the system PbClz-KC1 had been found by Duke and Fleming’ to have unequal cation mobilities that should have given rise to substantially larger liquid junction potentials6than the [‘lessthan 1 mV” reported by Murgulescu and Marchidan.6 I n an attempt to identify the source of this discrepancy, Behl and Egans carried out additional emf measurements on PbC12-KC1. They found results consistent with the transference measurements of Duke and Fleming.’ Since capillary tubing had been used to isolate the electrode compartments described by Murgulescu and Marchidan, while porous materials of relatively high internal surface area were used both in the emf measurements of Behl and Egan and in the transference work of Duke and Fleming (as well as in most other transference determinations), the possibility that such materials introduced a “wall effect” on the relative cation mobilities could not be ruled out. The present studies are part of a thorough investigation of transport properties of the systems silver bromide-alkali bromide, for which equal cation mobilities were also indicated by Murgulescu’s emf measurements. The Journal of Physical Chemistry, Vol. 7 4 , No. 16, 1970
The concentration dependence of the equivalent conductance in AgBr-KBr has been foundgJOto be remarkably similar to that of LiC1-KC1. In both systems A shows such strongly negative deviations from additivity of the pure salt values that conductance vs. composition isotherms pass through a minimum. It would therefore be surprising if cation mobilities in AgBrKBr were equal at all concentrations. The aim of this work has been to determine the relative mobilities of the cations in this system with good precision over substantial ranges of composition and temperature, employing a Hittorf-type transference method in which no frits or other porous materials separate the compartments. I n addition, some relatively crude emf measurements on concentration cells with transference have been included to check for consistency with values calculated using the experimental transference numbers obtained in this work. (1) This work is part of a program sponsored by the U. 5. Atomic Energy Commission. (2) C. T. Moynihan and R. W. Laity, J. Phys. Chem., 68, 3312 (1964). (3) (a) F. Lantelme and M. Chemla, Bull. SOC.Chim. Fr., 2200 (1963) ; (b) E. P. Honig and J. A. A. Ketelaar, Trans. Faraday Soc., 62, 190 (1966). (4) F. Lantelme and iM.Chemla, Electrochim. Acta, 10, 663 (1965). (5) R. W. Laity and C. T. Moynihan, J . Phys. Chem., 67, 723 (1963). (6) I. G. Murgulescu and D. I. Marchidan, Russ. J . Phys. Chem., 34, 2534 (1960); Stud, Cercet. Chim., 8 , 383 (1960). (7) F. R. Duke and R. A. Fleming, J. Electrochem. Soc., 106, 130 (1959).
(8) W. K. Behl and ,J. J. Egan, J. Phys. Chem., 71, 1764 (1967). (9) B. S. Harrap and E. Heymann, Trans. Faraday SOC.,51, 259 (1955). (10) S. Petruoci and R. W. Laity, to be published.
CATIONMOBILITIES IN SILVERBROMIDE-POTASSIUM BROMIDE MELTS
3113
Experimental Section’’ Materials. Matheson Coleman and Bell purified
with transference over a wide range of compositions quickly and easily.
AgBr was used without further purification. The KBr was Baker reagent grade. Salt mixtures were prepared by heating the solids together in the transference vessel slowly (2 days) to 300” under vacuum, then melting under dry nitrogen. The composition could then be varied by adding one of the pure salts which had also been dried at 300”. KCN was reagent grade from either Matheson Coleman and Bell or Baker. Apparatus. The transference vessel, furnace, and devices for regulating and measuring temperature were those employed by Moynihan and Laity.’ As anodes, both bromine and silver electrodes were used. To avoid difficulties resulting from dendritic growth of silver, only bromine electrodes were used as cathodes. Bromine vapor was introduced into a porous carbon cathode by first passing a stream of dry nitrogen through a liquid bromine trap. A bromine anode was simply a short graphite rod. A silver anode consisted of 99.99% silver wire about ‘/*in. in diameter. A sheath enclosing the contents of each electrode compartment was made from a Pyrex tube, tapered at the bottom so that contact to the bulk was made through a capillary 3 to 4 cm long and about 1 mm in diameter. This capillary was bent upward so that the salt could not run out of the compartment as the cell was raised at the end of a run. Run procedure was similar to that of Aloynihan and Laity’ except that cathode, as well as anode, compartments were analyzed. Analysis. Several analytical techniques were investigated. By far the greatest accuracy and precision were obtained using a completely gravimetric method in which KBr was first leached with hot water from a previously weighed sample consisting of both salt and electrode material fragments. After reweighing, the AgBr was dissolved in excess KCN solution and the remaining material weighed a third time. Some mixtures were analyzed as many as 15 times. I n such cases the standard deviation in mole fraction of silver bromine was found to be less than one part per thousand. Emf Measurements. Except for the use of silver metal electrodes in both compartments, essentially the same apparatus and materials as had been used in the transport number experiments were employed in the emf experiments. The procedure consisted of putting different concentrations of salt on each side of a cell, immersing the cell in a molten salt bath, monitoring the emf of the cell until it became stable, and removing and analyzing the salt in the compartments as in the transport number experiments. Although this was a rather crude method, it was possible to investigate the approximate effect of cation mobility differences on the emf of concentration cells
Calculation of Results Mobility Ratios. Since the assignment of transport numbers depends on the choice of reference frame, which is arbitrary in molten salts,12 it is convenient for the purpose of comparing cation mobilities to choose the ~ ,t o 0 and transport number of the bromide ion, t ~equal hence assign cation transference numbers such that tag -tK l = 1. The actual transport numbers of each cation relative to bromide must vary from 1 to 0 as the concentration changes from pure salt to infinite dilution. Thus it is more instructive to describe results of transference experiments in a way that reflects any variations of mobility with concentration. However, it is desirable to make use of a quantity whose value is not dependent on the reliability of conductance measurements. Thus, Moynihan and Laity1 employed the “per cent mobility difference,” Q. Present results will be expressed in terms of the mobility ratio R, defined as R = X A ~ / X K , where X i is the equivalent conductance of cation i relative to Br. R is related to Q by Q = 100(R - 1). It is calculated from experimental data by the relation
E=----$ A
~ K
NA&K where $ is the “transport fraction” whose calculation from experimental data is described by Moynihan and Laity’ for the case where halogen electrodes are used. An analogous expression can be employed to obtain the same quantity when the anode is silver metal. Calculation of Emf from Thermodynamic and Transport Data. The basic equation for the emf of the concentration cell Ag((AgBr KBr)A[\ (AgBr KBr)B(/Ag is
+
+
s* E
&oell
=
F
A
Nz
d In a1
where 1 refers to Ag, 2 to K, and A and B to two different concentrations, l 3 B richer in AgBr. To distinguish the explicit dependence of the emf on activity coefficients and on transport number values it is instructive to divide the total emf into a sum of four “contributions” : EN, E y , E,, and &7,.
I. For an ideal solution with equal cation mobilities, &I
= EN, where
(11) For a more complete description of apparatus and procedure see A. S. Tenney 111, Ph.D. Thesis, ltutgers University, 1970. (12) R. W. Laity, “Fused Salt Transport Numbers” in “The Encyclopedia of Electrochemistry,” C. A . Hampel, Ed., H. Iteinhold Publishing Corp., New York, N. Y., 1964. (13) R. W. Laity, J. Amer. Chem. Soc., 79, 1849 (1957).
The Journal of Physical Chemistry, Vol. 74, No. 16,1970
RICHARDW. LAITYAND ALBERTS. TENNEY
3114 1.8
11. For a nonideal solution with equal cation mobilities, €11 = E N E,, where
+
Integration in this case (as in many molten salt mixtures) is facilitated by the fact that the system is thermodynamically “regular.” Thus Hildebrand and Salstrom have shown that RT In y1 = AN22in a mixture of AgBr with alkali bromides, A being a constant whose value is -1480 cal mol-’ in AgBr-KBr.14 GII is the emf predicted for a cell in which cation mobilities are equal over the concentration range from A to B. 111. For an ideal solution with unequal cation mobilities, 81x1 = E N E,, where
+
(3)
The value of &/NZ is obtained from the results of the transport number experiments. From the values of R measured for AgBr-KBr, it was found that 4 2 / N zcould be represented within experimental precision as a linear function of N1 over the concentration range studied in the emf experiments. IV. Finally, for nonideal solutions with unequal cat&$ &, where ion mobilities, EIV = E N E,
+ + +
may be considered an additional “correction” that is required wherever cation mobilities are unequal in a nonideal system. By comparison of EIV with €11 it is Ey,, may be taken as the seen that the quantity E, “liquid junction potential.” Since E I V includes all four contributions to the emf, it is equivalent to the quantity designated at the beginning of this section.
+
Results and Discussion The results for the cation mobility ratios a t four temperatures are plotted in Figure 1 as functions of equivalent fraction AgBr. They may be summarized as ~ 0.72 (only the eutectic follows: at 350” and N A = region was accessible), R = 1.69 f 0.04; at 450” and 0.555 N a g 50.9, R = 0.67 0.89NA, f 0.04; at 500” and 0 . 5 5 5 N a g 5 0.75, R = 0.58 0.85N~f , 0.03; at 550” and 0.55 1)for N I > 0.5, while at 550”, E(+ is more mobile for NI < 0.8. To assign numerical values to cationic mobilities or conductances (relative to Br) it is necessary to know the equivalent conductance of each mixture as well as the transport numbers. Using the results of Laity and Petrucci,’O we find the concentration dependence of the individual ionic conductances shown in Figure 2. Both the temperature and composition dependence of the relative cation mobilities in AgBr-KBr are remarkably similar to those in KC1-LiCll and in alkali nitrates.2-4 I n all of these systems both mobilities increase monotonously with increasing concentration of the better-conducting (when pure) salt. The mobility of the cation of this salt has significantly greater concentration dependence than that of the other cation, resulting in the “crossover” of mobilities indicated for our system by each pair of isotherms in Figure 2. As the temperature is increased, the crossover point moves toward higher concentrations of the better-conducting salt. This means that the mobility of the cation of this salt is less temperature dependent than that of the other cation. Thus, the apparent “activation energy” for conductance of Ag+ (based on the temperature dependence of is less than that of K + a t all concentrations studied, as shown by the isotherms of E plotted in Figure 3. Perhaps more noteworthy in this system, however, is the fact that while both E *hK and E apparently decrease with increasing KBr concentration, the Efn (the quantity obtained from conductance measurements alone) increases. This apparent anomaly is due to the trivial fact that as one ionic species increases in concentration, it contributes more to the conductivity of the mixture. Results of emf measurements on concentration cells with transference are presented in Table I along with values calculated for each of the “components” indicated. I n view of the relatively poor precision of the observed emf’s, their accuracy is not expected to be
*
J
Figure 3. Activation energies for Amixt and for individual cationic conductances in molten. AgBr f KBr mixtures at 500’.
much better than =k2 mV. For example, although the second and sixth runs were performed on identical concentrations at nearly identical temperatures, the emf’s measured differed by more than 1 mV. The uncertainties in the concentrations determined by direct analysis of overall electrode compartment contents, as well as in the emf measurement itself, were not nearly large enough to account for such discrepancies. The main source of error was probably attributable t o the difficulty of maintaining uniform concentrations within the electrode compartments. The mixing that resulted from both interdiffusion and the mass flow between compartments that took place as each was stirred between emf readings may not have been negligible in some of these experiments; in such cases the concentrations analyzed were not necessarily identical with those that determined the emf at the electrodes. I n an effort to reduce this error several experiments were performed in which excess solid KBr in one compartment (whose temperature was accurately known) fixed the liquid concentration a t a value which could be taken from the phase diagram. Unfortunately, the uncertainty in the ~ at a particular temperature available N A value amounted to about .t0.01.15 To test whether the emf results were consistent with the transport number results, it mas necessary to study a concentration range over which E, and E,, were large compared to the uncertainties in the method. This accounts for the choices of composition and temperature at which our emf experiments were conducted. Note that a crossover in cation mobilities within the interval spanned by the electrode compartment compositions The Journal of Physical Chemistry, Vol. 7 4 t N o . 16, 1.970
RICHARD W. LAITYAND ALBERTS.TEXNEY
3116
Table I: Observed and Calculated Emf's for the Concentration Cell with Transference Agl AgBr
+ KBr (A)/(AgBr+ KBr ( B ) I A ~
7----Concns---l
of predicted emfs, mV---
----Components
Temp,
NAg
Run
OC
A
B
EN
6,
1 2 3 4 5 6 7 8 9 10
455 453 452 45 1 482 45 1 431 443 447 446
0.500 0. 52" 0.796 0.636 0.628 0. 52" 0.541 0.726 0.53" 0 53"
1.000 1.000 1.000 0.918 0.907 1.000 0.665 1.000 1.000 1.000
44 41 14 23 24 41 13 20 39 39
16 15 3 8 9 15 6 5 14 14
NAK
I
E+
-8 -8 -4 -5 -4 -8 -2 -5 -8 -8
-Predicted
emf's, mV-
E,,
E11
EIV
-3 -3 -1 -2 -2 -3
60 56 17 31 33 56 19 25 53 53
49 45 12 24 27 45 16 19 43 43
-1 -1
-2 -2
a Determined from phase diagram9 pure solid KBr was in contact with these solutions. coarse fritted Pyrex disk.
Obsd emf's, mV Eexp
50.9 43.2 12.0 26.6 29. Ob 42.1 13.2 16.5 41.5 44.5
' Compartments were separated by a
would result in a decrease of the liquid junction potenE, eventually becomes greater than -E+. Thus, for the large concentration differences needed to obtain exE,,. tial E, perimental emf's of sufficient magnitude for valid comSeveral sources of error contribute to the uncertainty The parisons of E,, with predicted values, contributions due in values tabulated for the components of EIV. to the nonideality of the solution comprise as much as random error in the activity coefficients reported by one third of the total, while the (negative) contribuHildebrand and Salstrom14 is about 4%, which gives rise to =t4Y0uncertainty in the values calculated for E,,, tions to EIV due to unequal cation mobilities, E, are generally less than one-fourth the magnitudes of E, and E,,. More seriously, the uncertainty in our and G I V . own values of R results in uncertainties of about f15% &+ E,, has been called the "liquid junction potenin &, and E?,, From these figures the total uncertial." It reaches a maximum of only about -11 mV, tainty in predicted emf values is about *l% (
