Richard W. Laity Princeton University Princeton, N e w Jersey
Electrochemistry of Fused Salts
In spite of a relatively long history of endeavor, including especially rapid growth in recent years, our knowledge and understanding of molten salt electrochemistry fall far short of levels established some 30 years ago for aqueous systems. The need for an entirely different approach to seemingly familiar problems is one reason for this. Concepts which rely on the presence of an inert solvent (for example, ionic "transference numbers") must either he redefined or discarded altogether. Even the straightforward measurement of unambiguouslydefined quantities has yielded some unexpected results, yet to be explained. Although the scope of the term "electrochemistry" is not well defined, a unifying feature of the specific subjects to be surveyed in this contribution is their relevance to the operation of an electrochemical cell. Two broad subheadings provide a basis for classification: electrolytes and electrodes. The latter includes the former to some extent, since it is the "half-cell," not just the electrode material, that is under consideration. It is natural to separate the discussion of electrolytic solutions from that of electrochemical reactions. Within each of these categories at least one additional distinction is worth making: equilibrium properties and phenomena can be treated independently of dynamic processes. This review of electrochemical phenomena in fused salt systems will therefore be divided into four subsections, dealing with both thermodynamic and kinetic aspectsof both electrolyte and electrode systems. The universal acquaintance of chemists with the electrochemistry of aqueous solutions will serve as a point of departure in each area. After briefly refreshing the reader on experimental observations and theoretical interpretations in the more familiar electrolytic solutions, corresponding considerations in pure and mixed fused salts will be reviewed. Thermodynmmics of Fused Electrolytes
Although the thermodynamic activity of a solution Presented as part of the Symposium on Recent Advances in the Chemistry of Fused Salts, before the Division of Chemical Edu1961 cation at the 139th ACS Meetine. , -Mxrrh. -. -, St,. -~~ Innis. The author is indebted to the U.S. Atomic Energy Commission for financial support which helped make this review possible. ~
~
component is defined in terms of its vapor pressure (at= fugacity of i vapor/standard fugacity), the partial pressure of a salt over its aqueous solution is negligibly small a t room temperature. Salt activities in this medium are therefore determined either by measurement of water vapor pressure followed by application of the Gibbs-Duhem relation, or by indirect methods such as measurement of emf in reversible galvanic cells. It is useful to define a mean ionic activity coefficient y+, in terms of at and the electrolyte concentration. In dilute solutions of strong electrolytes the dependence of 7 + , on concentration is found to he a function of the charge types of the constituent ions, nearly independent of specific chemical properties. For an electrolyte of any charge type, y * . decreases in direct proportion to the square root of increasing solute concentration. Debye and Hiickel accounted for these observations quantitatively by equating the change in free energy of the system to the electrostatic work done in bringing together a statistically distrihuted assembly of charged spheres in a dielectric medium. Experimental observations in more concentrated aqueous solutions are less readily generalized, nor has a satisfactory theory been developed to explain the results for any specific system. One reason for interest in molten salts is the possibility of approaching concentrated electrolytic solutions from the other direction. By studying the effects of adding a little water or other inert "solvent" to a fused salt (under sufficient pressure to maintain the former in solution), it may be possible to develop a general approach to the theory of concentrated electrolytes. Fairly extensive studies have been made on the thermodynamic properties of molten salts mixed with one another. I n contrast with aqueous solutions, volatility a t experimental temperatures may actually he sufficient to nermit direct measurement of salt vavor vressures. This approach to determining activities is seldom used in melts, however. In fact, it is now evident that it would be apt to give misleading results, due to the recently-discovered tendency of simple salt molecules to form dimers and trimers in the gaseous state (like NaKM (1). The most accurate activity figures available for salt mixtures have been determined by
. .
Volume 39, Number 2, February 1962
/ 67
emf measurements. Phase diagrams are often used for less precise estimates. In order to discuss results of activity measurements on ionic melts it is useful to establish a standard for "ideal" behavior. By analogy with other systems, the definition can be based on an idealized model for calculating the relevant relationships. The model proposed by Temkin (2) will be described shortly. It leads to a particularly simple expression for the activity of a salt A,B,: ~ A B =
XA"XB"'
(1)
systems (melts composed of a t least two diierent cationic and two different anionic species) have not yet been reported. I t is nevertheless possible to infer departures from ideality by consideration of thermodynamic data for the pure salts. This follows from the fact that a system composed, for example, of the ions Na+, K+, C1-, and Br- is actnally a ternary system, so that any of the four salts NaC1, NaBr, KC1, or KBr can be considered a particular "mixture" of the other three. Thus, if the free energy change for the permutation of ions represented by NaBr
+ KC1
-
KBr
+ NaCl
where X A = number of A cations/total number of (each saltpure liquid at a common temperature) is cations and is called the "cation fraction" of A. The not zero, the system cannot be ideal. An analysis of anion fraction X s is similarly defined. Equation (1) alkali halide data in this way has indicated some sysprovides the basis for a definition of the salt activity tematic trends in the small but real departures from a coefficient 7 , which can also be expressed as r+'"+", ideality (5). mean ionic activity coefficient. Simply let am repreAlthough there is no general theory of molten salt sent the activity of a real salt, and insert on the right mixtures analogous to that of Dehye and Hiickelforthe hand side whatever factor is required by experiment to more familiar electrolytic solutions, some progress has preserve the equality. Models leading to relations been made in understanding the observations listed other than equation (1) have also been proposed (3'). above. The Temkin model resembles the conventional For mixtures of two salts of the same valence type, all approach to mixing of crystalline lattices, postulating such relations usually become mathematically indisa fixed number of cation "sites" in each of the pure tinguishable from (I), thus providing a universally acsalts, not accessible to anions, and vice versa. The total ceptable standard for ideality in such melts. For of sites of each type is assumed to remain consalts of different valence types (e.g., N ~ C ~ - C ~ C ~ Snumber ), however, discrepancies between calculated activities stant on mixing the salts, all species of like-charged ions being distributed randomly over available sites. become appreciable near the middle of the concentration range. While it is difficult to generalize the exThis gives for the entropy of mixing. perimental results for the few systems that have been studied, observed activities usually seem to agree best with those calculated from equation (1). I n any case (1) is the simplest equation that has been derived where X1 refers to either cation or anion fraction, the from a theoretical model, and the one commonly used summation being taken over all ionic species. The as the basis for thermodynamic ideality in molten salts. enthalpy of mixing neutral salts is taken to be zero, The salt mixtures most commonly studied experijust as in other ideal solutions. Kote, however, that mentally are those composed of two salts having one ions are the units employed in calculating entropy ion in common. Deviations from ideality in such changes, while the statement AH = 0 refers only to systems are often found to be small, exceptions occurmixing of uncharged ionic combinations. The free ring when the attraction of a particular pair of ions energy change calculated from these two postulates has a significantly covalent character. Some degree of leads, of course, directly to equation (1). non-ideality is usually present, nevertheless. Trends in In contrast with theories of thermodynamic behavior such deviations can often be correlated with position in aqueous solution, the Temkin approach is typical of in the periodic table, e.g., the activity coefficient of NaI those that have been applied to molten salts; it treats varies systematically as the "solvent" or "solute" is evaluation of AH and A S separately, rather than atchanged from NaF to NaCl to NaBr I n contrast tempting to evaluate A F directly. Since the former with aqueous electrolytes, whatever trends are estabquantities can both be determined experimentally, it is lished when either component is dilute normally conpossible to establish the extent to which each continue into the middle of the concentration range. tributes to the non-ideality of the solution. Although A classic example of these generalizations is found in data of the requisite accuracy have been slow in comthe work of Hildebrand and Salstrom (4) on mixtures of ing, very careful calorimetric measurements reported AgBr with various alkali bromides. I n every case the recently by Kleppa and Hersh (6) have demonstrated solutions were found to be "regular"; that is' that in molten alkali nitrate mixtures, the important factor is the slightly exothermic character of the mixing RT in 71 = AX? (2) process. These workers have also found a striking where A is a constant, independent of composition and correlation of the magnitudes of AH in different mixtemperature. Values of A , which measures the heat of tures with ionic size parameters. Their results were mixing, varied systematically with ion size, being consist,ent with F@rland'shypothesis that the principal positive for alkali cations smaller than Ag+ and prosource of heat is the reduction on mixing of coulombic gressively more negative for the rest. repulsion between cations (7). Activity measurements on the simplest reciprocal This section should not be concluded without mention of recent theoretical and experimental work by Blander, Braunstein, and co-workers on systems of somewhat 1 Subscript 1 in equation ( 2 ) refers to either salt; subscript 2 greater complexity (8). The effects on thermodynamic refers to the other salt. 68 / Journol of Chemicol Education
activity of varying concentrations of Ag+ and C1- in alkali nitrate "solvents" were investigated. Here the two ions mentioned have an "extra-coulombic attraction" which tends to stabilize their association with one another. I t was found that by assuming reasonable coordination numbers in a "quasi-lattice" model this association could be characterized and experimental results explained quantitatively in terms of a single interaction-energy parameter. Snch advances may provide the opening wedge to an understailding of more extensively "covalent," molten salt systems, such as AgC1-PbCl,. Here, curiously enough, the experimental value of each y is very nearly unity over the entire range of composition. Tmnsport Properties
Rather than attempting to consider the whole range of properties that fall under this heading, the present review will deal principally with the single concept of primary interest to electrochemistry-t,hat of ionic mohility. Actually two different concepts of ionic mohility in aqueous solutions can be developed from a phenomenological approach. The first is based on tracer-diffusion measurements, normally characterized by an ionic "self-diffusion" coefficient. This concept will be referred to here as "diffusional mobility." As electrolyte concentration increases, the diffusional mobility of a given ion is found to decrease, and to become more dependent on the nature of other species present. The second concept will be called "electrical mobility." I n an electrolytic solntion whose equivalent conductance is given by A, the electrical mobility of an ion i can be described by fit = t , A / 5 , or simply by A, = &A, where ti is the transference number of i. At infinite dilution the diffusional and electrical mohilities of any ion have a simple relationship t,o one another:
where R is the molar gas constant, T the absolute temperatnre, and 2,5 the charge on one mole of i. Equation (3) is known as the Kernst-Einstein relation. Even though the behavior of p i with increasing concentration is similar to that of Di,the two mobilities do not decrease a t the same rate, so that (3) is valid only at infinite dilution. Although there are no definite rules concerning the values of the limiting mobilities of ions in aqueous solution, it is possible to make some semi-quantitative generalizations. Taking the familiar "crystal radii" as measures of ionic size, it is found that small ions like Li+ have relatively low mobilities, as do those with radii substantially larger than the dimensions of water molecules, such as NleaN+. Maximum mobility is therefore reached by ions of intermediate size, a rather broad plateau including all the larger alkali and halide ions. The exceptions in aqueous solution are H + and OH-, which have very much larger mohilities than any other ions. Charge is also an important factor; increasing the charge of smaller ions generally is accompanied by decreased mobility. The theoretical approach of Debye and Hiickel, later extended by Onsager and others, makes use of the "ion atmosphere" coucept originally developed in ex-
plaining thermodynamic activities. This cloud of opposite charge around each ion arises from its tendency to attract those of the other sign into its vicinity, while repelling like-charged ions. Opposing the Coulomb forces is the randomizing effect of thermal motion. The resulting charge distribution is best characterized by the "radius" of the ion atmospherethe dist.ance a t which a thin shell of equal but opposite charge would produce the same force on the central ion. This radius varies inversely with the square root of concentration. When an electric field is applied, the atmosphere is distorted, producing a local ficld contrary to the applied field. The ion then moves slower than in an atmosphere of greater radius. This is calculated to be one of the important factors in the decrease of electrical mobility with increasing concentration. Including additional effects not discussed here, the theory is quantitatively successful in describing the concentration dependence of equivalent conductance in dilute electrolytes. At infinite dilution where diffusional and electrical mobilities are essentially equivalent [equation (3)], the ion moves through a medium of pure water. The Stokes-Einstein equation for the mobility of a sphere in a continuous medium of viscosity 1)
is adequate to explain the results for ions whose radii r, are large compared with the dimensions of water molecules. The same presumably applies to very small and highly charged ions, except that r , becomes an effective "hydrated radius" which takes account of the strong attraction for neighboring water dipoles. At the present time, however, there is no generally accepted theoretical basis for predicting the limiting mobilities of any but the very large ions. This statement includes the ions H+ and OH-, which apparently move through water by a different mechanism. The concept of ionic mobility in fused salts has proved to be elusive. To understand why, it is necessary to realize that the solvent plays an essential role in defining the aqueous mohilities. I n order to specify any velocity a frame of reference must be selected. The velocities of ions are always referred to the coordinate system of the medium in which they are dispersed. The absence of such a component in ionic melts thus makes it impossible to assign mobilities in a manner operationally consistent with the definitions used previously. One may therefore inquire whether analogous quantities can be defined for fused salts which offer the same conceptual advantages. Now in aqueous solution, the self-diffusion coefficient is a measure of the random (Brownian) motion of the ion, equal to one-sixth the mean square distance traveled through the solution per unit time. Ions in fused salts have a similar thermal motion relative to the hulk of the melt, so that diffusional mobility should again be a useful concept. As for electrical mobility, its possible value in fused salts is suggested by the following experimental values of A in pure alkali halides at 800°C: Salt LiCl NaCl
A (cmvohm equiv.)
KC1
Volume 39, Number 2, February 1962
/
69
There is a temptation to conclude that these melts are essentially cation conductors, i.e., the cations have substantially larger electrical mobilities than the anions. Before attempting to make this statement quantitative, however, one should realize that each of the salts listed above constitutes a unique medium, so that the numbers given cannot he strictly comparable. This is best demonstrated by making use of some additional data: Salt NaBr KBr
A (em'!ohm eauiv.) . .
138.0
100.5
Now the mobility difference between chloride and hromide can be calculated in two ways: AN.CI - A N ~ B=~ -3.3 and - A K B= ~ +10.0. It is apparent that no self-consistent table comparable to that of limiting mohilities in aqueous solutions could be developed for the electrical mobilities of ions in pure fused salts. However, this does not preclude the possibility of dividing A for a given salt into meaningful ionic constituents. Just as the concept of diffusional mobility could he of theoretical value in both types of system, the usefulness of individual ion conductances in developing a theory of fused salt conductivity appears promising. Specifically, since ions are generally thought to move by a series of jumps between successive potential energy minima, it should be important to compare the frequency and length of such jumps for different species. Operationally-defined mohilities which accurately reflect these microscopic parameters are presumably the quantities sought in the various types of molten-salt "transference number" experiments that have been reported in the literature. Since the subject of reference frames is not adequately discussed in these works, it is desirable to consider some possibilities here. Lacking a solvent, one may attempt first to use the ions themselves as the basis for a reference frame. This approach is immediately successful in tracer-diffusion, where there is no net flux of any one species relative to any other; the only relative motions involve different isotopes of species whose total concentration is constant throughout. Choosing the reference frame in which all ionic species present have zero velocity gives the same value of D ito each interdiffusing isotope of a given species, thus providing an unambiguous basis for assigning diffusional mobilities. When an electric field is applied across a melt of uniform composition, however, there is a net flux of cationic species relative to anionic species. This is what makes it possible to determine a total equivalent conductance A, even though there is no obvious way of subdividing this quantity into ionic contributions. Any one species might be choscn for reference, but this assigns to it a mobility of zero. Taking some kind of average ionic velocity for reference is an equally arbitrary procedure,. giving only - electrical mobilities of trivial significance. Having failed to find a suitable reference for electrical mohilitv within the melt. one mav next seek externallv imposed references. A variety of these have actually been employed. Those in which the electrodes or the walls of thecell serve as reference give trivial mobilities, depending on electrode reaction or cell geometry. The use of a porous plug or capillary fine enough to restrain liquid flow has been shown to give results which cannot 70 / Journal o f Chemical Education
he predicted from such simple a priori considerations. To what extent mobilities defined by this method are consistent with the theoretical objectives discussed above, however, remains to he established. This is where the problem of assigning electrical mobilities from the results of transference experiments stands today. Another approach has been the attempt to employ straightforwardly defined diffusional mobilities as basis for these more elusive quantities. Direct application of the Nernst-Einstein relation [equation (3) ] has given values of ht for both cation and anion in a number of pure salts. Unfortunately, the sum of these quantities always comes out greater than the experimental A for the salt. This is not surprising when one realizes that the electrically migrating ion moves against a stream of oppositely-charged ions that is stationary during the diffusion experiment, an effect which accounts for the failure of the Nernst-Einstein relation in aqueous solutions of finite concentration. Ways of "correcting" the diffusional mobility to take account of this added interference have recently been discussed by the author (9). It is appropriate to indicate the sort of generalizations about fused salts that can be made from available diffusion and conductance data. For example, there seems to be some correlation between diffusional mobility and ionic radius, just as in aqueous electrolytes. This t i e , however, the smaller the ion, the greater its mobility. The conclusion is based on typical results for more than one ionic constituent of the same melt, so that a common "medium" is involved. Also analogous to aqueous electrolytes is the tendency of diffusional mobility to decrease with increasing charge. The same effects of ionic size and charge seem to be present in electrical mobilities, as reflected by values of A in pure salts. The size effect was evident in the alkali halide figures tabulated above. The alkaline earth halides show the effect of charge; values of A are generally around half those for alkali halides at the same temperature. In a few cases, such as the halides of zinc and mercury, conductance is still smaller by an order of magnitude or more. Although no operational definition for "degree of dissociation" has been put forward for pure molten salts, the substantially greater diffusional mobilities found for the "ions" suggest that diffusion of uncharged entities like HgClz or ZnBr2may account for some of the obsewed transport. Some values representative of these and other observations on pure salts are collected in Table 1. Table 1.
Some Ionic Transport Parameters in Pure Fused Salts ( 1 0 )
D+
Salt
X
lo5 Temp (cmg! (cma/ ( " C ) ohm eauw.) sec) A
'Figures not available.
D- X lo6 (cma/ see)
EL* (kcall mole)
The last column of Table 1 indicates the temperature dependence of equivalent conductance. When In A is plotted against 1/T, a straight line is generally obtained. Multiplying the slope of this line by R gives the figures listed under En*. This quantity is commonly called the "activation energy for conductance," identified (in a way that has not been well defined) with the height of the energy barrier to ionic migration. I n contrast with aqueous electrolytes, the activation energy for conductance of fused salts is generally lower than that for viscous flow of the same salts. Activation energies for diffusion, on the other hand, are more nearly the same as EA*in both types of electrolyte. I n a t least two cases (AgNOs and NH4NOa), conductance isotherms of salt-water systems have been obtained all the way from infinite dilution to the pure molten salt (If). I n both cases the value of A was found to decrease continually with increasing concentration of salt. The total decrease in A for AgNOa was almost 20-fold, the rate of decrease being greatest a t the dilute end. When two fused salts are mixed, the conductance of the melt is usually less than would be predicted by assuming additivity of pure salt values. This interesting and rather unexpected behavior is illustrated in the figure for mixtures of KC1 with each of three other alkali halides. The negative deviation from additivity seems to be greatest when the pure salt conductances are furthest apart. No satisfactory explanation has yet been put forward to account for the behavior of A in fused salt mixtures. Nor has there been any theoretical work on the conductance of fused salts to which a little inert "solvent" has been added. I t is possible that these problems may be dealt with before the more general problem of describing the magnitudes of observed mobilities in terms of microscopic properties of the ions. Although this was seen to be a useful way of organizing the approach to transport theory in aqueous electrolytes, there has been a tendency for workers in the moltensalt field to concentrate on the latter problem. Simple models for ionic transport, such as motion of charged spheres through a continuous medium with the viscosity of the melt, have been vitiated by experimental data. Since q and Dl generally have different temperature dependences, the value of r , calculated from the Stokes-Einstein relation, equation (4), is somewhat arbitrary. It is interesting to note, however, that such "Stokes radii" are always about the right order of magnitude-usually 15-50% less than crystallographic radii of the same ions. This may be taken as evidence that the unit of transport is the simple ion, rather than more complex species. There is little doubt that each ion tends to be closely surrounded by species of opposite charge. The folly of attempting to use the Debye-Hiickel approach is evident, however, when one tries their equation for calculating the thickness of the ion atmosphere. Inserting typical fused ~alt~parameters, one calculates a "radius" of less than 0.2A. This is even smaller than the radius of the central ion! I n view of the failure of the Poisson-Boltzmann equation (on which the Debye-Hiickel theory is based) to take account of short-range repulsive forces, this result is not surprising. The closeness with which ions are packed together in
a melt and the success of quasi-crystalline models in predicting thermodynamic behavior have suggested to some workers the possibility that "vacancies" (holes of ionic size in the structure of the liquid) are the mobile units of transport (1%). The fact that this concept has been so successful in accounting for transport properties in ionic crystals indicates to this reviewer, however, that it is not likely to prove useful in melts. For transport properties, as opposed to thermodynamic or equilibrium properties, primarily differentiate the liquid from the solid salt. It therefore seems unlikely that the microscopic details of transport are basically similar in both states, differing only in extent or degree. Experimental evidence seems to bear this out; employing the technique used to add more vacancies t o ionic crystals ("doping" a uni-univalent salt with divalent ions) generally decreases the conductance of fused salts. Thus, in developing transport theory, it would seem more logical either to ignore the behavior of solids, or to focus attention on the differences in structure of the two phases. Electrode Poieniiols
The discussion of electrodes given here will he somewhat brief for two reasons: First, the topics surveyed in the previous section are of greater interest to this reviewer. Second, the subject of electrodes in fused salt systems has been treated extensively in a recent publication (5). All of the points touched upon below are elaborated more fully in the reference cited. The familiar table of standard electrode potentials in aqueous solutions provides a basis for calculating the emf of any reversible galvanic cell. This is made possible by choosing a reference state for defining the activity coefficient of an ion in such a way that it is independent of the nature of any other ions present. Such a state can never be realized, of course, but is approached as the electrolyte nears infinite dilution. Values of standard potentials in aqueous solution are therefore obtained by an extrapolation process, and will here be designated Elo. The potentials reflect the ease with which various substances are reduced, employing a voltage scale that is calibrated by taking E,' = 0 for the reduction of hydrogen. Entries from the standard electromotive force series in aqueous solutions were used to calculate the figures listed in the first column of Table 2. The magnitude of each E,' has been shifted by 1.360 volts, the potential of the chlorine electrode relative to hydrogen. This does not affect the observed order of values of E f O , which has been found to correlate fairly well with the ease of adding electrons to the same substances in the gaseous state (i.e., electron affinities and negative ionization potentials). This shows that the energy changes accompanying condensation of gases and hydration of ions are less important than that for electron addition. It is not possible to construct a table of standard potentials for fused salts in which the value of Eo for each ion is independent of the nature of other ions present. The reason for this is obvious; there is no inert solvent relative to which ionic concentrations can be extrapolated to infinite dilution. Tables of standard electrode potentials in fused salts have nevertheless been developed, using several alternative approaches to the problem of defining E D . The first is Volume 39, Number 2, February 1962
/
71
Table 2.
Order iu aqueous solution
(!I.
Ei m aqueous s o h at 25'
(2
Standard Electrode Potentials Referred to Chlorine (51
E, 1n pure fused chlorides at 1000'
($1
E, m
pure fused ehloridy at 700
to restrict the list to reducible cations, taking the anion to be the same in every case. A table of potentials based on the free energies of formation of pure metal chlorides has been made up by Hamer and co-workers (IS). Some of their figures appear in the second column of Table 2 under the heading Eno,the subscript referring to pure salts. The potential of the chlorine electrode was taken as zero in assigning these values. This is because a new reference standard is needed in fused salts to take the place of the hydrogen electrode. Since the figures listed for aqueous potentials are also referred to chlorine, it is of interest to compare them. Besides the change in the environment of each ion in the standard state (from water to chloride ion), these figures reflect also a change of almost 1000 degrees in temperature, any accompanying changes of state of the pure metals, and a change in assignment of "unit concentration" from 1.0 molal to unit mole fraction. The degree of correlation in the examples listed is striking, nevertheless. Except for the positions of Cd+%and Go+%,the order is the same. Some idea of the temperature effect can be gained by comparing columns 2 and 3, the latter figures being based on experimental decomposition potentials a t (or extrapolated to) 700° by Delimarskii (14). Potentials determined by this method in molten salts are usually not far fromreversible values. The decrease noted for most of the Eno with decreasing temperature is to be expected for potentials referred to the gaseous chlorine electrode. The effect on XVoof changing the anion is shown in columns 4 and 5 , the figures again being based on decomposition potentials reported by Delimarskii (14). This time, however, a secondary reference had to be nsed to put all potentials on the "chlorine scale." The potential for Na+ was chosen to be -3.39 volts, the same as its value in pure NaCl at this temperature. On this scale the potential of bromine in pure NaBr is -0.41, while that of iodine in NaI is -0.97. These figures were subtracted from the respective decomposition potentials of the bromides and iodides of the ions listed to obtain the entries in columns 4 and 5. On comparing potentials for the different anions, an interesting effectis noted; the total range of potentials becomes more and more compressed on passing from chlorides to bromides to iodides. By taking a melt of specified composition as the 'I solvent," it is possible to establish a fused-salt electromotive force series employing exactly the same method used in aqueous solution. All ions except 72 / Journal of Chemical Education
)(.:
E, m
pure fused bromides at 700'
(2).
E, m
pure fused iodides at 700'
(fj
Ei ~n KCI-NaC1 at 450'
(a).
Ei ~n KCI-Livl at 450
constituents of the solvent can then be taken to infinite dilution, thereby allowing a set of Eioto be determined. Two such series are listed in columns 6 and 7 of Table 2 for different solvent media a t the same temperature. The solvents in each case are entectic mixtures of the two salts listed a t the top of the column. All of these figures were obtained by extrapolating direct measurements of cell emf's (15, 16). Rather than use molalilies, however, concentration units of cation f r a e t i a have been e m p l ~ y e d . ~Comparison of the figures in columns 6 and 7 seems to indicate that changing one of the solvent cations from Na+ to Li+ has little effect. Theoretical efforts to "explain" differences among electromotive force series arising from a change of standard state, or even differences accompanying changes of solvent, do not constitute a separate field of endeavor. All such changes can be completely described in terms of thermodynamic "mixing" parameters-activities or activity coefficients in part,icular. The latter quantities, which have already been discussed, are simpler to deal with theoretically than changes of electrode potential. Almost the same statements can be made with regard to the effect of temperature on emf series, except that here changes in standard free energy of salt formation with temperature must also be taken into account. One area where additional theoretical work has been required is in writing appropriate expressions for emf's of fused-salt cells with transference. The problem arises a t the liquid junction, where the "electrical mobilities" of the ions present are important in establishing the potential. Transference numbers are nsed in the emf expressions for such cells in aqueous solutions; fused-salt transference numbers have not been unambiguously defined (see preceding section). The necessary "theory" to deal with this problem is not microscopic, but involves straightforward application of principles from the thermodynamics of irreversible processes. I t has been elaborated by the author, both from a rigorous point of view and in tcrms of appropriate quasi-thermodynamic concepts (5). Ahsolute ionic mobilities turn out to be irrelevant, the important transport parameters being mobilities of constituent ions relative to m e another. I n general, it is found that the magnitndes of liquid junction potentials in molten salts are likely to be smaller than typical
'
This change of units can actually switch the order of neighhoring entries in the table (see reference6, p. 561).
aqueous-solution values, a conclusion consistent with experimental observations. Kinetics of Electrode Reactions
The rates of electrode reactions are measured by the current density, and thus can be adjusted to almost any value a t will. The kinetic parameter of interest is the voltage required to achieve a specific current, or rather the departure of the electrode potential from its equilibrium value. The classical method of studying such "overvoltages" is to pass constant direct current through the electrode and observe the polarization under steady-state conditions. When controlled by "activation" only (i.e., a slow step in the electrochemical reaction), the observed overvoltage usually conforms to the Tafel equation, which can be written in the form
where Eois the reversible potential, i the cathodic or anodic current density (depending on the direction of current flow applied), and a an empirical parameter usually lying between 0 and 2. Since iois the cathodic or anodic current density a t the equilibrium potential (i.e., when there is no net current because cathodic equals anodic current), it is known as the "exchange current." This current is sensitive to a number of factors, such as adsorption of species from solution and catalytic activity of the electrode surface. Typical values for hydrogen overvoltage range from 10-1%amp cm-2 (on mercury) to 0.003 amp cm-2 (on platinum). Reactions not involving gases may have very much higher exchange currents. When the value of io is large compared with the current drawn a t the electrode, i/ioin equation (,5) is nearly unity, so that no activation polarization is observed. Until recently such reactions were simply classified as 'Lfast," and not studied further. However, a number of techniques for studying fast electrode reactions have now been developed. Some of these involve, for example,
Conductance irothermr
+ NoCl; and A. KI.
for KCI-alkali halide mixtures at 800% 0.LiClr Omta of V m Arlsdalen and Yoffe ( 1 8 ) .
disturbing the steady-state by interruption of the direct current, superposition of an alternating current, or addition of short pulses of higher current. The develop ment and use of these new tools for the understanding of electrode reaction mechanisms is responsible for a substantial fraction of the research activity in electrochemistry today. With the possible exception of some early studies involving evolution of chlorine gas a t carbon electrodes, attempts to measure overvoltage in molten salt systems by the classical method have generally proved fruitless. Polarization observed a t the highest currents feasible could be completely accounted for by factors other than activation (such as I R losses). Additional evidence for unusually high exchange currents was the ease of achieving reversibility found for many electrodes in fused salts. I n the search for suitable fuel cell systems it was observed that with molten salt electrolytes even carbonaceous substances could be oxidized a t potentials close to calculated reversible values. Only very recently, however, have experimental studies been carried out which indicate the actnal magnitudes of these exchange currents. Work reported by Laitinen, Tischer, and Roe (17)on electrode reactions in molten LiC1-KC1 eutectic yielded (extrapolated) molar exchange currents ranging from 8 amp cm-= for Bi+=/ Bi(1iq) to 210 amp em-= for Cd+2/Cd. It is apparent that a major factor i n producing such high exchange currents in fused salts is simply high temperahre, which of course accelerates all reactions. The absence of an interfacial layer of water dipoles and the lack of any necessity for reacting ions to alter or shed their "hydration spheres" may also contribute. Much more work remains to be done before the details of electrode reaction mechanisms in fused salts can be fully elaborated. Literature Cited
( I ) BERKOWITZ, J., AND CHUPKA, W. A,, J. Chem. Phys., 29, 653 (1958). (2) TEMKIN, M. I., Zhur. Fiz. Khim., 20,105 (1946). T.,Disc. Faraday Soe., No. 32 (in press). (3) F~RLAND, E. J.. J . Am. Chem. (4) J. H.. AND SALSTROM. . . HILDEBRAND. SOL, 54,4257 (1932). (5) LAITY, R. W., "Electrodes in Fused Salt Systems," Chap. 12 in "ReferenceElectrodes: Theory and Practice," IVES, D. J. G., AND JANE,G . J., Editom, Academic Press, New York, 1961. (6) KLEPPA,0. J., AND HERSH,L. S., J. Chem. Phys., 64, 1937 (1960); KLEPPA,0. J., AND HERSH,L. S., Disc. Faraday Soe., No. 32 (in press). (7) F ~ R L A N T., D , "On the Properties of Some Mixtures of Fused Sdtlts," Nwges Tekniske Vilenskapsakadai, Oslo, Series 2. No. 4 (1957). ~, (8) BLANDER, M., AND BRAUNSTEIN, J., Ann. N. Y . Acad. S e i , 70,838 (1960). (9) LAITY,R. W., Disc. Faraday Soc., No. 32 (in press). (10) LAITY,R. W., Ann. N. Y . Acad. Sci., 7 9 , 997 (1960). (11) CAMPBELL, A. N., ETAL.,Can. J. Chem., 32, 1051 (1954). (12) BOCKRIS, J. O'M., ETAL.,PIOC.Roy. SOC.,AZ55, 558 (1960). M. S., AND RUBIN, B., J. (13) HAMER,W. H., MALMBERG, Electroehem. Soe.. 103. 8 f195fi). , , D E L I ~ S K IYu. I , K., 2hur. Ftz. Khim., 29, 28 (1955). T. R., J . Eleclroehem. Soe., FLENGAS, S. N., AND INORAHAM, 106,714(1959). LAITINEN, H. A,, AND LIU, C. H., J. Am. Chem. Soc., 80, 1015 (1958). i LAITINEN,H. A,, TISCHER, R. P., AND ROE, D. K., J. Eleclrochem. Soc., 107,546 (1960). VANARTSDALEN, E. R., AND YAFPE,I. S., J. Phys. Chem., 59,118 (1955). Volume 39, Number 2, February 1962
/
73
