Another way to write [2] is obtained in making use of [1], [3], and [4], thus (d~) T = --FA-d~A~ --rc + d~co~ --F [~ --AH] d~r [7] in which d~A~ = d~A- § d~ + ; d~coH = d~c + --d~ + According to the definition e : FH+ and assumption I"H+ = 0, Eq. [6] transforms into Eq.[1] of Frumkin et aI., and relations [3] and [4] of this work are readily inferred and may be extended to the case where H + is not only in state of contact adsorption (r'~+ ~ 0). From [6] it is observed that at ~-and #c+ constant, [r'n+ + e] and [AH-e] are thermodynamically independent variables. Therefore, by exact differential property, d~ could be written in terms of these coordinates, or by introducing an analytical change of coordinates* in terms of either [AH -}-r'n+] and If'H+ ~-e] or A H and rH+, according to the approximation of Frumkin. Equation [12] of Frumkin with X -1 the pseudocapacitance of adsorption and y-1 a capacitance of the double layer suggests that such change of coordinates has been used. Equation [10] of Frumkin et al. may be easily shown to follow from Eq. [7] given above. *With X = [AI~ --e]; Y = [F'• + e] and U = X + Y; V = Y the J'acobian $(X,Y/U,V) of the transformation X,u ~ U,V is unity.
ABSTRACTThe influence of "bulk" ion pairing on electrode processes is easily detected when its main effect is to decrease the activity of the depolarizer. On the other hand, when association with the adsorbed ions of the supporting electrolyte forms a more electroactive entity, it is known that it can be more difficult to distinguish between direct discharge, or via ion pairs. However, a broad intercomparison (under strictly identical experimental conditions) of the influence of the nature and concentration of the supporting cation (Li +, Na +, K +, Cs +, Mg 2+, Ca 2+, Ba 2+) on depolarizers of various electronic charge, allows to detect the abnormal behaviors, which are not determined by the pure "static" ~ effect. An indirect method has also been used, which essentially consists in modifying the double layer profile by adding, at constant concentration, increasing amounts of tensioactive ions having the same charge as the electrode, e.g., iodide at not too negative charge densities.The occurrence of chemical ion pairing as a concomitant rate-determining factor in electrode processes is generally easily detected from the effect of suitable composition changes at constant double layer structure: a typical case is the action of the sulfate ion on cation reduction, recently studied in our laboratory (15). However, it has been pointed out (1, 2) that, in the case of anion reduction proceeding at sufficiently negative potentials in not too concentrated solutions, the variations of the apparent rate constant produced by changing the concentration of the supporting electrolyte can be referred either to the usual ~ effect acting on the "bulk" species or to a prior charge-decreasing process involving ion-pairing with the supporting cations, which helps to circumvent the repulsive interaction with the electrode. In some cases, sudden chang...
