The Temperature Dependence of the Properties of Electrolyte Solutions. IV. Determination of Cationic Transference Numbers in Methanol, Ethanol, Propanol, and Acetonitrile at Various Temperatures

Electric conductivities of 1:1 electrolytes in liquid methanol along the liquid–vapor coexistence curve up to the critical temperature. I. NaCl, KCl, and CsCl solutions

The molar conductivities Lambda of NaCl, KCl, and CsCl in liquid methanol were measured in the concentration range of (0.3-2.0) x 10(-3) mol dm(-3) and the temperature range of 60-240 degrees C along the liquid-vapor coexistence curve. The temperature range corresponds to the solvent density range of (2.78-1.55)rhoc, where rhoc = 0.2756 g cm(-3) is the critical density of methanol. The concentration dependence of Lambda at each temperature and density (pressure) has been analyzed by the Fuoss-Chen-Justice equation to obtain the limiting molar conductivity Lambda0 and the molar association constant KA. For all the electrolytes studied, Lambda0 increased almost linearly with decreasing density at densities above 2.0rhoc, while the opposite tendency was observed at lower densities. The relative contribution of the nonhydrodynamic effect on the translational friction coefficient zeta was estimated in terms of Deltazeta/zeta, where the residual friction coefficient Deltazeta is the difference between zeta and the Stokes friction coefficient zetaS. At densities above 2.0rhoc, Deltazeta/zeta increased with decreasing density though zeta and Deltazeta decrease, and the tendencies are common for all the ions studied. The density dependences of zeta and Deltazeta/zeta were explained well by the Hubbard-Onsager (HO) dielectric friction theory based on the sphere-in-continuum model. At densities below 2.0rhoc, however, the experimental results cannot be explained by the HO theory.

Role of alkali metal cation size in the energy and rate of electron transfer to solvent-separated 1:1 [(M+)(acceptor)] (M+ = Li+, Na+, K+) ion pairs

The effect of cation size on the rate and energy of electron transfer to [(M(+))(acceptor)] ion pairs is addressed by assigning key physicochemical properties (reactivity, relative energy, structure, and size) to an isoelectronic series of well-defined M(+)-acceptor pairs, M(+) = Li(+), Na(+), K(+). A 1e(-) acceptor anion, alpha-SiV(V)W(11)O(40)(5-) (1, a polyoxometalate of the Keggin structural class), was used in the 2e(-) oxidation of an organic electron donor, 3,3',5,5'-tetra-tert-butylbiphenyl-4,4'-diol (BPH(2)), to 3,3',5,5'-tetra-tert-butyldiphenoquinone (DPQ) in acetate-buffered 2:3 (v/v) H(2)O/t-BuOH at 60 degrees C (2 equiv of 1 are reduced by 1e(-) each to 1(red), alpha-SiV(IV)W(11)O(40)(6-)). Before an attempt was made to address the role of cation size, the mechanism and conditions necessary for kinetically well behaved electron transfer from BPH(2) to 1 were rigorously established by using GC-MS, (1)H, (7)Li, and (51)V NMR, and UV-vis spectroscopy. At constant [Li(+)] and [H(+)], the reaction rate is first order in [BPH(2)] and in [1] and zeroth order in [1(red)] and in [acetate] (base) and is independent of ionic strength, mu. The dependence of the reaction rate on [H(+)] is a function of the constant, K(a)1, for acid dissociation of BPH(2) to BPH(-) and H(+). Temperature dependence data provided activation parameters of DeltaH = 8.5 +/- 1.4 kcal mol(-1) and DeltaS = -39 +/- 5 cal mol(-1) K(-1). No evidence of preassociation between BPH(2) and 1 was observed by combined (1)H and (51)V NMR studies, while pH (pD)-dependent deuterium kinetic isotope data indicated that the O-H bond in BPH(2) remains intact during rate-limiting electron transfer from BPH(2) and 1. The formation of 1:1 ion pairs [(M(+))(SiVW(11)O(40)(5-))](4-) (M(+)1, M(+) = Li(+), Na(+), K(+)) was demonstrated, and the thermodynamic constants, K(M)(1), and rate constants, k(M)(1), associated with the formation and reactivity of each M(+)1 ion pair with BPH(2) were calculated by simultaneous nonlinear fitting of kinetic data (obtained by using all three cations) to an equation describing the rectangular hyperbolic functional dependence of k(obs) values on [M(+)]. Constants, K(M)(1)red, associated with the formation of 1:1 ion pairs between M(+) and 1(red) were obtained by using K(M)(1) values (from k(obs) data) to simultaneously fit reduction potential (E(1/2)) values (from cyclic voltammetry) of solutions of 1 containing varying concentrations of all three cations to a Nernstian equation describing the dependence of E(1/2) values on the ratio of thermodynamic constants K(M)(1) and K(M)(1)red. Formation constants, K(M)(1), and K(M)(1)red, and rate constants, k(M)(1), all increase with the size of M(+) in the order K(Li)(1) = 21 < K(Na)(1) = 54 < K(K)(1) = 65 M(-1), K(Li)(1)red = 130 < K(Na)(1)red = 570 < K(K)(1)red = 2000 M(-1), and k(Li)(1) = 0.065 < k(Na)(1) = 0.137 < k(K)(1) = 0.225 M(-1) s(-1). Changes in the chemical shifts of (7)Li NMR signals as functions of [Li(5)1] and [Li(6)1(red)] were used to establish that the complexes M(+)1 and M(+)1(red) exist as solvent-separated ion pairs. Finally, correlation between cation size and the rate and energy of electron transfer was established by consideration of K(M)(1), k(M)(1), and K(M)(1)red values along with the relative sizes of the three M(+)1 pairs (effective hydrodynamic radii, r(eff), obtained by single-potential step chronoamperometry). As M(+) increases in size, association constants, K(M)(1), become larger as smaller, more intimate solvent-separated ion pairs, M(+)1, possessing larger electron affinities (q/r), and associated with larger k(M)(1)() values, are formed. Moreover, as M(+)1 pairs are reduced to M(+)1(red) during electron transfer in the activated complexes, [BPH(2), M(+)1], contributions of ion pairing energy (proportional to -RT ln(K(M)(1)red/K(M)(1)) to the standard free energy change associated with electron transfer, DeltaG degrees (et), increase with cation size: -RT ln(K(M)(1)red/K(M)(1)) (in kcal mol(-1)) = -1.2 for Li(+), -1.5 for Na(+), and -2.3 for K(+).