Ion pairing in solutions of sodium tetraphenylborate

Conductance data are presented for sodium tetraphenylborate (NaBPh₄) in three solvent systems: water-dimethyl sulfoxide, water-acetone, and acetone-dimethyl sulfoxide. These and other data from the literature were first analyzed by the three-parameter equation Λ^′=Λ₀+Aτ²+Bτ³, where $$Lambda prime = [Lambda (obs.) + beta _0 c^{1/2} (1 + 0.5tau ln 2tau )]/[1 - alpha _0 c^{1/2} + (tau ^2 /3) ln 2tau ]$$ Here, β₀ is the Onsager electrophoresis coefficient, α_oc^1/2 the limiting relaxation term, τ=e²κ/2DkT, κ^?1 is the Debye-Hückel distance, andA andB are empirical constants. The fact that three parameters are necessary to reproduce the data shows that ion pairing is not negligible for NaBPh₄ solutions despite the fact that the conductance curve lies above the limiting tangent even in ethanol (D=24.30). The quantity Λ_o is the limit of Λ^′ at zero concentration; the sum Aτ²+Bτ³ represents the part of the observed conductance from which the pairing constantK _Λ and the distance parameterR are derived. Conductance experiments should therefore be designed so that this sum is as large as possible, subject to the restriction that the highest concentration should not exceed 10^?7D³ (where the effects of short-range three-ion interactions are no longer negligible). Pairing constants for NaBPh₄ in the various solvents range from 4.6 in water to 70 in a mixture of Me₂SO and Me₂CO with dielectric constantD=23.80. The dependence ofE _s (the difference in free energy between solvent-separated pairs and contact pairs) on solvent composition is different for aprotic solvents and for mixtures containing water; for the latter, theE _s/kT vs. l/D plot shows a maximum while for the former the curve is monotone descending. The Walden produces (Λ_oη=limiting conductance times viscosity) plotted againstD ^?1 follow the same pattern.