Ion Pairing of Quaternary Salts in Solvent Mixtures

Conductances at 25.00°C are reported for the following systems: tetrabutylammonium bromide in dimethyl sulfoxide-acetone mixtures (Bu4NBr in Me2SO–Me2CO); tetraphenylphosphonium bromide (Ph4PBr) in water Me2SO, Me2CO, and in the mixtures H2O–Me2SO, Me2SO–Me2CO and Me2CO–H2O; Ph4PCl in Me2SO, Me2CO, H2O–Me2SO, and Me2SO–Me2CO; and tetrapropylammonium bromide (Pr4NBr) in Me2SO and Me2CO. The data were analyzed using the Fuoss 1978 equation which is based on the coupled equilibria: (unpaired ions)(solvent-separated pairs)(contact pairs). The conductimetric pairing constantK A =K R(l+K s) is the product of two factors:K R, which describes the first (diffusion controlled) equilibrium andK s=exp(–E s/kT), which describes the second (system-specific) equilibrium. Ions with overlapping cospheres (of diameterR) are defined as paired: their center-to-center distancer lies in the rangearR; contact pairs (r=a) are ions which have one ion of opposite charge as a nearest neighbor, all other nearest and next nearest neighbors being solvent molecules. The quantityE s is the difference in free energy between the states defined byr=R andr=a. For the Me2SO–Me2CO systems,E s is positive for solutions in Me2SO and decreases through zero to negative values as the fraction of the less polarizable acetone increases. For solutions in waterE s is also positive. On addition of Me2SO or Me2CO,E s initially increases, goes through a maximum, and then decreases to negative values as the fraction of the less polarizable component increases. The decrease is an electrostatic effect, common to all the systems. The initial increase inE s appears when the small water molecules surrounding solvent-separated pairs are replaced by organic molecules which have greater volumes than water.