Measurements of F-19 and H-1 nuclear spin-lattice relaxation times from aqueous solutions of PF6- and (H3C)(4)N+ containing small concentrations of nitroxide free radicals were made at applied magnetic field strengths ranging from 0.00025 to 7.05 T to directly determine the form of the frequency-dependent spectral densities that modulate relaxation. This magnetic relaxation dispersion (MRD) technique may provide detailed information concerning molecular dynamics over the time scale range from milliseconds to picoseconds. The MRD data compare well to a theory for translational diffusion of hard spheres, one that accounts for the intermolecular electrostatic potential between ionic solutes. Theoretically accessible parameters are extracted, and the treatment of the intermolecular potential as a reduction (increase) in the number of effective translational encounters between ions of like (unlike) charge is discussed. Represented by a mean field, the relatively long range Coulombic interaction does not impose spatial conditions on the diffusion equation through which the short-range magnetic dipole-dipole interactions are correlated. Calculated distances of closest approach are approximately 6.5 Angstrom and are consistent with the dimensions expected for a sterically impeded encounter between the nuclear spin probes and the nitroxide centered paramagnetic spin density. Comparison of the (H3C)(4)N+ and PF6- data provides a means of quantifying the Coulombic potential, which has a more dramatic effect on the F-19 relaxation of the polarizable PF6-.