17O nuclear magnetic resonance study of the rotational motion of the sulphate ion in aqueous solution

Abstract

Linewidths of ¹⁷O n.m.r. spectra of the sulphate ion in D₂O solutions have been measured at temperatures ranging from 4 to 70 °C. The dependence of the linewidth on concentration has been investigated in various alkali-metal and tetra-alkylammonium sulphate solutions. The electric-field gradient at the oxygen site of an isolated sulphate ion has been calculated using the ab initio molecular-orbital method. This gave a field gradient of 1.52 atomic unit for the component along the O—S bond. The field gradient at the sulphate oxygen caused by a nearby single positive charge has also been calculated. This calculation showed that the fluctuation of the field gradient caused by the movement of the surrounding ions and water molecules is of secondary importance in its effect on the ¹⁷O linewidth of the sulphate ion in aqueous solutions. The rotational correlation times of the sulphate ion, τ, in solution have been obtained from the measured linewidths and the calculated field gradient (1.52 a.u.). A plot of the rotational correlation time at infinite dilution, τ(0), against the ratio of viscosity to temperature (η/T) curved downward at low temperatures. τ(0) values at various temperatures are well represented by the Arrhenius relation with an activation energy of 13 kJ mol^–1 for rotation of the sulphate ion. The rotational correlation time of the sulphate ion increased with increasing salt concentration and showed a good correlation with the decrease in mobility of water molecules in the hydration sphere of the cation contained in the solution.