Nuclear Magnetic Resonance Study of the Proton Transfer in Water

Abstract

Measurements of the nuclear relaxation in water are reported. The transverse relaxation rate (1/T₂) of the proton resonance is pH dependent. The effect is shown to be due to a spin‐spin splitting of the proton resonance by O¹⁷ (spin 5/2), which is only partially averaged out by proton exchange. The increase of relaxation rate is observable in natural water (0.037% O¹⁷), and becomes very appreciable in water enriched in O¹⁷. Additional information can be obtained by measuring relaxation rates in the presence of an rf field H₁, using a method due to Solomon. A study of the width of the O¹⁷ resonance as a function of pH is in quantitative agreement with the results of the proton resonance. The observations provide a direct determination of the rate constants of the exchange reactions: $${\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_3{\mathrm{O}}^{+}\to {\displaystyle {lim}_{k_1}}{\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{H}}_2\mathrm{O}\hspace{0.17em}\mathrm{and}\hspace{0.17em}{\mathrm{H}}_2\mathrm{O}+{\mathrm{HO}}^{-}\to {\displaystyle {lim}_{k_2}}{\mathrm{HO}}^{-}+{\mathrm{H}}_2\mathrm{O}.$$ It is found that k₁=(10.6±4)×10⁹ liter mole⁻¹ sec⁻¹ and k₂=(3.8±1.5)×10⁹ liter mole⁻¹ sec⁻¹. The spin‐spin interaction between H and O¹⁷ in water is determined as 92±15 cps. In the Appendices, theoretical equations for the exchange contribution to the relaxation rate are derived.