Kinetic studies on the vanadium(II)–titanium(IV) and titanium(III)–vanadium(IV) redox reactions in aqueous solutions

Abstract

The one-equivalent reduction of titanium(IV) by vanadium(II) ions has been studied at temperatures in the range 20–40 °C by the stopped-flow method and shown to be independent of hydrogen-ion concentration [H⁺]= 0·35–1·85M, I= 2·0M(LiClO₄). The rate law is as in (i). –d[V^II]/dt= d[Ti^III]/dt=k₂₄[V^II][Ti^IV](i) At 25 °C, k₂₄= 1·95 l mol^–1 s^–1 and activation parameters, ΔH^‡= 12·7 ± 0·4 kcal mol^–1and ΔS^‡=–14·6 ± 1·3 cal K^–1 mol^–1, are consistent with a process which is vanadium(II)-substitution controlled. The one-equivalent reduction of vanadium(IV) by titanium(III) ions has also been studied by the stopped-flow method at temperatures 15–45 °C. Since titanium(III) stock solutions were made up in aqueous HCl, it was necessary to investigate the effect of chloride ions on the rate of the reaction. Data obtained at ionic strength I= 0·5M(LiClO₄) fit the rate law (ii), where, at 25 °C, K_a= 0·34 l mol^–1 s^–1, K_b= 0·037 s^–1, and K_c= 0·72 l² mol^–2 s^–1. –d[V^IV]/dt=K₃₄[Ti^III][V^IV]=(k_a+K_b[H⁺]^–1+K_c[Cl^–])[Ti^III][V^IV](ii) Activation parameters for all the three paths in equation (ii) have been determined.