Question #45041

Consider the disproportionation of a metastable oxyacid $\ce{H_2MO_3(aq)}$ into $\ce{MO_4^{2-}(aq)}$ and solid metal $\ce{M(s)}$ in an aqueous buffer at 298 K.

The standard reduction potentials are given as: $\ce{MO_4^{2-}(aq) + 4H+(aq) + 2e- <=> H_2MO_3(aq) + H_2O(l)} \quad E^\circ = 1.15 \text{ V}$ $\ce{H_2MO_3(aq) + 4H+(aq) + 4e- <=> M(s) + 3H_2O(l)} \quad E^\circ = 1.445 \text{ V}$

Calculate the value of $\log_{10} K'$ for the disproportionation reaction at equilibrium in a buffer solution of $\text{pH} = 2.0$, where the conditional equilibrium constant is defined as $K' = \frac{[\ce{MO_4^{2-}}]^2}{[\ce{H_2MO_3}]^3}$.

(Given: $\frac{2.303 RT}{F} = 0.059 \text{ V}$ at 298 K)