Question #45016

A half-cell is prepared by dissolving $0.055\text{ mol}$ of \ce{Na2CrO4} and $0.050\text{ mol}$ of \ce{CrCl3} in $1.0\text{ L}$ of a buffer solution at $298\text{ K}$. The buffer is formulated such that its pH is exactly equal to the pH of a $1.0 \times 10^{-8}\text{ M}$ \ce{HCl} aqueous solution.

Given: $\bullet$ $E^\circ_{\ce{Cr2O7^{2-}}/\ce{Cr^{3+}}} = 1.33\text{ V}$ $\bullet$ $K_{eq}$ for $2\ce{CrO4^{2-}} + 2\ce{H+} \rightleftharpoons \ce{Cr2O7^{2-}} + \ce{H2O}$ is $9.07 \times 10^{13}$ $\bullet$ $\frac{2.303 RT}{F} = 0.059\text{ V}$ at $298\text{ K}$ $\bullet$ $K_w = 1.0 \times 10^{-14}$ $\bullet$ $\sqrt{401} \approx 20.0$, $\log(1.05) \approx 0.02$

Calculate the reduction potential of this half-cell. (Assume the buffer capacity is sufficient to maintain the pH constant).