Question #44733

A $1.0 \text{ L}$ acidic aqueous solution contains \ce{Sn^{4+}} and \ce{Sn^{2+}} ions. The initial concentration of \ce{Sn^{2+}} is equal to the hydrogen ion concentration of a $0.10 \text{ M}$ aqueous solution of a monobasic weak acid \ce{HA}. For \ce{HA}, the molar conductivity is $3.90 \text{ S cm}^2 \text{ mol}^{-1}$ and the limiting molar conductivity is $390 \text{ S cm}^2 \text{ mol}^{-1}$ at $298 \text{ K}$.

The initial reduction potential of the \ce{Sn^{4+}/Sn^{2+}} couple in the solution is $E^\circ_{\ce{Sn^{4+}/Sn^{2+}}} + 0.0295 \text{ V}$.

A constant current of $1.93 \text{ A}$ is passed through the solution using inert electrodes to selectively reduce \ce{Sn^{4+}} to \ce{Sn^{2+}}$. Assuming no change in volume, what is the time required for the reduction potential of the couple to become$E^\circ_{\ce{Sn^{4+}/Sn^{2+}}} - 0.0295 \text{ V}$?

(Given: $\frac{2.303 RT}{F} = 0.059 \text{ V}$ at $298 \text{ K}$, $1 \text{ F} = 96500 \text{ C mol}^{-1}$)