Chapter 17, Problem 90AP

Consider a galvanic cell for which the anode reaction is
3 $\text{Pb}\left(s\right)\to {\text{Pb}}^{2+}\left(1.0\times {10}^{-2}\text{M}\right)+2e^{-}$

and the cathode reaction is
${\text{VO}}^{2+}\left(0.10\text{M}\right)+2{\text{H}}_{\text{3}}{\text{O}}^{+}\left(0.10\text{M}\right)+e^{-}\to {\text{V}}^{3+}\left(1.0\times {10}^{-5}\text{M}\right)+3{\text{H}}_{\text{2}}\text{O}\left(\mathcal{l}\right)$

The measured cell potential is 0.640 V.
Calculate $E°$ for the ${\text{VO}}^{2+}|V^{3+}$ half-reaction, using $E°\left({\text{Pb}}^{2+}|\text{Pb}\right)$ from Appendix E.

Calculate the equilibrium constant (K) at 25°C for thereaction

$\text{Pb}\left(s\right)+2{\text{VO}}^{2+}\left(aq\right)+4{\text{H}}_{\text{3}}{\text{O}}^{+}\left(aq\right)\underset{}{\overset{}{\rightleftarrows }}{\text{Pb}}^{2+}\left(aq\right)+2{\text{V}}^{3+}\left(aq\right)+6{\text{H}}_{\text{2}}\text{O}\left(\mathcal{l}\right)$