For the reaction $2{\text{Ag}}^{+}+\text{Cu}\to 2\text{Ag}+{\text{Cu}}^{2+}$, the standard Gibbs free energy change is $-41.4\text{ kJ/mol}$ at $298\text{ K}$. Calculate the equilibrium constant for the reaction.

Solution

1. The relation is $\Delta G^0=-RT\ln K_{\text{eq}}$.
2. $-41400\text{ J/mol}=-(8.314\text{ J/K mol})\cdot (298\text{ K})\cdot \ln K_{\text{eq}}$.
3. $\ln K_{\text{eq}}=\frac{41400}{2477.57}\approx 16.7$.
4. $K_{\text{eq}}=e^{16.7}\approx 1.8\times 10^7$.
5. Rounding to the nearest order of magnitude, the answer is (A).