Question #44513

A redox half-cell is prepared at $298\text{ K}$ by mixing $50\text{ mL}$ of $0.40\text{ M } \ce{Fe_2(SO_4)_3}$ and $50\text{ mL}$ of $0.10\text{ M } \ce{FeSO_4}$. In this highly concentrated electrolyte medium, the solution exhibits significant non-ideal behavior. The single-ion activity coefficients are determined to be $\gamma_{\ce{Fe^{3+}}} = 0.01$ and $\gamma_{\ce{Fe^{2+}}} = 0.10$. Given the standard reduction potential $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.770\text{ V}$ and $\frac{2.303 RT}{F} = 0.059\text{ V}$, calculate the actual reduction potential of this half-cell. (Given: $\log 2 = 0.301$, $\log 5 = 0.699$)