Question #44451

Consider the following redox equilibrium involving generic metal ions at $298\text{ K}$: $\ce{M^{3+} + N^{+} <=> M^{2+} + N^{2+}}$ In an aqueous medium (dielectric constant $\epsilon_r = 80$), the standard cell potential for this reaction is $E^\circ_{\text{aq}} = -0.10\text{ V}$. The solvent is then replaced with an organic solvent (dielectric constant $\epsilon_r = 20$). Assume that the standard Gibbs free energy of the reaction in the gas phase remains unchanged, and the solvation energy is governed entirely by the Born solvation model.

Given: All ions are perfectly spherical with an identical effective ionic radius $r$. The Born constant for these ions is $\frac{N_A e^2}{8 \pi \epsilon_0 r F} = 4.0\text{ V}$.

Determine the new standard cell potential $E^\circ_{\text{org}}$ in the organic solvent and the spontaneous direction of the reaction under standard conditions.