Question #44110

A solution is prepared by mixing $0.10\text{ moles}$ of $\ce{Fe^{3+}}$, $0.10\text{ moles}$ of $\ce{Fe^{2+}}$, and $1.30\text{ moles}$ of a diprotic ligand $\ce{H_2L}$ in $1.0\text{ L}$ of water at $298\text{ K}$. The solution is buffered at $\text{pH} = 2.0$. Given the standard reduction potential $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.77\text{ V}$. For the ligand $\ce{H_2L}$, the acid dissociation constants are $K_{a1} = 1.0 \times 10^{-2}$ and $K_{a2} = 1.0 \times 10^{-6}$. The formation constants for the metal complexes are $\beta_2 = 2.0 \times 10^{20}$ for $\ce{[FeL_2]^-}$ and $K_f = 1.0 \times 10^8$ for $\ce{[FeL]}$. Assuming that the complexes formed are exclusively $\ce{[FeL_2]^-}$ and $\ce{[FeL]}$, and that the buffer components do not interact with the metals, calculate the equilibrium reduction potential of the $\ce{Fe^{3+}/Fe^{2+}}$ couple in this solution.\n\n(Take $\frac{2.303 RT}{F} = 0.06\text{ V}$ and $\log 2 = 0.30$)