Question #44775

An iron pipeline is exposed to a corrosive aqueous medium at $298\text{ K}$. The medium is buffered at $\text{pH} = 8.0$ and contains a total dissolved Cr(VI) concentration of $0.1\text{ M}$ (i.e., $[\ce{CrO4^{2-}}] + 2[\ce{Cr2O7^{2-}}] = 0.1\text{ M}$). The concentration of $\ce{Cr^{3+}}$ is $10^{-2}\text{ M}$ and $\ce{Fe^{2+}}$ is $10^{-3}\text{ M}$.

Given the following standard reduction potentials and equilibrium constant: $E^\circ_{\ce{Cr2O7^{2-}/Cr^{3+}}} = +1.33\text{ V}$ $E^\circ_{\ce{Fe^{2+}/Fe}} = -0.44\text{ V}$ $\ce{Cr2O7^{2-}(aq) + H2O(l) \rightleftharpoons 2CrO4^{2-}(aq) + 2H+(aq)}$, $K_{eq} = 10^{-14}$

Assume $\frac{2.303 RT}{F} = 0.06\text{ V}$.

Calculate the cell potential ($E_{cell}$) for the oxidation of iron by the Cr(VI) species in this medium.