Question #44079

A localized corrosion cell forms on a structural iron beam exposed to an aerated aqueous solution of $0.1\text{ M } AlCl_3$ at $298\text{ K}$. The anodic process involves the oxidation of $Fe(s)$ to $Fe^{2+}(aq)$, while the cathodic process is the reduction of $O_2(g)$ to $OH^-(aq)$. Given the standard reduction potentials: $E^\circ_{Fe^{2+}/Fe} = -0.44\text{ V}$ and $E^\circ_{O_2/OH^-} = +0.40\text{ V}$. The first hydrolysis constant ($K_h$) of $[Al(H_2O)_6]^{3+}$ is $1.0 \times 10^{-5}$. Assume the partial pressure of $O_2(g)$ is $1\text{ bar}$, the local concentration of $Fe^{2+}$ is $1.0 \times 10^{-2}\text{ M}$, and $K_w = 1.0 \times 10^{-14}$. Calculate the operating cell potential ($E_{cell}$) of this corrosion cell. (Take $\frac{2.303 RT}{F} = 0.06\text{ V}$ at $298\text{ K}$).