Question #44759

A student sets up the following concentration cell at $T$ K to model localized electrochemical corrosion:

$\ce{Cu(s) | Cu+ (aq, 0.002 M) || Cu+ (aq, 0.2 M) | Cu(s)}$

The student assumes that $\ce{Cu+}$ is perfectly stable in aqueous solution and calculates the theoretical electromotive force of the cell as $E_{ideal}$. However, $\ce{Cu+}$ undergoes spontaneous disproportionation. The system is allowed to reach chemical equilibrium in both half-cells before any current is drawn. The actual measured electromotive force of the cell is $E_{real}$.

Given standard reduction potentials at $T$ K: $E^\circ_{\ce{Cu+/Cu}} = 0.52 \text{ V}$ and $E^\circ_{\ce{Cu^{2+}/Cu}} = 0.34 \text{ V}$.

Assume activity coefficients are unity and $\frac{2.303 RT}{F} = 0.06 \text{ V}$. Identify the correct set of values for $(E_{ideal}, E_{real}, \log_{10} K_{eq})$, where $K_{eq}$ is the equilibrium constant for the disproportionation of $\ce{Cu+}$.