Question #44737

Consider the following electrochemical cell operating in a mixed aqueous-organic solvent at $298 \text{ K}$:

$\ce{Zn(s) | ZnSO4 (0.1 M) || CuSO4 (0.1 M) | Cu(s)}$

Due to the lower dielectric constant of the solvent, significant ion-pairing occurs, preventing complete dissociation. The observed Van't Hoff factors ($i$) for the $0.1 \text{ M}$ $\ce{ZnSO4}$ and $0.1 \text{ M}$ $\ce{CuSO4}$ solutions are $1.40$ and $1.04$, respectively.

Given standard reduction potentials: $E^\circ_{\ce{Zn^{2+}/Zn}} = -0.76 \text{ V}$ and $E^\circ_{\ce{Cu^{2+}/Cu}} = +0.34 \text{ V}$.

Assume the activity coefficients of the free, un-paired ions are unity, and that ion-pairing is the sole reason for the deviation of $i$ from the ideal stoichiometric value. (Take $\frac{2.303 RT}{F} = 0.06 \text{ V}$)

What is the cell potential, $E_{\text{cell}}$?