Question #44790

An electrolytic cell is used for the deposition of copper from an aqueous \ce{CuSO4} solution. The cell contains a porous barrier separating two \ce{HCl} solutions with concentrations $C_1 = 10^{-3} \text{ mol cm}^{-3}$ and $C_2 = 1 \text{ mol m}^{-3}$, which creates a Liquid Junction Potential ($E_{LJP}$). The transport number of \ce{H+} is $0.80$.

The applied potential across the cell is $E_{app} = 1.08 \text{ V}$. The $E_{LJP}$ acts as an opposing potential, reducing the effective current efficiency for copper deposition to $\eta = \left(1 - \frac{E_{LJP}}{E_{app}}\right) \times 100\%$.

A total charge of $1.93 \times 10^7 \text{ C}$ per cubic meter of the cathode compartment volume is passed. The volume of the cathode compartment is $10 \text{ L}$. Assuming ideal behavior, calculate the mass of copper deposited at the cathode.

(Given: $\frac{2.303 RT}{F} = 0.06 \text{ V}$ at $298 \text{ K}$, $F = 96500 \text{ C mol}^{-1}$, Atomic mass of Cu = $63.5 \text{ g mol}^{-1}$. The LJP for a single electrolyte is given by $E_{LJP} = (t_+ - t_-) \frac{2.303 RT}{F} \log \frac{C_1}{C_2}$)