Question

Like any piece of apparatus, an electrolytic cell operates at less than$\text{100\%}$efficiency. A cell depositing$\text{Cu}$from a${\text{Cu}}^{\text{2 +}}$bath operates for$\text{10 h}$with an average current of$\text{5.8 A}$. If$\text{53.4 g}$of copper is deposited, at what efficiency is the cell operating?

Short answer

At $\text{77.66\%}$efficiency the cell is operating.

Step-by-step solution

Concept Introduction

An electrolytic cell is an electrochemical device that employs electrical energy to help a non-spontaneous redox reaction take place. Electrolytic cells are electrochemical cells that can be used to electrolyze a variety of substances.

A galvanic cell, or voltaic cell, is an electrochemical cell that converts the chemical energy of spontaneous redox reactions into electrical energy.

Information Provided

• The reaction is ${\text{Cu}}^{\text{2 +}}{\text{(aq) + 2e}}^{\text{-}}\rightleftharpoons \text{Cu(s)}$
• The mass of Cu deposited is$\text{53.4 g}$
• The Current is$\text{5.8A(A = C/s)}$
• Cell is operated for$\text{10h(10h}·\frac{\text{3600s}}{\text{1h}}\text{= 3.6}·{\text{10}}^{\text{4}}\text{s)}$
• Faraday constant: charge of of electrons ($\text{F = 96485 C/mole}$)

Efficiency of the Cell

First find the charge –

$$\begin{gathered} \text{Current =}\frac{\text{Charge}}{\text{Time}} \\ \text{Charge = Current}·\text{Time} \\ \text{= 5.8 C/s}·\text{3.6}·{\text{10}}^{\text{4}}\text{s} \\ \text{= 2.088}·{\text{10}}^{\text{5}}\text{C} \end{gathered}$$

The number of moles of electrons is –