Q21.120 CP - Chemistry: Molecular Nature Of Matter And Change

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?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 ($\text{F = 96485 C/mole}$)

Step 3: 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 –