Question

In a galvanic cell, one half-cell consists of a zinc strip dipped into a $\mathbf{\text{1.00M}}$solution of$\mathbf{\text{Zn}}{\left({\text{NO}}_{\text{3}}\right)}_{\mathbf{\text{2}}}$. In the second half-cell, solid indium adsorbed on graphite is in contact with a$\mathbf{\text{1.00M}}$solution of$\mathbf{\text{In}}{\left({\text{NO}}_{\text{3}}\right)}_{\mathbf{\text{3}}}$. Indium is observed to plate out as the galvanic cell operates, and the initial cell potential is measured to be$\mathbf{\text{0.425V}}$at${\mathbf{\text{25}}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$.

(a) Write balanced equations for the half-reactions at the anode and the cathode.

(b) Calculate the standard reduction potential of an${\mathbf{\text{In}}}^{\mathbf{\text{3+}}}\mathbf{\text{|In}}$half-cell. Consult Appendix E for the reduction potential of the${\mathbf{\text{Zn}}}^{\mathbf{\text{2+}}}\mathbf{\text{|Zn}}$electrode.

Short answer

1. Balanced equation for the half-cell reaction at the anode –

$\text{Zn(s)}\to {\text{Zn}}^{\text{2+}}{\text{(aq)+2e}}^{\text{-}}$

Balanced equation for the half-cell reaction at the cathode –

${\text{In}}^{\text{3+}}{\text{(aq)+3e}}^{\text{-}}\to \text{In(s)}$

1. The standard reduction potential of${\text{In}}^{\text{3+}}\text{|In}$ half-cell is ${\text{E}}_{\text{cathode}}^{\text{°}}\text{=-0.338V}$.

Step-by-step solution

Concept Introduction

An oxidation process in which electrons are lost or a reduction reaction in which electrons are gained is known as a half-cell reaction. The processes take place in an electrochemical cell, where electrons are lost at the anode via oxidation and consumed at the cathode via reduction.

Balanced Equations for cathode and anode

The balanced cathode half-cell reaction for the reduction of${\text{In}}^{\text{3+}}$–

${\text{In}}^{\text{3+}}{\text{(aq)+3e}}^{\text{-}}\to \text{In(s)}$

The anode half-cell reaction for the oxidation of$\text{Zn}$–

$\text{Zn(s)}\to {\text{Zn}}^{\text{2+}}{\text{(aq)+2e}}^{\text{-}}$

Therefore, the reactions of anode and cathode are $\text{Zn(s)}\to {\text{Zn}}^{\text{2+}}{\text{(aq)+2e}}^{\text{-}}$and ${\text{In}}^{\text{3+}}{\text{(aq)+3e}}^{\text{-}}\to \text{In(s)}$respectively.

Calculation for Standard Reduction Potential

The formula for Cell Potential (cathode) is –

$\begin{array}{c}{\text{E}}_{\text{cell}}^{\text{°}}{\text{=E}}_{\text{cathode}}^{\text{°}}{\text{-E}}_{\text{anode}}^{\text{°}}\\ {\text{E}}_{\text{cathode}}^{\text{°}}{\text{=E}}_{\text{cell}}^{\text{°}}{\text{+E}}_{\text{anode}}^{\text{°}}\mathrm{...}\left(1\right)\end{array}$

The cell potential is:${\text{E}}_{\text{cell}}^{\text{°}}\text{=-0.425V}$.

The cell potential for Anode is:${\text{E}}_{\text{anode}}^{\text{°}}\text{=-0.763V}$.

Plugging in the values in Equation –

$\begin{array}{c}{\text{E}}_{\text{cathode}}^{\text{°}}\text{=-0.425+(-0.763V)}\\ \text{=-0.338V}\end{array}$

Therefore, the value for the standard reduction potential is obtained as ${\text{E}}_{\text{cathode}}^{\text{°}}\text{=-0.338V}$.