Question

In a galvanic cell, one half-cell consists of gaseous chlorine bubbled over a platinum electrode at a pressure of $\mathbf{\text{1.00atm}}$into a$\mathbf{\text{1.00atm}}$solution of. The second half-cell has a strip of solid gallium immersed in a$\mathbf{\text{1.00MGa}}{\left({\text{NO}}_{\text{3}}\right)}_{\mathbf{\text{3}}}$solution. The initial cell potential is measured to be$\mathbf{\text{1.918V}}$at${\mathbf{\text{25}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$, and as the cell operates, the concentration of chloride ion is observed to increase.

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

(b) Calculate the standard reduction potential of a${\mathbf{\text{Ga}}}^{\mathbf{\text{3+}}}\mathbf{\mid }\mathbf{\text{Ga}}$half-cell. Consult Appendix E for the reduction potential of the${\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}\mathbf{\mid }{\mathbf{\text{Cl}}}^{\mathbf{\text{-}}}$ electrode.

Short answer

The cathode half -cell reaction for the reduction of${\text{Cl}}_{\text{2}}$

${\text{Cl}}_{\text{2}}{\text{(g)+2e}}^{\text{-}}\to {\text{2Cl}}^{\text{-}}\text{(aq)}$

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

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

(b) The standard reduction potential of${\text{Ga}}^{\text{3+}}\mid \text{Ga}$ = $\text{-0.558V}$.

Step-by-step solution

Definition of cathode and anode cell.

The flow of current defines both of them.

Cathode cell: The current departs a polarised electrical device through a cathode, which is an electrode.

Anode cell: A current enters a polarised electrical device through an anode, which is an electrode.

Finding balanced equations for the half-reactions at the anode and the cathode.

The cathode half -cell reaction for the reduction of${\text{Cl}}_{\text{2}}$

${\text{Cl}}_{\text{2}}{\text{(g)+2e}}^{\text{-}}\to {\text{2Cl}}^{\text{-}}\text{(aq)}$

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

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

Calculation of the standard reduction potential of a  half-cell.

Consider the given information and find the standard reduction potential,

$\begin{array}{c}{\text{E}}_{\text{cell}}^{\text{à}}\text{=1.918V}\\ {\text{E}}_{\text{cathode}}^{\text{o}}\text{=1.36V}\\ {\text{E}}_{\text{cell}}^{\text{o}}{\text{=E}}_{\text{cathode}}^{\text{]}}{\text{-E}}_{\text{anode}}^{\text{o}}\\ {\text{E}}_{\text{anode}}^{\text{o}}{\text{=E}}_{\text{eathode}}^{\text{o}}{\text{-E}}_{\text{cell}}^{\text{o}}\\ {\text{E}}_{\text{anode}}^{\text{o}}\text{=1.36V-1.918V=-0.558V}\end{array}$

Thus, the standard reduction potential of${\text{Ga}}^{\text{3+}}\mid \text{Ga}$ = $\text{-0.558V}$.