Find the potentials of the following electrochemical cell:

\(Cd|C{d^{2 + }},M = 0.10||N{i^{2 + }},M = 0.50|Ni\)

We can use Nernst equation;

\({E_{cell}} = {E_{cell}} - \frac{{0.05915}}{n}.\log \frac{{product}}{{reac\tan t}}\)

Standard electrical potential,

\(C{d^{2 + }} + 2{e^ - } \to Cd,\) E = -0.403V

\(N{i^{2 + }} + 2{e^ - } \to Ni,\) E = -0.257V

Calculate the standard electrode potential,

\(\begin{aligned}{l}{E_{cell}} &= {E_{cathode}} - {E_{anode}}\\{E_{cell}} &= \left( { - 0.257V} \right) - \left( { - 0.403V} \right)\\{E_{cell}} &= - 0.146V\end{aligned}\)

We have reaction,

\(Cd + N{i^{2 + }}\left( {0.5M} \right) \to Ni + C{d^{2 + }}(0.1M)\)

We can see that\(N{i^{2 + }}\)is our reactant and\(C{d^{2 + }}\)is our product,

\(\begin{aligned}{l}{E_{cell}} &= {E_{cell}} - \frac{{0.05915}}{n}.\log \frac{{product}}{{reac\tan t}}\\{E_{cell}} &= - 0.146V - \frac{{0.05915}}{2}.\log \frac{{(0.1M)}}{{(0.5M)}}\\{E_{cell}} &= 0.167V\end{aligned}\)