Find the observed EMF of the cell \(\mathrm{Cd}\left|\mathrm{Cd}^{2+}(0.01 \mathrm{M}) \| \mathrm{Cd}^{2+}(0…
Find the observed EMF of the cell \(\mathrm{Cd}\left|\mathrm{Cd}^{2+}(0.01 \mathrm{M}) \| \mathrm{Cd}^{2+}(0.01 \mathrm{M})\right| \mathrm{Cd}\) under conditions, internal resistance of \(4 \Omega\) and producing a current of \(0.15 \mathrm{~A}\).
(Given, \(E^{\circ} \mathrm{Cu}^{2+} / \mathrm{Cu}=0.35 \mathrm{~V}\)
and \(\quad E_{\mathrm{Cd}^{2+} / \mathrm{Cd}}^{\circ}=-0.4 \mathrm{~V}\) )
\(0.75 \mathrm{~V}\)
\(0.15 \mathrm{~V}\)
\(0.6 \mathrm{~V}\)
\(0.9 \mathrm{~V}\)
Solution
The cell representation is
\(\mathrm{Cd} / \mathrm{Cd}^{2+}(0.01 \mathrm{M}) \| \mathrm{Cu}^{2+}(0.01 \mathrm{M}) \mid \mathrm{Cu}\)
Note In the statement of the question, this portion is written as
\({ }^" \mathrm{Cd}^{2+}(0.01 \mathrm{M}) \mid \mathrm{Cd}\) " which is wrong.
The cell reaction is
\(\begin{gathered}
\mathrm{Cd}(s)+\underset{(0.01 \mathrm{M})}{\mathrm{Cu}^{2+}} \longrightarrow \underset{(0.01 \mathrm{M})}{\mathrm{Cd}^{2+}}+\mathrm{Cu}(s) \\
Q=\frac{\left[\mathrm{Cd}^{2+}\right][\mathrm{Cu}]}{[\mathrm{Cd}]\left[\mathrm{Cu}^{2+}\right]}=\frac{0.01 \times 1}{1 \times 0.01}=1
\end{gathered}\)
\(\begin{aligned}
E_{\text {cell }} & =\left(E_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}-E_{\mathrm{Cd}^{2+} / \mathrm{Cd}}^{\circ}\right)-\frac{0.0591}{2} \log Q \\
& =[0.35-(-0.40)]-0 \quad[\because \log Q=\log \mathrm{l}=0] \\
& =0.75 \mathrm{~V} \\
\Rightarrow E_{\text {cell }}^{\text {obscrved }} & =E_{\text {intemal }}-E_{\text {extemal }} \\
& =0.75-(\text { resistance } \times \text { current }) \\
& =0.75-(4 \times 0.15)=(0.75-0.60) \mathrm{V} \\
& =0.15 \mathrm{~V}
\end{aligned}\)