The cell, $\mathrm{Zn}\left|\mathrm{Zn}^{2+}(1 \mathrm{M}) \| \mathrm{Cu}^{2+}(1 \mathrm{M})\right|…

The cell, $\mathrm{Zn}\left|\mathrm{Zn}^{2+}(1 \mathrm{M}) \| \mathrm{Cu}^{2+}(1 \mathrm{M})\right| \mathrm{Cu}\left(\mathrm{E}_{\text {cell }}^0=1.10 \mathrm{~V}\right)$, was allowed to be completely discharged at $\mathrm{298~K}$. The relative concentration of $\mathrm{Zn}^{2+}$ to $\mathrm{Cu}^{2+}\left[\frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}\right]$ is
  1. antilog $(24.08)$
  2. $37.3$
  3. $10^{37.3}$
  4. $9.65 \times 10^4$

Solution

$\begin{aligned} & \mathrm{E}_{\mathrm{cell}}=\mathrm{E}_{\mathrm{cell}}^{\circ}-\frac{0.0591}{\mathrm{n}} \log \mathrm{Q} \\ & \text { Where } \mathrm{Q}=\frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]} \end{aligned}$ For complete discharge $\mathrm{E}_{\text {cell }}=0$ So $\mathrm{E}_{\text {cell }}^{\circ}=\frac{0.591}{2} \log \frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}$ $\Rightarrow\left|\frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}\right|=10^{37.3}$ Hence, (C) is correct.

Asked in: JEE Main 2007

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