Question

The cell, $Zn/Zn^{2 +}\left(\right.1M\left.\right)\left|\right.\left|\right.Cu^{2 +}\left(\right.1M\left.\right)/Cu\left(\right.E_{c e l l}^{0}=1.10V\left.\right)$ was allowed to be completely discharged at 298K. The relative concentration of $Zn^{2 +}$ to $Cu^{2 +}\left(\frac{\left[Z n^{2 +}\right]}{\left[C u^{2 +}\right]}\right)$ is $10^{x}$ . The value of $x$ is:

( $Take\frac{2.303 R T}{F}=0.059$ Round off your answer up to one decimal)

Answer 1

$\mathrm{E}_{\text {cell }}=0 ; \text { when cell is completely discharged } $ $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^0-\frac{0.059}{2} \log \left[\frac{\left.\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}\right] $
$0=1.1-\frac{0.059}{2} \log \left[\frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}\right] $
$ \log \left[\frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}\right]=\frac{2 \times 1.1}{0.059}=37.3 $
$\frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]}=10^{37.3}=10^{\mathrm{x}} $
$ \therefore \mathrm{x}=37.3$