Question

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

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

Answer 1

Answer: 37

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