Question

The cell, $Zn\left|Zn^{2+}\left(1M\right)\right|\left|Cu^{2+}\left(1M\right)\right|Cu\left(E^{0}_{cell}=1.10V\right), $ was allowed to be completely discharged at $298 \,K$. The relative concentration of $Zn^{2+} to Cu^{2+}\left[\frac{\left[Zn^{2+}\right]}{\left[Cu^{2+}\right]}\right]$ is

• A. antilog $(24.08)$
• B. $37.3$
• C. $10^{37.3}$
• D. $9.65 × 10^4$

Answer 1

Answer: (C)

$E_{cell}=E^{o}_{cell}-\frac{0.0591}{n}log\,Q$
Where $Q =\frac{\left[Zn^{2+}\right]}{\left[Cu^{2+}\right]}$
For complete discharge $E_{cell}=0$
So $E^{o}_{cell}=\frac{0.591}{2}log \frac{\left[Zn^{2+}\right]}{\left[Cu^{2+}\right]}$
$\Rightarrow \left|\frac{\left[Zn^{2+}\right]}{\left[Cu^{2+}\right]}\right|=10^{37\,.3}$