Question

The cell, $Zn|Z{n}^{2+}\left(1M\right)||C{u}^{2+}\left(1M\right)|$ $Cu(E_{cell}^0=1.10V)$, was allowed to be completely discharged at 298 K. 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 :

• A. $9.65\times {10}^4$
• B. $antilog\left(24.08\right)$
• C. ${10}^{37.2}$
• D. ${10}^{37.3}$

Answer 1

The correct option is C ${10}^{37.2}$

The expression for the cell potential is $E_{cell}=E_{cell}^0-\frac{0.0592}{n}log\frac{\left[{Zn}^{2+}\right]}{\left[{Cu}^{2+}\right]}$.

When the cell is fully discharged, its cell potential drops to zero. Hence,

$0.0V=1.10V-\frac{0.0592}{2}log\frac{\left[{Zn}^{2+}\right]}{\left[{Cu}^{2+}\right]}$

$log\frac{\left[{Zn}^{2+}\right]}{\left[{Cu}^{2+}\right]}=\frac{1.10}{0.0296}=37.2$

$\frac{\left[{Zn}^{2+}\right]}{\left[{Cu}^{2+}\right]}={10}^{37.2}.$