Question

The normal oxidation potential of a referred to the standard hydrogen electrode is $0.76volt$ and of copper is $-0.34volt$ at ${25}^{\circ }C$. When excess of zinc is added to solution of copper sulphate, the zinc displaces copper equilibrium is reached. What is the ratio of concentration $Z{n}^{2+}$ to $C{u}^{2+}$ ions at equilibrium?

Answer 1

The reaction is,
$Zn+CuS{O}_4\to Cu+ZnS{O}_4$
or $Zn+C{u}^{2+}\to Cu+Z{n}^{2+}$
$E_{cell}=E_{cell}^{\circ }-\frac{0.0591}{2}\log \frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}$
At equilibrium, $E_{cell}=0$
$E_{cell}^{\circ }=\frac{0.0591}{2}\log \frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}$
or $\log \frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}=\frac{2\times E_{cell}^{\circ }}{0.0591}$
$(E_{cell}^{\circ }=0.76+0.34=1.10volt)$
$=\frac{2\times 1.10}{0.0591}=37.225$
$\frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}=1.679\times {10}^{37}:1$.