Question

The standard reduction potential of $E _{ Bi ^{3+} / Bi }^{0} ; \& E _{ Cu ^{2+} / Cu }^{0}$ are $0.222 V \& 0.34 V$ respectively. A mixture of salt of $Bi ^{3+} \& Cu ^{2+}$ at unit concentration each is electrolysed at $25^{\circ} C$. To what value can $\left[ Cu ^{2+}\right]$ be brought down before bismuth starts to deposit during electrolysis?

• A. 0.266 M
• B. $10^{-4} M$
• C. $10^{4} M$
• D. $10^{8} M$

Answer 1

Answer: (B)

Though $Cu ^{2+}$ has higher $E _{\text {red }}^{0}$. Than $Bi ^{3+}$ but stile $Bi ^{3+}$ can be deposited if either the reduction potential of $Cu ^{2+}$ is lowered or reduction potential of $Bi ^{3+}$ is raised.

$Bi ^{2+}+3 e ^{-} \rightarrow Bi \,\,\,Cu ^{2+}+2 e ^{-} \rightarrow Cu$

$E _{red}=0.222-\frac{0.06}{3} \log \frac{1}{\left[ Bi ^{3+}\right]}$

$E _{ red }=+0.34-\frac{0.06}{2} \log \frac{1}{\left[ Cu ^{2+}\right]}$

$E _{ red }=0.222-\frac{0.06}{3} \log \left[ Bi ^{3+}\right]$

$E _{ red }=+0.34+\frac{0.06}{2} \log \left[ Cu ^{2+}\right]$

Since $\left( Cu ^{2+}\right)$ has to be brought down,

$0.222=+0.34+\frac{0.06}{2} \log \left[ Cu ^{2+}\right]$

$-\frac{0.118 \times 2}{0.06}=\log \left[ Cu ^{2+}\right]$

$-4=\log \left[ Cu ^{2+}\right]$

$\Rightarrow \left[ Cu ^{2+}\right]=10^{-4} M$