Question

The standard reduction potential of $E_{B{i}^{3+}/Bi}^0;\&E_{C{u}^{2+}/Cu}^0$ are $0.222V\&0.34V$ respectively. A mixture of salt of $B{i}^{3+}\&C{u}^{2+}$ at unit concentration each is electrolysed at $25^{\circ }C$. To what value can $\left[C{u}^{2+}\right]$ 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 $C{u}^{2+}$ has higher $E_{\text{red }}^0$. Than $B{i}^{3+}$ but stile $B{i}^{3+}$ can be deposited if either the reduction potential of $C{u}^{2+}$ is lowered or reduction potential of $B{i}^{3+}$ is raised.

$B{i}^{2+}+3e^{-}\to BiC{u}^{2+}+2e^{-}\to Cu$

$E_{red}=0.222-\frac{0.06}{3}\log \frac{1}{\left[B{i}^{3+}\right]}$

$E_{red}=+0.34-\frac{0.06}{2}\log \frac{1}{\left[C{u}^{2+}\right]}$

$E_{red}=0.222-\frac{0.06}{3}\log \left[B{i}^{3+}\right]$

$E_{red}=+0.34+\frac{0.06}{2}\log \left[C{u}^{2+}\right]$

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

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

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

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

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