Question

The electrolysis of BiO⁺ produces pure bismuth. How long would it take to produce 10.0 g of Bi by the electrolysis of a BiO⁺ solution using a current of 25.0 A?

Short answer

Thetime needed to plate out Bi is 554 s.

Step-by-step solution

Calculating the moles of electron

The reduction reaction can be denoted as,

${\mathrm{BiO}}^{+}+2{\mathrm{H}}^{+}+3{\mathrm{e}}^{-}\to \mathrm{Bi}+{\mathrm{H}}_2\mathrm{O}$

The mole number of electrons can be denoted as,

$\begin{array}{rcl}\mathrm{Moles} \mathrm{of} \mathrm{electron}& =& (1 0 \mathrm{g} \mathrm{Bi})\left(\frac{1 \mathrm{mol} \mathrm{Bi}}{209 \mathrm{g} \mathrm{Bi}}\right)\left(\frac{3 \mathrm{mol}}{1 \mathrm{mol}}\right)\\ & =& 0.1435 \mathrm{mol}\end{array}$

The charge needed for the release of electrons are as follows,

$\begin{array}{rcl}\mathrm{Charge}& =& (0.1435\mathrm{mol})\left(\frac{96485 \mathrm{C}}{1 \mathrm{mol}}\right)\\ & =& 1.385\times {10}^4\mathrm{C}\end{array}$

Calculating the time required for plate out

The time required to plate out can be calculated as,

$\begin{array}{rcl}Time& =& (1.385\times {10}^{4}C)\left(\frac{1 s}{25 C}\right)\\ & =& 554 s\end{array}$