# An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current.

Question:

An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current. As per the following equation $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+14 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}$ The amount of $\mathrm{Cr}^{3+}$ obtained was $0.104 \mathrm{~g}$. The efficiency of the process (in \%) is (Take : $\mathrm{F}=96000 \mathrm{C}$, At. mass of chromium =52) ___________.

Solution:

(60)

Charge $(Q)=\mathrm{It}=2 \times 8 \times 60=960 \mathrm{C}$

$\Rightarrow \frac{960}{96000}=0.01 \mathrm{~F}$

$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+14 \mathrm{H}^{+}+6 e^{-} \longrightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}$

$0.01 \mathrm{~F}$ $\frac{1}{3} \times 0.01$ mole

Theoritical mass of $\mathrm{Cr}^{3+}=\frac{1}{3} \times \frac{960}{96000} \times 52=0.173 \mathrm{~g}$

So, efficiency $=\frac{\mathrm{W}_{\text {actual }}}{\mathrm{W}_{\text {Theoritical }}} \times 100=\frac{0.104}{0.173} \times 100=60 \%$