Electrochemistry 1 Question 39
38. Chromium metal can be plated out from an acidic solution containing $\mathrm{CrO}_{3}$ according to the following equation.
$$ \mathrm{CrO}{3}(a q)+6 \mathrm{H}^{+}(a q)+6 e^{-} \longrightarrow \mathrm{Cr}(s)+3 \mathrm{H}{2} \mathrm{O} $$
Calculate (i) How many grams of chromium will be plated out by $24,000 \mathrm{C}$ and (ii) How long will it take to plate out $1.5 \mathrm{~g}$ of chromium by using 12.5 A current?
(1993, 2M)
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Solution:
- Molar mass of $\mathrm{Cr}=52 \mathrm{~g}$
Equivalent mass of $\mathrm{Cr}=\frac{52}{6} \mathrm{~g}$
(i) Mass of Cr deposited on passing 24000 Coulombs
$$ =\frac{24000}{96500} \times \frac{52}{6} \mathrm{~g}=2.15 \mathrm{~g} $$
(ii) Number of gram equivalent of $\mathrm{Cr}=\frac{1.5}{52} \times 6=\frac{9}{52}$
$\Rightarrow$ Coulombs required for $1.5 \mathrm{~g} \mathrm{Cr}=\frac{9}{52} \times 96500=I t$
$$ \Rightarrow \quad t=\frac{9 \times 96500}{52 \times 12.5} \mathrm{~s}=22.27 \mathrm{~min} $$
