# Solve the following

Question:

$108 \mathrm{~g}$ of silver (molar mass $108 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is deposited at cathode from $\mathrm{AgNO}_{3}(\mathrm{aq})$ solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at $273 \mathrm{~K}$ and 1 bar pressure from water by the same quantity of electricity is _______________ .

Solution:

(5.68)

No. of moles of silver deposited.

$=\frac{108}{108}=1 \mathrm{~mol}$

$\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag}$

$1 \mathrm{~F}$ charge is required to deposit 1 mole of $\mathrm{Ag}$

2 F charge deposit $\rightarrow \frac{1}{2}$ moles of oxygen

$1 \mathrm{~F}$ charge will deposit $\rightarrow \frac{1}{4}$ moles of oxygen

$\mathrm{V}_{\mathrm{O}_{2}}=\frac{n \mathrm{RT}}{\mathrm{P}}$

$=\frac{1}{4} \times \frac{0.08314 \mathrm{~L} \text { bar } \mathrm{K}^{-1} \mathrm{~mol}^{-1} \times 273 \mathrm{~K}}{1 \mathrm{bar}}$

$=\frac{1}{4} \times 22.7$

$\mathrm{V}_{\mathrm{O}_{2}}=5.675 \mathrm{~L}$