The drain cleaner, Drainex contains small bits of aluminium which react with caustic soda to produce dihydrogen. What volume of dihydrogen at $20^{\circ} C$ and one bar will be released when $0.15 g$ of aluminium reacts?

204 m L

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200 m L

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203 m L

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400 m L

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Solution

The correct option is D $203 m L$
The reaction between aluminium and caustic soda is :

$2 A l 2 \times 27 = 54 g + 2 N a O H + 2 H_{2} O \to 2 N a A l O_{2} + 3 H_{2} 3 \times 22.4 L a t S T P$

$∴ 54 g$ of $A l$ produces $H_{2}$ at $S T P = 3 \times 22.4 L$

$0.15 g$ of $A l$ will produce $H_{2}$ at $S T P$

$= \frac{3 \times 22.4}{54} \times 0.15 = 0.186 L$

At STP Given conditions
$P_{1} = 1 a t m$ $P_{2} = 1 b a r = 0.987 a t m$
$V_{1} = 0.186 L$ $V_{2} = ?$
$T_{1} = 273 K$ $T_{2} = 273 + 20 = 293 K$

Applying ideal gas equation,

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

$\frac{1 \times 0.1867}{273} = \frac{0.987 \times V_{2}}{293}$

$V_{2} = \frac{293}{0.987} \times \frac{1 \times 0.1867}{273} = 0.2030 L = 203 m L$ .

Therefore, the correct option is C.

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