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Standard XII

Chemistry

Concentration Terms

A gas known t...

Question

A gas known to be a mixture of propane $(C_{3} H_{5})$ and methane $(C H_{4})$ is contained in a vessel of unknown. volume V, at a temperature T and exert a pressure of 320 mm of Hg. The gas is burnt in excess 02 an all the carbon is recovered a $C O_{2}$ . The $C O_{2}$ is found to have a pressure of 448 mm Hg in a volume V, at the same temperature T. Calculate the mole fraction of propane in the original mixture. (Assume ideal behavior of all gases) (Report your answer by multiplying 10)

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Solution

$C_{3} H_{8} + 5 O_{2} ⟶ 3 C O_{2} + 4 H_{2} O$
Let moles of $C_{3} H_{8}$ be $x$ $3 x$
$C H_{4} + 2 O_{2} ⟶ C O_{2} + 2 H_{2} O$
Let moles of $C H_{4}$ be $y$ $y$
Before reaction, mixture contained $C_{3} H_{8}$ and $C H_{4}$
Total moles $= x + y$
$P = 320$ $m m H g$
From ideal gas equation is $P V = n R T$
$⟹ 320 \times V = (x + y) R T$ (equation $01$ )
Pressure exerted by recovered $C O_{2} = 448$ $m m H g$
Total moles of $C O_{2} = (3 x + y)$
$∴$ Using $P V = n R T$
$⟹ 448 \times V = (3 x + y) R T$ (equation $2$ )
equation $01$ is divided by $02$
$\frac{320 V}{448 V} = \frac{(x + y) R T}{(3 x + y) R T}$
$⟹ 960 x + 320 y = 448 x + 448 y$
$⟹ 512 x = 128 y$
$⟹ y = 4 x$
$MolesfractionofC3H8=MolesofpropaneTotalmolesofmixture=xx+y$
Putting $y = 4 x$
$⟹ X_{C_{3} H_{8}} = \frac{x}{5 x}$
$⟹ X_{C_{3} H_{8}} = \frac{1}{5} \times 10$
$⟹ X_{C_{3} H_{8}} = 2$

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