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Ideal Gas Equation

An ideal gase...

Question

An ideal gaseous mixture of ethane ( $C_{2} H_{6}$ ) and ethene ( $C_{2} H_{4}$ ) occupies 28 litre at 1 atm and 273 K. The mixture reacts completely with 128 gm $O_{2}$ to produce $C O_{2}$ and $H_{2} O$ . Mole fraction at $C_{2} H_{4}$ in the mixture is:

A

0.6

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B

0.4

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C

0.5

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D

0.8

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Solution

The correct option is D 0.4
$C_{2} H_{6} + 3.5 O_{2} \to 2 C O_{2} + 3 H_{2} O$
$C_{2} H_{4} + 3 O_{2} \to 2 C O_{2} + 2 H_{2} O$
Let vol. of ethane is $x$ ,
$22.4 \times 4 = 3.5 x + 3 (28 - x)$
$\Rightarrow x = 11.2$ litre
at constant T and P , $V \propto n$ ;
$∴$ Mole fraction of $C_{2} H_{6}$ in mixture
$= \frac{11.2}{28} = 0.4$

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