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Characteristics of Chemical Reaction

An ideal gas ...

Question

An ideal gas is mixture of $C_{2} H_{6}$ and $C_{2} H_{4}$ occupies $28$ l at $1$ atm $8273$ k. The mixture reacts completely with $128$ g of $O_{2}$ to produce $C O_{2}$ pf water vapour. Mole fraction of $C_{2} H_{6}$ in the mixture will be:

A

0.4

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B

0.6

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C

0.2

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D

0.8

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Solution

The correct option is A 0.4
Given $P = 1 a t m$
$V = 28 l$
$T = 8273$
$128 g$ of $O_{2}$ produce $C O_{2}$
mixture of $C_{2} H_{6}$ & $C_{2} H_{4}$
$P V = n R T$
$1 \times 28 = n \times 0.082 \times 8273$
total moles $= 0.04127$
$C_{2} H_{6} + C_{2} H_{4} = 0.04127$
$a + b = 0.04127... (1)$
$C_{2} H_{6} + \frac{7}{2} O_{2} \to 2 C O_{2} + 3 H_{2} O$
$C_{2} H_{4} + 3 O_{2} \to 2 C_{2} + 2 H_{2} O$
$\frac{7 a}{2} + 3 b = \frac{128}{32} . . . (2)$
find value of a & b from $e q^{n} (1)$ & $(2)$
mole fraction of $C_{2} H_{6} = \frac{a}{t o t a l m o l e s}$

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