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Dalton's Law of Partial Pressures

A mixture of ...

Question

A mixture of ethane (C₂H₆) and ethene (C₂H₄) occupies 40 litre at 1 atm
and 400 K. The mixture reacts completely with 130 g of oxygen to produce
carbon dioxide gas and water vapour. Assuming ideal gas behavior, the mole
fraction of C₂H₄ and C₂H₆ in the mixture is__

A

0.34; 0.66

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B

0.66; 0.34

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C

0.5; 0.5

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D

0.6; 0.4.

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Solution

The correct option is C 0.34; 0.66
Mixture of $C_{2} H_{6}$ and $C 2 H_{4}$
$P V = n R T$
$1 \times 40 = n \times 0.082 \times 400$
Total mole of $(C_{2} H_{6} + C_{2} H_{4}) = 1.2195$
$C_{2} H_{6} + C_{2} H_{4} = 1.2195$
a+b=1.2195-------(1)
$C_{2} H_{6} + 7 / 2 O_{2} \to 2 C O_{2} + 3 H_{2} O$
$C_{2} H_{4} + 3 O_{2} \to 2 C O_{2} + 2 H_{2} O$
$7 a / 2 + 3 b = 130 / 32$ ------(2)
From (1) & (2)
a=0.808
b=0.4115
Mole fraction of $C_{2} H_{6}$ =0.8081.2195=0.66
Mole fraction of $C_{2} H_{4}$ =0.34

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