Question

An ideal gaseous mixture of ethane $\left( C _{2} H _{6}\right)$ and ethene $\left( C _{2} H _{4}\right)$ occupies $28$ litre at $1 \,atm$ and $273 \,K$. The mixture reacts completely with $128 \,g O _{2}$ to produce $CO _{2}$ and $H _{2} O$. Mole fraction at $C _{2} H _{6}$ in the mixture is:

• A. 0.6
• B. 0.4
• C. 0.5
• D. 0.8

Answer 1

Answer: (B)

$ C _{2} H _{6}+3.5 O _{2} \rightarrow 2 CO _{2}+3 H _{2} O$
$ C _{2} H _{4}+3 O _{2} \rightarrow 2 CO _{2}+2 H _{2} O$
Let volume of ethane is $x$ litre.
$22.4 \times 4=3.5 x+3(28-x) $
$\Rightarrow x=11.2 $ litre
at constant $ T$ and $P , V \propto n $
$\Rightarrow $ Mole fraction of $ C _{2} H _{6}$ in mixture
$=\frac{11.2}{28}=0.4$