Question

A mixture of an alkane and $C_2{H}_6$ has volume $24$ cc at a given temperature and pressure. To burn completely, the mixture required $114$ cc of oxygen. The combustion product, $C{O}_2$ occupied $72$ cc. Considering complete combustion, find which of the following is/are correct? Consider all volumes are measured at same temperature and presssure (ideal behaviour).

• A. The alkane is $C_2{H}_6$
• B. The alkane is $C_3{H}_8$
• C. The mole % of $C_3{H}_6$ is $50\%$
• D. The vapour density of the mixture is $21.5$

Answer 1

Answer: (B), (C), (D)

The alkane is $C_3{H}_8$
The mole % of $C_3{H}_6$ is $50\%$
The vapour density of the mixture is $21.5$

$C_3{H}_6+C_n{H}_{2n+2}$
(x)cc (24-x)cc
$\Rightarrow C_3{H}_6+\frac{9}{2}{O}_2\to 3C{O}_2+3H_{2}O$
xcc 3x
$\Rightarrow C_n{H}_{2n+2}+\frac{3n+2}{2}{O}_2\to nC{O}_2+(n+2)H_{2}O$
$(24-x)\frac{3n+1}{2}\times (24-x)n(24-x)$
$\Rightarrow \frac{9}{2}x+\frac{3n+1}{2}(24-x)=114$ .....(i)
$3x+n(24-x)=72$ ...(ii)
$\Rightarrow \text{From (i) and (ii)}$
$x=12andn=3$
$\Rightarrow alkane$

$=C_3{H}_8\text{and mole}$%$of{C}_3{H}_6(C_6{H}_6$%$)=\frac{12}{24}\times 100$

$=50$%

Average molar mass $=\frac{44+42}{2}$
$=43$
$\Rightarrow Vapourdensity=\frac{43}{2}$

$=21.5$