Question

A gas with formula $C_n{H}_{2n+2}$ diffuses through the porous plug at a rate one sixth of the rate of diffusion of hydrogen gas under similar condition. The formula of gas is:

• A. $C_2{H}_6$
• B. $C_{10}{H}_{22}$
• C. $C_5{H}_{12}$
• D. $C_9{H}_{14}$

Answer 1

The correct option is C $C_5{H}_{12}$

Mol. wt of $C_n{H}_{2n+2}=12n+2n+2$
$=14n+2$
$=2(7n+1)$
From $r\propto \frac{1}{\sqrt{M}}$
$\frac{r_g}{r_{H_2}}=\frac{M_{H_2}}{M_g}$
$\Rightarrow \frac{1}{6}=\sqrt{\frac{2}{2(7n+1)}}$
$\Rightarrow 36=7n+1\Rightarrow n=5$
$\therefore C_n{H}_{2n+2}=C_5{H}_{12}$