Question

At identical temperature and pressure, the rate of diffusion of hydrogen gas is $3\sqrt{3}$ times that of a hydrocarbon having molecular formula $C_n{H}_{2n-2}$. What is the value of ${}^{\prime }{n}^{\prime }$ ?

• A. 1
• B. 4
• C. 3
• D. 8

Answer 1

Answer: (B)

$\frac{r_{H_2}}{r_{C_n{H}_{2n-2}}}=\sqrt{\frac{M_{C_n{H}_{2n-2}}}{M_{H_2}}}$
$=\sqrt{\frac{M_{C_n{H}_{2n-2}}}{2}}$
$\because \sqrt{\frac{M_{C_n{H}_{2n-2}}}{2}}=3\sqrt{3}=\sqrt{27}$
$\Rightarrow M_{C_n{H}_{2n-2}}=27\times 2=54$
Hence, $12n+(2n-2)\times 1=54$
$\Rightarrow 14n=56$
$\Rightarrow n=4$
Thus, hydrocarbon is $C_4{H}_6$.