Question

If the speed of sound in a mixture of $2$ moles of Helium and $2$ moles of Hydrogen at temperature $\frac{972}{5}K$ is $n\times 100m{s}^{-1}$, then the value of $n$ is (Take, $R=\frac{25}{3}Jmo{l}^{-1}{K}^{-1}$ )

• A. 9
• B. 10
• C. 100
• D. 90

Answer 1

Answer: (A)

Given, $T=\frac{972}{5}K,R=\frac{25}{3}Jmo{l}^{-1}{K}^{-1}$
Molecular mass of the mixture
$=\frac{n_{He}{M}_{He}+n_H{M}_H}{n_{He}+n_H}$
$\because n_{He}=2$ moles, $n_H=2$ moles
$M_{He}=4,M_H=2$
$\therefore$ Molecular mass of the mixtures,
$M=\frac{2\times 4+2\times 2}{2+2}$
$=\frac{8+4}{4}=3gm/mole$
$\because$ Degree of freedom of mixture
$f=\frac{2\times 3+2\times 5}{2+2}=4$
$\because f_{\text{mix }}=1+\frac{2}{f}=1.5$
$\because \text{ Speed of sound }=\sqrt{\frac{f_{textmix}RT}{M}}$
$=\sqrt{\frac{1.5\times \frac{25}{3}\times \frac{972}{5}}{3\times 10^{-3}}}$
$=900=n\times 100m/s$
Hence, $n=9$