Question

Velocity of hydrogen at NTP is $v$. What will be the velocity of sound in a mixture of hydrogen and oxygen in the ratio $4:1$ at NTP is :

• A. $v$
• B. $2v$
• C. $v/2$
• D. $v/4$

Answer 1

Answer: (C)

$v/2$

Velocity of sound in gas is given by

$v=\sqrt{\frac{\gamma RT}{M}}$.

For NTP, v is proportional to $\frac{1}{\sqrt{M}}$.

$M_{H_2}=2\text{gm/mol}\text{and}{M}_{O_2}=32\text{gm/mol}$.

Therefore molar mass of the mixture is

$M_{mix}=\frac{4\times 2+32\times 1}{4+1}=8\text{gm/mol}$.

Hence, $\frac{v_{H_2}}{v_{mix}}=\sqrt{\frac{M_{mix}}{M_{H_2}}}=\sqrt{\frac{8}{2}}=2$.

$\Rightarrow v_{mix}=\frac{v}{2}$

Ans: C