Question

The rms speed of hydrogen molecule at a certain temperature is $v$ . If the temperature is doubled and hydrogen gas dissociates into atomic hydrogen, the rms speed will become

• A. $v$
• B. $\frac{v}{2}$
• C. $2v$
• D. $\sqrt{2} \, v$

Answer 1

Answer: (C)

Let the molar mass of $H_{2}$ is $M$ .
Hydrogen gas is dissociated into atomic hydrogen.
It molar mass is equal to $\frac{M}{2}$ .
$v_{r m s}=\sqrt{\frac{3 R T}{M}}$
$\frac{v_{1}}{v_{2}}=\sqrt{\frac{T_{1}}{M_{O_{1}}} \times \frac{M_{O_{2}}}{T_{2}}}$
$T_{2}=2T_{1} \, and \, M_{O_{2}}=\frac{M_{O_{1}}}{2}=\frac{M}{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\sqrt{\frac{T_{1}}{M} . \frac{M / 2}{2 T_{1}}}=\sqrt{\frac{1}{4}}$
$v_{2}=2v_{1}=\text{2} v$