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 $\frac{M}{2}$ .
$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\frac{v_1}{v_2}=\sqrt{\frac{T_1}{M_{O_1}}\times \frac{M_{O_2}}{T_2}}$
$T_2=2T_{1}and{M}_{O_2}=\frac{M_{O_1}}{2}=\frac{M}{2}$
$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{T_1}{M}.\frac{M/2}{2T_1}}=\sqrt{\frac{1}{4}}$
$v_2=2v_1=\text{2}v$