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)

2v

Answer 2

Let the molar mass of $H _{2}$ is $M$. $\because$ Hydrogen gas is dissociated into atomic hydrogen. $\therefore$ It molar mass is equal to $\frac{ M }{2}$. $\because v_{ rms }=\sqrt{\frac{3 RT }{ M }}$ $\therefore \frac{ v _{1}}{ v _{2}}=\sqrt{\frac{ T _{1}}{ M _{ O _{1}}}} \times \frac{ M _{ O _{2}}}{ T _{2}}$ $\because T _{2}=2 T _{1} \text { and } M _{ O _{2}}=\frac{ M _{ O _{1}}}{2}=\frac{ M }{2}$ $\Rightarrow \frac{ v _{1}}{ v _{2}}=\sqrt{\frac{ T _{ l }}{ M }} \cdot \frac{ M / 2}{2 T _{1}}=\sqrt{\frac{1}{4}}$ $\therefore v _{2}=2 v _{1}$