Question

The root mean square velocity of hydrogen molecules at $300K$ is $1930$ metre / sec. Then the r.m.s velocity of oxygen molecules at $1200K$ will be

• A. 482.5 metre/sec
• B. 965 metre/sec
• C. 1930 metre/sec
• D. 3860 metre/sec

Answer 1

Answer: (B)

Root-mean square-velocity is given by
$v_{rms}=\sqrt{\frac{3RT}{M}}$
i.e., $v_{rms}\propto \sqrt{\left(\frac{T}{M}\right)}$
$\therefore \frac{\left(v_{rms}\right)O_2}{\left(v_{rms}\right)H_2}=\sqrt{\left[\frac{T_{O_2}}{T_{H_2}}\times \frac{M_{H_2}}{M_{O_2}}\right]}=\frac{1}{2}$
$\therefore \left(v_{rms}\right)O_2=\left(v_{rms}\right)H_2\times \frac{1}{2}=\frac{1930}{2}=965m/s$