Question

The rms speed of oxygen at room temperature is about $500m/s$. The rms speed of hydrogen at the same temperature is about

• A. $125m/s$
• B. $2000m/s$
• C. $8000m/s$
• D. $31m/s$

Answer 1

The correct option is B $2000m/s$

Rms speed $v_{rms}=\sqrt{\frac{3RT}{M}}$

$⟹v_{rms}\propto \frac{1}{\sqrt{M}}$ for constant $T$

Thus we get $\frac{v_{H_2}}{v_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}}$

Given : $v_{O_2}=500m/s$

We know, $M_{H_2}=2g/mol$ and $M_{O_2}=32g/mol$

$\therefore$ $\frac{v_{H_2}}{500}=\sqrt{\frac{32}{2}}=4$

$⟹v_{H_2}=4\times 500=2000m/s$