Question

The root mean square speed of hydrogen molecules at 300 K is 1930 m/s. Then the root mean square speed of oxygen molecules at 900 K will be

• A. $1930\sqrt{3}m/s$
• B. 836 m/s
• C. 643 m/s
• D. $\frac{1930}{\sqrt{3}}m/s$

Answer 1

Answer: (B)

836 m/s

Answer 2

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

∴ $\frac{v_{H_{2}}}{v_{O_{2}}} = \sqrt{\frac{T_{H_{2}}}{M_{H_{2}}} \times \frac{M_{O_{2}}}{T_{O_{2}}}}$

⇒ $\frac{1930}{v_{O_{2}}} = \sqrt{\frac{300}{2} \times \frac{32}{900}}$

⇒ $v_{O_{2}} = \frac{1930 \times \sqrt{3}}{4} = 836m ⥂ / ⥂ s$.