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Question: A cubical box with porous walls containing an equal number of \(O_{2}\) and H<sub>2</sub> molecules ...

A cubical box with porous walls containing an equal number of O2O_{2} and H2 molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature T. The ratio of vrmsv_{rms}of O2O_{2}molecules to that of the vrmsv_{rms}of H2 molecules, found in the chamber outside the box after a short interval is

A

122\frac{1}{2\sqrt{2}}

B

14\frac{1}{4}

C

12\frac{1}{\sqrt{2}}

D

2\sqrt{2}

Answer

14\frac{1}{4}

Explanation

Solution

Temperature remain constant so

vrms∝1Mv_{rms} \propto \frac{1}{\sqrt{M}}̃ vO2vH2=MH2MO2=116=14\frac{v_{O_{2}}}{v_{H_{2}}} = \sqrt{\frac{M_{H_{2}}}{M_{O_{2}}}} = \sqrt{\frac{1}{16}} = \frac{1}{4}