JEE MainChemistryEasy / Moderate/ Tough tPhysical Chemistry

The average velocity of gas molecules is 400 m/sec calculate its
r.m.s. velocity at the same temperature

Show answer and solution

U_{av} = \sqrt{\frac{8RT}{\pi M}}

and

U_{rms} = \sqrt{\frac{3RT}{M}}

\therefore\frac{U_{av}}{U_{rms}} = \sqrt{\frac{8RT}{\pi M}} \times \sqrt{\frac{M}{3RT}} = \sqrt{\frac{8}{3\pi}} = 0.9216

U_{av} = 0.9216 \times U_{rms}

Given

U_{av} = 400m/s

U_{rms} = \frac{400}{0.9216} = 434.02m/s

Source: Grass-G / CH-28 Chemistry Paper FST 16 Jan.docx

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