(C) The average kinetic energy $E$ for one mole of an ideal gas is given by $E = \frac{3}{2}RT$. The root mean square velocity is given by $u_{rms} =

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$u_{rms} = \sqrt{\frac{2E}{M}}$

(C) The average kinetic energy $E$ for one mole of an ideal gas is given by $E = \frac{3}{2}RT$. The root mean square velocity is given by $u_{rms} = \sqrt{\frac{3RT}{M}}$. From the kinetic energy equation,we have $RT = \frac{2E}{3}$. Substituting this into the $u_{rms}$ equation: $u_{rms} = \sqrt{\frac{3}{M} \times \frac{2E}{3}} = \sqrt{\frac{2E}{M}}$.

Class 11 Chemistry States of Matter Kinetic molecular theory of gases and Molecular collisions

Medium

For one mole of a monoatomic gas with molar mass $M$,the root mean square velocity is $u_{rms}$. What is the relationship between $u_{rms}$ and the average kinetic energy $E$?

A
$u_{rms} = \sqrt{\frac{3E}{2M}}$
B
$u_{rms} = \sqrt{\frac{2E}{3M}}$
C
$u_{rms} = \sqrt{\frac{2E}{M}}$
D
$u_{rms} = \sqrt{\frac{E}{3M}}$

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Kinetic molecular theory of gases and Molecular collisions

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For one mole of a monoatomic gas with molar mass $M$,the root mean square velocity is $u_{rms}$. What is the relationship between $u_{rms}$ and the average kinetic energy $E$?

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