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(D) The $rms$ velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass.Since the number of

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$\frac{1}{\sqrt{m}}$

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(D) The $rms$ velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass.Since the number of moles $n = \frac{m}{M}$,where $m$ is the total mass of the gas,we can write $M = \frac{m}{n}$.Substituting this into the $rms$ velocity formula: $v_{rms} = \sqrt{\frac{3RT}{(m/n)}} = \sqrt{\frac{3RTn}{m}}$.For a fixed amount of gas at a constant temperature,$T$,$R$,and $n$ are constants.Therefore,$v_{rms} \propto \frac{1}{\sqrt{m}}$.

At a given temperature,the $rms$ velocity of a gas molecule of mass $m$ is proportional to:

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Derive the equation of $v_{rms}$ in terms of molar mass.

When the rms velocity of a gas is denoted by $V$,which of the following relations is true? ($T=$ absolute temperature of the gas)

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