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(D) The $RMS$ velocity of gas molecules can be calculated using the following expressions: $1$. $v_{rms} = \sqrt{\frac{3P}{d}}$,where $P$ is pressure

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all of these

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(D) The $RMS$ velocity of gas molecules can be calculated using the following expressions: $1$. $v_{rms} = \sqrt{\frac{3P}{d}}$,where $P$ is pressure and $d$ is density. $2$. $v_{rms} = \sqrt{\frac{3PV}{M}}$,where $V$ is volume and $M$ is molar mass (since $PV = nRT = \frac{m}{M}RT$,and $d = \frac{m}{V}$,thus $P = \frac{dRT}{M}$). $3$. $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the ideal gas constant and $T$ is the temperature. Since all three expressions are mathematically equivalent for an ideal gas,the correct option is $D$.

The $rms$ speed at $NTP$ of the species can be calculated from the expression

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