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  4. If the vrms is 30R1/2 at 27° C then calculate the molar mass of gas in kilogram

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Q. If the $v_{rms}$ is $30R^{1/2}$ at $27^\circ\,C$ then calculate the molar mass of gas in kilogram

States of Matter

Solution:

$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\sqrt{30^{2} R}=\sqrt{\frac{3RT}{M}}$
$\Rightarrow 30\times30R=\frac{3R\times300}{M}$
$\Rightarrow M=\frac{3\times300}{30\times30} 1\,g$
$=0.001\,Kg$