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Q)

The root mean square of a gas at 300K is $3\sqrt{R}$. The molar mass of this gas in $Kg mol^{-1}$ is

$(a)\;1\qquad(b)\;10\qquad(c)\;100\qquad(d)\;1000$

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A)
Toolbox:
  • The behaviour of gases has been expressed in terms of various gas laws obtained experimentally i.e Boyle's law , Charles law , Pressure-temperature law , Dalton's law of partial pressure , Graham's law of diffusion and Avogadro's hypothesis . Later on Maxwell derived kinetic equation $PV = \large\frac{1}{3}mnu^2$ , theoretically by assuming the concept of molecules and their motion . The term u represents root mean square speed of molecule.
$U_{rms} = \sqrt{\large\frac{3RT}{m}}$
$\therefore 3\times \sqrt{R} = \sqrt{\large\frac{3RT}{m}}$
or $9R = \large\frac{3RT}{m}$
or $m = \large\frac{3\times300}{9}$
$100 Kg mol^{-1}$
Hence answer is (C)
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