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Molecular Speeds - Vrms, Vavg, Vmps

The RMS spe...

Question

The $R M S$ speed of the molecules of a gas of density 4 $k g m^{- 3}$ and pressure $1.2 \times 10^{5} N m^{- 2}$ is :

120 m s^{- 1}

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300 m s^{- 1}

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600 m s^{- 1}

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900 m s^{- 1}

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Solution

The correct option is D $300 m s^{- 1}$
$V_{r m s} = \sqrt{\frac{3 R T}{M}}$
$P V = W / M R T \Rightarrow P M = W / V R T = d R T \Rightarrow M = d R T / P$
$V_{r m s} = \sqrt{\frac{3 P R T}{d R T}} = \sqrt{\frac{3 P}{d}} = \sqrt{\frac{3 \times 1.2 \times 10^{5}}{4}} = \sqrt{90000} = 300 m s^{- 1}$

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