First slide

Rms speed

Question

The rms speed of oxygen molecule in a gas at 27°C would be given by [UK PMT 2015]

Easy

A

483 ${ms}^{- 1}$
B

966 ${ms}^{- 1}$
C

4.83 ${ms}^{- 1}$
D

9.66 ${ms}^{- 1}$

Solution

The rms speed is given by
$v_{rms} = \sqrt{\frac{3 R T}{Molecular weight}}$
$= \sqrt{\frac{3 \times 8.3 \times (273 + 27)}{2 \times 16 \times 10^{- 3}}} = \sqrt{\frac{3 \times 8.3 \times 300}{32 \times 10^{- 3}}}$
$\Rightarrow$ $v_{r m s} = 483 m s^{- 1}$

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