The rms speed of oxygen molecule in a vessel at particular...

The RMS speed is given by

${v}_{rms} = \sqrt{\dfrac{3RT}{M}}$

The average speed is given by

${v}_{avg} = \sqrt{\dfrac{8RT}{\piM}}$

The ratio is

$⇒ \dfrac{{v}_{rms}}{{v}_{\text{avg}}} = \sqrt{\dfrac{\dfrac{3RT}{M}}{\dfrac{8RT}{\piM}} =}\sqrt{\dfrac{3\pi}{8}} = \sqrt{\dfrac{3}{8} \times \dfrac{22}{7}} ⇒ \dfrac{{v}_{rms}}{{v}_{\text{avg}}} = \sqrt{\dfrac{33}{28}}$

Comparing it with the given value \left(1 + \dfrac{5}{x}\right)\dfrac{1}{2}$,</p><p>$\dfrac{{v}_{rms}}{{v}_{\text{avg}}} = \sqrt{1 + \dfrac{5}{28}} ⇒ x = 28