Question

The most probable speed of an oxygen molecule in the gas phase at room temperature is 450 m/s. The root-mean-square speed (urms) is therefore equal to 450 m/s. much greater than 450 m/s. slightly less than 450 m/s. much less than 450 m/s. slightly greater than 450 m/s.

Answer 1

Explanation:

We have,

The most probable speed of an oxygen molecule in the gas phase at room temperature is 450 m/s.

The formula of the most probable speed of a gas molecule is given by :

$v_p=\sqrt{\dfrac{2RT}{M}}$

So,

$450=\sqrt{\dfrac{2RT}{M}}\\\\\dfrac{RT}{M}=\dfrac{450^2}{2}\\\\\dfrac{RT}{M}=101250\ .....(1)$

The RMS speed of the gas molecule is given by :

$v_{rms}=\sqrt{\dfrac{3RT}{M}}\\\\v_{rms}=\sqrt{3\times \dfrac{RT}{M}}$

Use equation (1) in above equation :

$v_{rms}=\sqrt{3\times \dfrac{RT}{M}}\\\\v_{rms}=\sqrt{3\times 101250} \\\\v_{rms}=551.13\ m/s$

It is clear that the RMS speed of the gas molecule is greater than 450 m/s.