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

Step-by-step 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{(2RT)/(M)}`

So,

`450=\sqrt{(2RT)/(M)}\\\\(RT)/(M)=(450^2)/(2)\\\\(RT)/(M)=101250\ .....(1)`

The RMS speed of the gas molecule is given by :

`v_(rms)=\sqrt{(3RT)/(M)}\\\\v_(rms)=\sqrt{3* (RT)/(M)}`

Use equation (1) in above equation :

`v_(rms)=\sqrt{3* (RT)/(M)}\\\\v_(rms)=√(3* 101250) \\\\v_(rms)=551.13\ m/s`

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