One mole of oxygen occupies a volume of 24 L at `20^(@) C` and 1 atm pressure. What is the rms speed of an oxygen? Find the total translational kinetic energy and the total momentum of the molecules.

Explanation

`pV = (1)/(3) Mv_(rms)^(2)`
or `v_(rms) = sqrt((3pV)/(M))`
`= sqrt((3 xx (1.013 xx 10^(5)) xx 24 xx 10^(-3))/(32 xx 10^(-3))) = 477 m s^(-1)`
`U = (3)/(2) RT = (3)/(2) xx 8.3 xx (273 + 20) = 3647.8 J`
Momentum `= M overline c = Mv_(rms) (overline c ~~ v_(rms))`
`= (32 xx 10^(-3)) xx 477 = 15 g m s^(-1)`