Hydrogen gas is contained in a closed vessel at `1atm(100kPa)` and `300K`.
(a) Calculate the mean speed pf the molecules.
(b) Suppose the molecules strike the wall with this speed making an average angle of `45^(@)` with it. How many molecules strike each square metre of the wall per second?

Explanation

Given: `P = 100 k Pa = 100 xx 10^(3) = 10^(5) N//m^(2), T = 300 K`
Molecular mass of hydrogen gas, `M_(0) = 2 g = 2 xx 10^(-3) kg`
(a) Mean speed `bar(v) = sqrt((8 R T)/(pi M_(0)))`
`= sqrt((8 xx 8.3 xx 300)/(pi xx 2 xx 10^(-3)))`
`= 1781 m//s`
(b) Mass of hydrogen molecule
`m = (M_(0))/(N_(A)) = (2 xx 10^(-3))/(6.023 xx 10^(23)) = 0.33 xx 10^(-26) kg`

Change in momentum of molecule
`Delta p = 2 m bar(v) cos 45^(@) = sqrt(2) mv`
If `n` molecules strike the wall per second
Force exerted by molecules
`F = n Delta p`
Pressure `=` Force`//`area `= n' Deltap = n'. sqrt(2) mv`
`n' = n` umber of molecule`// m^(2)//s`
`P = sqrt(2) n' mv`
`n' = (P)/(sqrt(2) mv) (10^(5))/(sqrt(2) xx 0.33 xx 10^(-26) xx 1781)`
=`1.2 xx 10^(28)`