For oxygen gas at `27^(@)C` and 1 atm pressure, calculate
The number of collisions per cubic metre per second. The collision diameter of oxygen molecule is 361 picometre.

Explanation

Molar mass of oxygen `= 32 xx 10^(-3) kg mol^(-1)`
`1.0 atm = 1.01325 xx 10^(5) Nm^(-2)`,
`T= 27^(@)C= 300K, d= 361pm= 361 xx 10^(-12)m= 3.61xx 10^(-10)m`
Average velocity, `u_(avg)= ((8RT)/(pi M))^(1/2)= =[((8)(8.314 JK^(-1)mol^(-1))(300K))/((3.1416)(32xx 10^(-3)kg mol^(-1)))]^(1/2)= 447.0 m`
Collision frequency, `Z_(1)= sqrt(2) pi d^(2) u_(avg) P"/"kt =((1.4142)(3.1416)(3.61xx 10^(-10)m)^(2)(447.0 ms^(-1)(1.01325 xx 10^(5)N m^(-2))))/((1.38xx 10^(-23)JK^(-1))(300K))=6.33 xx 10^(9)s^(-1)`.