The mean free path l of a molecule is the average distance that a molecule trave

Question

The mean free path l of a molecule is the average distance that a molecule travels before colliding with another molecule. It is given by l = 1/squareroot 2 pi d^2 N_V where d is the diameter of the molecule and N_V is the number of molecules per unit volume. The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f, is given by f = V_avg/l (a) If the diameter of an oxygen molecule is 2.00 times 10^-10 m, find the mean free path of the molecules in a scuba tank that has a volume of 12.5 L and is filled with oxygen at a gauge pressure of 103 atm at a temperature of 23.5 degree C. m (b) What is the average time interval between molecular collisions for a molecule of this gas? s

Explanation / Answer

Given that

pressure P=103 atm=103*1.013*10^5=104.339*10^5 pa

temperature T=273+23.5=296.5 K

diameter d=2*10^-10 m

now we find the mean free path

mean free path =KT/1.414*3.14*(2*10^-10)^2*104.339*10^5

=1.38*10^-23*296.5/1853*10^-15

=0.221*10^-8 m

=2.21 nm

now we find the time

time =2.21*10^-9/3*10^8=0.074sec

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