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 one another. It is given by

l = 1/pv(2) d^2Nv

where d is the diameter of the molecule and Nv 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 is given by

f = vavg/l

a) if the diameter of an oxygen molecule is 2.00x10^-10m, find the mean free path of molecules in a scuba tank that has a colume of 12.0L and filled with oxygen at a guage pressure of 100atm and 298K.

b)What is the average time interval between molecular collisions for a molecule of this gas.

This is what I got for part A.

n = PV/RT
n/V = P/RT
= 100x101x10^3/8.314x298 = 4076.5

4076.5x6.02x10^23 = 2.45x10^27 = Nv

Then plug everything in and I get 2.28x10^-9m for l.

Im not sure if thats right so I didnt attempt part b so any help would be appriciated thanks.
The mean free path l of a molecule is the average distance that a molecule travels before colliding with one another. It is given by l = 1/pv(2) d^2Nv where d is the diameter of the molecule and Nv 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 is given by f = vavg/l a) if the diameter of an oxygen molecule is 2.00x10^-10m, find the mean free path of molecules in a scuba tank that has a colume of 12.0L and filled with oxygen at a guage pressure of 100atm and 298K. b)What is the average time interval between molecular collisions for a molecule of this gas. This is what I got for part A. n = PV/RT n/V = P/RT = 100x101x10^3/8.314x298 = 4076.5 4076.5x6.02x10^23 = 2.45x10^27 = Nv Then plug everything in and I get 2.28x10^-9m for l. Im not sure if thats right so I didnt attempt part b so any help would be appriciated thanks.

Explanation / Answer

a) you are right, L = 2.28*10^-9 m b) vavg = sqrt[8RT/(pi*M)] where M = 32*10^-3 kg/mol vavg = 444 m/s t = L/vavg = 5.14*10^-12 s

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