Question

Calculate the mean free path of air molecules at a pressure of 3.00×10−13 atm and a temperature of 304 K . (This pressure is readily attainable in the laboratory.) Model the air molecules as spheres with a radius of 2.00×10−10 m .

Answer 1

153273.68816 m

Step-by-step explanation:

k = Boltzmann constant =
`1.3* 10^(-23)\ J/K`

T = Temperature = 304 K

P = Pressure =
`3.8* 10^(-13)\ atm`

r = Radius =
`2* 10^(-10)\ m`

d = Diameter= 2r =
`2* 2* 10^(-10)\ m=4* 10^(-10)\ m`

Mean free path is given by

`\lambda=(kT)/(\sqrt2\pi d^2P)\\\Rightarrow \lambda=(1.38* 10^(-23)* 304)/(\sqrt2 \pi (4* 10^(-10))^2* 3.8* 10^(-13)* 101325)\\\Rightarrow \lambda=153273.68816\ m`

The mean free path of the air molecule is 153273.68816 m