By now much will the mean free path of a gas molecule in a vessel at constant `T` change if the pressure is reduced by `10%`?

Options

A. `10%` increase
B. `10%` decrease
C. `11.1%` increase
D. `11.1%` decrease

Explanation

`lambda prop (T)/(P)`
`lambda(mean free path)=(overline (c ))/(sqrt(2)pi sigma^(2)overline(c )N)=(1)/(sqrt(2) pi sigma^(2)N^(*))`
` :. Lambda prop (1)/(sigma^(2))` (`sigma=` molecular diameter, `overline(c )=` average velocity)
`lambda=(KT)/(sqrt(2)pi sigma^(2)P)(K= Boltzmann constant =(R)/(N)=1.38xx10^(-23)JK^(-1)mol^(-1))`
`lambda prop (1)/(P)` (at constant `T`)
`lambda prop T` (at constant `P`)
`lambda_(1)P_(1)=lambda_(2)P_(2), (lambda_(1))/(T_(1))=(lambda_(2))/(T_(2))`
`:. lambda_(1)P_(1)=lambda_(2)xx0.9 P_(1)`
` implies lambda_(1)=0.9lambda_(2) implies lambda_(2)=1.11 lambda_(1)`
`:. lambda_(2)=111.1 %`
Increases in `lambda_(2)=111.1-100=11.1%`
This shows `lambda` will increase by `1//9`, if `P` is reduced by `10%`.