An ideal gas is confined in a container. The initial mean free path of the gas molecules is . If half the mass of the gas is allowed to escape and the volume of the container is simultaneously doubled, what will be the new mean free path of the gas molecules?

Step-by-step solution

The mean free path ( ) of gas molecules is given by: = 1 2 d^2 n where n is the number density of the gas molecules. The number density is defined as the number of molecules per unit volume, n = N V . When half the mass of the gas escapes, the new number of molecules becomes N' = N 2 . When the volume of the container is doubled, the new volume becomes V' = 2V . The new number density is: n' = N' V' = N 2 2V = N 4V = n 4 Since the mean free path is inversely proportional to the number density ( 1 n ), the new mean