Question

Calculate the pressures, P, in atmospheres at which the mean free path, l, of a hydrogen molecule will be 3.50 μm, 3.50 mm, and 3.50 m at 20.0 °C. The diameter of a H2 molecule is 270 pm.

Answer 1

The pressure P is

P = kT / (2^1/2 L·pi·d²)

Re/write as

P · L = const where const. = kT / (2^1/2 pi·d²)

Calculate const. as

Const = 1.38 x 10^-23J/K x 293 K / (1.41 x 3.14 x 2.7² x 10^-20 m²) =

           = (404/ 32.3) x10^-3 =

           = 12.5 x10^-3 m.Pa

For L = 3.50x10^-6 m

P = 12.5 x10^-3 m.Pa /3.50x10^-6 m = 3.57x10³ Pa

For L = 3.50x10^-3 m

P = 12.5 x10^-3 m.Pa /3.50x10^-3 m = 3.57 Pa

For L = 3.50 m

P = 12.5 x10^-3 m.Pa /3.50 m = 3.57x10^-3 Pa

Note : 1Pa = 9.8692×10⁻⁶ atm