PHYSICAL CHEMISTRY IN BRIEF

CHAP. 10: TRANSPORT PROCESSES [CONTENTS] 346

10.5.5 Knudsen region

The relation (10.18) for the mean free path can be rewritten to the form

`=

RT

√

2 π σ^2 p NA

, (10.25)

whereNA is the Avogadro constant. The mean free path is thus inversely proportional to
pressure, and at very low pressures it may exceed the dimensions of the containing vessel. In
this case we speak about theKnudsen pressure region. In the Knudsen region the formulas
of the preceding section are inapplicable. In this region, collisions between molecules do not
occur and transport quantities lose their physical meaning, just like in an ideal gas.

Example

Calculate the pressure at which the mean free path of argon molecules at a temperature of 300

K would equal 1 cm. Substitute argon molecules with hard spheres of 0.34 nm in diameter.

Solution

From equation (10.25) we obtain

p=

8. 31 × 300

√

2 × 3. 14 ×(0. 34 × 10 −^9 )^2 × 0. 01 × 6. 02 × 1023

= 0. 8 Pa.