Modern Engineering Thermodynamics

18.4 Intermolecular Collisions 733
where r is the effective radius of the kinetic theory spherical molecule. Typical values for the effective radius of
simple molecules are given in Table 18.1.
The collision frequency F is the number of collisions per unit time made by the moving molecule, determined
from
F = σV
N 8 1/2
rms
V 3π
where N/V = N o /v = pN o /RT = p/kT is the number of molecules per unit volume, σ is the molecular collision
moving cross section, and V rms istherootmeansquarevelocityofthe average molecule. The molecular mean
free path λ is defined to be the distance traveled between molecular collisions, calculated from
λ =
1
ðN/VÞσ
(18.15)
Table 18.1 Typical Values of the Effective Molecular Radius
Molecule
Effective Radius, r (m)
He
Ne
Ar
H 2
N 2
O 2
Br 2
Cl 2
F 2
I 2
HBr
HCl
HF
HI
H 2 O
CO
NO
CO 2
NH 3
CH 4
1.37 × 10 −10
1.30 × 10 −10
1.82 × 10 −10
0.74 × 10 −10
1.10 × 10 −10
1.21 × 10 −10
2.28 × 10 −10
1.99 × 10 −10
1.41 × 10 −10
2.67 × 10 −10
1.41 × 10 −10
1.27 × 10 −10
0.92 × 10 −10
1.60 × 10 −10
1.50 × 10 −10
1.13 × 10 −10
1.15 × 10 −10
2.30 × 10 −10
2.22 × 10 −10
2.07 × 10 −10
Source: Material drawn from the JANAF Thermochemical Tables, first ed., 1961, Thermal Research Laboratory,
Dow Chemical Corporation, Midland, MI. Reprinted by permission.
WHAT ARE ATOMIC AND MOLECULAR RADII?
The distance from the center of the nucleus to the outer electron shell of an atom is called the atomic radius of that atom.
The distance from the nucleus to the outer shell depends on the electrostatic attraction that the nucleus exerts on the electrons
of the outer shell. The atomic radii increase as you move down in the periodic table, as electrons fill outer electron
shells. However, the atomic radii decrease as you move from left to right, across the periodic table, even though more electrons
are added to atoms. This is because the increasing nuclear charge “pulls” the electron clouds inward, making the
atomic radii smaller.
Molecules are much more complex and much less spherical. There are various techniques for measuring molecular geometry
such as the effective molecular size a molecule displays in a solution. However, a molecule’s diameter can be estimated
as the cube root of the volume it sweeps out as it moves through space.