Page 22 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:35 9in x 6in b985-ch01 Elementary Physical Chemistry

State of Matter. Properties of Gases 7

28.0 × 10 −3 kg/mol gives
2 −2
)
c rms =(3 × 8.3145 × kg m s K −1 mol −1 × 298 K/28 × 10 −3 kg mol −1 1/2
= 515.2ms −1
We now have a relation between the macroscopic quantity T and the
microscopic property, c. Since the average energy of molecule is ε =
1 m c we immediately obain
2
2
2
PV = N ε (1.13a)
3
and for one mole,

2
PV = RT = N A ε (1.13b)
3
where N A is Avogadro’s number. Finally,

3
ε = RT/N A (1.13c)
2
Defining R/N A as Boltzmann’s constant (k =1.38 × 10 −16 erg K −1
molcule −1 )gives
3
ε = kT (1.14)
2

Comment 1: Temperature is not associated with the kinetic energy
of a single molecule, but with the average kinetic energy of a large
number of molecules. It is a statistical concept.

Comment 2: So far we have dealt only with average speeds. Actually,
the speeds of molecules vary enormously. Molecules slow down as they
collide with one another, speed up afterwards, etc. An expression of
the distribution of speeds was derived by Maxwell.A schematic
diagram of the variation of speed with temperature is depicted in
Fig. 1.2.

1.8. Molecular Collisions

The mean free path, λ, is the average distance (of molecules) between
collisions. The collision frequency, z, is the rate at which single molecule