Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

5.2 Kinetic gas theory 105
I Kinetic energy distribution function: We may substitute for in Eq. 5.64:
= 1 2 2 (5.72)
µ 12 2
y =
(5.73)
y
µ 12 2
= × 1 µ 12 1
2 × ( ) −12 = ( ) −12 (5.74)
2
µ 12 1
y = ( ) −12 (5.75)
2
Insertion into Eq. 5.64 gives (see Fig. 5.5)
( ) =
y
µ 32 µ
µ 12 µ 12
2
× 4 × − 1 1
×
(5.76)
2
2
µ 32 1
( ) =2
( ) 12 − (5.77)
I
Figure 5.5: Maxwell-Boltzmann distribution function for the kinetic energy.
The fraction of molecules with 0 is temperature dependent.