– for a bimolecular process involving species A and B the number of collisions is
[8], p. 606:
z II ¼ V AB Á pd
2
AB ½A½B ¼ k
gk
II ½A½B:
ð2:3:5Þ
Here V AB ¼
ffiffiffiffiffiffiffi ffi
8RT
pl AB
q
is the average relative velocity of the species A and B,
d AB = (d A + d B )/2, d A , d B are the gas kinetic diameters of the species A and B;
l AB is the reduced mass (see (2.2.21)) for identical species l A 2 ¼ 1=2m A , k
gk
II ¼
V AB Á pd
2
AB is the gas-kinetic rate constant;
– for a termolecular process involving species A, B, and C the number of collisions is are:
z III ¼ 8
ffiffi ffi
2
p p
3
2 d
2
AB d
2
BC d
ffiffiffiffiffiffi
RT
p
1
l AB
þ
1
l BC
½A½B½C ¼ k
gk
III ½A½B½C: ð2:3:6Þ
Here, d is the distance that species A and B approach to C; this is a particular
value of the order of molecular sizes (0.1 nm). The physical meaning of the
gas-kinetic rate constant is clear: if one wishes to count the number of collisions,
then one has to multiply this constant by the product of the concentrations of the
colliding partners.
Combining (2.3.4–2.3.6), one sees that the rates of bimolecular and termolecular
processes are
r II $ k
gk
II ½A½B exp ÀE a =RT
ð
Þ ;
r III $ k
gk
III ½A½B½C exp ÀE a =RT
ð
Þ ;
respectively (the E and E
0 are designated here as E a and called activation
energies). Clearly, not every the collision can be ‘effective’, and this circumstance can be taken into account in some approximation by a coefficient, which
again in some approximation is independent of temperature. This coefficient is
called with the steric factor P. Do not let his name mislead a reader, most often
the reason for its difference from unit is not some geometric factors, but the
forbiddance of the process. We will meet with these things more than once. As
part of these approximations and according to (2.1.23):
r II ¼ Pk
gk
II ½A½B exp ÀE a =RT
ð
Þ ;
ð2:3:7Þ
and, similarly,
r III ¼ Pk
gk
III ½A½B½C exp ÀE a =RT
ð
Þ ;
ð2:3:8Þ
(one has to remember that T
1/2 is ‘hidden’ in k
gk
II , k
gk
III ).
2.3 Arrhenius Equation
25
[8], p. 606:
z II ¼ V AB Á pd
2
AB ½A½B ¼ k
gk
II ½A½B:
ð2:3:5Þ
Here V AB ¼
ffiffiffiffiffiffiffi ffi
8RT
pl AB
q
is the average relative velocity of the species A and B,
d AB = (d A + d B )/2, d A , d B are the gas kinetic diameters of the species A and B;
l AB is the reduced mass (see (2.2.21)) for identical species l A 2 ¼ 1=2m A , k
gk
II ¼
V AB Á pd
2
AB is the gas-kinetic rate constant;
– for a termolecular process involving species A, B, and C the number of collisions is are:
z III ¼ 8
ffiffi ffi
2
p p
3
2 d
2
AB d
2
BC d
ffiffiffiffiffiffi
RT
p
1
l AB
þ
1
l BC
½A½B½C ¼ k
gk
III ½A½B½C: ð2:3:6Þ
Here, d is the distance that species A and B approach to C; this is a particular
value of the order of molecular sizes (0.1 nm). The physical meaning of the
gas-kinetic rate constant is clear: if one wishes to count the number of collisions,
then one has to multiply this constant by the product of the concentrations of the
colliding partners.
Combining (2.3.4–2.3.6), one sees that the rates of bimolecular and termolecular
processes are
r II $ k
gk
II ½A½B exp ÀE a =RT
ð
Þ ;
r III $ k
gk
III ½A½B½C exp ÀE a =RT
ð
Þ ;
respectively (the E and E
0 are designated here as E a and called activation
energies). Clearly, not every the collision can be ‘effective’, and this circumstance can be taken into account in some approximation by a coefficient, which
again in some approximation is independent of temperature. This coefficient is
called with the steric factor P. Do not let his name mislead a reader, most often
the reason for its difference from unit is not some geometric factors, but the
forbiddance of the process. We will meet with these things more than once. As
part of these approximations and according to (2.1.23):
r II ¼ Pk
gk
II ½A½B exp ÀE a =RT
ð
Þ ;
ð2:3:7Þ
and, similarly,
r III ¼ Pk
gk
III ½A½B½C exp ÀE a =RT
ð
Þ ;
ð2:3:8Þ
(one has to remember that T
1/2 is ‘hidden’ in k
gk
II , k
gk
III ).
2.3 Arrhenius Equation
25