K c ¼ K ¼
Q
k F
m
0
k
k;c
Q
i F
m i
i;c
Á exp
Q
0
0
RT
ð2:2:12bÞ
(concentration units, species/cm
3 )
K p ¼
Q
k F
m
0
k
k;p =N A
Q
i F
m i
i;p =N A
Á exp
Q
0
0
RT
ð2:2:12cÞ
(concentration units, mol/cm
3 ).
Here, F
m i
i =N A and F
m
0
k
k =N A are the partition functions of the i-th and k’-th species,
respectively, the indices p and c denote that the corresponding partition functions
refer to the standard state at a pressure of 1 atm and 1 mol/cm
3 , respectively; Q
0
0 is
the thermal effect of the reaction at T = 0 K, equal to the difference between the
internal energy of the reactants and products at this temperature ÀDU
0
0
À
Á
[3], p. 362.
The correctness of (2.2.12a–2.2.12c) seems to be quite understandable:
– in these equations, the Boltzmann factor is present, the need for which is
undeniable;
– as regards the partition function, then, as is known from statistical physics, if
one analyzes system states with the same energy (the Boltzmann factor is taken
into account!), then all these states are equally probable in a thermodynamically
equilibrium system, regardless of the degree of freedom (electronic, vibrational,
rotational or translational). Naturally, it is necessary to take into account the
degeneracies of these states. One can see another manifestation of these laws of
nature in Sect. 3.1 in which the detailed balance principle is considered.
The partition function of a species is equal to the product of the functions
corresponding to different forms of energy. This statement also seems to be
indisputable; indeed, in each molecular electronic state can be many vibrational
states corresponding to vibrational degrees of freedom, and in each vibrational state
there can be many rotational levels, and each of the species in each rovibronic state
moves, etc.
It follows from (2.2.11–2.2.12) that if one knows the spectroscopic constants of
the reactants and products, then the equilibrium constants for the process in which
they are involved can be calculated.
Let us determine the partition function for the reaction
I 2 X0
þ
g ; v X ; J X
$
M 2I 5p
5 2 P J
À
Á
ð2:2:13Þ
J = 3/2 (E = 0), 1/2 (E = 0.9427 eV (7603.1 cm
−1 ) are the components of the
spin–orbit splitting (Fig. 2.2) [7], p. 25.
18
2 General Kinetic Rules for Chemical Reactions, Collisional …
Q
k F
m
0
k
k;c
Q
i F
m i
i;c
Á exp
Q
0
0
RT
ð2:2:12bÞ
(concentration units, species/cm
3 )
K p ¼
Q
k F
m
0
k
k;p =N A
Q
i F
m i
i;p =N A
Á exp
Q
0
0
RT
ð2:2:12cÞ
(concentration units, mol/cm
3 ).
Here, F
m i
i =N A and F
m
0
k
k =N A are the partition functions of the i-th and k’-th species,
respectively, the indices p and c denote that the corresponding partition functions
refer to the standard state at a pressure of 1 atm and 1 mol/cm
3 , respectively; Q
0
0 is
the thermal effect of the reaction at T = 0 K, equal to the difference between the
internal energy of the reactants and products at this temperature ÀDU
0
0
À
Á
[3], p. 362.
The correctness of (2.2.12a–2.2.12c) seems to be quite understandable:
– in these equations, the Boltzmann factor is present, the need for which is
undeniable;
– as regards the partition function, then, as is known from statistical physics, if
one analyzes system states with the same energy (the Boltzmann factor is taken
into account!), then all these states are equally probable in a thermodynamically
equilibrium system, regardless of the degree of freedom (electronic, vibrational,
rotational or translational). Naturally, it is necessary to take into account the
degeneracies of these states. One can see another manifestation of these laws of
nature in Sect. 3.1 in which the detailed balance principle is considered.
The partition function of a species is equal to the product of the functions
corresponding to different forms of energy. This statement also seems to be
indisputable; indeed, in each molecular electronic state can be many vibrational
states corresponding to vibrational degrees of freedom, and in each vibrational state
there can be many rotational levels, and each of the species in each rovibronic state
moves, etc.
It follows from (2.2.11–2.2.12) that if one knows the spectroscopic constants of
the reactants and products, then the equilibrium constants for the process in which
they are involved can be calculated.
Let us determine the partition function for the reaction
I 2 X0
þ
g ; v X ; J X
$
M 2I 5p
5 2 P J
À
Á
ð2:2:13Þ
J = 3/2 (E = 0), 1/2 (E = 0.9427 eV (7603.1 cm
−1 ) are the components of the
spin–orbit splitting (Fig. 2.2) [7], p. 25.
18
2 General Kinetic Rules for Chemical Reactions, Collisional …