14 Chemical Kinetics - Notes, Chemistry, Engineering, Semester Class 12 Notes | EduRev

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Class 12 : 14 Chemical Kinetics - Notes, Chemistry, Engineering, Semester Class 12 Notes | EduRev

 Page 1


14 
Chemical Kinetics 
14.1 Introduction 
Up until now it has been assumed that chemical reactions take place very rapidly, and that 
the equilibrium conditions are reached instantaneously. While most combustion processes 
are extremely fast, often their speed is not such that combustion can be considered to be 
instantaneous, compared with the physical processes surrounding them. For example, the 
combustion in a reciprocating engine running at 6000 rev/min has to be completed in 
about 5 ms if the engine is to be efficient. Likewise, combustion in the combustion 
chamber of a gas turbine has to be rapid enough to be completed before the gas leaves the 
chamber. Such short times mean that it is not possible for all the gases in the combustion 
chamber to achieve equilibrium - they will be governed by the chemical kinetics of the 
reactions. 
Chemical kinetics plays a major role in the formation of pollutants from combustion 
processes. For example, oxygen and nitrogen will coexist in a stable state at atmospheric 
conditions, and the level of oxides of nitrogen (NO,) will be negligible. However, if the 
oxygen and nitrogen are involved in a combustion process then they will join together at 
the high temperature to form NO, which might well be frozen into the products as the 
temperature drops. This NO, is a pollutant which is limited by legislation because of its 
initant effects. NO, is formed in all combustion processes, including boilers, gas turbines, 
diesel and petrol engines; it can be removed in some cases by the use of catalytic 
converters. 
It was shown in Chapters 12 and 13 that significant dissociation of the normal products 
of combustion, carbon dioxide and water can occur at high temperature. The values 
shown were based on the equilibrium amounts of the substances, and would only be 
achieved after infinite time; however, the rates at which chemical reactions occur are 
usually fast and hence some reactions get close to equilibrium even in the short time the 
gases are in the combustion zone. An analysis of the kinetics of reactions will now be 
presented. 
14.2 Reaction rates 
Reaction rates are governed by the movement and breakdown of the atoms or molecules in 
the gas mixture: reactions will occur if the participating ‘particles’ collide. The number of 
Page 2


14 
Chemical Kinetics 
14.1 Introduction 
Up until now it has been assumed that chemical reactions take place very rapidly, and that 
the equilibrium conditions are reached instantaneously. While most combustion processes 
are extremely fast, often their speed is not such that combustion can be considered to be 
instantaneous, compared with the physical processes surrounding them. For example, the 
combustion in a reciprocating engine running at 6000 rev/min has to be completed in 
about 5 ms if the engine is to be efficient. Likewise, combustion in the combustion 
chamber of a gas turbine has to be rapid enough to be completed before the gas leaves the 
chamber. Such short times mean that it is not possible for all the gases in the combustion 
chamber to achieve equilibrium - they will be governed by the chemical kinetics of the 
reactions. 
Chemical kinetics plays a major role in the formation of pollutants from combustion 
processes. For example, oxygen and nitrogen will coexist in a stable state at atmospheric 
conditions, and the level of oxides of nitrogen (NO,) will be negligible. However, if the 
oxygen and nitrogen are involved in a combustion process then they will join together at 
the high temperature to form NO, which might well be frozen into the products as the 
temperature drops. This NO, is a pollutant which is limited by legislation because of its 
initant effects. NO, is formed in all combustion processes, including boilers, gas turbines, 
diesel and petrol engines; it can be removed in some cases by the use of catalytic 
converters. 
It was shown in Chapters 12 and 13 that significant dissociation of the normal products 
of combustion, carbon dioxide and water can occur at high temperature. The values 
shown were based on the equilibrium amounts of the substances, and would only be 
achieved after infinite time; however, the rates at which chemical reactions occur are 
usually fast and hence some reactions get close to equilibrium even in the short time the 
gases are in the combustion zone. An analysis of the kinetics of reactions will now be 
presented. 
14.2 Reaction rates 
Reaction rates are governed by the movement and breakdown of the atoms or molecules in 
the gas mixture: reactions will occur if the participating ‘particles’ collide. The number of 
Reaction rates 277 
collisions occurring in a mixture will be closely related to the number densities (number 
per unit volume) of the 'particles'. The number density can be defined by the molar 
concentration, c, which is the amount of substance per unit volume. This is obviously a 
measure of the number of particles per unit volume since each amount of substance is 
proportional to the number of molecules; this is illustrated in Fig 14.1. The molar 
concentration will be denoted by enclosing the reactant or product symbol in [ 1. 
.. . 
0. 
. 
. 0. 
.O . 
. 
.. 
1: 'd.1 
Fig. 14.1 Diagrammatic representation of molar concentration. Molar concentration in (a) is 
approximately half that in (b) 
Reactions occur when two, or more, reactants are capable of reacting. Many simple 
chemical reactions are second order, e.g. 
kf 
A+B-C+D 
kb 
(14.1) 
kf 
C02 + H2-H20 + CO 
kb 
where the first reaction is a general one and the second is an example based on the water 
gas reaction (chosen because the same number of reactants and products exist on both 
sides). 
These reactions can be written as 
(14.2) 
where A,, A,, .. . etc are the elements or compounds involved in the reaction, and 
Y,, v2, . . . etc are the respective stoichiometric coefficients. Equation (14.2) can be further 
generalised to 
(14.3) 
where q = total number of species being considered, v' represents the stoichiometric 
coefficients of the reactants, and Y" that of the products. 
In this case q has been taken as the same on both sides of the equation because it is 
assumed that the same species can exist on both sides. If a species does not exist on one of 
the sides it is represented by a stoichiometric coefficient of zero (Y = 0). For example, 
(14.4) CO, + H, wH,O + CO 
Page 3


14 
Chemical Kinetics 
14.1 Introduction 
Up until now it has been assumed that chemical reactions take place very rapidly, and that 
the equilibrium conditions are reached instantaneously. While most combustion processes 
are extremely fast, often their speed is not such that combustion can be considered to be 
instantaneous, compared with the physical processes surrounding them. For example, the 
combustion in a reciprocating engine running at 6000 rev/min has to be completed in 
about 5 ms if the engine is to be efficient. Likewise, combustion in the combustion 
chamber of a gas turbine has to be rapid enough to be completed before the gas leaves the 
chamber. Such short times mean that it is not possible for all the gases in the combustion 
chamber to achieve equilibrium - they will be governed by the chemical kinetics of the 
reactions. 
Chemical kinetics plays a major role in the formation of pollutants from combustion 
processes. For example, oxygen and nitrogen will coexist in a stable state at atmospheric 
conditions, and the level of oxides of nitrogen (NO,) will be negligible. However, if the 
oxygen and nitrogen are involved in a combustion process then they will join together at 
the high temperature to form NO, which might well be frozen into the products as the 
temperature drops. This NO, is a pollutant which is limited by legislation because of its 
initant effects. NO, is formed in all combustion processes, including boilers, gas turbines, 
diesel and petrol engines; it can be removed in some cases by the use of catalytic 
converters. 
It was shown in Chapters 12 and 13 that significant dissociation of the normal products 
of combustion, carbon dioxide and water can occur at high temperature. The values 
shown were based on the equilibrium amounts of the substances, and would only be 
achieved after infinite time; however, the rates at which chemical reactions occur are 
usually fast and hence some reactions get close to equilibrium even in the short time the 
gases are in the combustion zone. An analysis of the kinetics of reactions will now be 
presented. 
14.2 Reaction rates 
Reaction rates are governed by the movement and breakdown of the atoms or molecules in 
the gas mixture: reactions will occur if the participating ‘particles’ collide. The number of 
Reaction rates 277 
collisions occurring in a mixture will be closely related to the number densities (number 
per unit volume) of the 'particles'. The number density can be defined by the molar 
concentration, c, which is the amount of substance per unit volume. This is obviously a 
measure of the number of particles per unit volume since each amount of substance is 
proportional to the number of molecules; this is illustrated in Fig 14.1. The molar 
concentration will be denoted by enclosing the reactant or product symbol in [ 1. 
.. . 
0. 
. 
. 0. 
.O . 
. 
.. 
1: 'd.1 
Fig. 14.1 Diagrammatic representation of molar concentration. Molar concentration in (a) is 
approximately half that in (b) 
Reactions occur when two, or more, reactants are capable of reacting. Many simple 
chemical reactions are second order, e.g. 
kf 
A+B-C+D 
kb 
(14.1) 
kf 
C02 + H2-H20 + CO 
kb 
where the first reaction is a general one and the second is an example based on the water 
gas reaction (chosen because the same number of reactants and products exist on both 
sides). 
These reactions can be written as 
(14.2) 
where A,, A,, .. . etc are the elements or compounds involved in the reaction, and 
Y,, v2, . . . etc are the respective stoichiometric coefficients. Equation (14.2) can be further 
generalised to 
(14.3) 
where q = total number of species being considered, v' represents the stoichiometric 
coefficients of the reactants, and Y" that of the products. 
In this case q has been taken as the same on both sides of the equation because it is 
assumed that the same species can exist on both sides. If a species does not exist on one of 
the sides it is represented by a stoichiometric coefficient of zero (Y = 0). For example, 
(14.4) CO, + H, wH,O + CO 
278 Chemical kinetics 
can be represented by 
4 b4 
v:,~i-.C V;A, 
i= 1 kb i=l 
(14.5) 
where q=4 
vij = stoichiometric coefficient of i in reaction j 
A,=C02 v\=l v’~=O 
A, = H2 v;=1 v;=o 
A,= CO vk=O v:=1 
A,=H,O v;=O ~l;=l 
The law of mass action, which is derived from the kinetic theory of gases, states that the 
rate of formation, or depletion, of a species is proportional to the product of molar 
concentrations of the reactants, each raised to the power of its stoichiometric coefficient. 
Hence the rate of formation of species j, for an elementary reaction, is 
Rj a [Al]”J[A2]’*J [A,]” 
or 
n 
Rj=n[Ai]” for(j= 1, ... s) 
i= 1 
and s = total number of simultaneous reactions. 
Equation (14.6) may be written as 
n 
Rj=k,n[AJyJ for(j= 1, ... s) 
i= 1 
(14.6) 
(14.7) 
where kj is the rate constantfor the reaction. In eqns (14.1) to (14.5) the reaction was 
described as having a forward and backward direction, with rates k, and kb. The reaction 
shown in eqn (14.7) can be described in this way as 
n 
R, = bj 
[A,]’” 
for (j = 1, . . . s) (14.8) 
i= 1 
and 
n 
Rbj = kbj n [A,]” for (j = 1,. . . S) (14.9) 
The rate of change with time of species i is proportional to the change of the 
stoichiometric coefficients of Ai in the reaction equation (the system is effectively a first 
order one attempting to achieve the equilibrium state). Thus, for the forward direction 
i= 1 
(14.10) 
Page 4


14 
Chemical Kinetics 
14.1 Introduction 
Up until now it has been assumed that chemical reactions take place very rapidly, and that 
the equilibrium conditions are reached instantaneously. While most combustion processes 
are extremely fast, often their speed is not such that combustion can be considered to be 
instantaneous, compared with the physical processes surrounding them. For example, the 
combustion in a reciprocating engine running at 6000 rev/min has to be completed in 
about 5 ms if the engine is to be efficient. Likewise, combustion in the combustion 
chamber of a gas turbine has to be rapid enough to be completed before the gas leaves the 
chamber. Such short times mean that it is not possible for all the gases in the combustion 
chamber to achieve equilibrium - they will be governed by the chemical kinetics of the 
reactions. 
Chemical kinetics plays a major role in the formation of pollutants from combustion 
processes. For example, oxygen and nitrogen will coexist in a stable state at atmospheric 
conditions, and the level of oxides of nitrogen (NO,) will be negligible. However, if the 
oxygen and nitrogen are involved in a combustion process then they will join together at 
the high temperature to form NO, which might well be frozen into the products as the 
temperature drops. This NO, is a pollutant which is limited by legislation because of its 
initant effects. NO, is formed in all combustion processes, including boilers, gas turbines, 
diesel and petrol engines; it can be removed in some cases by the use of catalytic 
converters. 
It was shown in Chapters 12 and 13 that significant dissociation of the normal products 
of combustion, carbon dioxide and water can occur at high temperature. The values 
shown were based on the equilibrium amounts of the substances, and would only be 
achieved after infinite time; however, the rates at which chemical reactions occur are 
usually fast and hence some reactions get close to equilibrium even in the short time the 
gases are in the combustion zone. An analysis of the kinetics of reactions will now be 
presented. 
14.2 Reaction rates 
Reaction rates are governed by the movement and breakdown of the atoms or molecules in 
the gas mixture: reactions will occur if the participating ‘particles’ collide. The number of 
Reaction rates 277 
collisions occurring in a mixture will be closely related to the number densities (number 
per unit volume) of the 'particles'. The number density can be defined by the molar 
concentration, c, which is the amount of substance per unit volume. This is obviously a 
measure of the number of particles per unit volume since each amount of substance is 
proportional to the number of molecules; this is illustrated in Fig 14.1. The molar 
concentration will be denoted by enclosing the reactant or product symbol in [ 1. 
.. . 
0. 
. 
. 0. 
.O . 
. 
.. 
1: 'd.1 
Fig. 14.1 Diagrammatic representation of molar concentration. Molar concentration in (a) is 
approximately half that in (b) 
Reactions occur when two, or more, reactants are capable of reacting. Many simple 
chemical reactions are second order, e.g. 
kf 
A+B-C+D 
kb 
(14.1) 
kf 
C02 + H2-H20 + CO 
kb 
where the first reaction is a general one and the second is an example based on the water 
gas reaction (chosen because the same number of reactants and products exist on both 
sides). 
These reactions can be written as 
(14.2) 
where A,, A,, .. . etc are the elements or compounds involved in the reaction, and 
Y,, v2, . . . etc are the respective stoichiometric coefficients. Equation (14.2) can be further 
generalised to 
(14.3) 
where q = total number of species being considered, v' represents the stoichiometric 
coefficients of the reactants, and Y" that of the products. 
In this case q has been taken as the same on both sides of the equation because it is 
assumed that the same species can exist on both sides. If a species does not exist on one of 
the sides it is represented by a stoichiometric coefficient of zero (Y = 0). For example, 
(14.4) CO, + H, wH,O + CO 
278 Chemical kinetics 
can be represented by 
4 b4 
v:,~i-.C V;A, 
i= 1 kb i=l 
(14.5) 
where q=4 
vij = stoichiometric coefficient of i in reaction j 
A,=C02 v\=l v’~=O 
A, = H2 v;=1 v;=o 
A,= CO vk=O v:=1 
A,=H,O v;=O ~l;=l 
The law of mass action, which is derived from the kinetic theory of gases, states that the 
rate of formation, or depletion, of a species is proportional to the product of molar 
concentrations of the reactants, each raised to the power of its stoichiometric coefficient. 
Hence the rate of formation of species j, for an elementary reaction, is 
Rj a [Al]”J[A2]’*J [A,]” 
or 
n 
Rj=n[Ai]” for(j= 1, ... s) 
i= 1 
and s = total number of simultaneous reactions. 
Equation (14.6) may be written as 
n 
Rj=k,n[AJyJ for(j= 1, ... s) 
i= 1 
(14.6) 
(14.7) 
where kj is the rate constantfor the reaction. In eqns (14.1) to (14.5) the reaction was 
described as having a forward and backward direction, with rates k, and kb. The reaction 
shown in eqn (14.7) can be described in this way as 
n 
R, = bj 
[A,]’” 
for (j = 1, . . . s) (14.8) 
i= 1 
and 
n 
Rbj = kbj n [A,]” for (j = 1,. . . S) (14.9) 
The rate of change with time of species i is proportional to the change of the 
stoichiometric coefficients of Ai in the reaction equation (the system is effectively a first 
order one attempting to achieve the equilibrium state). Thus, for the forward direction 
i= 1 
(14.10) 
Chemical kinetics of NO 279 
and, for the backward direction 
Hence the net rate of formation of Ai is 
[A,]'' - kbj n [Ai]" 
d [Ail j 
i= 1 
Consider the following rate controlled reaction equation: 
kf 
vaA + vbB-vcC + vdD 
kb 
The net rate of generation of species C is given by 
-- d[C1 - [kf[A]'"[B]" - kb[c]''[DP] 
dt 
(14.11) 
(14.12) 
(14.13) 
( 14.14) 
Using the notation [A]/[Al, = a, [Bl/[B], = /3, [Cl/[Cl, = y and [Dl/[Dl, = 6, where 
the suffix e represents equilibrium concentrations, gives 
(14.15) d [ C ] /d t = k, a "0/3"b[A ] 2 [ B 12 - kbyVc 6 vd [ C 1,'. [ D ] 2 
At equilibrium 
k,[A]:[B]? = k,[C],'.[D],'d= Rj 
Therefore the net rate is 
(14.16) 
d[C]/dt = Rj[av~/3vb - y"C6vd1 (14.17) 
14.3 Rate constant for reaction, k 
The rate constant for the reaction, k, is related to the ability of atoms or ions to combine. 
In combustion engineering this will usually occur when two or more particles collide. 
Obviously the collision rate is a function of the number of particles per unit volume, and 
their velocity of movement, i.e. their concentration and temperature. Most chemical 
reactions take place between two or three constituents because the probability of more than 
three particles colliding simultaneously is too small. It has been found experimentally that 
most reactions obey a law like that shown in Fig 14.2. 
This means that the rate constant for the reaction can be defined by an equation of the 
form 
(14.18) 
This equation is called the Arrhenius equation. The factor A is called the pre- 
exponential factor, or the frequency factor, and is dependent on the rate at which 
collisions with the required molecular orientation occur. A sometimes contains a 
temperature term, indicating that the number of collisions is related to the temperature in 
those cases. The term E in the exponent is referred to as the activation energy. The values 
of A and E are dependent on the reactions being considered, and some values are 
k = Ae - E/RT 
Page 5


14 
Chemical Kinetics 
14.1 Introduction 
Up until now it has been assumed that chemical reactions take place very rapidly, and that 
the equilibrium conditions are reached instantaneously. While most combustion processes 
are extremely fast, often their speed is not such that combustion can be considered to be 
instantaneous, compared with the physical processes surrounding them. For example, the 
combustion in a reciprocating engine running at 6000 rev/min has to be completed in 
about 5 ms if the engine is to be efficient. Likewise, combustion in the combustion 
chamber of a gas turbine has to be rapid enough to be completed before the gas leaves the 
chamber. Such short times mean that it is not possible for all the gases in the combustion 
chamber to achieve equilibrium - they will be governed by the chemical kinetics of the 
reactions. 
Chemical kinetics plays a major role in the formation of pollutants from combustion 
processes. For example, oxygen and nitrogen will coexist in a stable state at atmospheric 
conditions, and the level of oxides of nitrogen (NO,) will be negligible. However, if the 
oxygen and nitrogen are involved in a combustion process then they will join together at 
the high temperature to form NO, which might well be frozen into the products as the 
temperature drops. This NO, is a pollutant which is limited by legislation because of its 
initant effects. NO, is formed in all combustion processes, including boilers, gas turbines, 
diesel and petrol engines; it can be removed in some cases by the use of catalytic 
converters. 
It was shown in Chapters 12 and 13 that significant dissociation of the normal products 
of combustion, carbon dioxide and water can occur at high temperature. The values 
shown were based on the equilibrium amounts of the substances, and would only be 
achieved after infinite time; however, the rates at which chemical reactions occur are 
usually fast and hence some reactions get close to equilibrium even in the short time the 
gases are in the combustion zone. An analysis of the kinetics of reactions will now be 
presented. 
14.2 Reaction rates 
Reaction rates are governed by the movement and breakdown of the atoms or molecules in 
the gas mixture: reactions will occur if the participating ‘particles’ collide. The number of 
Reaction rates 277 
collisions occurring in a mixture will be closely related to the number densities (number 
per unit volume) of the 'particles'. The number density can be defined by the molar 
concentration, c, which is the amount of substance per unit volume. This is obviously a 
measure of the number of particles per unit volume since each amount of substance is 
proportional to the number of molecules; this is illustrated in Fig 14.1. The molar 
concentration will be denoted by enclosing the reactant or product symbol in [ 1. 
.. . 
0. 
. 
. 0. 
.O . 
. 
.. 
1: 'd.1 
Fig. 14.1 Diagrammatic representation of molar concentration. Molar concentration in (a) is 
approximately half that in (b) 
Reactions occur when two, or more, reactants are capable of reacting. Many simple 
chemical reactions are second order, e.g. 
kf 
A+B-C+D 
kb 
(14.1) 
kf 
C02 + H2-H20 + CO 
kb 
where the first reaction is a general one and the second is an example based on the water 
gas reaction (chosen because the same number of reactants and products exist on both 
sides). 
These reactions can be written as 
(14.2) 
where A,, A,, .. . etc are the elements or compounds involved in the reaction, and 
Y,, v2, . . . etc are the respective stoichiometric coefficients. Equation (14.2) can be further 
generalised to 
(14.3) 
where q = total number of species being considered, v' represents the stoichiometric 
coefficients of the reactants, and Y" that of the products. 
In this case q has been taken as the same on both sides of the equation because it is 
assumed that the same species can exist on both sides. If a species does not exist on one of 
the sides it is represented by a stoichiometric coefficient of zero (Y = 0). For example, 
(14.4) CO, + H, wH,O + CO 
278 Chemical kinetics 
can be represented by 
4 b4 
v:,~i-.C V;A, 
i= 1 kb i=l 
(14.5) 
where q=4 
vij = stoichiometric coefficient of i in reaction j 
A,=C02 v\=l v’~=O 
A, = H2 v;=1 v;=o 
A,= CO vk=O v:=1 
A,=H,O v;=O ~l;=l 
The law of mass action, which is derived from the kinetic theory of gases, states that the 
rate of formation, or depletion, of a species is proportional to the product of molar 
concentrations of the reactants, each raised to the power of its stoichiometric coefficient. 
Hence the rate of formation of species j, for an elementary reaction, is 
Rj a [Al]”J[A2]’*J [A,]” 
or 
n 
Rj=n[Ai]” for(j= 1, ... s) 
i= 1 
and s = total number of simultaneous reactions. 
Equation (14.6) may be written as 
n 
Rj=k,n[AJyJ for(j= 1, ... s) 
i= 1 
(14.6) 
(14.7) 
where kj is the rate constantfor the reaction. In eqns (14.1) to (14.5) the reaction was 
described as having a forward and backward direction, with rates k, and kb. The reaction 
shown in eqn (14.7) can be described in this way as 
n 
R, = bj 
[A,]’” 
for (j = 1, . . . s) (14.8) 
i= 1 
and 
n 
Rbj = kbj n [A,]” for (j = 1,. . . S) (14.9) 
The rate of change with time of species i is proportional to the change of the 
stoichiometric coefficients of Ai in the reaction equation (the system is effectively a first 
order one attempting to achieve the equilibrium state). Thus, for the forward direction 
i= 1 
(14.10) 
Chemical kinetics of NO 279 
and, for the backward direction 
Hence the net rate of formation of Ai is 
[A,]'' - kbj n [Ai]" 
d [Ail j 
i= 1 
Consider the following rate controlled reaction equation: 
kf 
vaA + vbB-vcC + vdD 
kb 
The net rate of generation of species C is given by 
-- d[C1 - [kf[A]'"[B]" - kb[c]''[DP] 
dt 
(14.11) 
(14.12) 
(14.13) 
( 14.14) 
Using the notation [A]/[Al, = a, [Bl/[B], = /3, [Cl/[Cl, = y and [Dl/[Dl, = 6, where 
the suffix e represents equilibrium concentrations, gives 
(14.15) d [ C ] /d t = k, a "0/3"b[A ] 2 [ B 12 - kbyVc 6 vd [ C 1,'. [ D ] 2 
At equilibrium 
k,[A]:[B]? = k,[C],'.[D],'d= Rj 
Therefore the net rate is 
(14.16) 
d[C]/dt = Rj[av~/3vb - y"C6vd1 (14.17) 
14.3 Rate constant for reaction, k 
The rate constant for the reaction, k, is related to the ability of atoms or ions to combine. 
In combustion engineering this will usually occur when two or more particles collide. 
Obviously the collision rate is a function of the number of particles per unit volume, and 
their velocity of movement, i.e. their concentration and temperature. Most chemical 
reactions take place between two or three constituents because the probability of more than 
three particles colliding simultaneously is too small. It has been found experimentally that 
most reactions obey a law like that shown in Fig 14.2. 
This means that the rate constant for the reaction can be defined by an equation of the 
form 
(14.18) 
This equation is called the Arrhenius equation. The factor A is called the pre- 
exponential factor, or the frequency factor, and is dependent on the rate at which 
collisions with the required molecular orientation occur. A sometimes contains a 
temperature term, indicating that the number of collisions is related to the temperature in 
those cases. The term E in the exponent is referred to as the activation energy. The values 
of A and E are dependent on the reactions being considered, and some values are 
k = Ae - E/RT 
280 Chemical kinetics 
11 T 
Fig. 14.2 Relationship between reaction rate and temperature 
introduced below. The significance of the activation energy, E, is shown in Fig 14.3, 
where it can be seen to be the energy required to ionise a particular molecule and make it 
receptive to reacting. It appears in the exponential term because not all activated molecules 
will find conditions favourable for reaction. 
Activation 
Enthalpy (or internal energy) 
of reaction, Q, (or Q, ) 
Progress of reaction 
Fig. 14.3 Schematic interpretation of activation energy 
14.4 Chemical kinetics of NO 
The chemical kinetics for the formation of NO are relatively well understood, and will be 
developed here. The chemical kinetics for other pollutants can be derived in a similar way 
if the necessary reaction rates are available, although it should be recognised that most 
other pollutants are produced by reactions between the oxygen in the air and a constituent 
of the fuel (e.g. carbon or sulfur). The formation of NO in combustion processes can occur 
from two sources: thermal NO and prompt NO. Thermal NO is formed by the combination 
of the oxygen and nitrogen in the air, and will be produced even if there is no nitrogen in 
the fuel itself. This section will restrict itself to considering thermal NO. Prompt NO is 
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