Module 2: Genesis and Mechanism of Formation of Engine Emissions
Lecture 4: Mechanisms of Nitrogen Oxides Formation
Rate Constants for Zeldovich Mechanism
The rate constants for the above reactions in units of cm3/mol-s and temperature in K are given in Table 2.1
Table 2.1
Reaction rates for NO formation mechanism, cm3/mol-s, T in K
Reaction
Forward
Reverse
O + N2 ↔ NO +N
k1= 1.8 x 1014 x
exp (-38,370/T)
k -1 = 3.8 x 1013 x
exp(- 425/T)
N + O2 ↔ NO + O
k2 = 1.8 x 1010T x
exp (- 4680/T)
k -2 = 3.8 x 109 T x
exp(- 20,820/T)
N + OH ↔ NO + H
k3 = 7.1 x 1013 x
exp (- 450/T)
k -3 = 1.7 x 1014 x
exp(- 24,560/T)
Rate of NO Formation The rate of formation of NO using the three reactions (2.1) to (2.2) can be expressed by the following equation;
[NO] = k1 [O][N2] – k -1 [NO][N] + k2 [N][O2] – k -2 [NO][O] + k3 [N][OH] – k -3 [NO][H]
(2.4)
[] denotes the concentration of species in moles/cm3.
(i)
Steady – state approximation of [N]: Rate of formation and destruction of N is small relative to its concentration. Concentration of atomic N is of the order of 10-8 mole fraction only, which is much smaller compared to the other reacting chemical species.
(ii)
O, OH, O2 and O concentrations are governed by chemical equilibrium considerations as the reactions governing concentration of these species are very fast at the combustion temperatures..
Steady state assumption of [N] leads to,
[N] = + k1 [O][N2] – k -1 [NO][N] – k2 [N][O2] + k -2 [NO][O] - k3 [N][OH] + k -3
(2.5)
[NO][H] = 0
Use of Eqs. 2.4 and 2.5 yield the rate of NO formation,
[NO] = k1 [O][N2] – k -1 [NO][N] + k2 [N][O2] – k -2 [NO][O] + k3 [N][OH] – k -3 [NO][H] 
