Question

For the thermal NO (Zeldovich) mechanism, the rate-limiting step in the NO formation process is O + N2 → NO + N. The reaction rates for the following temperature are T-1000K: k-4.41- 10-3 cm3 mol s-1 T-1200K: k-2.59 cm3 mol s1 Show the following relation for the production rate of NO to be true, assuming that the concentrations of 02 and O atoms are in equilibrium (O 20) and the N2 concentration is not changing: dINO] -9.3 1017exp 68690K dt cm.s

Answer 1

Formation of Nitrogen Oxides Nitric oxide is the major component of NOx emissions from the internal combustion engines. During combustion, three probable sources of NO formation are By oxidation of atmospheric (molecular) nitrogen at high temperatures in the post-flame burned gases ( Thermal NO (ii) Prompt NO (iii) Fuel NO Formed at the flame front within the flame reaction zone Oxidation of fuel-bound nitrogen at relatively low temperatures Thermal NO is the dominant source of nitrogen oxides in IC engines Thermal NO NO is formed in the high temperature burned gases behind the flame front. The rate of formation of NO increases exponentially with the burned gas temperature although, it is slower compared to the overall rate of combustion Kinetics and Modelling of Thermal NO Formation The following three reactions commonly referred to as the extended Zeldovich mechanism govern the formation of thermal NO 2 (2.2) (2.3) 3 k1, k2 and k3 are the reaction rate constants for the forward reactions and k.1, k.2 and k.3 are for the reverse reactions The original Zeldovich mechanism consisted of the first two reactions (2.1) and (2.2) and the third reaction (2.3) was added by Lavoie. The forward part of the first reaction (2.1) is highly endothermic with high activation energy of about 314 kJ /mol and is a rate determining reaction in NO 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 i Table 2.1 Table 2.1 Reaction rates for No formation mechanism, cm3/mol-s, T in K Reaction Forward Reverse ki- 1.8 x 1014x k2 1.8 x 1010Tx k3 7.1 x 1013x k.1 -3.8 x 1013 exp (-38,370/T) exp (- 4680/T) exp (- 450/T) exp(- 425/T) k.2 3.8 x 10 Tx exp(- 20,820/T) k.3 1.7 x 1014x N + OHNO H 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 [OI[N21 - k -1 [NO][N] + k2 [N]IO21-k-2 [NOj[O] + k3 [N][OH] - k dt (2.4) 3 INO[H] 3 l denotes the concentration of species in moles/cm Steady state approximation of [N]: Rate of formation and destruction of N is small relative (i) 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. O, OH, O2 and O concentrations are governed by chemical equilibrium considerations as the (ii) reactions governing concentration of these species are very fast at the combustion temperatures.. Steady state assumption of [N] leads to, [Nk1 [O]IN2l- k.1 [NO][N] - k2 [N][O2] dt k.2 [NOIIO] k3 [N][OH] +k-3 (2.5) Use of Eqs. 2.4 and 2.5 yield the rate of NO formation, [NO] 2 (k1 [OJ[N2]- k-1 [NOI[N]) dt (2.6)

and from Equation 2.5 steady state concentration of N (2.7) From the assumption of equilibration of O, OH, H and O2, (2.9) O1OH IOIINOJ INJIOH] e equilibrium k2 k.j Eliminating [N] and [H using equations 2.7 and 2.8, the equation 2.6 gives, (2.10) dt where K= (kl/k-1)(k2/k-2) įs equilibrium constant for the reaction N2 + O2艹2NO The NO formation rates may be calculated by Eq. 2.10 using equilibrium concentrations of O, O2, OH and N2. Most of NO formation takes place in the burned gases behind the flame front after combustion is completed locally. The rate of NO formation being much slower than the combustion rates, the NO formation process may be decoupled from combustion process and rate of formation of NO can be calculated assuming equilibrium concentrations of O, O2, OH and N2 By introducing equilibrium assumption in the calculations, the Eq. 2.10 is further simplified by using the following notations, where R1 is the reaction rate using equilibrium concentrations for the reaction (2.1) Similarly, Using the above notations the Eq. 2.10 is simplified to give rate of formation of NO as below,

[NO] = dt where w = R1/( R2+ R3)

NO Formation is a Function of Temperature and 02 From Eq. 2.11 the initial rate of NO formation when [NO]/[NO]e<< 1; (2.12) The concentration of atomic oxygen at equilibrium, using reaction 2 O2 O is given by; 1/2 (2.13) Ole 1/2 Equilibrium constant K p(O) is 31090 Kp()-3.6x1 0, exp (2.14) Using value of k1 from Table 2.2 and, the Eqs. 2.13 and 2.14 the initial rate of NO formation then reduces to d[NO] 1.3x10 1/2 (2.15) dt