Question

# 1. Consider the following chain mechanism for the high-temperature formation of NO (a regulated pollutant) through the Zeldovich mechanism: where ki = 1.82 x 10¹4 exp[-(76,241 cal/mol)/RºT) and k2 = 1.8 x 10¹ (T/K)exp[-(9300 cal/mol)/RºT) where both rate constants are given in units of cm³/mol/s. a) Write out the expressions for d[NO]/dt and d[N]/dt assuming that the above reactions only proceed in the forward direction (10 points). b) Assuming N is a quasi-steady state species and assuming that the concentrations of O, O₂, and N₂ are at their equilibrium values for a specified temperature and composition, show that d[NO]/dt = 2k1/[O]q[N₂]eq (5 points) c) Write out the expression for [N]s from part (b) (5 points). d) For the conditions given below, under the assumptions above, how long does it take form 50 ppm of NO? (Note that ppm = parts per million = 106 x mole fraction) (20 points) T=2100 K, p = 0.167 kg/m³, MW = 28.778 kg/kmol, Xo.q=7.6 x 105, Xoz.eq=3.025 x 10³, XN2.q=0.726 e) Calculate the value of the reverse reaction rate constant for (R1) at T = 2100 K (10 points). f) For your calculations in part D, is that assumption that the reverse reaction is negligible valid? Similarly, is the assumption that N is a quasi-steady state species valid? Please be quantitative. (10 points) g) For the conditions of part D, determine numerical values for [N]ss and XN. (5 points)  Fig: 1