Question

1. In the stratosphere, nitric oxide radical (·NO) is produced and consumed by the following reactions:

k1 N2O + O* ––––> 2·NO

k2 ·NO + O3 ––––> ·NO2 + O2

k3 ·NO2 + O –––––––> ·NO + O2

a.(3) Based on the rate laws for these reactions, write an equation for the steady-state concentration of nitric oxide radical (·NO) in the stratosphere. The rate constant for reaction 2 (k2) varies with temperature and has an Arrhenius constant (A) of 1.8 x 10-12 cm3 molecule-1 s-1 and an activation energy (Ea) of 11.4 kJ mol-1.

b.(4) Calculate the rates of reaction 2 at the top (0C, P = 0.001 atm) and bottom (–60°C, P = 0.1 atm) of the stratosphere assuming that xO3 = 1 ppm and x·NO = 5 ppb. (Note that you need to use the energy-specific gas constant, R = 8.314 x 10-3 kJ mol-1 K-1, to calculate rate constants with the Arrhenius equation.)

c.(2) Estimate the residence times of ·NO at the top and bottom of the stratosphere. d.(1) Show which physical factor, temperature or pressure, was most responsible for the difference in the rate of reaction 2 at the two altitudes.

Answer 1

d[NO]/dt =2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O]
       
      on applying steady state approximation on NO
       d[NO]/dt = O
       2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O] = O
        hence,
   2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
                             k2[O3]
      
      
             But k2= Ae^(-Ea/RT)
             and A= 1.8 x 10^(-12) cm3 and Ea= 11.4 kJ mol-1.
            So
2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
   1.8 x 10^(-12)e^(-11.4/RT)
       d[NO]/dt =2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O]
       
      on applying steady state approximation on NO
       d[NO]/dt = O
       2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O] = O
        hence,
                      2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
                             k2[O3]
      
      
             But k2= Ae^(-Ea/RT)
             and A= 1.8 x 10^(-12) cm3 and Ea= 11.4 kJ mol-1.
            So
   2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
   1.8 x 10^(-12)e^(-11.4/RT)
       d[NO]/dt =2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O]
       
      on applying steady state approximation on NO
       d[NO]/dt = O
       2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O] = O
        hence,
                      2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
                             k2[O3]
      
      
             But k2= Ae^(-Ea/RT)
             and A= 1.8 x 10^(-12) cm3 and Ea= 11.4 kJ mol-1.
            So
2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
1.8 x 10^(-12)e^(-11.4/RT)
       d[NO]/dt =2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O]
       
      on applying steady state approximation on NO
       d[NO]/dt = O
       2k1[O*][N2O]-k2[NO][O3]+k3[NO2][O] = O
        hence,
   2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
                             k2[O3]
      
      
             But k2= Ae^(-Ea/RT)
             and A= 1.8 x 10^(-12) cm3 and Ea= 11.4 kJ mol-1.
            So
   2k1[O*][N2O]+k3[NO2][O]
                [NO]= ________________________
1.8 x 10^(-12)e^(-11.4/RT)