Consider the Chapman mechanism for the dynamics of atmospheric ozone, O_3, which

Question

Consider the Chapman mechanism for the dynamics of atmospheric ozone, O_3, which is given by Where the reaction rate constants for the conditions of interest are k_1 = 7.76 times 10^-6 cm^6/(molecule^2 s) k_2 = 4.66 times 10^-6 cm^3/(molecule s) k_3 = 5.00 times 11^-11 s^-1 k_4 = 2.50 times 10^-4 s^-1 while M denotes any molecule in the system. The initial composition of the system at time t = 0 is as follows (where the chemical symbol in parenthesis denotes the composition of that species in molecules per cm^3): (N_2)_o = 13.9 times 10^16 molecules/cm^3 (O_2)_o= 3.7 times 10^16 molecules/cm^3 (O_3)_o= 1.0 times 10^12 molecules/cm^3 While evaluation of (M) can proceed under the approximation that (O)

Explanation / Answer

4. Mechanism for ozone

(a) d[O3]/dt = k1[O][O2][M]

d[O2]/dt = k2[O][O3]

d[O]/dt = k3[O2]

(b) Steady state apporimation of [O], formation consumption

k3[O2] + k4[O3] = k1[O][O2][M] + k2[O][O3]

[O] = (k3[O2] + k4[O3])/(k1[O2][M] + k2[O3])

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