Problem 21
In class we talked about Chapman chemistry, which was proposed to explain the presence of ozone in the stratosphere. The four chemical
equations are:

                                             O2 + hn O + O                                 J1

                                             O + O2 + M  O3 + M                         k2

                                             O3 + hn O + O2                                J3

                                              O + O3  O2 + O2                               k4

(a) It is convenient to define odd-oxygen as [Ox] = [O] + [O3]. Write rate expressions for [O], [O3], and [Ox], and show that when d[Ox]/dt = 0
(i.e. steady state), only reactions 1 and 4 appear in the expression.

(b) Assume that the rates of the second and third reactions are equal. Calculate the ratio of [O]/[O3]. Use J3 = 1x10-2 s-1 and k2 = 1x10-33 cm6 molec-2 s-1.
Do this calculation for densities of [M] = 2.0x1018 molec cm-3 and [M] = 1.0x1017 molec cm-3.

(c) At what altitude is the ratio of [O]/[O3] = 1? You can estimate the altitude (z) using the formula z = 7 ln(2.7x1019/[M]), in km. Remember that
[O2] = 0.21[M].