## Od mo m

The rate coefficient for this reaction is (Table B.2)

Vd)+m = 3-2 x 10-11 exp(70/r) M = 02 = 1.8 x 10'nexp(110/r) M = N2

The mean lifetime of O('D) against reaction with M is

Choosing 30 km (T = 227 K), and noting that M consists of 0.2102 + 0.79 N2, [M] = 3.1 x 1017 molecules cm-3 (Table 5.1), we obtain t0(.d) = 10"7 s

Consequently, O('D) is effectively converted instantaeously to ground-state O, and the photodissociation of 03 by both reactions 3 and 3' (above) can be considered to produce entirely ground-state O atoms.

Finally, O and 03 react to reform two 02 molecules:

The mechanism (reactions 1-4 above) for production of ozone in the stratosphere was proposed by Chapman (1930) and bears his name.

The rate equations for [O] and  in the Chapman mechanism are d = 2j0l[O2] - £2[M] +j03 - MOHOs] (5.1)

dt ¿[O3] dt ki[O][M] -7O3 - ^4 (5.2)

Once an oxygen atom is generated in reaction 1 (above), reactions 2 and 3 proceed rapidly. The characteristic time for reaction of the O atom in reaction 2 is

where k2 is assumed to be expressed as a termolecular rate coefficient (cm6 molecule"2 s-1). The rate coefficient is (Table B.2)

k2 = 6.0 x 10~34 (r/300)"2'4 cm6 molecule"2 s"1 Let us evaluate x2 at z = 30 and 40 km. Since  = 0.21 [M] at any altitude, we obtain t2 =---j (5.4)

We find z, km T, K [M], molecules cm-3 k2 (cm6 molecule-2 s-1) x2 (s)

The overall photolysis rate of ozone, Jo3> is the sum of the rates of the reactions 3 and 3' above, and the overall lifetime of 03 against photolysis is

Evaluating x3 at 30 km and 40 km at a solar zenith angle of 0° (see Figure 4.15) yields z, km_Jo3^o, s-1_jo3->o('d)» s-'_s

Thus, the photolytic lifetime of an 03 molecule is on the order of 10 min at these altitudes. However, this lifetime is not the overall lifetime of 03. Once 03 photodissociates, the O atom formed can rapidly reform 03 in reaction 2; thus, 03 photolysis alone does not lead to a loss of 03. Only reaction 4 truly removes 03 from the system. The lifetime of 03 against reaction 4 is

where k4 = 8.0 x 10-12 exp(-2060/T) cm3 molecule-1 s 1 (Table B.l). To estimate t4, we need [O], Let us assume, for the moment, that once an O atom is produced in reaction 1, reactions 2 and 3 cycle many times before reaction 4 has a chance to take place. If, indeed, there is rapid interconversion between O and 03, it is useful to view the sum of O and 03 as a chemical family (see Section 3.6). The sum of O and 03 is given the designation odd oxygen and is denoted Ox. The odd-oxygen family can be depicted as shown in Figure 5.2. The rapid interconversion between O and 03 leads to a pseudo-steady-state relationship between the O and 03 concentrations:

From the values of k2, [M], and jo{, we can estimate the / ratio. For example, at 30 and 40 km:

As altitude increases, [M] decreases, so the / ratio becomes larger at higher altitudes. Regardless, 03 is the dominant form of odd oxygen below ~ 50 km.

The lifetime of odd oxygen O t can be found from the ratio of its abundance to its rate of disappearance: 