Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 352

E XAMPLE 6.24 E FFECT OF CFC S OURCE R EDUCTION ON THE F UTURE
A TMOSPHERIC C ONCENTRATION

Figure 6.47 represents the entire atmosphere as a single box that receives CFCs at a
constant production rate of S tot mol/cm 2 y. Even though the rate of CFC production
has declined since the Montreal Protocol was signed, no significant depletion of CFCs
in the stratosphere has yet been noted because of its low reactivity. The long lifetime
of CFCs guarantees a continuous but slow increase in atmospheric concentration even
after the Montreal Protocol. Let us assume that for several decades the rate of release,
S tot , can be assumed to be constant. The only mechanism by which CFCs are removed
from the system involves photolysis reactions.
Let the overall rate constant for the reaction of a CFC be k(y − 1 ) and its concentration
be [CFC] (mol/m 3 of air). From Section 6.3.1.1, using w v = u = w p = 0 and r i =
− k [CFC], we have the following differential equation:

d [ CFC ]
d t

S tot
Z s .

+ k [ CFC ]= (6.186)

Solving the above equation with the initial condition that at t = 0, [ CFC ]=[ CFC ] 0 ,
we obtain

S tot

[ CFC ]=[ CFC ] 0 e − kt

kZ s ( 1 − e − kt ) .

+ (6.187)

Note that S tot /kZ s = Q s /kV atm , where Q s is the source strength in mol/y and V atm is
the atmospheric volume (m 3 ) .At some time in the future, the CFC concentration should
reach a steady state, that is, as t →∞ , [CFC] ss → S tot /kZ s . Hence,

1 − [ CFC ] ss
[ CFC ] 0

e − kt .

[ CFC ]
[ CFC ] 0 =

[ CFC ] ss
[ CFC ] 0 +

(6.188)

Since [CFC], [CFC] 0 , and [CFC] ss are concentrations in moles of CFC per m 3 of air,
they are easily converted to conventional units of ratio of volume of CFC to air (either

Atmosphere

Z s

CFC → Products

S tot

Surface sources

FIGURE 6.47 Box model for the production and dissipation of CFCs in the
atmosphere.