Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 317

1.2 × 10 − 5 mol/m 3 (background CO). The equation is [ A ]= 2.04 × 10 − 4 ( 1 −
e − t/ 2 ) + 1.2 × 10 − 5 e − t/ 2 .Thesteady-stateconcentration[A] ss is2.04 × 10 − 4 mol/m 3 .
Figure 6.28 depicts the change in CO with time. If the contribution from automobiles
is negligible, the [A] in the CSTR is continually diluted.

E XAMPLE 6.14 A N I NDOOR A IR P OLLUTION M ODEL

In this case we consider a pollutant that may not only react, but also has a source within
the indoor atmosphere. We disregard both w v and w p . The overall mass balance in this
case is

d [ A ]
d t =

U
L · ( [ A ] 0 −[ A ] ) +

S A
H − k [ A ] .

(6.134)

Theterm U/L = (UWH)/(LWH) = G/V iscalledtheairexchangerate, I a and S A /H =
(S A LW)/(LWH) = S TOT /V , where S TOT is the surface source strength expressed in
μ g/s. Using the initial condition, [ A ]=[ A ] initial at t = 0, we obtain

[ (S TOT /V) +[ A ] 0 I a ]
I a + k

1 − e − (I a + k)t

+[ A ] initial e − (I a + k)t . [ A ]= (6.135)

The steady-state concentration ( t →∞ ) is

[ (S TOT /V) +[ A ] 0 I a ]
I a + k

[ A ] ss = . (6.136)

For the special case where [A] 0 = 0 and k = 0 (conservative pollutant) and where
unsteady state is applicable,

S TOT
I a V

1 − e − I a t .

[ A ]= (6.137)

If a room of total volume V = 1000 m 3 where a gas range emits 50 mg/h of NO x
is considered for an air exchange rate I a = 0.2 h − 1 , and a first-order rate of loss
at 0.1 h − 1 , we have at steady state, [A] ss = ( 50 / 1000 )/( 0.2 + 0.1 ) = 0.16 mg/m 3 =

160 μ g/m 3 .

E XAMPLE 6.15 A G LOBAL M IXING M ODEL

Globally the stratosphere and the atmosphere are considered to be separate compart-
ments (boxes) with internal mixing, but with slow exchange between the two boxes
(Warneck, 1999; Reible, 1998). This is one of the reasons why nonreactive chemicals
(e.g., CFCs) released to the troposphere slowly make their way into the stratosphere
where they participate in other reactions (e.g., with ozone). If the slow exchange rate
is represented G (see Figure 6.29), the rate of change in concentration in each CSTR is
continued