Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 335

Consider an aqueous droplet falling through the atmosphere. There are five
processes that must be considered. These are (see Seinfeld, 1986; Schwartz and
Freiberg, 1981):

(i) Diffusion of solute in the gas phase, characterized by the diffusion
constant, D g .
(ii) Mass transfer across the air-water interface of the droplet characterized
by the mass transfer coefficient, k mt , and the progress toward equilibrium
at the interface. The latter is characterized by the air-water equilibrium
constant, K aw .
(iii) For a species such as SO 2 , its dissolution in the aqueous phase is imme-
diately followed by a dissociation reaction. The dissociation is as follows:
[SO 2 ·

k 1
K 2 H + +

HSO 3 []

, for which the equilibrium concentration
of [SO 2 · H 2 O] aq can be obtained (see Section 5) from

H 2 O ] aq

[SO 2 · H 2 O] − [SO 2 · H 2 O] eq

H 2 O ] eq = e −α t ,

[ SO 2 ·

H 2 O ] −

[ SO 2 ·

HSO 3 ] eq ) .
(iv) If the droplet is not well mixed, then diffusion within the aqueous phase
will play a role. This is characterized by the diffusion constant, D w .
(v) The final item to be considered is chemical reaction within the droplet.
This is what we discussed earlier and is characterized by the reaction rate
constant,

1 ([H + ] eq +[

where α = k 1 + k

−

1
[S ( VI ) ]

d [S ( VI ) ]
d t

=−

k .

Seinfeld (1986) has analyzed each of these steps in detail. He derived an equation
for the characteristic time ( τ ) in each case. Table 6.10 summarizes the expressions for
τ . The terms, their definitions, and typical values are also given. If the characteristic

time for any one step is larger than that for the chemical reaction within the droplet,
then equilibrium will not be achieved in that step and the observed rate at which
the products are formed will be smaller than the reaction rate. This has interesting
consequences as far as acid rain is concerned.
From Table 6.21, one observes that for S(IV) oxidation in a 10- μ m droplet, τ r is

larger than all other values and hence the conversion is reaction limited. In general,

for all practical purposes

τ

τ g and τ d are small. τ i , τ a ,or τ r is then rate limiting. Unless

the droplets are much smaller, τ a is large compared with τ i and τ r . τ r is both pH and

species dependent.

E XAMPLE 6.21 S CAVENGING OF C ONSERVATIVE P OLLUTANTS BY R AIN OR F OG

Consider rain or fog drops falling through the atmosphere. Each drop reaches terminal
velocity determined by its size and scavenges pollutants as they drop to the surface.
continued