Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 282

solution to give NH 4 OH. Another example is the reaction and transport of gases
(CO 2 ,O 2 ) and volatile species in soil. As a general example, consider a compound
A in air that diffuses in air and reacts transforming to a compound B. There are three
steps involved:

gas diffusion
−−−−−−−→ A g A σ ,

k A
−→

(6.37)

A B ,

σ σ

liquid diffusion
−−−−−−−−→

B σ B aq .

Depending on which of the above reactions is slow, the overall rate will vary.
Fortheheterogeneousreactionschemeconsideredabove,thebulkgasphasewillbe
well mixed with a concentration C A , whereas the solute concentration at the interface
is C A . The change occurs across a very thin film of thickness

δ near the interface. The

diffusive flux of A to the interface is given by

C g

A − C A ,

D AL
δ

n A,diff = (6.38)

where D AL is the diffusion constant of A in solution. D AL / is the film transfer

coefficient forA. More appropriately we can define a general mass transfer coefficient
k c to represent this term.
The first-order surface reaction rate is given by

δ

C A . r

σ =

k (6.39)

σ

At steady state, the flux to the interface must be the same as the reactive loss at the
surface. This gives

k c C A
k c +

C A k c = . (6.40)

k

σ

The rate of the reaction at steady state is

k σ k c C g

A

r σ =

k c .

(6.41)

k σ +

There are two limiting conditions for the above rate: (i) if diffusion is controlling,
k

k c C A ; and (ii) if reaction is controlling, k C A .

σ

k c , r →

σ

k c , r

σ →

k

σ