Environmental Engineering Reference
In-Depth Information
7.2 Law of Mass Action for Kinetic Reactions
As mentioned above, chemical reactions often are described by a so-called
kinetic
formulation. The term kinetic is used in order to distinguish the description from the
equilibrium or thermodynamic formulation. In the latter case an equilibrium condi-
tion is used to characterise the relationship between the participating species. The
thermodynamic formulation is equivalent to the formulation of isotherms, which
was introduced in Chap. 6.
In the kinetics approach the rate term itself is expressed in terms of concen-
trations of the chemical species. Different formulations of such kinetic laws can be
found in concerned publications that are valid for certain reactions under certain
conditions and a certain parameter range. The most common formulation is the
kinetic version of the
Law of Mass Action
. The equilibrium version of that law is
presented in the following chapter.
For the reaction example (
7.2
) the law of mass action formulation is:
q ¼
k
c
a
c
b
(7.8)
with a reaction-characteristic parameter
is a characteristic for
the 'speed' of the reaction. For fast reactions, k has a high value. For slow reactions
it is a small number.
The increase of the rate with the concentration, as expressed by (
7.8
), is an
expected behavior. For a reversible reaction
aþb
!
k
. The parameter
k
2
c
, the rate law is given by:
q ¼
k
!
c
a
c
b
þ
k
c
2
(7.9)
c
There appear different reaction parameters for reaction and back-reaction:
k
!
and
k
. Moreover, the stoichiometric number for the involvement of a species
in the reaction appears in form of an exponent of the concentration; two for
species
c
. The rate increases proportionally to the respective power of the concen-
tration if the stoichiometric number exceeds one. Equations (
7.8
) and (
7.9
) are
special cases of the general form
q ¼
k
!
Y
reactants
i
c
a
i
þ
k
Y
products
j
c
a
j
j
(7.10)
where the stoichiometric numbers are denoted as
a
j
. Equation (
7.10
)isnot
the most general formulation of the law of mass action. In fact, it turns out to be
valid only for the small and moderate concentration range. If the fluid is highly
mineralized, i.e. when concentrations of dissolved species are high, inhibition
due to competition between species has to be taken into account. Then activi-
ties replace concentrations in the above expressions. Further details are given
in Chap. 9.
a
i
and
