Biomedical Engineering Reference
In-Depth Information
where
d D
[
]
d C
[
]
d A
[
]
d B
[
]
v
=
;
v
=
;
v
= -
;
v
= -
(7.4)
D
C
A
B
d t
d t
d t
d t
7.3.1.2 Rate Laws
Rate of reaction is essential to determine the kinetics of the reaction; it is also a
guide to the mechanism of the reaction, for any proposed mechanism should be
consistent with the observed rate law. Formally, the rate of reaction is a function of
the concentration of the species present in the reaction [3]
(7.5)
v
=
([
f A B C D
],[
],[
],[
])
For gases, the rate of reaction can be deduced from gas kinetics theory [4] and
is expressed by the simple expression
(7.6)
v
= [
k A B
][
]
In a liquid phase, the reaction rate is more empirical and is often—but not al-
ways—obtained by an expression of the type
a
b
(7.7)
v
= [
k A B
] [
]
where
k
,
a,
and
b
are coefficients independent of time. The parameter
k
is called the
rate constant.
7.3.1.3 Reaction Order
If a reaction rate is described by a formula of the type (7.7)—and this is a frequent
case—it is possible to define the order of the reaction with respect to a species by its
exponent, and an overall reaction order by the sum of the exponents corresponding
to each species
(7.8)
o a b
= +
Note that the order is not necessarily an integer; for example, the reaction rate
may be
1
2
v
=
k A B
[
]
[
]
and the order of the reaction is 3/2. Some reactions may obey a zero order rate law,
i.e. the reaction rate does not depend on the concentrations of the species, just on
the parameter
k
. Some comments on the “constant”
k
are needed at this stage.
First, the unit of
k
depends on the order of the reaction. For a zero order
reaction,
k
is expressed in mole/m
3
is for a first-order reaction,
k
is dimension-
ally a frequency and expressed in s
-1
; for a second order reaction, the unit of
k
is
m
3
/mol/s.
