Environmental Engineering Reference
In-Depth Information
The rate equation can also be written as a product of two factors, one dependent on the
temperature (k
f
) and the other on the concentrations of the reactants:
=k
f
Y
n
p
i
r
f
=k
f
×f M½
ð
,M½
,
…
Þ
M½
ð
Eq
:
5
:
2
Þ
i=1
where k
f
is called the
reaction rate coefficient
or
rate constant
(Arrhenius), p
i
is the reaction order with respect to species
M
i
,and
X
n
i=1
p
i
is the total reac-
tion order.
We also have to take into account the reverse reaction, so the reaction rate can be
written as
p
1
M½
p
2
p
m
M
m+1
p
m+1
r
=
r
f
−
r
b
=k
f
M½
−
k
b
M½
½
ð
Eq
:
5
:
3
Þ
The reaction rate is influenced by:
1. The
nature
of the reactants
2. The
concentration
of the reactants
3. The
temperature
4. The presence of
catalysts
The first point concerns the nature of the chemical bonds of the species involved. To
understand the influence of the other factors, the way a reaction takes place should be
well known. A necessary condition for a reaction to take place is the collision of the
reactant molecules, having kinetic energy due to the thermal energy. Thus, the higher
the concentration of the reactants, the higher the probability that a reaction takes place,
because of the larger number of collisions. However, the reaction rate does not depend
on the number of collisions alone, because otherwise we would observe high rates for
every reaction. The collision must be a successful collision. This means that, given the
right orientation of the molecules at the moment of the collision, the collision has to be
strong enough to break the existing bonds and to exceed the repulsive barriers of the
molecules. The minimum amount of kinetic energy needed is called the activation
energy. Not every collision is successful as not every molecule has the same kinetic
energy. For example, the velocities of the particles of a gas at a certain temperature
continuously change due to the high number of collisions, and theoretically, they
assume all the values between zero and infinite, according to the Maxwell
Boltzmann
law. This law is represented in Figure 5.1a. Here, the area of each rectangle of very
small size (at its limit, infinitesimal) is the number of particles with a certain kinetic
energy close to a certain value
E
1
. The sum of all the infinitesimal rectangles on
the interval zero
-
infinite is the total number of particles. The hatched area in
Figure 5.1b represents the number of particles with a kinetic energy greater or equal
to the activation energy E
a
; the lower the activation energy, the higher the reaction rate
as more molecules will be ready to react. If the temperature increases, the distribution
curve moves to the left (the percentage of particles with higher kinetic energy
—
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