Environmental Engineering Reference
In-Depth Information
involvement of the catalyst in the process. Actually, the fact that the reaction rate
increases by the presence of a catalyst can only be explained if the catalyst combines
with the reactants and the reaction takes place through elementary reactions where the
transition states formed require a lower activation energy than the uncatalyzed reac-
tion. This concept is graphically explained by Figure 5.3.
The lower the activation energy required for the molecules to react, the higher the
number of molecules that can react, which results in a higher reaction rate as shown in
Figure 5.4.
For a first-order reaction, the time needed to halve the reactant concentration is
t
2
=
ln2
ð
Eq
:
5
:
38
Þ
k
where k is the rate coefficient in the Arrhenius expression Equation (5.4). Now, if,
e.g., the activation energy of an uncatalyzed reaction at 400
C is 200,000 J
mol
−1
mol
−1
for its catalyzed counterpart, their rate coefficients are:
and 120,000 J
200
,
000
120
,
000
k
1
=k
0
e
−
and k
2
=k
0
e
−
8
:
31 × 673
:
15
8
:
31 × 673
:
15
so
120
,
000
8
:
31 × 673
:
15
k
1
=
e
−
t
1,
1
=
k
2
=
2
t
2,
1
6×10
6
=1
:
200
,
000
8
:
31 × 673
:
15
e
−
=
2
[AB]
E
a
E
″
a
E
′
a
A+B
C+D
Reaction path
FIGURE 5.3
How a catalyst affects the activation energy of a reaction (E
a
, activation energy
of the noncatalyzed reaction; E
0
a
,E
0
a
, activation energies of the elementary reactions with
catalyst) (Source: Reproduced with permission from Pasquetto and Patrone, 1999, vol.3. ©
Zanichelli editore S.p.A).
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