Biomedical Engineering Reference
In-Depth Information
1
E
max
d
q ¼
d
E
s
(9.119a)
where
q
is the available (vacant) active site fraction. Integrating
Eqn (9.119a)
, we obtain
E
s
¼ E
max
q
(9.119b)
which can be rewritten for adsorption of a single species
E
s
¼ E
max
ð
1
q
A
Þ
(9.120)
i.e. the adsorbed molecules exhibit an adsorption heat fluctuation (
E
s
) linearly related to the
site coverage. Using
Eqn (9.32)
,
DH
ad
ðq
A
Þ¼DH
ad
E
s
¼ DH
ad
E
max
ð
1
q
A
Þ
(9.121)
Therefore, one can imagine that the activation energy of adsorption should be linearly related
to the site coverage as well,
E
ad
ðq
A
Þ¼E
ad
þ E
a
q
A
(9.122)
where
E
ad
(
q
A
) is the activation energy of adsorption for A when the fractional surface
coverage of A is
q
A
. It is expected that at lower coverage, the activation energy is lower.
The activation energy increases as the coverage is increased.
E
ad
is the activation energy of
adsorption for A when no A has been adsorbed on the surface, and
E
a
is a positive scaling
constant. Since (see
Eqn 9.5
)
DH
ad
¼ E
ad
E
des
(9.123)
Substitute
Eqn (9.122)
into
Eqn (9.123)
, we have
E
des
ðq
A
Þ¼E
ad
DH
ad
ðq
A
Þ¼E
ad
DH
ad
þ E
max
ðE
max
E
a
Þq
A
(9.124)
We now derived at the activation energies for the adsorption and desorption as a function of
the surface coverage. Since we expect the desorption activation energy to decrease with
increasing coverage, i.e.
ðE
max
E
a
Þ <
0
(9.125)
We have
0
< E
a
< E
max
(9.126)
This forms the basis for studying the kinetics involving nonideal surfaces.
One example of kinetics involving the application of the nonideal surfaces theory is the
ammonia synthesis from Nitrogen and Hydrogen. The synthesis of ammonia has changed
the world food production (V. Smil, 2001). The Haber
e
Bosch process has remained the domi-
nant process in generating ammonia from nitrogen separated from air and hydrogen. Over
an Iron catalyst or a promoted Ru/C catalyst:
N
2
þ
2s
%
2
N
$s
(9.127a)
H
2
þ
2
s
%
2
H
$s
(9.127b)
H
$s þ
N
$s
%
NH
$s þ s
(9.127c)
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