Biomedical Engineering Reference
In-Depth Information
TABLE 9.7
Some Examples of Rate Expressions with Multilayer Adsorption Where Surface Reaction Is the
Rate-Limiting Step
Overall reaction
Rate expression
1) Isomerization
A
b ¼ K
A
C
A
þ K
B
C
B
N
C
A
C
B
=K
eq
1
1
½
1
þ Nð
1
bÞb
r ¼ k
s
cK
A
C
s
B
%
Nþ
1
b
1
ð
1
cÞb cb
(
1
)
2
b ¼ K
A
C
A
þ K
B
C
B
þK
C
C
C
þ K
D
C
D
2) Bimolecular
A
N
C
A
C
B
C
C
C
D
=
K
eq
ð
½
1
þ Nð
1
bÞb
r ¼ k
s
c
2
K
A
K
B
C
2
s
þ
B
C
þ
D
%
2
Nþ
1
1
ð
1
cÞb cb
1
bÞ
(
1
)
2
3) Bimolecular
(dissociative)
1
2
A
2
þ
1
2
A
2
þ K
B
C
B
þK
C
C
C
þ K
D
C
D
1
2
A
2
C
C
1=2
A
2
C
B
C
C
C
D
=K
eq
ð
N
½
1
þ Nð
1
bÞb
b ¼ K
r ¼ k
s
c
2
K
1=2
A
2
K
B
C
2
s
2
Nþ
1
1
ð
1
cÞb cb
1
bÞ
B
%
C
þ
D
4) Bimolecular (Eley
Rideal) A
b ¼ K
A
C
A
þ K
C
C
C
N
C
A
C
B
C
C
=
K
eq
1
1
½
1
þ Nð
1
bÞb
r ¼ k
s
cK
A
C
s
þ
B
C
%
b
Nþ
1
1
ð
1
cÞb cb
For chemical reactions with surface reaction as the limiting step, some examples of the
reaction rates are listed in
Table 9.7
when multilayer adsorption is employed to model the
nonideality of the surfaces.
9.5. KINETICS OF REACTIONS ON SURFACES WHERE THE SOLID
IS EITHER A PRODUCT OR REACTANT
In the previous section, we have learned that with solid catalysis the surface active centers
are not generated or consumed during reaction. When solid phase is one of the reactants, for
example, dissolution reactions, combustion reactions, or products, for example vapor depo-
sition, the active centers on the surface changes. The change of surface active centers could
lead to changes in the kinetic analysis. In this section, we shall use the reactions on woody
biomass to focus our discussions.
Renewable biomass has increasingly become the chemical and energy source for
commodity and chemical industry. Reactions involving biomass are usually heterogeneous
with the biomass being solid. Pulp and paper are the earliest and remaining application.
Based on the surface reaction theory, Liu (e.g. S. Liu “A Kinetic Model on Autocatalytic
Reactions in Woody Biomass Hydrolysis”,
J. Biobased Materials and Bioenergy
,2,135
e
147,
2008) inserted LWWH type of kinetics into bleaching, pulping, and extraction reactions
involving wood and fibers. A series of studies followed resulted in simplestic kinetic
relationships. A brief review of the kinetics of “acid-hydrolysis” and hot water extraction
is shown here as an example of reactions involving surfaces. There are multitudes of
chemical components in wood that participate in the reactions. At high temperatures,
water molecule can be activated and directly attack carbohydrates, resulting thermal-
hydrodepolymerization. In the case of acid hydrolysis, hydrogen ions act as catalyst to
soften the glycosidic bonds and induce their depolymerization. The glycosidic bond
breakage is enhanced when the breakaway oligomers are attracted away from the solid
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