Biomedical Engineering Reference
In-Depth Information
We need only to determine [
$
CH
3
] before the rate expression is determined. We observe
that addition of
Eqns (6.66)
þ
(6.68)
leads to
3
2
0 ¼
k
1
½
CH
CHO
2
k
4
½$
CH
(6.70)
3
Solving for [
$
CH
3
], we obtain
k
1=2
1
1=2
½$
CH
3
¼
½
CH
3
CHO
(6.71)
2
k
4
Substituting
Eqn (6.71)
into
Eqn (6.69)
, we obtain the rate for the overall reaction
k
1=2
1
3=2
r
¼
k
3
½$
CH
3
½
CH
3
CHO
¼
k
½
CH
3
CHO
(6.72)
3
2
k
4
k
3
(k
1
/2k
4
)
1/2
.
Therefore, we predict 3/2 order kinetics with an effective rate coefficient k
¼
6.6. KINETICS OF ACID HYDROLYSIS
We have learned the derivation of kinetic equations based on a given mechanism. Next, we
apply this technique to a slightly more complex situation: acid hydrolysis of polymers in an
aqueous medium. Acid hydrolysis can be described as
O
H
O
% H
2
(6.73)
2
O
/
HX
n
OH
ð
aq
Þþ
H
HX
m
OH
ð
aq
Þþ
HX
s
OH
ð
aq
Þ
(6.74)
2
H
þ
ð
H
þ
ð
HX
n
OH
ð
aq
Þþ
aq
Þ %
HX
n
OH
$
aq
Þ
(6.75)
H
þ
ð
H
þ
ð
$
Þþ
ð
Þ /
$
Þþ
ð
Þ
(6.76)
HX
n
OH
aq
H
O
aq
HX
m
OH
aq
HX
s
OH
aq
2
H
þ
þ
O
%
O
þ
H
H
(6.77)
2
3
O
þ
ð
O
þ
ð
HX
n
OH
ð
aq
Þþ
H
aq
Þ %
HX
n
OH
$
H
aq
Þ
(6.78)
3
3
O
þ
ð
H
þ
ð
HX
n
OH
$
H
aq
Þ /
HX
m
OH
$
aq
Þþ
HX
s
OH
ð
aq
Þ
(6.79)
3
n;H
2
O* is activated water molecule; H
3
O
þ
and H
þ
are considered to have the
same catalytic effect; HX
n
OH represents an n-unit oligomer,
where m
þ
s
¼
i.e. for example, xylan:
H(
OC
5
H
8
O
3
.
The monomers can further decompose into other products. For example, sugars can dehy-
drate in the presence of protons to dehydrated products such as furfural, humic acid, levu-
linic acid, etc.
e
O
e
C
5
H
8
O
3
e
)
n
OH, X
¼
H
þ
ð
H
þ
þ
(6.80)
The reaction
(6.74)
shows that the breaking of intermonomer bonds is random. If all the
intermonomer bonds are equally active, the rate of formation of one particular m-oligomer
from an n-oligomer is given by
HX
OH
$
aq
Þ/
other dehydration products
1
O
r
m; n/mð
6
:
74
Þ
¼
k
C
n
½
(6.81)
H
ð2Þ
2
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