Biomedical Engineering Reference
In-Depth Information
Intermediate formation in the liquid phase as shown in
Eqn (9.155)
:
(9.172)
where
K
H
is the equilibrium constant of reaction
(9.155)
or for H
þ
to be chemically associated
with HX
n
OH in the extract liquor;
C
n-H
þ
is the concentration HX
n
OH in the extraction liquor
that is chemically associated with H
þ
; and
C
n
is the concentration of HX
n
OH in the extraction
liquor.
The dissolution reaction rate, based on reactions
(9.148), (9.154), and (9.159)
, is given by:
C
nH
þ
¼ K
H
C
n
C
H
þ
k
en
K
S
½
H
2
O
K
S
C
H
þ
r
qs;qn
/
qs
¼ k
en
q
n
þ k
e
q
nH
þ
¼
þ K
S
C
H
þ
þ k
en
q
n
(9.173)
1
1
þ K
S
C
H
þ
where
r
q
s,
q
n
/
q
s
is the rate of formation of
s
-oligomer on the solid phase from the
n
-oligomer
on the solid phase. The hydrolysis reaction rate, based on
(9.155), (9.156), (9.157), (9.163), and
(9.164)
, can be written as
H
2
O
þk
h
K
H
C
H
þ
ÞC
n
r
s;n
/
s
¼
2
ðk
h
½
(9.174)
Here,
r
s,n
/
s
is the rate of formation of
s
-oligomer in aqueous phase from the
n
-oligomer in
aqueous phase. The factor 2 is resulted from the fact that either 2 mol of s-oligomers are
formed from breaking one bond or breaking of two different bonds in the n-oligomer can
each lead to one s-oligomer.
While there are n-bonds can be broken from an n-oligomer on the solid phase, there is only
one bond can be broken at any given time. Letting
k
E
¼ n
k
en
K
S
½
H
2
O
K
S
C
H
þ
þ K
S
C
H
þ
þ k
en
(9.175)
1
1
þ K
S
C
H
þ
and,
H
2
O
k
H
¼ k
h
K
H
½
K
H
C
H
þ
þ K
H
C
H
þ
þ k
h
(9.176)
1
1
þ K
H
C
H
þ
we obtain
k
E
r
qs;qn
/
qs
¼
n
q
n
(9.177)
k
E
r
s;qn
/
s
¼
n
q
n
(9.178)
r
s;n
/
s
¼
2k
H
C
n
(9.179)
Neglecting the condensation reactions, we obtain the formation of s-xylo-oligomers in the
liquor as:
X
X
N
N
r
s
¼
r
s;n
/
s
þ
r
s;qn
/
s
r
s;s
/c
1is1
(9.180)
n¼s
n¼sþ
1
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