Biomedical Engineering Reference
In-Depth Information
This reaction and its reverse take place readily in basic aqueous solution. This reaction
follows the form
A
þ
B
#
C
þ
D
(3.43)
Next, consider the addition of water to an olefin to form an alcohol,
RCH
¼
CH
2
þ
H
O
#
RCH
CH
OH
(3.44)
2
2
2
which can be written as
(3.45)
In many situations, we carry out these reactions in dilute aqueous solutions, where there is
a large excess of water. The concentration of pure liquid water is 55 mol/L, and the concen-
tration of water in liquid aqueous solutions is nearly constant even when the above solutes
are added up to fairly high concentrations. The reaction is essentially forward and the reverse
reaction is negligible. The rates of these forward reactions are
A
þ
B
#
C
r
¼
k
½
CH
COOC
H
5
½
H
O
(3.46)
3
2
2
and
r
¼
k
½
RCH
¼
CH
2
½
H
O
(3.47)
2
respectively. However, since change in the concentration of water [H
2
O] is usually immeasur-
ably small whenever water is a solvent, we may simplify these reactions to
CH
COOC
H
5
/
CH
COOH
þ
C
H
OH
;
r
¼
k
½
CH
COOC
H
5
(3.48)
3
2
3
2
5
3
2
and
RCH
¼
CH
2
/
RCH
CH
OH
;
r
¼
k
½
RCH
¼
CH
2
(3.49)
2
2
These reactions do not satisfy total mass conservation because the mole of water is omitted as
a reactant. We have also redefined a new rate coefficient as k
k[H
2
O] by grouping the nearly
constant [H
2
O] with k. After grouping the concentration of the solvent [H
2
O] into the rate
coefficient, we say that we have a pseudo first-order rate expression.
It is fairly common to write reactions in this fashion, omitting H
2
O from the chemical
equation and the rate, so these reactions become of the type
¼
A
/
C
þ
D
;
r
¼
kC
A
(3.50)
and
(3.51)
respectively. Thus, in addition to isomerization, there are in fact a number of reactions that
we write approximately as A
A
/
C
;
r
¼
kC
A
products, so our use of these simple rate expres-
sions is in fact appropriate for a large number of reaction systems.
Reaction rate expressions are always empirical, which means that we use whatever
expression gives an accurate enough description of the problem at hand. No reactions are
as simple as these expressions predict if we need them to be correct to many decimal places.
Further, all reaction systems in fact involve multiple reactions, and there is no such thing as
/
BorA
/
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