Biomedical Engineering Reference
In-Depth Information
The rate of the reverse reaction, r
2
, is similarly written in terms of C
C
and C
D
, the concentration of C and D, respectively:
k
back
C
C
C
D
r
2
5
(7.30)
When the reaction begins, the concentration of the reactants A and B is
high and that of the product C and D is low. So the forward reaction rate r
1
is initially much higher than r
2
, the reverse reaction rate, because the product
concentrations are relatively low. The reaction in this state is not in equilib-
rium, as r
1
.
r
2
. As the reaction progresses, the forward reaction increases
the buildup of products C and D. This increases the reverse reaction rate.
Finally, a stage comes when the two rates are equal to each other (r
1
5
r
2
).
This is the equilibrium state. At equilibrium:
There is no further change in the concentration of the reactants and the
products.
The forward reaction rate is equal to the reverse reaction rate.
The Gibbs free energy of the system is at minimum.
The entropy of the system is at maximum.
Under equilibrium state, we have
r
1
5
r
2
k
back
C
C
C
D
k
for
C
A
C
B
5
(7.31)
7.4.1.1 Reaction Rate Constant
A rate constant, k
i
, is independent of the concentration of reactants but is
dependent on the reaction temperature, T. The temperature dependency of
the reaction rate constant is expressed in Arrhenius form as:
E
RT
k
A
0
exp
(7.32)
5
2
where A
0
is a preexponential constant, R is the universal gas constant, and
E is the activation energy for the reaction.
The ratio of rate constants for the forward and reverse reactions is the
equilibrium constant, K
e
. From
Eq. (7.31)
we can write
C
C
C
D
C
A
C
B
k
for
k
back
5
K
e
5
(7.33)
The equilibrium constant, K
e
, depends on temperature but not on pres-
sure.
Table 7.4
gives values of equilibrium constants and heat of formation
of some gasification reactions (Probstein and Hicks, 2006, pp. 62
64).
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