Biomedical Engineering Reference
In-Depth Information
concentration A that is not converted to C 1 .Using Eqn (6.41) ,wearriveatthereaction
rate expression for the overall reaction (6.32) as
r
¼
r C ¼
r
2 ¼
k
C
AB ¼
k
K
C
C
(6.42)
2
2
1
A
B
Therefore, we have shown that if the second step is rate liming, the overall reaction rate is
of second order and the rate constant is the product of the rate constant of the second reaction
and the equilibrium constant of the first step.
What happens if step 1, or reaction (6.30) , is really the rate-limiting step? That the reaction
(6.31) is fast is equivalent to say that any AB* formed in the reaction system is immediately
converted to C and thus the concentration of AB* is zero. Thus, the overall reaction rate is
then
r
¼
r
A ¼
r
1 ¼
k
C
C
(6.43)
1
A
B
The reaction rate is equivalent to the forward rate of reaction step 1.
We are now comfortable in approximate the reaction rates if one or more reaction steps are
rate-limiting while others are fast.
6.3.2. Pseudosteady-State Hypothesis
In a reaction system, there are species that are of particular interest to us, while there are
also species that are of less interest from a practical point of view. For example, in the
simplistic reaction system we use, reactions (6.30) and (6.31) , reactants A and B are to be
supplied, while C is the product of interest, based on the overall reaction (6.32) . We are
not interested in the value of AB* from a practical standpoint. One can also look at this
from a different standpoint. There are species formed in the reaction system that have
very low level of concentration and upon completion of the reaction system there is no trace
of, or only negligible amount of, them. We call these species intermediates. In most reaction
systems, the intermediates formed can hardly be detected with even sophisticated measuring
tools available today. Because the concentrations of the intermediates are very low, one can
assume that their net rates of formation are zero. This is the essence of pseudosteady-state
hypothesis (PSSH).
In reaction system (6.30) and (6.31) , species AB* is an intermediate, that is
0 ¼
r
AB ¼
r
1
r
2 ¼
k
C
C
B
k
C
AB
k
C
AB
(6.44)
1
A
1
2
1 If the assumption K 1 is not invoked, one needs to find the concentrations of “free” A and B to be used in Eqn
(6.38) . The measurable concentrations of A and B are given by (via mass balance).
C AT ¼
C A þ
C AB
C AB
These two equations must be solved together with Eqn (6.38) to express the concentration of C AB* as
a function of the overall concentrations of A and B. This may be more important at the beginning of the reaction
(measurable concentration of A and B change “sharply” while very little product C is formed) and toward the
completion of the reaction.
C BT
¼
C B
þ
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