Environmental Engineering Reference
In-Depth Information
5.3.1 I SOLATION M ETHOD
Consider a reaction involving two reactants A and B. Let the rate be r
=
k [A][B],
where the overall order of the reaction is two. If, however,
[
B
][
A
]
, throughout
constant (k ) and
the reaction, [B] remains constant in relation to [A]. Hence k
[
B
]∼
k [A]. This is called the pseudo-first-order rate . If the rate were more
complicated such as, for example,
=
the rate is r
2
k 1 [
A
]
r
=
,
(5.27)
k 2 [
B
]+
k 3
k [A] 2 , where k is called the pseudo-second-orderrate .The dependence
of r on each reactant can be isolated in turn to obtain the overall rate law.
we have r
=
5.3.2 I NITIAL R ATE M ETHOD
This is used in conjunction with the isolation method described above.The velocity or
rate of an n th-order reaction withA isolated may be generally expressed as r
k [A] n .
=
Hence we have log r
n log [A]. The slope of the plot of log r versus log [A]
will give n . This is most conveniently accomplished by measuring initial rate at
different initial concentrations. In Figure 5.2a, the slope of [A] versus time as t
=
log k
+
0
gives the initial rate, r 0 . The log of initial rate is then plotted versus the log of initial
concentration to obtain the slope, n (Figure 5.2b).
5.3.3 I NTEGRATED R ATE L AWS
The most common method of obtaining the order and rate of a reaction is the method
of integratedratelaws.Theinitialratesdonotoftenportraythefullratelaw,especially
(a)
(b)
Initial rate
[A]
n
log k
t
log [A] 0
FIGURE 5.2 (a) Concentration versus time for various [A] 0 values. (b) Logarithm of initial
rate versus logarithm of initial concentrations. The slope is the order of the reaction and the
intercept gives the logarithm of the rate constant for the reaction.
 
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