Environmental Engineering Reference
In-Depth Information
1.2
[A]/[A
0
]
[B]/[A
0
]
[C]/[A
0
]
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
t
/min
FIGURE 5.6
Change in concentrations of A, B, and C with time for a series reaction A
→
B
→
C.
growth (which is termed the
induction period
) followed by an exponential increase
to [A]
0
.
In those cases where there are several intermediates involved in a reaction, such
as occurs in most chemical reactions in air and water environments, the derivation of
the overall rate expression will not be quite as straightforward as described above.
The intermediate (e.g., B above) is necessarily of low concentration and is assumed
to be constant during the reaction. This is called the
pseudo
-
steady-state approxi-
mation
(
PSSA
). It allows us to set d[B]/d
t
to zero. Thus, at pseudo-steady-state we
can obtain
B
∗
]+
−
k
2
[
k
1
[
A
]=
0,
(5.43)
k
1
k
2
[
k
1
k
2
[
B
∗
]=
]
0
e
−
k
1
t
.
[
A
]=
A
Hence
e
−
k
1
t
)
.
[
C
]=[
A
]
0
(
1
−
(5.44)
Comparing with the exact equations for [B] and [C] given in Table 5.1, we observe
that the exact solutions approximate the steady-state solution only if
k
2
k
1
in other
words, when the reactivity of B is so large that it has little time to accumulate. The
difference between the exact and approximate solutions can be used to estimate the
departure from steady state.
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