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Lecture 32
1
Going Beyond Initial Rates
(28.58)
Before we explore how rate laws can be deduced, we will examine the
variation in rate laws with longer times and temperature.
Implicitly we know that reactions must “end”.
For a large set of
reactions, reactants and products can come into equilibrium or at least a
quasiequilibrium where
A
B
B
In a general sense, this reaction is “reversible” (reactant to product and
vice versa), but not in a thermodynamic sense.
If we initially start with A, such that
[ ]
[ ]
,
f
d A
A
B
k
A
dt
B

=
(we’re assuming 1
st
order kinetics,
k
f
=forward rxn rate const.)
As the concentration of B builds up, the rate will slow as the reverse
reaction A
B occurs.
i.e. B “back reacts” to form A so
[ ]
[ ] [ ]
r
k
reverse rate constant
f
r
d A
k
A
k B
dt

=

=
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2
( 29
1
1
note the text has
f
r
k
k
k
k
A
B
A
B

I
A
I
A
[ ]
[ ]
At some point, the net consumption of A stops, i.e.
0
Also
0 and the system is in dynamic equilibrium.
d A
dt
d B
dt

=
=
[ ]
[ ]
Now at equilibrium we know
but from our rate law, we have:
eq
c
eq
B
K
A
=
[ ]
[ ]
[ ] [ ]
[ ]
[ ]
0
so
f
r
eq
eq
eq
f
c
r
eq
d A
d B
k
A
k B
dt
dt
B
k
K
A
k

=
=
=

=
=
Lecture 32
3
[ ] [ ] [ ] [ ] [ ] [ ]
0
0
If at time
0
and
0, then at any time, t,
t
A
A
B
B
A
A
=
=
=
=

[ ]
[ ] [ ] [ ] [ ] [ ]
{ }
( 29
[ ] [ ]
0
0
f
r
f
r
f
r
r
d A
k
A
k B
k
A
k
A
A
k
k
A
k A
dt

=

=


=
+

[ ]
( 29
[ ] [ ]
0
(see HW problem 2832)
f
r
r
d A
dt
k
k
A
k A
= 
+

[ ] [ ] [ ]
( 29
(
29
[ ] [ ] [ ]
0
where
A
at equilibrium
f
r
k
k t
eq
eq
eq
A
A
A
e
A
A

+
=

+
=
[ ] [ ]
( 29
[ ] [ ]
( 29
( 29
0
ln
ln
f
r
eq
eq
A
A
A
A
k
k t

=


+
Plot has slope of –(k
f
+k
r
)
Fig 28.5
This shows the time dependence of [A] and [B].
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4
What if the reaction is really fast with respect to mixing, so we can’t do
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This note was uploaded on 04/13/2008 for the course CHEM 444 taught by Professor Jameslis during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 JamesLis
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