Derivation of Kinetic Rate Laws
Consider a general chemical reaction whose balanced equation is
a
A
+
b
B
+
...
→
e
E
+
f
F
+
where a, b, e, and f are the stoichiometric coefficients. Introduce a variable
w
which is a measure
of the difference in concentration from the initial value:
w
=
1
a
([A]
0
−
[A])
=
1
b
([B]
0
−
[B])
=
...
(1)
=
1
e
([E]
−
[E]
0
)
=
1
f
([F]
−
[F]
0
)
=
where the zero subscript denotes the initial concentration. The rate of the reaction can often be
written in as many equivalent forms as there are species in the stoichiometric equation. Let the
volume be constant. As the rate is the change in concentration,
Δ
w
, per change in time,
Δ
t
, take
the change in the variable
w
in Eq. (1) per change in time remembering that the initial concentra
tions are constant. One obtains for the rate
Rate
=
Δ
w
Δ
t
=−
1
a
Δ
[A]
Δ
t
1
b
Δ
[B]
Δ
t
=
=
1
e
Δ
[E]
Δ
t
=
1
f
Δ
[F]
Δ
t
=
Many reactions are found experimentally to have rates that can be expressed in terms of a
simple rate law
Rate
=
k
[A]
x
[B]
y
(2)
=
k
([A]
0
−
aw
)
x
([B]
0
−
bw
)
y
where Eq. (1) was used to solve for the concentrations (in the first line of Eq. (2)) in terms of the
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 Spring '08
 jursich
 Reaction, Chemical reaction, ΔT, Δt Δt, Δt f Δt

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