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Integrated Rate Laws – Changes in concentration over time –
Calculus applied to kinetics
Consider the general reaction:
A → B
Rate = −∆[A] / ∆
t
Rate =
k
[A]
−∆[A] / ∆
t
=
k
[A]
Using calculus, the expression is integrated over time to obtain the
integrated rate law for
first order reaction
:
ln ([A]
0
/ [A]
t
) =
kt
or
ln [A]
0
ln [A]
−
t
=
kt
second order reaction:
Rate =
[A] /
−∆
∆
t
=
k
[A]
2
Integrating over time:
(1 / [A]
t
)
(1 / [A]
−
0
) =
kt
zero order reaction:
Rate =
[A] /
−∆
∆
t
=
k
[A]
0
Integrating over time:
[A]
t
[A]
−
0
=
−
kt
Problem:
At 25
o
C, HI breaks down slowly to hydrogen and iodide:
rate =
k
[HI]
2
.
The rate constant at 25
o
C is 2.4 x 10
21
−
L/mol s.
If
∙
0.0100 mol of HI(
g
) is placed in a 1.0L container, how long will it
take for the concentration of HI to reach 0.00900 mol/L?
1
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View Full DocumentDetermine reaction order from integrated rate law
For a first order reaction:
ln [A]
0
ln [A]
−
t
=
kt
ln [A]
t
=
−
kt
+ ln [A]
0
y
=
mx
+
b
second order:
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 Spring '08
 Eisenstadt

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