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Reaction Order
Differential Rate Law
Integrated Rate Law
Linear Form
Characteristic
Kinetic Plot
Half-life
Expression
Units of
Rate Constant
Zero
-
d [A]
d t
= rate = k
[A] = [A]0 - k t
[A] = -k t + [A]0
[A] vs t
t½ =
[A]0
2k
mole L-1 sec-1
First
-
d [A]
d t
= rate = k [A]
[A] = [A]0 e- k t
ln[A] = -kt + ln[A]0
ln [A] vs t
t½ =
ln(2)
k
sec-1
Second
-
d [A]
d t
= rate = k [A]2
[A] =
[A]0
1 + k t [A]0
1
[A]
= k t +
1
[A]0
1/[A] vs t
t½ =
1
k[A]0
L mole-1 sec-1
The series of three graphs shown below illustrate the use of the characteristic kinetic plots.
The graph on the left shows [A] vs t plots for a zero-order (red line),
first-order (green line), and second-order (blue line) reaction.
The graph in the middle shows ln [A] vs t plots and the graph on the right shows 1/[A] vs t plots for each reaction order.