Integrated Rate Law
Appearance of NO
0.0080
0.0070
0.0060
[NO]
0.0050
0.0040
0.0030
0.0020
0.0010
0.0000
0
50
100
150
200
250
Time (s)
300
350
400
450
Integrated Rate Law:
A reaction is followed for an extended
period of time.
Method of Initial Rates
A reaction is followed for only the
first few moments of the reaction.
Advantages of the Method
of Initial Rate:
1. Useful when a reaction is reversible.
The reverse reaction won’t significantly
contribute to the first few moments
of the reaction.
2. Useful for very fast or very
slow reactions.
Advantages of the
Integrated Rate Method:
1. Useful for moderate length reaction.
2. Doesn’t require multiple experiments
to determine the order of the
reaction.
Common Uses of the Method
of Initial Rates:
1. To determine the order of the
reaction.
2. Find the rate constant, k .
Common Uses of the Method
of Integrated Rate Laws:
1. To determine the order of the
reaction.
2. Find the rate constant, k .
3. To determine the concentration
at a certain time.
4. To determine at what time a
certain concentration will be
reached.
Concentration of D over Time
Time(s)
[D] mol/L
0
0.2000
10
0.1904
20
0.1812
30
0.1725
40
0.1641
50
0.1562
60
0.1487
70
0.1415
80
0.1347
90
0.1282
100
0.1220
This is the raw data
collected during the
experiment
Start your analysis by
graphing [D] v. Time
Concentration of D over Time
0.2100
0.1900
0.1700
[D] mol/L
0.1500
0.1300
0.1100
0.0900
0.0700
0.0500
0
50
100
150
Time(s)
200
250
Concentration of D over Time
y = -0.0006x + 0.1848
R2 = 0.9737
0.2100
0.1900
0.1700
[D] mol/L
0.1500
0.1300
0.1100
0.0900
0.0700
0.0500
0
50
100
150
Time(s)
200
250
Concentration of D over Time
0.2100
The data do not form
a straight line.
0.1900
0.1700
The R2 value only has
one “9”.
0.1500
[D] mol/L
y = -0.0006x + 0.1848
RR22 == 0.9737
0.9737
0.1300
0.1100
This reaction is NOT
zero order!
0.0900
0.0700
0.0500
0
50
100
150
Time(s)
200
250
Next, convert your raw data to natural logs
and graph ln[D] v. time
Time(s)
[D] mol/L
Ln[D] mol/L
0
0.2000
-1.609
10
0.1904
-1.659
20
0.1812
-1.708
30
0.1725
-1.758
40
0.1641
-1.807
50
0.1562
-1.856
60
0.1487
-1.906
70
0.1415
-1.955
80
0.1347
-2.005
90
0.1282
-2.054
100
0.1220
-2.103
Natural Log of [D] over Time
-1.600
-1.800
Ln [D] mol/L
-2.000
-2.200
-2.400
-2.600
-2.800
-3.000
0
50
100
150
Time(s)
200
250
Natural Log of [D] over Time
y = -0.0049x - 1.6094
R2 = 1
-1.600
-1.800
Ln [D] mol/L
-2.000
-2.200
-2.400
-2.600
-2.800
-3.000
0
50
100
150
Time(s)
200
250
R2 = 1.0
The data DO form a
straight line.
The R2 value is 1.0.
This reaction is
first order.
Normally, when you get a straight line
you stop making graphs.
For teaching purposes, let’s go ahead
and look at the third kind of graph:
1/[D] v. time
Inverse [D] over time
18.000
16.000
1/[D] L/mol
14.000
12.000
10.000
8.000
6.000
4.000
0
50
100
150
time(s)
200
250
Inverse [D] over time
y = 0.0477x + 3.9571
R2 = 0.9737
18.000
16.000
1/[D] L/mol
14.000
12.000
10.000
8.000
6.000
4.000
0
50
100
150
time(s)
200
250