Enrichment - Rate Equations to
Determine Reaction Order
• The equation for a straight line is:
y  mx  b
• Compare this equation to the rearranged first
order rate-law.
Enrichment - Rate Equations
to Determine Reaction Order
y  mx  b
ln A  a k t  ln A0
• Now we can interpret the parts of the equation
as follows:
– y can be identified with ln[A] and plotted on the y-axis.
– m can be identified with –ak and is the slope of the
line.
– x can be identified with t and plotted on the x-axis.
Enrichment - Rate Equations to
Determine Reaction Order
• Example 16-9: Concentration-versus-time data
for the thermal decomposition of ethyl bromide
are given in the table below. Use the following
graphs of the data to determine the rate of the
reaction and the value of the rate constant.

C2 H5Brg  
 C2H4g   HBrg  at 700K
Enrichment - Rate Equations to
Determine Reaction Order
Time
(min)
[C2H5Br]
0
1.00
1
0.82
2
0.67
3
0.55
4
0.45
5
0.37
ln [C2H5Br] 0.00 -0.20 -0.40 -0.60 -0.80 -0.99
1/[C2H5Br]
1.0
1.2
1.5
1.8
2.2
2.7
Enrichment - Rate Equations
to Determine Reaction Order
• We will make three different graphs of the
data.
1 Plot the [C2H5Br] (y-axis) vs. time (x-axis)
– If the plot is linear then the reaction is zero
order with respect to [C2H5Br].
2 Plot the ln [C2H5Br] (y-axis) vs. time (xaxis)
– If the plot is linear then the reaction is first
order with respect to [C2H5Br].
3 Plot 1/ [C2H5Br] (y-axis) vs. time (x-axis)
– If the plot is linear then the reaction is second
Enrichment - Rate Equations
to Determine Reaction Order
• Plot of [C2H5Br] versus time.
– Is it linear or not?
[C2H 5Br]
[C2H5Br] vs. time
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
Time (min)
4
5
Enrichment - Rate Equations
to Determine Reaction Order
• Plot of ln [C2H5Br] versus time.
– Is it linear or not?
ln [C2H5Br] vs. time
0
ln [C 2H5Br]
-0.2
0
1
2
3
-0.4
-0.6
-0.8
-1
-1.2
Time (min)
4
5
Enrichment - Rate Equations
to Determine Reaction Order
• Plot of 1/[C2H5Br] versus time.
– Is it linear or not?
1/[C2H5Br] vs. time
1/[C 2H5Br]
3
2
1
0
0
1
2
3
Time (min)
4
5
Enrichment - Rate Equations
to Determine Reaction Order
• Note that the only graph which is linear is the plot of
ln[C2H5Br] vs. time.
– Thus this is a first order reaction with respect
to [C2H5Br].
• Next, we will determine the value of the rate constant
from the slope of the line on the graph of ln[C2H5Br] vs.
time.
– Remember slope = y2-y1/x2-x1.
y 2 - y1  0.80  (0.20)
slope 

x 2 - x1
4  1 min
 0.60
slope 
 0.20 min -1
3 min
Enrichment - Rate Equations to
Determine Reaction Order
• From the equation for a first order reaction we
know that the slope = -a k.
– In this reaction a = 1.
slope  -0.20  -k
Thus the rate constant k  0.20 min .
-1
Enrichment - Rate Equations
to Determine Reaction Order
• The integrated rate equation for a reaction that is
second order in reactant A and second order
overall.
1
1

akt
A A0
• This equation can be rearranged to:
1
1
akt
A
A0
Enrichment - Rate Equations to Determine
Reaction Order
• Compare the equation for a straight line and the
second order rate-law expression.
y  mx  b
1
1
akt
A
A0
• Now we can interpret the parts of the equation as follows:
– y can be identified with 1/[A] and plotted on the y-axis.
– m can be identified with a k and is the slope of the line.
– x can be identified with t and plotted on the x-axis
– b can be identified with 1/[A]0 and is the y-intercept.
Enrichment - Rate Equations
to Determine Reaction Order
• Example 16-10: Concentration-versustime data for the decomposition of nitrogen
dioxide are given in the table below. Use
the graphs to determine the rate of the
reaction and the value of the rate constant

2 NO2 g  
 2 NOg   O2g  at 500K
Enrichment - Rate Equations
to Determine Reaction Order
Time
(min)
[NO2]
0
1.0
1
0.53
2
0.36
3
0.27
4
0.22
5
0.18
ln [NO2]
0.0
-0.63
-1.0
-1.3
-1.5
-1.7
1/[NO2]
1.0
1.9
2.8
3.7
4.6
5.5
Enrichment - Rate Equations
to Determine Reaction Order
•
Once again, we will make three different graphs
of the data.
1. Plot [NO2] (y-axis) vs. time (x-axis).
– If the plot is linear then the reaction is zero order with
respect to NO2.
2.
3.
Plot ln [NO2] (y-axis) vs. time (x-axis).
•
If the plot is linear then the reaction is first order with
respect to NO2.
Plot 1/ [NO2] (y-axis) vs. time (x-axis).
– If the plot is linear then the reaction is second order
with respect to NO2.
Enrichment - Rate Equations
to Determine Reaction Order
• Plot of [NO2] versus time.
– Is it linear or not?
[NO2]
[NO2] vs. time
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
Time (min)
4
5
Enrichment -Rate Equations
to Determine Reaction Order
• Plot of ln [NO2] versus time.
– Is it linear or not?
ln [NO2] vs. time
0
0
1
2
3
ln [NO2]
-0.5
-1
-1.5
-2
Time (min)
4
5
Enrichment - Rate Equations
to Determine Reaction Order
• Plot of 1/[NO2] versus time.
– Is it linear or not?
1/[NO2]
1/[NO2] vs.time
6
5
4
3
2
1
0
0
1
2
3
Time (min)
4
5
Enrichment - Rate Equations
to Determine Reaction Order
• Note that the only graph which is linear is
the plot of 1/[NO2] vs. time.
• Thus this is a second order reaction with
respect to [NO2].
• Next, we will determine the value of the
rate constant from the slope of the line on
the graph of 1/[NO2] vs. time.
Enrichment - Rate Equations
to Determine Reaction Order
y 2 - y1 5.50  (1.90) 1 M
slope 

x 2 - x1
5  1 min
3.60 1 M
slope 
 0.90 1 M min
4 min
• From the equation for a first order reaction we
know that the slope = a k
– In this reaction a = 2.
slope  0.90  2 k
Thus the rate constant k  0.45 M
1
min
-1