1. Rates and Rate Laws

2. Factors that affect the Rate of a Reaction
The Physical state of the reactants
The Concentration of the Reactants
The Temperature of the Reaction
The Presence of a Catalyst

3. Reaction Rate
The change in concentration of a reactant or product per unit of time

4. 2NO2(g)  2NO(g) + O2(g) Reaction Rates: 1. Can measure
disappearance of
reactants
2. Can measure
appearance of
products
3. Are proportional
stoichiometrically

5. 2NO2(g)  2NO(g) + O2(g) [NO2] t Reaction Rates: 4. Are equal to the
slope tangent to
that point
5. Change as the
reaction proceeds,
if the rate is
dependent upon
concentration
[NO2] t

6. Rate Law Equation 2A (g) + 3 B (aq)  4 C (g)
As you write the rate equation remember that is based on changes in concentration so liquids or solids are not included in it.
Rate Law = k [A]2[B]3
K is the rate constant and is dependent on Temperature
The superscripts on the concentrations are the coefficients in the reaction. This is the best we can do without actual lab data to determine the effects of changing [A] and [B]

7. Rate Equivalent Equations
2A (g) + 3 B (aq)  4 C (g)
Using the equation above we can relate the equivalent rate changes between compounds.
Change in concentration over change in time
-[A] / 2t = - [B] / 3t = [C] / 4t
Notice the rates in the reactants are positive since they are disappearing and the products is positive since it is appearing.

8. Example 2A (g) + 3 B (aq)  4 C (g)
So as an example; What would be the rate of C if you knew the rate of disappearance of A was 4.2 M/s
-[A] / 2t = [C] / 4t
- (-4.2)/2 = Rate of C/4
Rate of C = 8.4 M/s

9. Writing a (differential) Rate Law
Problem - Write the rate law, determine the value of the rate constant, k, and the overall order for the following reaction:
2 NO(g) + Cl2(g)  2 NOCl(g)
Experiment
[NO]
(mol/L)
[Cl2]
Rate
Mol/L·s 1
0.250
1.43 x 10-6 2
0.500
5.72 x 10-6 3
2.86 x 10-6 4
11.4 x 10-6

10. Writing a Rate Law
Part 1 – Determine the values for the exponents in the rate law:
R = k[NO]x[Cl2]y
Experiment
[NO]
(mol/L)
[Cl2]
Rate
Mol/L·s 1
0.250
1.43 x 10-6 2
0.500
5.72 x 10-6 3
2.86 x 10-6 4
1.14 x 10-5
In experiment 1 and 2, [Cl2] is constant while [NO] doubles.
The rate quadruples, so the reaction is second order with respect to [NO]
 R = k[NO]2[Cl2]y

11. Writing a Rate Law
Part 1 – Determine the values for the exponents in the rate law:
R = k[NO]2[Cl2]y
Experiment
[NO]
(mol/L)
[Cl2]
Rate
Mol/L·s 1
0.250
1.43 x 10-6 2
0.500
5.72 x 10-6 3
2.86 x 10-6 4
1.14 x 10-5
In experiment 2 and 4, [NO] is constant while [Cl2] doubles.
The rate doubles, so the reaction is first order with respect to [Cl2]
 R = k[NO]2[Cl2]

12. Writing a Rate Law
Part 2 – Determine the value for k, the rate constant, by using any set of experimental data:
R = k[NO]2[Cl2]
Experiment
[NO]
(mol/L)
[Cl2]
Rate
Mol/L·s 1
0.250
1.43 x 10-6

13. Writing a Rate Law
Part 3 – Determine the overall order for the reaction.
R = k[NO]2[Cl2] 2 + 1
= 3
 The reaction is 3rd order
Overall order is the sum of the exponents, or orders, of the reactants

14. Determining Order with Concentration vs. Time data
(the Integrated Rate Law)
Zero Order:
First Order:
Second Order:

15. Solving an Integrated Rate Law
Time (s)
[H2O2] (mol/L)
1.00
120
0.91
300
0.78
600
0.59
1200
0.37
1800
0.22
2400
0.13
3000
0.082
3600
0.050
Problem: Find the integrated rate law and the value for the rate constant, k
A graphing calculator with linear regression analysis greatly simplifies this process!!
(Click here to download my Rate Laws program for theTi-83 and Ti-84)

16. Time vs. [H2O2] Time (s) [H2O2] 1.00 120 0.91 300 0.78 600 0.59 1200
1.00
120
0.91
300
0.78
600
0.59
1200
0.37
1800
0.22
2400
0.13
3000
0.082
3600
0.050
Regression results:
y = ax + b
a = x 10-4
b = 0.841
r2 =
r =

17. Time vs. ln[H2O2] Time (s) ln[H2O2] 120 -0.0943 300 -0.2485 600
120
300
600
1200
1800
-1.514
2400
-2.04
3000
-2.501
3600
-2.996
Regression results:
y = ax + b
a = x 10-4
b = -.005
r2 =
r =

18. Time vs. 1/[H2O2] Time (s) 1/[H2O2] 1.00 120 1.0989 300 1.2821 600
1.00
120
1.0989
300
1.2821
600
1.6949
1200
2.7027
1800
4.5455
2400
7.6923
3000
12.195
3600
20.000
Regression results:
y = ax + b
a =
b =
r2 =
r =

19. And the winner is… Time vs. ln[H2O2]
1. As a result, the reaction is 1st order
2. The (differential) rate law is:
3. The integrated rate law is:
4. But…what is the rate constant, k ?

20. Finding the Rate Constant, k
Method #1: Calculate the slope from the
Time vs. ln[H2O2] table.
Time (s)
ln[H2O2]
120
300
600
1200
1800
-1.514
2400
-2.04
3000
-2.501
3600
-2.996
Now remember:
 k = -slope
k = 8.32 x 10-4s-1

21. Finding the Rate Constant, k
Method #2: Obtain k from the linear regresssion analysis.
Regression results:
y = ax + b
a = x 10-4
b = -.005
r2 =
r =
Now remember:
 k = -slope
k = 8.35 x 10-4s-1

22. Rate Laws Summary Rate = k Rate = k[A] Rate = k[A]2 [A] = -kt + [A]0
Zero Order
First Order
Second Order
Rate Law
Rate = k
Rate = k[A]
Rate = k[A]2
Integrated Rate Law
[A] = -kt + [A]0
ln[A] = -kt + ln[A]0
Plot the produces a straight line
[A] versus t
ln[A] versus t
Relationship of rate constant to slope of straight line
Slope = -k
Slope = k
Half-Life

23. HW Problems [B] Rate of C in M/sec 1.00 4.00 2.00 8.00 3.00 9.00 1.50
A student has the following reaction; A(g) + 3 B (aq)  2 C(aq)
Given that the rate of C was 12.2 M/min. Find the rate of B
For the balanced equation above writer your predicted rate law.
Given the lab data below, find the integrated rate law including value of k and identify order.
[A]
[B]
Rate of C in M/sec
1.00
4.00
2.00
8.00
3.00
9.00
1.50 X
1.25 Y
25.00
4. Did the rate law that you obtained from the lab data match the one you predicted in #2?
5. Use the rate of C in Experiment 3 to find the rate of A.

24. HW Problems 1 cont
6. Given the lab Data below, write the rate law including value for k.
Experiment #
[A]
[B]
Rate of C m/min 1
0.10
2.00 x 10-3 2
0.20
4.00 x 10-3 3
0.30
4.86 x10-1

25. Homework #2
Given the following Lab Data, Identify order of the reaction and k value.
Time (seconds)
[A]
0.0
0.100
5.0
0.017
10.0
0.0090
15.0
0.0062
20.0
0.0047
2. In problem above find the Half Life of the reaction.

26. Homework #2 Continued Time ( Minutes) [CH4] 39 0.274 80. 0.238 140
3. Given the data below find the rate order of the reaction, the K value, Half Life and starting Concentration.
Time ( Minutes)
[CH4] 39
0.274
80.
0.238
140
0.190
210
0.146