1. KINETICS
The speed of a reaction

2. Kinetics The study of reaction rates.
Spontaneous reactions are reactions that will happen - but we can’t tell how fast.
Diamond will spontaneously turn to graphite – eventually.
Reaction mechanism – the steps by which a reaction takes place.

3. Reaction Rate Rate = Conc. of A at t2 -Conc. of A at t1 t2- t1
Rate = D[A] Dt
Change in concentration per unit time
For this reaction
N2 + 3 H2  2 NH3

4. As the reaction progresses the concentration of H2 goes down
Time

5. As the reaction progresses the concentration of N2 goes down 1/3 as fast. Check out the stoichiometry !
Concentration
[N2]
[H2]
Time

6. As the reaction progresses the concentration of the product, NH3 goes up.
Time

7. Calculating Rates Average rates are taken over long intervals.
Instantaneous rates are determined by finding the slope of a line tangent to the curve at any given point because the rate can change over time.
This is what is called in Calculus as a Derivative.

8. Average slope method
Concentration
D[H2] Dt
Time

9. Instantaneous slope method.
Concentration
D[H2]
D t
Time

10. Defining Rate
We can define rate in terms of the disappearance of the reactant or in terms of the rate of appearance of the product.
The stoichiometry is important.
In our example: N2 + 3 H2  2 NH3
-D [N2] = - 3 D[H2] = 2 D[NH3] Dt Dt Dt

11. Rate Laws Reactions are reversible.
As products accumulate they can begin to turn back into reactants.
Early on the rate will depend on only the amount of reactants present.
We want to measure the reactants as soon as they are mixed.
This is called the Initial rate method and time = 0.

12. Two key points to remember.
Rate Laws:
Two key points to remember.
The concentration of the products do not appear in the rate law because this is an initial rate so there are no products yet.
The order must be determined experimentally because it can’t be obtained from the equation.

13. 2 NO2  2 NO + O2
You will find that the rate will only depend on the concentration of the reactants.
Rate = k [NO2]n
This is called a rate law expression.
k is called the rate constant.
n is the order of the reactant - usually a positive integer.

14. 2 NO2  2 NO + O2 The rate of appearance of O2 can be said to be.
Rate' = D[O2] = k'[NO2] Dt
Because there are 2 NO2 for each O2
Rate = 2 x Rate'
So k[NO2]n = 2 x k'[NO2]n
So k = 2 x k'

15. Types of Rate Laws
Differential Rate law - describes how rate depends on concentration.
Integrated Rate Law - Describes how concentration depends on time.
For each type of differential rate law there is an integrated rate law and vice versa.
Rate laws can help us better understand reaction mechanisms.

16. Determining Rate Laws
The first step is to determine the form of the rate law (especially its order).
Must be determined from experimental data which is usually given.
For this reaction N2O5 (aq)  4 NO2 (aq) + O2 (g)
The reverse reaction won’t play a role

17. Now graph the data [N2O5] (mol/L) Time (s) 1.00 0 0.88 200 0.78 400
Now graph the data

18. To find rate we have to find the slope at two points
We will use the tangent method.

19. At .90 M the rate is (1.00 - .78) = 0.22 (0 - 400) - 400
= - 5.5x 10 -4

20. At .40 M the rate is (.52 - .31) = 0.22 (1000-1800) -800
= x 10 -4

21. Since the rate at twice the concentration is twice as fast, the rate law must be..
Rate = -D[N2O5] = k[N2O5]1 = k[N2O5] Dt
We say this reaction is first order in N2O5
First order means that the rate and the concentration are changing in a similar fashion.
The only way to determine order is to run the experiment.
So the Rate Law is Rate = k[N2O5]

22. The Method of Initial Rates
This method requires that a reaction be run several times.
The initial concentrations of the reactants are varied.
The reaction rate is measured just after the reactants are mixed.
Eliminates the effect of the reverse reaction.
In our problems, this isn’t a concern.

23. An Example of a Rate Law
For the reaction BrO Br H+1  3 Br2 + 3 H2O
The general form of the Rate Law is:
Rate = k[BrO3-1]n[Br-1]m[H+1]p
We use experimental data to determine the values of n, m, and p

24. Now we have to see how the rate changes with concentration
Initial concentrations (M)
Rate (M/s)
Br-1
BrO3-1
H+1
x 10-4
x 10-3
x 10-3
x 10-3
Now we have to see how the rate changes with concentration
Rate = k[BrO3-]1[Br-]1[H+]2

25. Remember our Formula ! Δ Concentration order = Δ Rate
In words, the change in concentration raised to the order of the exponent = the change in the rate.
Fortunately, most of the time, these can be solved on inspection. Eg. If the concentration is tripled and the rate is tripled, then 3x = 3 so x = 1.
HOWEVER…

26. Sometimes more drastic measures are needed.
Namely the law of logarithms.
Δ Concentration order = Δ Rate becomes
Order x (Log (conc.)) = Log (rate)
It is simple and works every time.
23 = log 2 = log x .301 = .903

27. Using data to create linear relationships
We can get more out of our data if we can create linear relationships (functions) from them.
Data is manipulated to create these linear relationships.
Obtaining a function gives us a way to determine many values in a straight-forward manner.

28. Integrated Rate Law
Expresses the reaction concentration as a function of time.
Form of the equation depends on the order of the rate law (differential).
Changes Rate = D [A]n Dt
We will mostly see n= 0, 1, and 2

29. First Order For the reaction 2 N2O5  4 NO2 + O2
We found the Rate = k[N2O5]1
If concentration doubles rate doubles.
If we integrate this equation with respect to time we get the Integrated Rate Law
ln[N2O5]t = - k t + ln[N2O5]0
ln is the natural log [N2O5]0 is the initial concentration.
Using ln in 1st order reactions gives us a straight line.

30. First Order General form Rate = D[A] / Dt = k[A] ln[A] = - kt + ln[A]0
In the form y = mx + b
y = ln[A] m = - k
x = t b = ln[A]0
A graph of ln[A] vs time is a straight line.

31. First Order Rates
By getting the straight line you can prove it is first order.
Often expressed in a ratio.

32. First Order
By getting the straight line you can prove it is first order.
Often expressed in a ratio

33. Half Life The time required to reach half the original concentration.
If the reaction is first order
[A] = [A]0/2 when t = t1/2

34. Half Life The time required to reach half the original concentration.
If the reaction is first order
[A] = [A]0/2 when t = t1/2
ln(2) = kt1/2

35. Half Life
t1/2 = 0.693/k
The time to reach half the original concentration does not depend on the starting concentration for first order reactions.
An easy way to find k.

36. Second Order Rate = -D[A] / Dt = k[A]2 Integrated rate law
1/[A] = kt + 1/[A]0
y= 1/[A] m = k
x= t b = 1/[A]0
A straight line if 1/[A] vs. t is graphed
Knowing k and [A]0 you can calculate [A] at any time.

37. Second Order Half Life
[A] = [A]0 /2 at t = t1/2

38. Zero Order Rate Law Rate = k[A]0 = k
Rate does not change with concentration.
Integrated [A] = -kt + [A]0
When [A] = [A]0 /2 t = t1/2
t1/2 = [A]0 / 2k

39. Zero Order Rate Law
Most often when reaction happens on a surface because the surface area stays constant.
Also applies to enzyme chemistry.
The material is said to be at the zeroeth order.

40. Concentration
Time

41. Concentration
k =
D[A]/Dt
D[A] Dt
Time

42. More Complicated Reactions
BrO Br H+1  3 Br2 + 3 H2O
For this reaction we found the rate law to be:
Rate = k[BrO3-][Br-][H+]2
To investigate this reaction rate we need to control the conditions.

43. Rate = k[BrO3-][Br-][H+]2
We set up the experiment so that two of the reactants are in large excess.
[BrO3-1]0= 1.0 x 10-3 M
[Br-1]0 = 1.0 M
[H+1]0 = 1.0 M
As the reaction proceeds [BrO3-1] changes noticably
[Br-1] and [H+1] don’t

44. Rate = k[BrO3-][Br-][H+]2
This rate law can be rewritten
Rate = k[BrO3-1][Br-1]0[H+1]02
Rate = k[Br-]0[H+1]02[BrO3-1]
Rate = k’[BrO3-]
This is called a pseudo first order rate law.
k = k’ [Br-]0[H+]02

45. Summary of Rate Laws Know your integrated rate laws.
Know how to find the order for the reaction
Know how to find k after you determine the orders.
As always, read the question carefully to make sure you are using all the given information.

46. Reaction Mechanisms
The series of steps that actually occur in a chemical reaction.
Kinetics can tell us something about the mechanism.
A balanced equation does not tell us how the reactants become products.
We will always want to find the rate determining step, which will usually be the slowest step in the mechanism.

47. Reaction Mechanisms 2 NO2 + F2  2 NO2F Rate = k[NO2][F2]
The proposed mechanism is
NO2 + F2  NO2F + F (slow)
F + NO2  NO2F (fast)
F is called an intermediate It is formed then consumed in the reaction, so it isn’t present in the given equation.

48. Reaction Mechanisms
Each of the two reactions is called an elementary step .
The rate for a reaction can be written from its molecularity .
Molecularity is the number of pieces that must come together.

49. Molecularity
Unimolecular step requires one molecule so the rate is first order.
Bimolecular step - requires two molecules so the rate is second order.
Termolecular step - requires three molecules so the rate is third order.
Termolecular steps are almost never heard of because the chances of three molecules coming into contact at the same time are miniscule.

50. A  Products Rate = k[A]
A + A  Products Rate= k[A]2
2A  Products Rate= k[A]2
A + B  Products Rate= k[A][B]
A + A + B  Products Rate= k[A]2[B]
2A + B  Products Rate= k[A]2[B]
A + B + C  Products Rate= k[A][B][C]

51. How to get rid of intermediates
Use the reactions that form them.
If the reactions are fast and irreversible - the concentration of the intermediate is based on stoichiometry.
If it is formed by a reversible reaction set the rates equal to each other.
A picture is worth 1,000 words here, so let’s check out the next slide.

52. Formed in reversible reactions
2 NO + O2  2 NO2
Mechanism
2 NO  N2O2 (fast) Step 1
N2O2 + O2  2 NO2 (slow) Step 2
rate = k2[N2O2][O2]
k1[NO]2 = k-1[N2O2]
rate = k2 (k1/ k-1)[NO]2[O2] =k[NO]2[O2]
NOTICE: Step 1 is in equilibrium so the rate of formation of the N2O2 is equal to the rate of formation of the 2 NO.

53. Formed in fast reactions
2 IBr  I2+ Br2
Mechanism
IBr  I + Br (fast)
IBr + Br  I + Br2 (slow)
I + I  I2 (fast)
What is the rate determining step ?
Rate = k[IBr][Br] but [Br]= [IBr]
Rate = k[IBr][IBr] = k[IBr]2

54. Collision theory Molecules must collide to react.
Concentration affects rates because collisions are more likely at higher concentrations.
Must collide hard enough.
Temperature and rate are related.
Only a small number of collisions produce reactions.

55. Potential
Energy
Reactants
Products
Reaction Coordinate

56. Activation Energy Ea Reaction Coordinate Potential Energy Reactants
Products
Reaction Coordinate

57. Reaction Coordinate Activated complex Potential Energy Reactants
Products
Reaction Coordinate

58. Potential
Energy }
Reactants DE
Products
Reaction Coordinate

59. Reaction Coordinate Br---NO Potential Br---NO Transition State Energy
2NO + Br 2
Reaction Coordinate

60. Terms
Activation energy - the minimum energy needed to make a reaction happen.
Activated Complex or Transition State - The arrangement of atoms at the top of the energy barrier.

61. Arrhenius Said the reaction rate should increase with temperature.
At high temperatures, more molecules have the energy required to get over the barrier.
The number of collisions with the necessary energy increases exponentially.

62. Arrhenius Number of collisions with the required energy = ze-Ea/RT
z = total collisions
e is Euler’s number (opposite of ln)
Ea = activation energy
R = ideal gas constant
T = temperature in Kelvin

63. Problems
Observed rate is less than the number of collisions that have the minimum energy.
Often due to Molecular orientation
Written into equation as p the steric factor.

64. O O O O O O O O O O No Reaction N N N N Br Br Br Br Br N N Br Br N Br

65. k = zpe-Ea/RT = Ae-Ea/RT
Arrhenius Equation
k = zpe-Ea/RT = Ae-Ea/RT
A is called the frequency factor = zp
ln k = -(Ea/R)(1/T) + ln A
Another line !!!!
ln k vs t is a straight line

66. Activation Energy and Rates
The final saga

67. Mechanisms and rates
There is an activation energy for each elementary step.
Activation energy determines k.
k = Ae- (Ea/RT)
k determines rate
Slowest step (rate determining) must have the highest activation energy.

68. This reaction takes place in three steps

69. Ea
First step is fast
Low activation energy

70. High activation energyEa
Second step is slow
High activation energy

71. Ea
Third step is fast
Low activation energy

72. Second step is rate determining

73. Intermediates are present

74. Activated Complexes or Transition States

75. Catalysts Speed up a reaction without being used up in the reaction.
Enzymes are biological catalysts.
Homogenous Catalysts are in the same phase as the reactants.
Heterogeneous Catalysts are in a different phase as the reactants.

76. How Catalysts Work
Catalysts allow reactions to proceed by a different mechanism - a new pathway.
New pathway has a lower activation energy.
More molecules will have this activation energy.
Do not change E

77. Heterogenous Catalysts
Hydrogen bonds to surface of metal.
Break H-H bonds H H H H H
Pt surface

78. Heterogenous Catalysts
Pt surface

79. Heterogenous Catalysts
The double bond breaks and bonds to the catalyst. H H H C C H H H H H
Pt surface

80. Heterogenous Catalysts
The hydrogen atoms bond with the carbon H H H C C H H H H H
Pt surface

81. Heterogenous Catalysts
Pt surface

82. Homogenous Catalysts
Chlorofluorocarbons catalyze the decomposition of ozone.
Enzymes regulating the body processes. (Protein catalysts)

83. Catalysts and rate
Catalysts will speed up a reaction but only to a certain point.
Past a certain point adding more reactants won’t change the rate.
Zero Order

84. Catalysts and rate. Rate
Rate increases until the active sites of catalyst are filled.
Then rate is independent of concentration
Concentration of reactants