1. Chemical Kinetics
Unit 10 – Chapter 12

2. Reaction Rate Change in concentration of a reactant over time
12.1
Reaction Rates
Reaction Rate
Change in concentration of a reactant over time
[A] means “concentration of A” in mol/L.

3. Decomposition of NO2 into O2 and NO.
12.1
Reaction Rates
Decomposition of NO2 into O2 and NO.

4. Instantaneous Rate Value of the rate at a particular time.
12.1
Reaction Rates
Instantaneous Rate
Value of the rate at a particular time.
Can be obtained by computing the slope of a line tangent to the curve at that point (1st derivative).

5. 12.2
Rate Laws: An Introduction
Rate Law
Shows how the rate depends on the concentration of the reactants (no equilibrium reactions…yet).
For the decomposition of nitrogen dioxide:
2NO2(g) → 2NO(g) + O2(g)
Rate = k[NO2]n
k = rate constant
n = order of the reactant

6. n must be determine experimentally.
12.2
Rate Laws: An Introduction
Rate Law
Rate = k[NO2]n
The concentrations of the products do not appear in the rate law because the reaction rate is being studied under conditions where the reverse reaction does not contribute to the overall rate (it is not an equilibrium reaction and the products do not sterically inhibit the reaction).
n must be determine experimentally.

7. 12.2
Rate Law: An Introduction
Types of Rate Laws
Differential Rate Law (rate law): shows how the rate of a reaction depends on concentrations.
Integrated Rate Law – shows how the concentrations of species in the reaction depend on time.

8. Method of Initial Rates
12.3
Determining the Form of the Rate Law
Method of Initial Rates
The value of the initial rate is determined for each experiment at the same value of t as close to t = 0 as possible.
Several experiments are carried out using different initial concentrations of each of the reactants, and the initial rate is determined for each run.
The results are then compared to see how the initial rate depends on the initial concentrations of each of the reactants.

9. Overall Reaction Order
12.3
Determining the Form of the Rate Law
Overall Reaction Order
The sum of the exponents in the reaction rate equation.
Rate = k[A]n[B]m
Overall reaction order = n + m
k = rate constant
[A] = concentration of reactant A
[B] = concentration of reactant B

10. ln[A] = –kt + ln[A]o First Order Rate Law
12.4
The Integrated Rate Law
First Order Rate Law
Rate = k[A]
Integrated:
ln[A] = –kt + ln[A]o
[A] = concentration of A at time t
k = rate constant
t = time
[A]o = initial concentration of A

11. 12.4
The Integrated Rate Law
Plot of ln [N2O5] vs. Time

12. First Order; Half Life k = rate constant Half–Life:
12.4
The Integrated Rate Law
First Order; Half Life
Half–Life:
k = rate constant
Half–life does not depend on the concentration of reactants.

13. [A] = concentration of A at time t k = rate constant t = time
12.4
The Integrated Rate Law
Second-Order
Rate = k[A]2
Integrated:
[A] = concentration of A at time t
k = rate constant
t = time
[A]o = initial concentration of A

14. Second Order; Half-Life
12.4
The Integrated Rate Law
Second Order; Half-Life
Half–Life:
k = rate constant
[A]o = initial concentration of A
Half–life gets longer as the reaction progresses and the concentration of reactants decrease.
Each successive half–life is double the preceding one.

15. 12.4
The Integrated Rate Law
Exercise
For a reaction aA  Products, [A]0 = 5.0 M, and the first two half-lives are 25 and 50 minutes, respectively.
Write the rate law for this reaction.
b) Calculate k.
c) Calculate [A] at t = 525 minutes.
rate = k[A]2
a) rate = k[A]2
We know this is second order because the second half–life is double the preceding one.
b) k = 8.0 x 10-3 M–1min–1
25 min = 1 / k(5.0 M)
c) [A] = 0.23 M
(1 / [A]) = (8.0 x 10-3 M–1min–1)(525 min) + (1 / 5.0 M)
k = 8.0 x 10-3 M–1min–1
[A] = 0.23 M

16. Rate = k[A]0 = k Integrated: [A] = –kt + [A]o Zero Rate Order
12.4
The Integrated Rate Law
Zero Rate Order
Rate = k[A]0 = k
Integrated:
[A] = –kt + [A]o
[A] = concentration of A at time t
k = rate constant
t = time
[A]o = initial concentration of A

17. [A]o = initial concentration of A
12.4
The Integrated Rate Law
Zero Order; Half-Life
Half–Life:
k = rate constant
[A]o = initial concentration of A
Half–life gets shorter as the reaction progresses and the concentration of reactants decrease.

18. 12.4
The Integrated Rate Law
Summary

19. NO2(g) + CO(g) → NO(g) + CO2(g)
12.5
Reaction Mechanisms
Reaction Mechanisms
Most chemical reactions occur by a series of elementary steps.
An intermediate is formed in one step and used up in a subsequent step and thus is never seen as a product in the overall balanced reaction.
NO2(g) + CO(g) → NO(g) + CO2(g)

20. Elementary Step (Molecularity)
12.5
Reaction Mechanisms
Elementary Step (Molecularity)
Unimolecular – reaction involving one molecule; first order.
Bimolecular – reaction involving the collision of two species; second order.
Termolecular – reaction involving the collision of three species; third order.

21. Rate-Determining Step A reaction is only as fast as its slowest step.
12.5
Reaction Mechanisms
Rate-Determining Step
A reaction is only as fast as its slowest step.
The rate-determining step (slowest step) determines the rate law and the molecularity of the overall reaction.
The sum of the elementary steps must give the overall balanced equation for the reaction.
The mechanism must agree with the experimentally determined rate law.

22. Decomposition of N2O5 2N2O5(g)  4NO2(g) + O2(g)
12.5
Reaction Mechanisms
Decomposition of N2O5
2N2O5(g)  4NO2(g) + O2(g)
Step 1: N2O NO2 + NO3 (fast)
Step 2: NO2 + NO3 → NO + O2 + NO2 (slow)
Step 3: NO3 + NO → 2NO2 (fast)
2( )

23. 12.5
Reaction Mechanisms
Reality Check
The reaction A + 2B  C has the following proposed mechanism:
A + B D (fast equilibrium)
D + B  C (slow)
Write the rate law for this mechanism.
rate = k[A][B]2

24. 12.6
A Model for Chemical Kinetics
Collision Model
Molecules must collide to react.
Main Factors:
Activation energy, Ea
Temperature
Molecular orientations
Activation Energy: Energy that must be overcome to produce a chemical reaction.

25. Change in Potential Energy
12.6
A Model for Chemical Kinetics
Change in Potential Energy

26. For Reactants to Form Products
12.6
A Model for Chemical Reactions
For Reactants to Form Products
Collision must involve enough energy to produce the reaction (must equal or exceed the activation energy).
Relative orientation of the reactants must allow formation of any new bonds necessary to produce products.

27. Arrhenius Equation Linear Version Ea = activation energy
12.6
A Model for Chemical Kinetics
Arrhenius Equation
A = frequency factor
Ea = activation energy
R = gas constant ( J/K·mol)
T = temperature (in K)
Linear Version

28. A substance that speeds up a reaction without being consumed itself.
12.7
Catalysis
Catalyst
A substance that speeds up a reaction without being consumed itself.
Provides a new pathway for the reaction with a lower activation energy.

29. Effect of a Catalyst on the Number of Reaction-Producing Collisions
12.7
Catalysis
Effect of a Catalyst on the Number of Reaction-Producing Collisions

30. Heterogeneous Catalyst
12.7
Catalysis
Heterogeneous Catalyst
Most often involves gaseous reactants being adsorbed on the surface of a solid catalyst.
Adsorption – collection of one substance on the surface of another substance.
Adsorption and activation of the reactants.
Migration of the adsorbed reactants on the surface.
Reaction of the adsorbed substances.
Escape, or desorption, of the products.

31. Exists in the same phase as the reacting molecules.
12.7
Catalysis
Homogeneous Catalyst
Exists in the same phase as the reacting molecules.
Enzymes are nature’s catalysts.

32. 12.1
Reaction Rates

33. 12.1
Reaction Rates

34. 12.1
Reaction Rates