1. Chemical Kinetics
Chapter 12

2. Reaction Rates Rate = Δ[A]/Δt
Rates of reactions are measured in the change of the amount of product or reactant per unit time
Usually measured in M/s…[ ] = molarity
Rate diminishes as the reaction proceeds

4. Comparing reactant change and product change
2 NO2 → 2 NO O2
Rate = Δ[NO2]/Δt
= Δ[NO]/Δt
= 2 (Δ[O2]/Δt)

5. Generalizations Reaction rates depend on several factors:
Nature of the reactant(s)
Temperature
Concentration of the reactants
Particle size for solid reactants

6. Rate Laws
A rate law (or differential rate law) is a mathematical expression that describes the relationship between the starting concentration of the reactants and the rate of the reaction
Rate = k [A]x[B]y
k is a temperature dependent rate constant that is unique to a reaction (determined by experiment)
X and Y are orders of reaction and are only determined experimentally

7. Determining a rate law A + B → C + D Trial [A] [B] Initial rate 1
1.35 x 10-7 M/s 2
0.010 M
2.70 x 10-7 M/s 3
0.200 M
5.40 x 10-7 M/s
Find the rate law for the reaction, including reaction order with
respect to each reactant, the rate constant and the
overall order of reaction.

8. Comparing trials 1 and 2, the concentration
of A is unchanged, but the concentration of B was
doubled and the rate doubled. Indicating that B has
an order of 1.
Comparing trials 2 and 3, the same is noted for A…
the rate doubles when A is doubled (with B constant). The order with respect to A is also 1.
The rate law: rate = k[A][B]
k is calculated by entering data into the law from one of the trials and solving for k.

9. Orders of Reaction
1st order: there is a direct relationship between the initial concentration of the reactant and the rate of reaction
2nd order: a squared relationship exists
3rd order: a cubed relationship exists
Zero order: no relationship between the reactant concentration and the rate.

10. Another example A + B + C → D + E Trial [A] [B] [C] rate 1 0.10 M
8.0 x 10-4 M/s 2
0.20 M
1.6 x 10-3 M/s 3
3.2 x 10-3 M/s 4

11. Integrated Rate Laws
The differential rate law (or rate law) relates the rate of the reaction to the initial reactant concentrations.
The integrated rate law relates the concentration of the reactant to elapsed time.

12. First-Order Laws Rate law: rate = k[A]
Integrated rate law: ln[A]t = -kt + ln[A]o
y = mx b
Notes:
A plot of ln[A]t vs t will give a straight line
k is the slope of the line
Many reactions and all radioactive decay follow this relationship
Half life: t1/2 = ln(2)/k

13. Second-Order Laws Rate Law: rate = k[A]2
Integrated rate law: 1 [𝐴 ] 𝑡 =𝑘𝑡+ 1 [𝐴 ] 0
Notes:
A plot of 1/[A]t vs t gives a straight line
k is the slope of the line
t 1/2 = 1/k[A]0

14. Zero-Order Laws Rate Law: rate = k[A]0 = k
Integrated Rate Law: [A]t = -kt + [A]0
Notes:
[A]t vs t gives a straight line
k is the slope of the line
Rate is independent of the starting concentration.
Often occurs with reactions occurring with a catalyst such as a metal grid or enzyme

15. Determining the Order of Reaction
If concentration and rate data are provided, analyze to find the order(s) of reaction to write the rate law. Solve for k using the rate law.
If concentration and time data are provided:
Plot the data against time using ln[A], 1/[A], and [A]…the most linear plot will be the order of reaction OR
Solve for k at least 2 times for each of the integrated laws…the trials that give the same k give the correct order of reaction

16. Collision Theory For a reaction to take place:
Particles must collide or break apart
The rate is dependent on the number of effective collisions
Effective collisions require
Proper orientation (active site)
Sufficient energy (activation energy)

17. Collision Theory and Rate
Anything that increases the number of effective collisions will increase the rate of a reaction
Nature of reactants…
Concentration of reactants
Temperature
Particle size
Catalysts and Inhibitors

18. Potential Energy Diagram
Negative ∆ H Positive ∆H

19. Activated Complex and Catalysts

20. Arrhenius Equation ln 𝑘 1 𝑘 2 = 𝐸 𝑎 𝑅 1 𝑇 2 − 1 𝑇 1
Allows the determination of activation energy for a reaction if the rate constants for two different temperatures are known from data.

21. Reaction Mechanisms
Reactions take place in a series of unimolecular or bimolecular elementary steps
Intermediates are chemical species that are not reactants or products, they are produced in one step and consumed in a later step
Catalysts and Inhibitors are not reactants or products, they are added at the beginning and reform during the reaction

22. Rate Determining Step The slowest step in the mechanism
The rate determining step will have stoichiometry that correlates with the experimentally determined rate law

23. Analyzing Mechanisms
NO2 + F2  NO2F + F (slow) NO2 + F  NO2F (fast) Net reaction: 2 NO2 + F2  2 NO2F Intermediate: F Rate law: rate = k[NO2][F2]

24. More… 1: NO2(g) + NO2(g) → NO3(g) + NO(g) (slow)
2: NO3(g) + CO(g) → NO2(g) + CO2(g) (fast)
Net reaction: NO2 + CO → NO + CO2
Intermediate: NO3
Catalyst: NO2
Rate law: rate = k[NO2]2

25. Mechanisms and PE Mechanism: Cl2  2Cl Cl + CO  COCl
Cl + COCl  COCl2
Notes:
Cl and COCl are intermediates
3rd step is rate-determining due
to the high Ea