1. Kinetics and Rate Law

2. RATE OF A REACTION
The speed with which the reactants disappear and the products form is called the rate of the reaction

3. May be expressed in terms of:
speed at which products appear or
speed at which reactants disappear.
Expressed as:(change in concentration)/time
Units are mol/L/s
The rate at any given moment is given by the slope of a tangent in concentration-time graph.

4. There are five principle factors that influence reaction rates:
Chemical nature of the reactants
Ability of the reactants to come in contact with each other
Concentration of the reactants
Temperature
Availability of of rate-accelerating agents called catalysts

5. Reaction Mechanism
A reaction mechanism is a series of steps by which a reaction takes place.
Each step involves the collision of two particles.
Each step is called an elementary process.
The slowest step in the reaction mechanism is called the rate -- determining step.
Mechanisms are determined experimentally

6. Reaction Mechanism
The rate law for elementary processes can be predicted.
The exponents for the rate law for elementary processes are the coefficients of the reactants in the chemical equation for the elementary process
Intermediate -- a substance that is produced in one step and is used up in a later step.

7. Reaction Mechanisms 2NO2 + F2 2NO2F Rate = k[NO2][F2]
The proposed mechanism is
NO2 + F NO2F + F (slow)
F + NO NO2F (fast)
F is called an intermediate It is formed then consumed in the reaction

8. 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.
Elementary steps add up to the balanced equation

9. How to get rid of intermediates
They can’t appear in the rate law.
Slow step determines the rate and the rate law
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.

10. 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.

11. Rate Laws Two key points
The concentration of the products do not appear in the rate law because this is an initial rate.
The order (exponent) must be determined experimentally,
can’t be obtained from the equation

12. Rate Law
The rate of a homogeneous reaction at any instant is proportional to the product of the molar concentrations of the reactants raised to a power determined from experiment

13. Rate Law Expresses the relationship between rate and concentration.
Order of the reaction -- can be positive, negative, zero, or a fraction.
Order with respect to a reactant -- its exponent in the rate law; determined experimentally
Overall order-- sum of exponents in rate law

14. The differential rate law is usually just called “the rate law.”
Rate Laws
Differential rate laws express (reveal) the relationship between the concentration of reactants and the rate of the reaction.
The differential rate law is usually just called “the rate law.”
Integrated rate laws express (reveal) the relationship between concentration of reactants and time

15. Suppose the experimental concentration-rate data for five experiments is:

16. The relationship between concentration and time can be derived from the rate law and calculus
Integration of the rate laws gives the integrated rate laws
Integrate laws give concentration as a function of time
Integrated laws can get very complicated, so only a few simple forms will be considered

17. 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 only work with n= 0, 1, and 2

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

19. First order reactions Rate law is: rate = k [A]
The integrate rate law can be expressed as:
[A]0 is [A] at t (time) = 0
[A]t is [A] at t = t
e = base of natural logarithms = …

20. Graphical methods can be used to determine the first-order rate constant, note

21. A plot of ln[A]t versus t gives a straight line with a slope of -k
The decomposition of N2O5. (a) A graph of concentration versus time for the decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant.

22. The simplest second-order rate law has the form
The integrated form of this equation is

23. Graphical methods can also be applied to second-order reactions
A plot of 1/[B]t versus t gives a straight line with a slope of k
Second-order kinetics. A plot of 1/[HI] versus time (using the data in Table 15.1).

24. The amount of time required for half of a reactant to disappear is called the half-life, t1/2
The half-life of a first-order reaction is not affected by the initial concentration

25. The half-life of a second-order reactions does depend on the initial concentration

26. COLLISIONS
Molecules must collide in order to react. The rate is determined by the number of effective collisions per second. In order for a collision to be effective, an activated complex must form.

27. Collision Theory Particles have to collide to react.
Have to hit hard enough
Things that increase this increase rate
High temperature – faster reaction
High concentration – faster reaction
Small particles = greater surface area means faster reaction

28. Unsuccessful Collisions
Collision Theory
Particle Orientation
Required Orientation
Unsuccessful Collisions
Successful Collision

29. In order for an activated complex to form, the molecules must have:
the proper orientation and
the proper amount of energy.
If the molecules do not have both of the above, no reaction will occur.
See graphs of endothermic and exothermic reactions.

30. The potential-energy diagram for an exothermic reaction
The potential-energy diagram for an exothermic reaction. The extent of reaction is represented as the reaction coordinate.

31. Activation energies and heats of reactions can be determined from potential-energy diagrams
Potential-energy diagram for an endothermic reaction. The heat of reaction and activation energy are labeled.

32. Collision Theory Activation Energy depends on reactants
low Ea = fast reaction rate Ea

33. An activated complex is an intermediate state formed by the interpenetration of the electron clouds of the molecules.

34. FACTORS AFFECTING RATE
1) Nature of the reactants -- Some reactions are fast by their nature and some are slow. Bonds must be broken, so the number and strength of bonds is a factor. In some cases ions must form or be rearranged.
2. Ability of the reactants to meet.
- Homogeneous system -- usually fast
- Heterogeneous- reaction at surface-slower

35. 3. Surface Area high SA = fast reaction rate
more opportunities for collisions
Increase surface area by…
using smaller particles
dissolving in water

36. 4. Temperature high temperature = fast reaction rate
Ten degree Celsius increase in temperature often doubles the rate
high KE
fast-moving particles give more collisions that result in the formation of an activated complex
more likely to reach activation energy

37. 5. Concentration (pressure for gases)
high concentration or pressure = fast reaction rate
more opportunities for collisions

38. There are two types of catalysts:
6) Catalyst -- A catalyst is a substance that changes the rate of a reaction without being permanently changed itself.
A catalyst changes the activation energy and changes the pathway of the reaction.
There are two types of catalysts:
Homogeneous -- same physical state as the reactants.
Heterogeneous -- reactants are adsorbed on surface; collisions can occur more easily.

39. Catalyst
substance that increases reaction rate without being consumed in the reaction
lowers the activation energy

40. The activation energy is related to the rate constant by the Arrhenius equation
k = rate constant
Ea = activation energy
e = base of the natural logarithm
R = gas constant = J mol-1 K-1
T = Kelvin temperature
A = frequency factor or pre-exponential factor

41. The Arrhenius equation can be put in standard slope-intercept form by taking the natural logarithm
A plot of ln k versus (1/T) gives a straight line with slope = -Ea/RT