1. Chemical Kinetics
Chapter 14

2. Factors that affect Reaction Rates
Kinetics is the study of how fast chemical reactions occur.
There are 4 important factors which affect rates of reactions:
reactant concentration,
temperature,
action of catalysts, and
surface area.

3. Reaction Rates
Speed of a reaction is measured by the change in concentration with time.
For a reaction A  B

4. Reaction Rates
At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present.
At t = 20 min, there is 0.54 mol A and 0.46 mol B.
At t = 40 min, there is 0.30 mol A and 0.70 mol B.

5. Reaction Rates
For the reaction A  B there are two ways of measuring rate:
the speed at which the products appear (i.e. change in moles of B per unit time), or
the speed at which the reactants disappear (i.e. the change in moles of A per unit time).

6. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)

7. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Reaction Rates
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
We can calculate the average rate in terms of the disappearance of C4H9Cl.
The units for average rate are mol/L·s or M/s.
The average rate decreases with time.
We plot [C4H9Cl] versus time.
The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve.
Instantaneous rate is different from average rate.
We usually call the instantaneous rate the rate.

8. Reaction Rates

9. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Reaction Rates
For the reaction:
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
we know
In general for:
aA + bB  cC + dD

10. NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)
Reaction Rates
In general rates increase as concentrations increase.
NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)

11. NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)
Rate Law
For the reaction
NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)
we note
as [NH4+] doubles with [NO2-] constant the rate doubles,
as [NO2-] doubles with [NH4+] constant, the rate doubles,
We conclude rate  [NH4+][NO2-].
Rate law:
The constant k is the rate constant.

12. Rate Law For a general reaction with rate law
we say the reaction is mth order in reactant 1 and nth order in reactant 2.
The overall order of reaction is m + n + ….
A reaction can be zeroth order if m, n, … are zero.
Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.

13. Rate Law
A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect.
A reaction is first order if doubling the concentration causes the rate to double.
A reacting is nth order if doubling the concentration causes an 2n increase in rate.
Note that the rate constant does not depend on concentration.

14. Rate Law
For a first order reaction, the rate doubles as the concentration of a reactant doubles.
A plot of ln[A]t versus t is a straight line with slope -k and intercept ln[A]0.
In the above we use the natural logarithm, ln, which is log to the base e.

15. Rate Law

16. Rate Law For a second order reaction with just one reactant
A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0
For a second order reaction, a plot of ln[A]t vs. t is not linear.

17. Rate Law: Half-Life
Half-life is the time taken for the concentration of a reactant to drop to half its original value.
For a first order process, half life, t½ is the time taken for [A]0 to reach ½[A]0.
Mathematically,

18. Rate Law
For a second order reaction, half-life depends in the initial concentration:

19. Rate vs. Temperature Most reactions speed up as temperature increases.
Examples
Food spoils when not refrigerated.
When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice.
The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light

20. Rate vs. Temperature
As temperature increases, the rate increases.

21. Rate vs. Temperature
Since the rate law has no temperature term in it, the rate constant must depend on temperature.
Consider the first order reaction CH3NC  CH3CN.
As temperature increases from 190 C to 250 C the rate constant increases from 2.52  10-5 s-1 to 3.16  10-3 s-1.

22. Collision Model
The collision model: in order for molecules to react they must collide.
The greater the number of collisions the faster the rate.
The more molecules present, the greater the probability of collision and the faster the rate.
The higher the temperature, the more energy available to the molecules and the faster the rate.
Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product.
In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.

23. Collision Model
Cl + NOCl  NO + Cl2

24. Collision Model
Arrhenius: molecules must posses a minimum amount of energy to react.
In order to form products, bonds must be broken in the reactants.
Bond breakage requires energy.
Activation energy, Ea, is the minimum energy required to initiate a chemical reaction.

25. Activation Energy Consider the rearrangement of methyl isonitrile:
In H3C-NC, the C-NC bond bends until the C-N bond breaks and the NC portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state.
The energy required for the above twist and break is the activation energy, Ea.
Once the C-N bond is broken, the NC portion can continue to rotate forming a C-CN bond

27. Activation Energy
From kinetic molecular theory, we know that as temperature increases, the total kinetic energy increases.
We can show the fraction of molecules, f, with energy equal to or greater than Ea is
where R is the gas constant (8.314 J/mol·K).

28. Activation Energy

29. Activation Energy
Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation:
k is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K.
A is called the frequency factor.
A is a measure of the probability of a favorable collision.
Both A and Ea are specific to a given reaction.

30. Activation Energy
If we have a lot of data, we can determine Ea and A graphically by rearranging the Arrhenius equation:
From the above equation, a plot of ln k versus 1/T will have slope of –Ea/R and intercept of ln A.

31. Activation Energy
If we do not have a lot of data, then we recognize

32. Reaction Mechanisms
The balanced chemical equation provides information about the beginning and end of reaction.
The reaction mechanism gives the path of the reaction.
Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction.

33. Reaction Mechanisms
Elementary step: any process that occurs in a single step.
Molecularity: the number of molecules present in an elementary step.
Unimolecular: one molecule in the elementary step,
Bimolecular: two molecules in the elementary step, and
Termolecular: three molecules in the elementary step.
It is not common to see termolecular processes (statistically improbable).

34. Reaction Mechanisms Some reaction proceed through more than one step:
NO2(g) + NO2(g)  NO3(g) + NO(g)
NO3(g) + CO(g)  NO2(g) + CO2(g)
Notice that if we add the above steps, we get the overall reaction:
NO2(g) + CO(g)  NO(g) + CO2(g)
If a reaction proceeds via several elementary steps, then the elementary steps must add to give the balanced chemical equation.
Intermediate: a species which appears in an elementary step which is not a reactant or product.

35. Reaction Mechanisms Rate Laws for Elementary Steps
The rate law of an elementary step is determined by its molecularity:
Unimolecular processes are first order,
Bimolecular processes are second order, and
Termolecular processes are third order.
Rate Laws for Multistep Mechanisms
Rate-determining step: is the slowest of the elementary steps.
Therefore, the rate-determining step governs the overall rate law for the reaction.

36. Reaction Mechanisms

37. Reaction Mechanisms 2NO(g) + Br2(g)  2NOBr(g)
The experimentally determined rate law is
Rate = k[NO]2[Br2]
Consider the following mechanism
The rate law is (based on Step 2):
Rate = k2[NOBr2][NO]

38. The rate law should not depend on the concentration of an intermediate (intermediates are usually unstable).
Assume NOBr2 is unstable, so we express the concentration of NOBr2 in terms of NOBr and Br2 assuming there is an equilibrium in step 1 we have
By definition of equilibrium:
Therefore, the overall rate law becomes
Note the final rate law is consistent with the experimentally observed rate law

39. Catalysts A catalyst changes the rate of a chemical reaction.
There are two types of catalysts:
homogeneous, and
heterogeneous.

40. Homogeneous Catalysis
The catalyst and reaction is in one phase.
Generally, catalysts operate by lowering the activation energy for a reaction.
Catalysts can operate by increasing the number of effective collisions.
That is, from the Arrhenius equation: catalysts increase k be increasing A or decreasing Ea.
A catalyst may add intermediates to the reaction.

41. Heterogeneous CatalySIs
The catalyst and reactants are in different phases.
Process
First step is adsorption (the binding of reactant molecules to the catalyst surface).
Adsorbed species (atoms or ions) are very reactive.
Molecules are adsorbed onto active sites on the catalyst surface.