1. Chem.414 - Physical Chemistry II
Spring 2016

2. Chemical Kinetics

3. Study of Chemical Kinetics
Rate of reaction
Dependence of concentration of species
Dependence of temp., pressure, catalyst
Control of reactions
Mechanisms [Dominating step (fast vs. slow)]
Guide to chemical intuition

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

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

6. EXCEL Time / s [N2O5] / M ln [N2O5] d[N2O5]/dt (tangential slope) 1
4. Consider the following N2O5 reaction:  2 N2O5(soln)  ---->  4 NO2(soln)  +  O2(g)      Let:    C = [N2O5]      (a) Using a graph of C vs. t, obtain tangential slopes and plot dC/dt vs. C. Calculate k after fitting with linear regression.     (b) Plot ln C vs. t. Calculate k after fitting with linear regression.     (c) Plot C vs. t. Fit the data with an appropriate function.  Display the equation in standard IRL form with the appropriate variable names for this reaction.     (d) Calculate half-live (t2) and life-time (t).   Compare them to the interpolated values from the plot of C vs. t.
Time / s
[N2O5] / M
ln [N2O5]
d[N2O5]/dt (tangential slope) 1
1.00 2
200
0.88 3
400
0.78 4
600
0.69 5
800
0.61 6
1000
0.54 7
1200
0.48 8
1400
0.43 9
1600
0.38 10
1800
0.34 11
2000
0.30
EXCEL

8. The Change of Concentration with Time
Isomeric Transformation of Methyl Isonitrile to Acetonitrile
First Order Reactions (to one component)

10. Differential and Integrated Rate Laws
n-th Order to One Component (Generalized Rate Laws)
Let: C = concentration of reactant A remaining at time t
Co = initial concentration of reactant A (i.e. t=0)
k = rate constant (units depends on n)
DRL:
IRL:

11. Differential and Integrated Rate Laws

12. Rate Law: First Order to One Component

14. The Change of Concentration with Time
Second Order Reactions

15. Rate Law: Second Order to One Component

16. Gas-Phase Decomposition of Nitrogen Dioxide
Time / s
[NO2] / M
0.0
50.0
100.0
200.0
300.0
Is this reaction first or second order?
k = unit?

17. Half-Lives, Rate Constants and Co

18. Half-Lives, Rate Constants and Co - II

19. Zeroth Order to One Component - Catalysis
Provide the DRL.
Determine the IRL.
Sketch the IRL: Co=1.00 mol L-1 , k = 5.00x10-3 mol L-1 s-1 .
Use Mathcad (or EXCEL) to generate the IRL graph.
Obtain the half-life expression.
How many half-lives would it take for the reaction to reach equilibrium (i.e. completion)? [ Hint: Solve the IRL for time when C=0. Confirm by graph. ]

21. Summary of Rate Laws to One-Component
First-Order
Second-Order
Zeroth-Order
DRL
(-dC/dt) kC
kC2 k
IRL
C = Co·e-kt
ln C = -kt + ln Co
1/C = kt + 1/Co
C = -kt + Co
Linear Equation
ln C vs. t
1/C vs. t
C vs. t
Linear Plot
Half-Life
ln(2)/k
1/kCo
Co/2k
Units on k
time-1
M-1 time-1
M time-1
m = -k
b = ln Co
m = k
b = 1/Co
m = -k
b = Co

22. Concentration and Rate
Exponents in the 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.

23. Method of Initial/Comparative Rates
Expt #
[NH4+]o / M
[NO2-]o / M
(Rate)o / M s-1 1
0.100
0.0050
1.35x10-7 2
0.0100
2.70x10-7 3
0.200
5.40x10-7

25. Three Component Rate Law
Expt #
[BrO3-]o / M
[Br-]o / M
[H+]o / M
(Rate)o / M s-1 1
0.10
8.0x10-4 2
0.20
1.6x10-3 3
3.2x10-3 4

26. Techniques for Multiple Component Rate Laws
Integration Approach: Second Order – First Order to each of two components
Flooding Technique: Rate = k [A]x [B]y [C]z

28. Applications of First-Order Processes
Radioactive Decay
Bacterial Growth
Interest and Exponential Growth
[Credit Card]
Loan Balance

31. Temperature and Rate The Arrhenius Equation
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 ( J K-1 mol-1) 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.

32. Temperature and Rate

33. 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.
Elementary Steps
Elementary step: any process that occurs in a single step.

34. Reaction Mechanisms Elementary Steps
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).

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. [example]

36. Reaction Mechanisms
Rate Laws for Elementary Steps

37. Rate Expressions If elementary steps:
-d[A]/dt = vk1[A]v[B]w – vk-1[C]x[D]y
-d[B]/dt = wk1[A]v[B]w – wk-1[C]x[D]y
d[C]/dt = xk1[A]v[B]w – xk-1[C]x[D]y
d[D]/dt = yk1[A]v[B]w – yk-1[C]x[D]y

38. d[NOBr]/dt = kobs[NO]2[Br2] (or) = kobs’[NO][Br2]
Reaction Mechanisms
Mechanisms with an Initial Fast Step
2NO(g) + Br2(g)  2NOBr(g)
The experimentally determined rate law can be:
d[NOBr]/dt = kobs[NO]2[Br2] (or) = kobs’[NO][Br2]
Consider the following mechanism

39. Spring 2014

40. Spring 2014

41. General Mechanism Overall Reaction: Proposed Mechanism:
Where: D = observable product
M = intermediate

44. Spring 2014

45. Spring 2014

46. Hydrogen-Iodine Reaction
Overall Reaction:
Proposed Mechanism:
Where: I• = free radical

49. Spring 2012

50. Spring 2012

51. Rice-Hertzfeld Free Radical Chain Reaction Mechanism
Overall Reaction:
Proposed Mechanism:

54. Kinetics

55. Catalysis

56. C2H4(g) + H2(g)  C2H6(g), H = -136 kJ/mol.
Catalysis
Heterogeneous Catalysis
Consider the hydrogenation of ethylene:
C2H4(g) + H2(g)  C2H6(g), H = -136 kJ/mol.
The reaction is slow in the absence of a catalyst.
In the presence of a metal catalyst (Ni, Pt or Pd) the reaction occurs quickly at room temperature.
First the ethylene and hydrogen molecules are adsorbed onto active sites on the metal surface.
The H-H bond breaks and the H atoms migrate about the metal surface.

57. Catalysis

58. Catalysis Enzymes Enzymes are biological catalysts.
Most enzymes are protein molecules with large molecular masses (10,000 to 106 amu).
Enzymes have very specific shapes.
Most enzymes catalyze very specific reactions.
Substrates undergo reaction at the active site of an enzyme.
A substrate locks into an enzyme and a fast reaction occurs.
The products then move away from the enzyme.

59. Catalysis
Enzymes
Only substrates that fit into the enzyme lock can be involved in the reaction.
If a molecule binds tightly to an enzyme so that another substrate cannot displace it, then the active site is blocked and the catalyst is inhibited (enzyme inhibitors).
The number of events (turnover number) catalyzed is large for enzymes ( per second).

60. Catalysis
Enzymes

61. Mechanism: Two Intermediates
Overall Reaction:
Experimentally found:
Proposed Mechanism:
Show that the proposed mechanism is consistent with the observed RL.

62. Mechanism
Overall Reaction:
Observed Rate Law:
Proposed Mechanism:

64. Chemical Kinetics