1. Chemistry: Kinetics! Dr. Ed Brothers
Chemistry and Physics for High School Students
Texas A&M (Qatar)
January 28, 2009

2. Where to get the slides?

3. Necessary Math Previously, we talked about logarithms 10x = y
log10(y) = x
You could define a logarithm in any base
34 = 81
log3(81) = 4

4. Necessary Math We can define the natural logarithm as:
loge(y) = ln(y) =x
We can define the natural logarithm graphically
This base, e, is used for a lot of things, such as exponential decay
e= …

5. 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
Catalysis
Mechanism

6. Reaction Rates
Speed of a reaction is measured by the change in concentration with time.
For a reaction A  B
Suppose A reacts to form B. Let us begin with 1.00 mol A.

7. Reaction Rates

8. Reaction Rates
At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B
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.

9. 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).

10. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Reaction Rates
Change of Rate with Time
Most useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional.
Consider:
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)

12. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Reaction Rates
Change of Rate with Time
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.

14. 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
Appearance of Product = Disappearance of Reactant

15. Concentration and Rate
In general rates increase as concentrations increase.
NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)

16. Concentration and Rate
For the reaction
NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)
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.
Note that the rate constant does not depend on concentration.

17. 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.

18. Concentration and Rate
Using Initial Rates to Determines Rate Laws
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.

19. The Change of Concentration with Time
First Order Reactions
Goal: convert rate law into a convenient equation to give concentrations as a function of time.
For a first order reaction, the rate doubles as the concentration of a reactant doubles.

20. The Change of Concentration with Time
First Order Reactions
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.
Recall the beginning of this lecture.

21. The Change of Concentration with Time
First Order Reactions

22. The Change of Concentration with Time
Second Order Reactions
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.

23. The Change of Concentration with Time
Second Order Reactions

24. The Change of Concentration with Time
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,

26. The Change of Concentration with Time
Half-Life
For a second order reaction, half-life depends in the initial concentration:

27. Temperature and Rate The Collision Model
Most reactions speed up as temperature increases. (E.g. 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.

28. Temperature and Rate The Collision Model
As temperature increases, the rate increases.

29. Temperature and Rate The Collision Model
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.
The temperature effect is quite dramatic. Why?
Observations: rates of reactions are affected by concentration and temperature.

30. Temperature and Rate The Collision Model
Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases.
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.

31. Temperature and Rate The Collision Model The Orientation Factor
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.
The Orientation Factor
In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.

32. Temperature and Rate The Orientation Factor Consider:
Cl + NOCl  NO + Cl2
There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.

33. Temperature and Rate
The Orientation Factor

34. Temperature and Rate Activation Energy
Arrhenius: molecules must posses a minimum amount of energy to react. Why?
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.

35. Temperature and Rate 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.

37. Temperature and Rate Activation Energy
The change in energy for the reaction is the difference in energy between CH3NC and CH3CN.
The activation energy is the difference in energy between reactants, CH3NC and transition state.
The rate depends on Ea.
Notice that if a forward reaction is exothermic (CH3NC  CH3CN), then the reverse reaction is endothermic (CH3CN  CH3NC).

38. Temperature and Rate Activation Energy
How does a methyl isonitrile molecule gain enough energy to overcome the activation energy barrier?

39. Temperature and Rate
Activation Energy Ea

40. Maxwell–Boltzmann Distributions
Temperature is defined as a measure of the average kinetic energy of the molecules in a sample.
At any temperature there is a wide distribution of kinetic energies.

41. Maxwell–Boltzmann Distributions
As the temperature increases, the curve flattens and broadens.
Thus at higher temperatures, a larger population of molecules has higher energy.

42. Maxwell–Boltzmann Distributions
If the dotted line represents the activation energy, as the temperature increases, so does the fraction of molecules that can overcome the activation energy barrier.
As a result, the reaction rate increases.

43. Maxwell–Boltzmann Distributions
This fraction of molecules can be found through the expression:
where R is the gas constant and T is the temperature in Kelvin .

44. activation energy; asserted solutions of salts contained ions.
Svante A. Arrhenius *
Developed concept of
activation energy; asserted
solutions of salts contained
ions. 1 1 1 1

45. 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 (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.

46. Temperature and Rate Determining the 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.

47. Temperature and Rate

48. Temperature and Rate Determining the Activation Energy
If we do not have a lot of data, then we recognize

49. 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.

50. 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).

51. Reaction Mechanisms Multistep 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)

52. Reaction Mechanisms Multistep Mechanisms
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.

53. 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.

54. Reaction Mechanisms
Rate Laws for Elementary Steps

55. Reaction Mechanisms 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.
Mechanisms with an Initial Fast Step
It is possible for an intermediate to be a reactant.
Consider
2NO(g) + Br2(g)  2NOBr(g)

56. Reaction Mechanisms Mechanisms with an Initial Fast Step
2NO(g) + Br2(g)  2NOBr(g)
The experimentally determined rate law is
Rate = k[NO]2[Br2]
Consider the following mechanism

57. Reaction Mechanisms Mechanisms with an Initial Fast Step
The rate law is (based on Step 2):
Rate = k2[NOBr2][NO]
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

58. Reaction Mechanisms Mechanisms with an Initial Fast Step
By definition of equilibrium:
Therefore, the overall rate law becomes
Note the final rate law is consistent with the experimentally observed rate law.

59. Catalysis A catalyst changes the rate of a chemical reaction.
There are two types of catalyst:
homogeneous, and
heterogeneous.
Chlorine atoms are catalysts for the destruction of ozone.
Homogeneous Catalysis
The catalyst and reaction is in one phase.

60. Catalysis Homogeneous Catalysis
Hydrogen peroxide decomposes very slowly:
2H2O2(aq)  2H2O(l) + O2(g)
In the presence of the bromide ion, the decomposition occurs rapidly:
2Br-(aq) + H2O2(aq) + 2H+(aq)  Br2(aq) + 2H2O(l).
Br2(aq) is brown.
Br2(aq) + H2O2(aq)  2Br-(aq) + 2H+(aq) + O2(g).
Br- is a catalyst because it can be recovered at the end of the reaction.

61. Catalysis Homogeneous Catalysis
Generally, catalysts operate by lowering the activation energy for a reaction.

62. Catalysis

63. Catalysis Homogeneous Catalysis
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.
Example: In the presence of Br-, Br2(aq) is generated as an intermediate in the decomposition of H2O2.

64. Catalysis Homogeneous Catalysis
When a catalyst adds an intermediate, the activation energies for both steps must be lower than the activation energy for the uncatalyzed reaction. The catalyst is in a different phase than the reactants and products.
Heterogeneous Catalysis
Typical example: solid catalyst, gaseous reactants and products (catalytic converters in cars).
Most industrial catalysts are heterogeneous.

65. Catalysis Heterogeneous Catalysis
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.

66. Catalysis

67. 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.

68. Catalysis Heterogeneous Catalysis Enzymes
When an H atom collides with an ethylene molecule on the surface, the C-C  bond breaks and a C-H  bond forms.
When C2H6 forms it desorbs from the surface.
When ethylene and hydrogen are adsorbed onto a surface, less energy is required to break the bonds and the activation energy for the reaction is lowered.
Enzymes
Enzymes are biological catalysts.
Most enzymes are protein molecules with large molecular masses (10,000 to 106 amu).

69. Catalysis Enzymes 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.

70. 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).

71. Catalysis
Enzymes

72. Chemistry: Molecules and Materials
Dr. Ed Brothers
Chemistry and Physics for High School Students
Texas A&M (Qatar)
January 28, 2009

73. Intermolecular Forces and Some Properties of Liquids
Cohesive Forces
Intermolecular forces between like molecules.
Adhesive Forces
Intermolecular forces between unlike molecules.
Surface Tension
Energy or work required to increase the surface area of a liquid.
Viscosity
A liquids resistance to flow
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General Chemistry: Chapter 13

74. Intermolecular Forces
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75. Intermolecular Forces
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76. 13-2 Vaporization of Liquids: Vapor Pressure
Chemistry 140 Fall 2002
13-2 Vaporization of Liquids: Vapor Pressure
Bonding atomic orbitals are shown in grey.
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77. Enthalpy of Vaporization
ΔHvap = Hvapor – Hliquid = - ΔHcondensation
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78. Boiling Point Mercury manometer Vapor pressure of liquid
Pvap independent of Vliq
Pvap independent of Vgas
Pvap dependent on T
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79. Vapor Pressure and Boiling Point
(e) (d) (c) (b) (a)
A =
ΔHvap R
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80. Clausius-Clapeyron Equation
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81. 13-3 Some Properties of Solids
Freezing Point
Melting Point
ΔHfus(H2O) = kJ/mol
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82. Sublimation ΔHsub = ΔHfus + ΔHvap = -ΔHdeposition Prentice-Hall © 2002
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83. 13-4 Phase Diagrams Iodine Chemistry 140 Fall 2002
OD represents the FUSION CURVE. There is little effect of pressure on melting point.
O is the triple point. A unique temperature and pressure at which three states of matter coexist.
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84. Phase Diagrams Carbon dioxide Chemistry 140 Fall 2002
Triple point is greater than one atmosphere, so we do not form liquid. Sublimation occurs.
Liquid present in fire extinguishers (P > 5.1 atm)
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85. Supercritical Fluids Prentice-Hall © 2002
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86. The Critical Point
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87. Critical Temperatures and Pressures
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88. Chemistry 140 Fall 2002
Water
Fusion curve (OD) has a negative slope. Unusual behavior. Ice skating.
Polymorphysm, the existence of a solid substance in more than one form. This is common.
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89. 13-5 Van der Waals Forces Instantaneous dipoles. Induced dipoles.
Electrons move in an orbital to cause a polarization.
Induced dipoles.
Electrons move in response to an outside force.
Dispersion or London forces.
Instaneous dipole – induced dipole attraction.
Related to polarizability.
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90. Phenomenon of Induction
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91. Instantaneous and Induced Dipoles
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92. Dipole Dipole Interactions
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93. 13-6 Hydrogen Bonding Prentice-Hall © 2002
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94. Hydrogen Bonding in HF(g)
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95. Hydrogen Bonding in Water
Chemistry 140 Fall 2002
Hydrogen Bonding in Water
Solid ice has lower density than liquid water. H-bonding holds the ice in a rigid but open structure.
Maximum density of water at 3.98 C.
around a molecule in the solid in the liquid
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96. Other examples of H-Bonds
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97. 13-7 Chemical Bonds as Intermolecular Forces
Chemistry 140 Fall 2002
13-7 Chemical Bonds as Intermolecular Forces
Network covalent solids. C allotropes: Diamond and Graphite
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98. Other Carbon Allotropes
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99. Interionic Forces
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100. 13-8 Crystal Structures Prentice-Hall © 2002
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101. Unit Cells in the Cubic Crystal System
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102. Holes in Crystals
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103. Hexagonal Close Packed (hcp)
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104. Coordination Number
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105. Counting Cell Occupancy
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106. X-Ray Diffraction
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107. X-Ray Diffraction
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108. Cesium Chloride
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109. Atomic Radii from Crystal Structures
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110. Sodium Chloride
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111. Holes in Crystals
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112. Prentice-Hall © 2002
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113. 13-9 Energy Changes in the Formation of Ionic Crystals
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114. NEXT TIME: Other Stuff