Kinetics

1
Kinetics

• or Reaction Rates

2
Change

• The ice melted.
• The Coke went flat.
• The nail rusted.

3
Expressing Change

• The ice melted.
• The Coke went flat.
• The nail rusted.

mL/min
g/min
g/min
4
Expressing Change

• Reaction Rate.
• Change in something divided by change in time

?amount ?time
5
Reaction Rate

• As a rxn occurs, what happens to the amount of
  reactant?

Rate ? reactant amt
?time
6
Reaction Rate

• Consider
• Mg(s) 2HCl(aq) ? MgCl2(aq) H2(g)

Rate ?mol Mg ?mol HCl
?t 2?t ?mol MgCl2 ?mol H2 ?t
?t
7
Reaction Rate of a one-way reaction

• Will be determined by looking at the reactants
  only
• Decreases as time progresses. Why?
• What eventually happens to the amount of
  reactant?

8
Reaction Rate of an equilibrium rxn

• Will be determined by looking at the reactants
  only
• Decreases as time progresses. Why?
• What eventually happens to the rate?
• Does the reaction stop?

9
Reaction Rate
2NO2(g) ? 2NO(g) O2(g)
10
Reaction Rate
11
Necessities of Reaction

• Proper orientation
• 2HI ? H2 I2

12
Necessities of Reaction

• Sufficient energy--Activation energy (Ea)

Activated Complex
Ea
Energy
2HI
?H
H2 I2
Rxn progress
13
Factors that affect Reaction Rate

• Concentration
• Temperature
• Surface Area
• Presence of a catalyst
• Rate-determining stepor the slowest step in a
  rxn mechanism

14
Rate Law

• Relates the rate as a function of the reactant(s)
• Units of rate are always mol/L-s unless otherwise
  stated
• Two types
• Differential
• Integrated

15
Differential Rate Law

• For the rxn A ? Bdifferential
• Rate kAx
• k is the rate law constantunits are dependent on
  the order
• x is the order of reactant A

16
Order

• may not be determined by looking at the
  coefficients of the reactants
• unless the rxn is the rate-determining step
• must be determined experimentally

17
Order

• If the rate does not change when the reactant is
  doubled, then the order is zero and rate is
  dependent solely on the value of k
• Rate kA0 or Rate k

18
Order

• If the rate doubles when the reactant is doubled,
  then the order is first and rate is dependent on
  the concentration of the reactant
• Rate kA1

19
Order

• If the rate quadruples when the reactant is
  doubled, then the order is second and rate is
  dependent on the square of the concentration of
  the reactant
• Rate kA2

20
Overall Order of Reaction

• is the sum of the individual orders
• When Rate kA0, the overall order is zero
• When Rate kA1, the overall order is one

21
Overall Order of Reaction

• If a differential rate law for the following rxn
• A B ? C
• is Rate kA1B2
• then the overall order is three
• What must the units of k be in this reaction?

22
Integrated Rate Law

• For the rxn
• 2N2O5 ? 4NO2 O2
• The following data were collected
• N2O5 Time(s)

1.00 0
0.88 200
0.78 400
0.69 600
0.61 800
23
Integrated Rate Law

• If we think the reactant is zero order
• Rate kN2O50
• Integrating the rate law gives us
• N2O5 -kt N2O5o

24
Integrated Rate Law

• If we plot Time vs. N2O5, then we get

25
Integrated Rate Law

• Since the plot gave a curve rather than a line,
  the order of the N2O5 cannot be zero.
• If we try looking at it as if it were first
  order, then we will need to integrate the rate
  law.

26
Integrated Rate Law

• If we think the reactant will be first order
• Rate kN2O51
• Integrating the rate law gives us
• ln N2O5 -kt lnN2O5o

27
Integrated Rate Law

• If we plot Time vs. lnN2O5, then we get

lnN2O5 (mol/L)
Time (s)
28
Integrated Rate Law

• Since the plot gave a line, the order of the N2O5
  is first or one.

29
Integrated Rate Law

• If we think the reactant will be
• second order
• Rate kN2O52
• Integrating the rate law gives us
• N2O5-1 kt N2O5o-1

30
Integrated Rate Law

• If we plot Time vs. N2O5-1, then we get

N2O5-1 (L/ mol)
Time (s)
31
1/2 Life

• First-order t½ 0.693
• k
• Second-order t½ __1__
• kAo
• Zero-order t½ Ao
• 2k

32
First-order Half-Life

• All first-order reactions have half-lives
  independent of the initial concentration of the
  reactant.
• All radioactive decays follow first-order
  kinetics.

33
First-order Half-Life Problem

• On November 23, 1999 I had Technetium-99 injected
  into my bloodstream for a bone scan. The
  half-life of Tc-99 is 6.0 hours.
• What percentage of the original amount of Tc-99
  is left in my body today?

34
Second-order Half-Life

• All second-order reactions have half-lives
  dependent on the initial concentration of the
  reactant.
• A second half-life will be longer than a first
  half-life because the initial concentration
  changes
• For each successive half-life, Ao is halved
  thus, for each successive half-life, the
  half-life is doubled

35
Second-order Half-Life Problem

• The decomposition of NOCl is a second- order
  reaction where
• k 4.00 x 10-8s-1.
• For an initial concentration of 0.50M, what is
  the half-life?
• How much is left after 1 x 108s?
• What is the half-life for an initial
  concentration of NOCl of 0.25M?

36
Zero-order Half-Life

• Most often occur when a catalyst is needed for
  the reaction to proceed.
• The catalyst determines how much reactant will be
  used.
• Since the rate is constant the half-life may be
  determined using either the rate law constant or
  the rate itself.

37
Reaction Mechanism

• Most reactions do not occur in a single step
• Rather, they happen in a series of steps called
  elementary steps
• The sum of the elementary steps gives the overall
  reaction.

38
Reaction Mechanism

• Intermediates are substances that are formed in
  one elementary step and consumed in a subsequent
  elementary step. They are rarely part of the
  rate law.
• Catalysts are substances added to a step that are
  also produced in a subsequent step. They are
  rarely part of the rate law.

39
Reaction Mechanism

• Rate-determining stepthe slowest step. If it is
  the first or only step, then the rate law may be
  written from its molecularity.
• The differential rate law may be written from the
  reactants in the rate-determining step.

40
Reaction Mechanism

• Consider the following elementary steps
• Step 1 OCl- H20 ? HOCl OH- fast
• Step 2 HOCl I- ? HOI Cl- slow
• Step 3 HOI OH- ? H20 OI- fast
• What is the overall balanced equation?
• What is the differential rate law?
• What substance(s) is an intermediate? A catalyst?

41
Reaction Mechanism

• What is the overall balanced equation?
• What is the differential rate law?
• What substance(s) is an intermediate? A catalyst?

OCl- I- ? Cl- OI-
Rate kI-
HOCl, HOI, OH- H2O
42
Reaction Mechanism

• A catalyst is a substance that increases the rate
  of reaction.
• It does so by lowering the Ea required for the
  reaction to occur.

43
A Catalysts Effect
Uncatalyzed
Ea
Catalyzed
Energy
Rxn progress
44
Reaction Mechanism
The reaction H2 Cl2 ? 2HCl occurs in four
steps. Step 1
energy
Cl
Cl
Cl
Cl
45
Reaction Mechanism
Step 2
46
Reaction Mechanism
Step 3
47
Reaction Mechanism
Step 4
48
energy
Cl
Cl
Cl
Cl
Cl
H
H
H
49
Collision Theory

• Molecules must move toward each other (through
  random motion).
• Molecules must hit with the proper orientation.
• Molecules must hit with sufficient energy.
• Molecules will separate after reaction occurs.

50
Collision Theory

• k Ae Ea/RT
• Take the ln of each side and

51
Collision Theory

• Plot 1/T vs. lnk to determine Ea or A.
• If you have two sets of data

ln k2 Ea 1 1_ k1 R T1
T2
52
Activation Energy

• for a one-way reaction

53
Activation Energy

• for a reversible reaction

54
Activation Energy Problem
Given the following kinetics data for the
reaction NO(g) O3(g) ? NO2(g)
02(g) Determine the activation energy.
55
Reaction Mechanism

• A series of elementary steps must satisfy two
  requirements for the reaction
• The sum of the elementary steps must give the
  overall balanced equation for the reaction.
• The mechanism must agree with the observed rate
  law.

56
Catalyst

• provides a surface whereby the reacting molecules
  might position themselves more favorably for
  collision
• lowers Ea
• Homogeneous (i.e. enzymes) are in the same phase
  as the reacting molecules
• Heterogeneous (i.e. Pt or Pd pieces in the
  catalytic converter of a car) are in a different
  phase and promote adsorption

57
Enzymes

• are proteins in living organisms that catalyze
  biological reactions.
• Salivary amylase
• Lactase

58
Inhibitors

• are elements or compounds used to decrease the
  rate of a reaction.
• Tetraethyl lead
• Oops! Along came catalytic converters
• Methyl t-butyl ether (MTBE) and ethanol

59
Collision Theory

• Concentration
• Temperature
• k is a measure of the fraction of collisions with
  sufficient energy to produce a reaction
• k Ae Ea/RT (Arrhenius equation)
• Afrequency factor (motion/orientation)
• Eaactivation energy (J/mol)

60
Reaction Mechanism Problem 1

• The balanced equation for the reaction of nitric
  oxide with hydrogen is
• 2NO 2H2 ? 2H20 N2
• The experimentally determined rate law is rate
  kNO2H2
• The following mechanism has been proposed

61
Reaction Mechanism Problem 1 (cont.)
k1

• NO H2 ? N H2O (slow)
• N NO ? N2O (fast)
• N2O H2 ? N2 H2O (fast)
• Is this mechanism consistent with the
• observed rate law?

k2
k3
62
Reaction Mechanism Problem 2
k1

• NO H2 N H2O (fast, with equal
  rates)
• N NO ? N2O (slow)
• N2O H2 ? N2 H2O (fast)
• Is this mechanism consistent with the
• observed rate law?

k-1
k2
k3
63
Reaction Mechanism Problem 3
k1

• NO H2 ? N H2O (fast)
• N NO ? N2O (fast)
• N2O H2 ? N2 H2O (slow)
• Is this mechanism consistent with the
• observed rate law?

k2
k3