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Chemical Kinetics
    Chapter 13
Chemical Kinetics

Thermodynamics – does a reaction take place?
Kinetics – how fast does a reaction proceed?

Reaction rate is the change in the concentration of a
reactant or a product with time (M/s).

                           A        B
              ∆[A]    ∆[A] = change in concentration of A over
     rate = -
               ∆t            time period ∆t
            ∆[B]      ∆[B] = change in concentration of B over
     rate =
             ∆t              time period ∆t

                      Because [A] decreases with time, ∆[A] is negative.

                                                                   13.1
A          B




                    time


         ∆[A]
rate = -
          ∆t

       ∆[B]
rate =
        ∆t


                               13.1
Br2 (aq) + HCOOH (aq)          2Br- (aq) + 2H+ (aq) + CO2 (g)




                                time


                                                       Br2 (aq)




                                              393 nm
393 nm                 Detector
 light
         ∆[Br2] α ∆Absorption
                                                                   13.1
Br2 (aq) + HCOOH (aq)        2Br- (aq) + 2H+ (aq) + CO2 (g)




                            slope of
                            tangent
                                        slope of
                                        tangent
                                                        slope of
                                                        tangent



                       ∆[Br2]          [Br2]final – [Br2]initial
      average rate = -        =-
                        ∆t                 tfinal - tinitial
instantaneous rate = rate for specific instance in time
                                                                   13.1
rate α [Br2]
 rate = k [Br2]
    rate
k=        = rate constant
    [Br2]
  = 3.50 x 10-3 s-1

                            13.1
2H2O2 (aq)       2H2O (l) + O2 (g)

                                    PV = nRT
                                n
                            P=     RT = [O2]RT
                                V
                                       1
                               [O2] =     P
                                      RT

                                  ∆[O2]    1 ∆P
                           rate =       =
                                   ∆t     RT ∆t



measure ∆P over time
                                                      13.1
2H2O2 (aq)   2H2O (l) + O2 (g)




                                 13.1
Reaction Rates and Stoichiometry

                        2A       B

Two moles of A disappear for each mole of B that is formed.

                    1 ∆[A]             ∆[B]
           rate = -             rate =
                    2 ∆t                ∆t


                  aA + bB       cC + dD

             1 ∆[A]    1 ∆[B]   1 ∆[C]   1 ∆[D]
    rate = -        =-        =        =
             a ∆t      b ∆t     c ∆t     d ∆t


                                                          13.1
Write the rate expression for the following reaction:

CH4 (g) + 2O2 (g)      CO2 (g) + 2H2O (g)


         ∆[CH4]    1 ∆[O2]   ∆[CO2]   1 ∆[H2O]
rate = -        =-         =        =
           ∆t      2 ∆t        ∆t     2   ∆t




                                                        13.1
The Rate Law
The rate law expresses the relationship of the rate of a reaction
to the rate constant and the concentrations of the reactants
raised to some powers.
                     aA + bB        cC + dD

                         Rate = k [A]x[B]y


                   reaction is xth order in A
                   reaction is yth order in B
                   reaction is (x +y)th order overall


                                                              13.2
F2 (g) + 2ClO2 (g)     2FClO2 (g)



   rate = k [F2]x[ClO2]y




Double [F2] with [ClO2] constant
Rate doubles
x=1
                                         rate = k [F2][ClO2]
Quadruple [ClO2] with [F2] constant
Rate quadruples
y=1
                                                               13.2
Rate Laws
•   Rate laws are always determined experimentally.

•   Reaction order is always defined in terms of reactant
    (not product) concentrations.

•   The order of a reactant is not related to the
    stoichiometric coefficient of the reactant in the balanced
    chemical equation.


                     F2 (g) + 2ClO2 (g)      2FClO2 (g)

                             rate = k [F2][ClO2] 1


                                                                 13.2
Determine the rate law and calculate the rate constant for
        the following reaction from the following data:
        S2O82- (aq) + 3I- (aq)    2SO42- (aq) + I3- (aq)

               [S2O82-]            Initial Rate
Experiment                 [I-]
                                       (M/s)      rate = k [S2O82-]x[I-]y
    1           0.08      0.034    2.2 x 10-4     y=1
    2           0.08      0.017    1.1 x 10-4     x=1
    3           0.16      0.017    2.2 x 10-4     rate = k [S2O82-][I-]

Double [I-], rate doubles (experiment 1 & 2)
Double [S2O82-], rate doubles (experiment 2 & 3)

                   rate          2.2 x 10-4 M/s
             k=             =                   = 0.08/M•s
                [S2O8 ][I ]
                      2- -
                              (0.08 M)(0.034 M)
                                                                     13.2
First-Order Reactions
                                       ∆[A]
     A         product        rate = -              rate = k [A]
                                        ∆t
                                                  ∆[A]
     rate   M/s                                 -      = k [A]
k=        =     = 1/s or s-1                       ∆t
      [A]   M
                                   [A] is the concentration of A at any time t
                                   [A]0 is the concentration of A at time t=0

         [A] = [A]0exp(-kt)                    ln[A] = ln[A]0 - kt




                                                                         13.3
The reaction 2A         B is first order in A with a rate
     constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A
     to decrease from 0.88 M to 0.14 M ?

                                                 [A]0 = 0.88 M
ln[A] = ln[A]0 - kt
                                                 [A] = 0.14 M
   kt = ln[A]0 – ln[A]
                               [A]0            0.88 M
                          ln              ln
       ln[A]0 – ln[A]          [A]             0.14 M
    t=                =               =                       = 66 s
              k                k          2.8 x 10 s-2   -1




                                                                       13.3
First-Order Reactions

The half-life, t½, is the time required for the concentration of a
reactant to decrease to half of its initial concentration.
                     t½ = t when [A] = [A]0/2

                                [A]0
                           ln
                                [A]0/2     ln2   0.693
                    t½ =                 =     =
                                k           k      k
     What is the half-life of N2O5 if it decomposes with a rate
     constant of 5.7 x 10-4 s-1?
           t½ = ln2 =        0.693
                                          = 1200 s = 20 minutes
                  k       5.7 x 10 s
                                  -4 -1


How do you know decomposition is first order?
                                         units of k (s-1)         13.3
First-order reaction
        A    product

  # of
half-lives   [A] = [A]0/n
    1             2

    2             4

    3             8

    4            16




                          13.3
Second-Order Reactions
                                ∆[A]
 A         product     rate = -               rate = k [A]2
                                 ∆t

   rate     M/s                             ∆[A]
k=        =   2 = 1/M•s
                                          -      = k [A]2
    [A] 2   M                                ∆t

  1     1              [A] is the concentration of A at any time t
     =      + kt
 [A]   [A]0            [A]0 is the concentration of A at time t=0


  t½ = t when [A] = [A]0/2

           1
  t½ =
         k[A]0


                                                                     13.3
Zero-Order Reactions
                                 ∆[A]
 A        product       rate = -               rate = k [A]0 = k
                                  ∆t

   rate                                      ∆[A]
k=        = M/s                            -      =k
    [A] 0
                                              ∆t

                        [A] is the concentration of A at any time t
 [A] = [A]0 - kt
                        [A]0 is the concentration of A at time t=0


  t½ = t when [A] = [A]0/2

         [A]0
  t½ =
          2k


                                                                      13.3
Summary of the Kinetics of Zero-Order, First-Order
         and Second-Order Reactions


                            Concentration-Time
 Order    Rate Law              Equation             Half-Life
                                                           [A]0
   0       rate = k             [A] = [A]0 - kt     t½ =
                                                            2k

   1     rate = k [A]         ln[A] = ln[A]0 - kt    t½ = ln2
                                                           k
                                1     1                    1
   2     rate = k [A]   2          =      + kt      t½ =
                               [A]   [A]0                k[A]0



                                                                  13.3
A+B        C+D

    Exothermic Reaction            Endothermic Reaction




The activation energy (Ea) is the minimum amount of
energy required to initiate a chemical reaction.
                                                      13.4
Temperature Dependence of the Rate Constant


                         k = A • exp( -Ea/RT )
                         (Arrhenius equation)
                      Ea is the activation energy (J/mol)
                      R is the gas constant (8.314 J/K•mol)
                      T is the absolute temperature
                      A is the frequency factor

                               Ea 1
                       lnk = -      + lnA
                               R T



                                                        13.4
Ea 1
lnk = -      + lnA
        R T




                     13.4
Reaction Mechanisms

The overall progress of a chemical reaction can be represented
at the molecular level by a series of simple elementary steps
or elementary reactions.

The sequence of elementary steps that leads to product
formation is the reaction mechanism.

               2NO (g) + O2 (g)       2NO2 (g)

             N2O2 is detected during the reaction!

       Elementary step:        NO + NO           N 2 O2
     + Elementary step:        N2O2 + O2         2NO2
       Overall reaction:       2NO + O2          2NO2
                                                           13.5
Intermediates are species that appear in a reaction
mechanism but not in the overall balanced equation.
An intermediate is always formed in an early elementary step
and consumed in a later elementary step.

    Elementary step:      NO + NO        N 2 O2
+ Elementary step:       N2O2 + O2       2NO2
    Overall reaction:    2NO + O2        2NO2

The molecularity of a reaction is the number of molecules
   reacting in an elementary step.
•   Unimolecular reaction – elementary step with 1 molecule
•   Bimolecular reaction – elementary step with 2 molecules
•   Termolecular reaction – elementary step with 3 molecules
                                                            13.5
Rate Laws and Elementary Steps

Unimolecular reaction     A      products      rate = k [A]

Bimolecular reaction    A+B        products    rate = k [A][B]

Bimolecular reaction    A+A        products    rate = k [A]2

Writing plausible reaction mechanisms:
•   The sum of the elementary steps must give the overall
    balanced equation for the reaction.
•   The rate-determining step should predict the same rate
    law that is determined experimentally.
The rate-determining step is the slowest step in the
sequence of steps leading to product formation.
                                                               13.5
The experimental rate law for the reaction between NO 2
      and CO to produce NO and CO2 is rate = k[NO2]2. The
      reaction is believed to occur via two steps:
        Step 1:         NO2 + NO2         NO + NO3
        Step 2:        NO3 + CO         NO2 + CO2
What is the equation for the overall reaction?
                    NO2+ CO          NO + CO2

What is the intermediate?
                               NO3

What can you say about the relative rates of steps 1 and 2?
           rate = k[NO2]2 is the rate law for step 1 so
               step 1 must be slower than step 2
                                                                13.5
A catalyst is a substance that increases the rate of a
chemical reaction without itself being consumed.
         k = A • exp( -Ea/RT )        Ea         k




   uncatalyzed                              catalyzed


                     ratecatalyzed > rateuncatalyzed
                              Ea‘ < Ea                   13.6
In heterogeneous catalysis, the reactants and the catalysts
are in different phases.
     •   Haber synthesis of ammonia
     •   Ostwald process for the production of nitric acid
     •   Catalytic converters

In homogeneous catalysis, the reactants and the catalysts
are dispersed in a single phase, usually liquid.

     •   Acid catalysis
     •   Base catalysis


                                                             13.6
Haber Process




                   Fe/Al2O3/K2O
N2 (g) + 3H2 (g)                  2NH 3 (g)
                     catalyst




                                              13.6
Ostwald Process
                     Pt catalyst
4NH3 (g) + 5O2 (g)                 4NO (g) + 6H2O (g)

    2NO (g) + O2 (g)          2NO2 (g)

2NO2 (g) + H2O (l)        HNO2 (aq) + HNO3 (aq)




                                                       Hot Pt wire
     Pt-Rh catalysts used                           over NH3 solution
      in Ostwald process                                           13.6
Catalytic Converters




                                   catalytic
CO + Unburned Hydrocarbons + O2   converter      CO2 + H2O

                               catalytic
                2NO + 2NO2    converter        2N2 + 3O2



                                                           13.6
Enzyme Catalysis




                   13.6
enzyme
uncatalyzed   catalyzed




                          13.6

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Chemical kinetics

  • 1. Chemical Kinetics Chapter 13
  • 2. Chemical Kinetics Thermodynamics – does a reaction take place? Kinetics – how fast does a reaction proceed? Reaction rate is the change in the concentration of a reactant or a product with time (M/s). A B ∆[A] ∆[A] = change in concentration of A over rate = - ∆t time period ∆t ∆[B] ∆[B] = change in concentration of B over rate = ∆t time period ∆t Because [A] decreases with time, ∆[A] is negative. 13.1
  • 3. A B time ∆[A] rate = - ∆t ∆[B] rate = ∆t 13.1
  • 4. Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g) time Br2 (aq) 393 nm 393 nm Detector light ∆[Br2] α ∆Absorption 13.1
  • 5. Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g) slope of tangent slope of tangent slope of tangent ∆[Br2] [Br2]final – [Br2]initial average rate = - =- ∆t tfinal - tinitial instantaneous rate = rate for specific instance in time 13.1
  • 6. rate α [Br2] rate = k [Br2] rate k= = rate constant [Br2] = 3.50 x 10-3 s-1 13.1
  • 7. 2H2O2 (aq) 2H2O (l) + O2 (g) PV = nRT n P= RT = [O2]RT V 1 [O2] = P RT ∆[O2] 1 ∆P rate = = ∆t RT ∆t measure ∆P over time 13.1
  • 8. 2H2O2 (aq) 2H2O (l) + O2 (g) 13.1
  • 9. Reaction Rates and Stoichiometry 2A B Two moles of A disappear for each mole of B that is formed. 1 ∆[A] ∆[B] rate = - rate = 2 ∆t ∆t aA + bB cC + dD 1 ∆[A] 1 ∆[B] 1 ∆[C] 1 ∆[D] rate = - =- = = a ∆t b ∆t c ∆t d ∆t 13.1
  • 10. Write the rate expression for the following reaction: CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (g) ∆[CH4] 1 ∆[O2] ∆[CO2] 1 ∆[H2O] rate = - =- = = ∆t 2 ∆t ∆t 2 ∆t 13.1
  • 11. The Rate Law The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. aA + bB cC + dD Rate = k [A]x[B]y reaction is xth order in A reaction is yth order in B reaction is (x +y)th order overall 13.2
  • 12. F2 (g) + 2ClO2 (g) 2FClO2 (g) rate = k [F2]x[ClO2]y Double [F2] with [ClO2] constant Rate doubles x=1 rate = k [F2][ClO2] Quadruple [ClO2] with [F2] constant Rate quadruples y=1 13.2
  • 13. Rate Laws • Rate laws are always determined experimentally. • Reaction order is always defined in terms of reactant (not product) concentrations. • The order of a reactant is not related to the stoichiometric coefficient of the reactant in the balanced chemical equation. F2 (g) + 2ClO2 (g) 2FClO2 (g) rate = k [F2][ClO2] 1 13.2
  • 14. Determine the rate law and calculate the rate constant for the following reaction from the following data: S2O82- (aq) + 3I- (aq) 2SO42- (aq) + I3- (aq) [S2O82-] Initial Rate Experiment [I-] (M/s) rate = k [S2O82-]x[I-]y 1 0.08 0.034 2.2 x 10-4 y=1 2 0.08 0.017 1.1 x 10-4 x=1 3 0.16 0.017 2.2 x 10-4 rate = k [S2O82-][I-] Double [I-], rate doubles (experiment 1 & 2) Double [S2O82-], rate doubles (experiment 2 & 3) rate 2.2 x 10-4 M/s k= = = 0.08/M•s [S2O8 ][I ] 2- - (0.08 M)(0.034 M) 13.2
  • 15. First-Order Reactions ∆[A] A product rate = - rate = k [A] ∆t ∆[A] rate M/s - = k [A] k= = = 1/s or s-1 ∆t [A] M [A] is the concentration of A at any time t [A]0 is the concentration of A at time t=0 [A] = [A]0exp(-kt) ln[A] = ln[A]0 - kt 13.3
  • 16. The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ? [A]0 = 0.88 M ln[A] = ln[A]0 - kt [A] = 0.14 M kt = ln[A]0 – ln[A] [A]0 0.88 M ln ln ln[A]0 – ln[A] [A] 0.14 M t= = = = 66 s k k 2.8 x 10 s-2 -1 13.3
  • 17. First-Order Reactions The half-life, t½, is the time required for the concentration of a reactant to decrease to half of its initial concentration. t½ = t when [A] = [A]0/2 [A]0 ln [A]0/2 ln2 0.693 t½ = = = k k k What is the half-life of N2O5 if it decomposes with a rate constant of 5.7 x 10-4 s-1? t½ = ln2 = 0.693 = 1200 s = 20 minutes k 5.7 x 10 s -4 -1 How do you know decomposition is first order? units of k (s-1) 13.3
  • 18. First-order reaction A product # of half-lives [A] = [A]0/n 1 2 2 4 3 8 4 16 13.3
  • 19. Second-Order Reactions ∆[A] A product rate = - rate = k [A]2 ∆t rate M/s ∆[A] k= = 2 = 1/M•s - = k [A]2 [A] 2 M ∆t 1 1 [A] is the concentration of A at any time t = + kt [A] [A]0 [A]0 is the concentration of A at time t=0 t½ = t when [A] = [A]0/2 1 t½ = k[A]0 13.3
  • 20. Zero-Order Reactions ∆[A] A product rate = - rate = k [A]0 = k ∆t rate ∆[A] k= = M/s - =k [A] 0 ∆t [A] is the concentration of A at any time t [A] = [A]0 - kt [A]0 is the concentration of A at time t=0 t½ = t when [A] = [A]0/2 [A]0 t½ = 2k 13.3
  • 21. Summary of the Kinetics of Zero-Order, First-Order and Second-Order Reactions Concentration-Time Order Rate Law Equation Half-Life [A]0 0 rate = k [A] = [A]0 - kt t½ = 2k 1 rate = k [A] ln[A] = ln[A]0 - kt t½ = ln2 k 1 1 1 2 rate = k [A] 2 = + kt t½ = [A] [A]0 k[A]0 13.3
  • 22. A+B C+D Exothermic Reaction Endothermic Reaction The activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction. 13.4
  • 23. Temperature Dependence of the Rate Constant k = A • exp( -Ea/RT ) (Arrhenius equation) Ea is the activation energy (J/mol) R is the gas constant (8.314 J/K•mol) T is the absolute temperature A is the frequency factor Ea 1 lnk = - + lnA R T 13.4
  • 24. Ea 1 lnk = - + lnA R T 13.4
  • 25. Reaction Mechanisms The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions. The sequence of elementary steps that leads to product formation is the reaction mechanism. 2NO (g) + O2 (g) 2NO2 (g) N2O2 is detected during the reaction! Elementary step: NO + NO N 2 O2 + Elementary step: N2O2 + O2 2NO2 Overall reaction: 2NO + O2 2NO2 13.5
  • 26. Intermediates are species that appear in a reaction mechanism but not in the overall balanced equation. An intermediate is always formed in an early elementary step and consumed in a later elementary step. Elementary step: NO + NO N 2 O2 + Elementary step: N2O2 + O2 2NO2 Overall reaction: 2NO + O2 2NO2 The molecularity of a reaction is the number of molecules reacting in an elementary step. • Unimolecular reaction – elementary step with 1 molecule • Bimolecular reaction – elementary step with 2 molecules • Termolecular reaction – elementary step with 3 molecules 13.5
  • 27. Rate Laws and Elementary Steps Unimolecular reaction A products rate = k [A] Bimolecular reaction A+B products rate = k [A][B] Bimolecular reaction A+A products rate = k [A]2 Writing plausible reaction mechanisms: • The sum of the elementary steps must give the overall balanced equation for the reaction. • The rate-determining step should predict the same rate law that is determined experimentally. The rate-determining step is the slowest step in the sequence of steps leading to product formation. 13.5
  • 28. The experimental rate law for the reaction between NO 2 and CO to produce NO and CO2 is rate = k[NO2]2. The reaction is believed to occur via two steps: Step 1: NO2 + NO2 NO + NO3 Step 2: NO3 + CO NO2 + CO2 What is the equation for the overall reaction? NO2+ CO NO + CO2 What is the intermediate? NO3 What can you say about the relative rates of steps 1 and 2? rate = k[NO2]2 is the rate law for step 1 so step 1 must be slower than step 2 13.5
  • 29. A catalyst is a substance that increases the rate of a chemical reaction without itself being consumed. k = A • exp( -Ea/RT ) Ea k uncatalyzed catalyzed ratecatalyzed > rateuncatalyzed Ea‘ < Ea 13.6
  • 30. In heterogeneous catalysis, the reactants and the catalysts are in different phases. • Haber synthesis of ammonia • Ostwald process for the production of nitric acid • Catalytic converters In homogeneous catalysis, the reactants and the catalysts are dispersed in a single phase, usually liquid. • Acid catalysis • Base catalysis 13.6
  • 31. Haber Process Fe/Al2O3/K2O N2 (g) + 3H2 (g) 2NH 3 (g) catalyst 13.6
  • 32. Ostwald Process Pt catalyst 4NH3 (g) + 5O2 (g) 4NO (g) + 6H2O (g) 2NO (g) + O2 (g) 2NO2 (g) 2NO2 (g) + H2O (l) HNO2 (aq) + HNO3 (aq) Hot Pt wire Pt-Rh catalysts used over NH3 solution in Ostwald process 13.6
  • 33. Catalytic Converters catalytic CO + Unburned Hydrocarbons + O2 converter CO2 + H2O catalytic 2NO + 2NO2 converter 2N2 + 3O2 13.6
  • 35. enzyme uncatalyzed catalyzed 13.6