Reaction Kinetics (2) by Y5AMwS1P

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									Physical Chemistry




                     Reaction Kinetics (2)

                       Xuan Cheng
                       Xiamen University

                                           1
Physical Chemistry                                                            Reaction
                Simple Order Reactions                                        Kinetics


 Order Reaction Rate Law                   k A  ak                             t1/2

 0         A P        r  ko          A  Ao  k At                        Ao
                                                                                 2k A

 1         A P
                     r  k A
                                                                                 ln 2
                                       A  Ao e         k At
                                                                                  kA

           A P                                  Ao
 2
                     r  k A     2   A                                       1
                                             1  k At Ao                    [ A]o k A

 n2       A P                n  A 
                                        1 n
                                                                              2 n 1  1
                     r  k    
                              A  A 
                                              1  Ao 1(n  1)k At
                                                        n
                                                                          (n  1)Ao 1 k A
                                                                                    n
                                  o


                                                                                           2
Physical Chemistry                                            Reaction
                                                              Kinetics
                 Typical Complex Reactions

           (1)       Reversible    Opposing           
                                                         kf
                                                   A  C
                     reaction      reaction              kb



           (2)       Consecutive      k       k
                     reaction            
                                   A 1 B  2 C


                                                    k1
                     Competing     Parallel       AC
           (3)
                     reaction      reaction         k
                                                    
                                                  A 2 D


                                                                     3
Physical Chemistry                                            Reaction
              Reversible First-Order Reactions                Kinetics

                     aA  bB    eE  fF                        (17.1)
    Consider the reverse reaction (opposing reaction)
                              kf
                           
                        A  C
                              kb

    the first order in both forward and back directions

              r f  k f [A]                   rb  kb [C ]


         d [ A]                        d [ A] 
                 r f  k f [ A]               rb  kb [C ]
         dt  f                         dt b

                                                                       4
Physical Chemistry                                                    Reaction
               Reversible First-Order Reactions                       Kinetics


             d [ A]  d [ A]    d [ A] 
                                      k f [ A]  kb [C ]          (17.31)
              dt     dt  f  dt b

           [C ]  [ A]            [C ]  [C ]o   A]  [ A]o 
                                                      [

                 [C ]  [C ]o  [ A]o  [ A]

                      k f [ A]  kb  C ]o  [ A]o  [ A]
              d [ A]
                                       [
               dt

              d [ A]
                      kb [C ]o  kb [ A]o  (k f  kb )[ A]              (17.32)
               dt

                                                                             5
Physical Chemistry                                                     Reaction
           Reversible First-Order Reactions                            Kinetics

              d [ A]
                      kb [C ]o  kb [ A]o  (k f  kb )[ A]                 (17.32)
               dt

                                  d [ A]
     At equilibrium,                     0             and      [ A]  [ A]eq
                                   dt
                kb[C]o  kb[ A]o  (k f  kb )[ A]eq                         (17.33)

                              (k f  kb ) A]eq  [ A]
                      d [ A]
                                          [
                       dt
                          [ A]  [ A]eq
                     ln                     (k f  kb )t
                          [ A]o  [ A]eq

                              
           [ A]  [ A]eq  [ A]o  [ A]eq e  jt             j  k f  kb   (17.34)
                                                                                 6
Physical Chemistry                                                        Reaction
             Reversible First-Order Reactions                             Kinetics


                                            
           [ A]  [ A]eq  [ A]o  [ A]eq e  jt                j  k f  kb       (17.34)

                                     A  Ao ek At                             (17.14)*
 Fig. 17.2
                AC                                         When [A]eq=0, kb=0
           [A]/[A]o              kf / kb=2
                                                                   Fig. 17.1(a)



                                                 [A]/[A]o

          [C]/[A]o
                        jt                                                     t
                                                                                       7
Physical Chemistry                                                              Reaction
                                                                                Kinetics
            Consecutive First-Order Reactions
   Consider two consecutive irreversible first-order reactions
                                        k            k
                                       
                                 A 1 B  2 C                                       (17.35)
                      r1  k1[ A]                            r2  k2 [ B]

                d [ B]                            d [ B] 
                         r1  k1[ A]                      r2  k2[ B]
                dt 1                              dt  2

                d [ B ]  d [ B ]   d [ B] 
                                          k1[ A]  k2[ B]
                 dt      dt 1  dt 2

    d [ A]                d [ B]                          d [C ] 
              k1[ A]             k1[ A]  k 2 [ B ]             k2 [ B]   (17.36)
    dt                    dt                              dt 
                                                                                       8
Physical Chemistry                                                                 Reaction
                Consecutive First-Order Reactions                                  Kinetics

     Let only A be present in the system at t = 0

                      [ A]o  0             [ B ]o  0            [C ]o  0            (17.37)
    d [ A]                   d [ B]                          d [C ] 
              k1[ A]                k1[ A]  k 2 [ B ]             k2 [ B]   (17.36)
    dt                       dt                              dt 

                                       d A / dt  k A A                           (17.11)

                                         A  Ao ek1t                              (17.38)

                            d [ B]             k t
                                     k1[ A]o e 1  k 2 [ B ]                        (17.39)
                            dt 

                                  k [ A]
   Integration              [ B]  1 o (e  k1t  e  k 2t ) ?                         (17.40)
                                  k 2  k1
                                                                                          9
Physical Chemistry                                                      Reaction
            Consecutive First-Order Reactions                           Kinetics

   At all times (conservation of matter)           [ A]  [ B]  [C ]  [ A]o

                                  A  Ao ek1t                              (17.38)
                             k [ A]
                       [ B]  1 o (e  k1t  e  k 2t )                         (17.40)
                             k 2  k1

                                 k2    k1t     k1       k 2t 
               [C ]  [ A]o 1 
                             k k e                  e        
                                                                                (17.41)
                                2   1         k2  k1          




                                                                                  10
Physical Chemistry                                      Reaction
          Consecutive First-Order               Reactions
                                                        Kinetics




           x  [ A] /[ A]o   y  [ B] /[ A]o   z  [C ] /[ A]o
        The intermediate’s concentration rises to a maximum, and
        then falls to zero  (the position of maximum: k1/k2) ?
        The concentration of the product C rises from zero and
        reaches [A]o
                                                                   11
Physical Chemistry                                                   Reaction
                                                                     Kinetics
          Consecutive First-Order Reactions
Suppose that in an industrial batch process a substance A produces the
desired product B which goes to decay to a worthless product C, each
stage of the reaction being first-order. At what time will product B be
present in greatest concentration?          k        k          k1  k 2
                                            
                                       A 1 B  2 C 
  The time dependence of [B]
                                k [ A]
                          [ B]  1 o (e  k1t  e  k 2t )               (17.40)
                                k 2  k1

                              k [ A]
                     [ B]max  1 o (e  k1t m ax  e  k 2t m ax )
                              k 2  k1
                                                d [ B]
   A maximum should occur at                           0
                                                 dt
                d [ B]  k1[ A]o
                                (k1e  k1t  k2e  k 2t )  0
                 dt     k2  k1
                                                                           12
Physical Chemistry                                                 Reaction
           Consecutive First-Order                         Reactions
                                                                   Kinetics

                     d [ B]  k1[ A]o
                                     (k1e  k1t  k2e  k 2t )  0
                      dt     k2  k1

     Since [A]o  0, k1  0, so k1ek1t  k2ek2t  0

                            ln k2  ln k1
                       tm 
                               k2  k1
                                            k [ A]
    The maximum concentration of B [ B]max  1 o (e  k1t m ax  e  k 2t m ax )
                                            k 2  k1
                                                  k2
                                          k1  k1  k 2
                         [ B]max  [ A]o  
                                         k 
                                                            ?
                                          2
   For a given value of k1 > k2, as k2 increases, both the time at
   which [B] is a maximum and the yield of B increase.
                                                                          13
Physical Chemistry                                                           Reaction
                 Competing First-Order Reactions                             Kinetics

  Consider two competing irreversible first-order reactions
                                    k                 k
                               
                             A 1 C               
                                                A 2 D                             (17.42)
                                                k1
                                                            C
                           A                                          Parallel reactions
                                                k2
                                                            D

                     r1  k1[ A]                         r2  k2 [ A]

             d [ A]                            d [ A] 
                      r1  k1[ A]                     r2  k2[ A]
             dt 1                              dt  2
                       d [ A]
                               k1[ A]  k2 [ A]  (k1  k2 )[ A]                (17.43)
                        dt

                                                                                     14
Physical Chemistry                                                              Reaction
               Competing First-Order                                     Reactions
                                                                                Kinetics

                     d [ A]
                             k1[ A]  k2 [ A]  (k1  k2 )[ A]                    (17.43)
                      dt

     Compare with                 d A / dt  k A A                              (17.11)

                                    A  Ao ek At                               (17.14)*


                               A  Ao e(k1  k2 )t
                         d [C ]                       ( k  k )t
       For C                      k1[ A]  k1[ A]o e 1 2
                         dt 

   t 0    Ao  0 ?        [C ] 
                                    k1[ A]o
                                    k1  k 2
                                               
                                             1  e  ( k1  k 2 )t                 (17.44)

                                                                                       15
Physical Chemistry                                                      Reaction
                                                                        Kinetics
             Competing First-Order Reactions
                              A  Ao e(k1  k2 )t
                                  k [ A]
                                  k1  k 2
                                             
                            [C ]  1 o 1  e  ( k1  k 2 )t               (17.44)

                       d [ D]                           ( k  k )t
       similarly                k 2 [ A]  k 2 [ A]o e 1 2
                       dt 

   t 0    Ao  0              k [ A]
                                 k1  k 2
                                              
                           [ D]  2 o 1  e  ( k1  k 2 )t                (17.45)

   Division of (17.44) and (17.45)
     At any time during the reaction
                                        [C ]      k1
                                                                           (17.46)
                                        [ D]      k2
                                                                              16
Physical Chemistry                                                      Reaction
                                                                        Kinetics
             Competing First-Order Reactions
                           k1                    k2
                       AC                A D                          (17.42)

  Consider the reverse reactions
                           k 1                  k2
                         
                      C  A                  
                                            D  A                         (17.47)

      Moreover             CD

    At equilibrium     K1  [C ] /[ A]  [C ]
                                                    Thermodynamic control
                       K 2 [ D] /[ A]  [ D]

 When any reverse reactions        [C ]     k1
                                                     Kinetic control       (17.46)
 or interconversion of C and       [ D]     k2
 D can be neglected
                                                                              17
Physical Chemistry                          Reaction
                                            Kinetics
                     Homework
         Page 591          Supplemental Material

                               Page 145, Prob. 16
             Prob. 17.13
                               Page 149, Prob. 30
                               Page 158, Prob. 68




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