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9.4: Untitled Page 220

  • Page ID
    18353
  • Chapter 9

    in which A  represents the activated form of azomethane or the so‐called reactive intermediate. On the basis of the analysis of Lindemann (1922) we explore the following set of elementary chemical kinetic schemata: k I

    Elementary chemical kinetic schema I:

    2 A

     A A

    (9‐45a)

    k II

    Elementary chemical kinetic schema II:

    A  

    B C

    (9‐45b)

    k III

    Elementary chemical kinetic schema III:

    A   A

     2 A

    (9‐45c)

    The schema represented by Eq. 9‐45a is illustrated in Figure 9‐8 where we see that a collision between two molecules of azomethane leads to the creation of the Figure 9‐8. Creation of a reactive intermediate for the decomposition of azomethane

    reactive intermediate denoted by (CH ) N  . Equation 9‐45a represents an 3 2

    2

    example of the situation illustrated by Eqs. 9‐40 and 9‐41, and one must be careful in terms of the stoichiometric interpretation. In this case we draw upon Figure 9‐8 to conclude that the stoichiometric schema associated with Eq. 9‐45a is the activation of an azomethane molecule that we represent in the form Stoichiometric schema:

    (CH ) N  (CH ) N 

    or

    A A

    (9‐46)

    3 2

    2

    3 2

    2

    Given this stoichiometric schema for the first elementary step, we see that Eq. 9‐45a leads to the following four representations:

    Elementary stoichiometric schema I:

    A

    A

    (9‐47a)

    k I

    Elementary chemical kinetic schema I:

    2 A

     A A

    (9‐47b)

    Reaction Kinetics

    409

    Elementary stoichiometry I:

    I

    I

    R

      R

    (9‐47c)

    A

    A

    Elementary chemical reaction rate equation I:

    I

    2

    R

      k c

    (9‐47d)

    A

    I A

    The second elementary step involves the decomposition of the activated molecule to form ethane and nitrogen according to:

    Elementary stoichiometric schema II:

    A   B C

    (9‐48a)

    k II

    Elementary chemical kinetic schema II:

    A  

    B C

    (9‐48b)

    Elementary stoichiometry II:

    II

    II

    II

    II

    R

      R ,

    R

      R

    (9‐48c)

    A

    B

    A

    C

    Elementary chemical reaction rate equation II:

    II

    R

      k c

    (9‐48d)

    A

    II A

    The final elementary step consists of the recombination of an activated molecule with azomethane to form two molecules of azomethane. This final step is described by the following representations:

    Elementary stoichiometric schema III:

    A   A

    (9‐49a)

    k III

    Elementary chemical kinetic schema III:

    A   A

    

     2 A

    (9‐49b)

    Elementary stoichiometry III:

    III

    III

    R

      R

    (9‐49c)

    A

    A

    Elementary chemical reaction rate equation III:

    III

    R

      k c c (9‐49d)

    A

    III A A

    According to Eq. 9‐32 the local net rates of production are given by I

    II

    R

    R

    R  III

    R

    (9‐50a)

    A

    A

    A

    A

    III

    I

    II

    R

    R

    R

    R

    (9‐50b)

    A

    A

    A

    A

    I

    II

    III

    R

    R

    R R

    (9‐50c)

    B

    B

    B

    B

    We now have a complete description of the reaction process for the schemata represented by Eqs. 9‐45, and from these results we would like to extract a representation for R in terms of c . The classic simplification of this algebraic B

    A

    410