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9.3: Untitled Page 219

  • Page ID
    18352
  • Chapter 9

    I

    I

    R

    R

    A

    B

    (9‐39)

    8

    3

    and a little thought will indicate that the general stoichiometric translation of Eq. 9‐34 is given by

    Elementary stoichiometry I

    (9‐40)

    I

    I

    I

    I

    I

    I

    R

    R

    R

    R

    R

    R

    A

    B

    A

    C

    A

    ,

     

    ,

    D

    This result is based on the assumption that species A , B , C and D are all unique species. For example, if species C is actually identical to species A the second of Eqs. 9‐40 takes the form

    I

    I

    R

    R

    Unacceptable stoichiometry:

    A

    A

     

    (9‐41)

    In this special case, it should be clear that Eq. 9‐34 cannot be used as a picture of the stoichiometry. If species B , C and D are all unique species, we can follow the same thought process that led to Eq. 9‐40 to conclude that the stoichiometric translation of Eq. 9‐36 is given by

    Elementary stoichiometry II

    (9‐42)

    II

    II

    II

    II

    R

    R

    R

    R

    B

    C

    B

    D

    II

    ,

     

    ,

    0

    A

    R

    Throughout our study of stoichiometry in Chapter 6 we used representations such as C H OH and CH OC H to identify the atomic structure of various 2

    5

    3

    2

    3

    molecular species, and with those representations it was easy to keep track of atomic species. The representations given by Eq. 9‐34 and Eq. 9‐36 are less informative, and we need to proceed with greater care when the atomic structure is not given explicitly.

    With the elementary stoichiometry now available in terms of Eq. 9‐40 and Eq. 9‐42, we can develop the local chemical reaction rate equations for species A and B on the basis of Eqs. 9‐35 and 9‐37. This leads to

     

     

     

    R

      k c c ,

    R

        k c c k c c

    (9‐43)

    A

    I A B

    B

     I A B

    II B C

    and the rate equations for the other species can be constructed in the same manner.

    index-416_1.png

    index-416_2.png

    index-416_3.png

    index-416_4.png

    Reaction Kinetics

    407

    9.1.3 Decomposition of azomethane and reactive intermediates We are now ready to return to the decomposition of azomethane to produce ethane and nitrogen. The rate equation given by Eq. 9‐29 is based on the work of Ramsperger (1927) and an explanation of that rate equation requires the existence of reactive intermediates (Herzfeld, 1919; Polanyi, 1920) or Bodenstein products (Frank‐Kamenetsky, 1940). Most chemical reactions involve reactive intermediate species, and this idea is illustrated in Figure 9‐7 where we have indicated the existence of an activated form of azomethane identified as (CH ) N  . This form exists in such small concentrations that it is difficult to 3 2

    2

    detect in the exit stream and thus does not appear in the representation of the global stoichiometry. A key idea here is that the expression for a chemical reaction rate is based on experiments, and when a specific chemical species cannot be detected experimentally it often does not appear in the first effort to construct a chemical reaction rate expression.

    Figure 9‐7 Local and global stoichiometry for decomposition of azomethane

    For simplicity we represent the molecular species suggested by Figure 9‐7 as A  (CH ) N ,

    B  C H ,

    C  N ,

    A   (CH ) N 

    (9‐44)

    3 2

    2

    2

    6

    2

    3 2

    2

    index-417_1.png

    index-417_2.png

    408