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9.11: Untitled Page 227

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    • Chapter 9

    These net rates of production can be used with Axiom I to analyze chemical reactors such as the batch reactors studied in Section 8.2.

    Hydrogen bromide reaction

    At this point we return to the hydrogen bromide reaction described briefly in Section 9.1 where Axiom II provided the result given by

    R

    H

    1 2

    Axiom II:

    2

     

    R

    (9‐95)

    HBr

    R

    1

     2

    2

    Br 

    

    pivot matrix

    Use of local stoichiometry along with the chemical kinetic schema given by Eq. 9‐15 did not lead to a chemical reaction rate equation that was in agreement with the experimental result indicated by Eq. 9‐19. Clearly the molecular process suggested by Figure 9‐3 is not an acceptable representation of the reaction kinetics and we need to explore the impact of reactive intermediates on the hydrogen bromide reaction. To do so, we propose the following chemical kinetic schemata:

    k I

    Elementary chemical kinetic schema I:

    Br

     2Br

    (9‐96a)

    2

    k II

    Elementary chemical kinetic schema II:

    Br  H

    

     HBr  H

    (9‐96b)

    2

    k III

    Elementary chemical kinetic schema III:

    H  Br

    

     HBr  Br

    (9‐96c)

    2

    k IV

    Elementary chemical kinetic schema IV:

    H  HBr

    

     H  Br (9‐96d)

    2

    k V

    Elementary chemical kinetic schema V:

    2Br

    

     Br

    (9‐96e)

    2

    Here we note that Eqs. 9‐96 are simply a more complex example of Eqs. 9‐81, thus we can follow the procedure outlined in the previous paragraphs assuming that the stoichiometric schemata are identical to the chemical kinetic schemata. We begin with the first elementary schema indicated by Eq. 9‐96a and our analysis of this schema leads to

    Reaction Kinetics

    423

    SCHEMA I

    k I

    Elementary chemical kinetic schema I:

    Br

     2Br

    (9‐97a)

    2

    I

    R

    Elementary stoichiometry I:

    I

    Br

    R

     

    (9‐97b)

    2

    Br

    2

    Elementary chemical reaction rate equation I:

    I

    R

      k c

    (9‐97c)

    Br

    I Br

    2

    2

    Elementary reference chemical reaction rate I:

    r

    k c

    (9‐97d)

    I

    I Br2

    The remaining schemata lead to an analogous set of equations given by SCHEMA II

    k II

    Elementary chemical kinetic schema II:

    Br  H

    

     HBr  H (9‐98a)

    2

    II

    II

    II

    II

    R

    R

    ,

    R

      R

    Elementary stoichiometry II:

    Br

    H2

    Br

    HBr (9‐98b)

    II

    II

    R

      R

    Br

    H

    Elementary chemical reaction rate equation II:

    II

    R

      k c c

    (9‐98c)

    Br

    II Br H2

    Elementary reference chemical reaction rate II:

    r

    k c c

    (9‐98d)

    II

    II Br H2

    SCHEMA III

    k III

    Elementary chemical kinetic schema III:

    H  Br

    

     HBr  Br (9‐99a)

    2

    III

    III

    III

    III

    R

    R

    ,

    R

      R

    H

    Br

    H

    HBr

    Elementary stoichiometry III:

    2

    (9‐99b)

    III

    III

    R

      R

    H

    Br

    Elementary chemical reaction rate equation III:

    III

    R

      k c c

    (9‐99c)

    H

    III H Br2

    Elementary reference chemical reaction rate III:

    r

    k c c

    (9‐99d)

    III

    III H B 2

    r

    424