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9.12: Untitled Page 228

  • Page ID
    18361
  • Chapter 9

    SCHEMA IV

    k IV

    Elementary chemical kinetic schema IV:

    H  HBr 

     H  Br (9‐100a)

    2

    IV

    IV

    IV

    IV

    R

    R

    ,

    R

      R

    Elementary stoichiometry IV:

    H

    HBr

    H

    H2

    (9‐100b)

    IV

    IV

    R

      R

    H

    Br

    Elementary chemical reaction rate equation IV:

    IV

    R

      k c c

    (9‐100c)

    H

    IV H HBr

    Elementary reference chemical reaction rate IV:

    r

    k c c

    (9‐100d)

    IV

    IV H HBr

    SCHEMA V

    k V

    Elementary chemical kinetic schema V:

    2Br

    

     Br

    (9‐101a)

    2

    V

    R

    Elementary stoichiometry V:

    Br

    V

      R

    (9‐101b)

    2

    Br

    2

    Elementary chemical reaction rate equation V:

    V

    R

      k

    2

    c

    (9‐101c)

    Br

    V Br

    Elementary reference chemical reaction rate V:

    r

    k c 2

    (9‐101d)

    V

    V Br

    We begin our analysis of Eqs. 9‐96 by listing the net molar rates of production of all five species in terms of the elementary rates of reaction according to I

    II

    III

    IV

    V

    R

    R

    R

    R

    R

    R

    (9‐102a)

    Br2

    Br2

    Br2

    B 2

    r

    Br2

    Br2

    I

    II

    III

    IV

    V

    R

    R

    R

    R

    R

    R

    (9‐102b)

    H2

    H2

    H2

    H2

    H2

    H2

    I

    II

    III

    IV

    V

    R

    R

    R

    R

    R

    R

    (9‐102c)

    HBr

    HBr

    HBr

    HBr

    HBr

    HBr

    I

    II

    III

    IV

    R

    R

    R

    R

    R

    R V

    (9‐102d)

    H

    H

    H

    H

    H

    H

    I

    II

    III

    IV

    V

    R

    R

    R

    R

    R

    R

    (9‐102e)

    Br

    Br

    Br

    Br

    Br

    Br

    At this point we can use the elementary chemical reaction rates to express the net rates of production according to

    Reaction Kinetics

    425

    R

      r  0  r

     0  1

    Br

    r

    (9‐103a)

    2

    I

    III

    V

    2

    R

    0  r

     0  r

     0

    (9‐103b)

    H2

    II

    IV

    R

    0  r

    r

    r

     0

    (9‐103c)

    HBr

    II

    III

    IV

    R

    0  r

    r

    r

     0

    (9‐103d)

    H

    II

    III

    IV

    R

     2 r r r

    r

    r

    (9‐103e)

    Br

    I

    II

    III

    IV

    V

    In matrix form these representations for the net rates of production are given by

    R

    r

    2

    Br

    1

    0 1

    0

    1 2 

     I 

    R

    H

    0

    1

    0

    1

    0

    r II 

    2

    R

    r

    HBr 

      0

    1

    1 1

    0   III 

    (9‐104)

    R

    0

    1 1 

    1

    0 

    r

    H 

     IV 

    2

    1

    1

    1

    R

    1  

    r

    Br 

     V 

    The compact form of this lengthy algebraic result can be expressed as R

     M r

    (9‐105)

    M

    in which R is the column matrix of all net rates of production, M is the M

    mechanistic matrix, and r is the column matrix of elementary chemical reaction rates. These quantities are defined explicitly by

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