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8.27: Untitled Page 216

  • Page ID
    18349
  • Chapter 9

    R

    2 k c

    c

    HBr

    H

    Br

    

    

    2

    2

    

    (9‐18)

    net rate of production

    chemical reaction rate

    

    

    chemical reaction rate equation

    In general, equations are unambiguous while verbal descriptions can sometimes be misleading. When in doubt, study the equations.

    Experimental studies of the reaction of hydrogen and bromine to form hydrogen bromide were carried out by Bodenstein and Lind (1907) in a well‐mixed batch reactor, and those experiments indicate that the net rate of production of hydrogen bromide can be expressed as

    k c

    c

    H2

    Br2

    Experimental:

    R

    (9‐19)

    HBr

    1  k  c

    c

    HBr

    Br

    2 

    This experimental result is certainly not consistent with the chemical reaction rate equation given by Eq. 9‐17, thus the picture represented by Eq. 9‐15 is not consistent with the kinetics of the real physical process. Clearly we need a new picture of the reaction of hydrogen with bromine to form hydrogen bromide, and that new picture is considered in Section 9.3.

    Decomposition of azomethane

    As another example of an apparently simple reaction, we consider the gas-phase decomposition of azomethane [ (CH ) N ] to produce ethane ( C H ) and 3 2

    2

    2

    6

    nitrogen ( N ). This reaction is illustrated in Figure 9‐4 where we have indicated 2

    that azomethane appears in both the input and the output streams.

    Figure 9‐4. Decomposition of azomethane

    Reaction Kinetics

    401

    The visual representation of the atomic matrix for this system is given by Molecular species 

    C H

    N

    (CH ) N

    2

    6

    2

    3 2

    2

    carbon

     2

    0

    2

    (9‐20)

    nitrogen

    0

    2

    2

    hydrogen

     6

    0

    6

    and use of this representation with Axiom II provides

    2 0 2

    R C

    0

    2 H6

     

    Axiom II:

    0 2 2 

    R

     

    0

    (9‐21)

    N

     

    2

    6 0 6

    0

     

    R

     

    (CH

    3 )2 N2 

    This can be expressed in terms of the row reduced echelon form of the atomic matrix to obtain

    1 0 1

    R C H

    0

    2

    6

     

    0 1 1 

    R

     

    0

    N2

     

    (9‐22)

    0 0 0

    0

      R

     

    (CH

    3 )2 N2 

    and a row‐row partition of this matrix leads to

    R

    C

    2 H6

    1 0 1

    0

    R

     

    N

     

    (9‐23)

    2

    0 1 1 

    0

    R

    (CH

    3 )2 N2 

    Use of the pivot theorem (see Sec. 6.4) allows us to express the net rates of production for ethane and nitrogen in terms of azomethane according to

    R

    C H

    1

    2

    6

     

    R

    (9‐24)

    (CH

    3 )2 N2

    R

     1

    N

    2

    

    pivot matrix

    and this result leads to the local stoichiometric relations given by Local Stoichiometry:

    R

      R

    ,

    R

      R

    (9‐25)

    C2H6

    (CH3)2N2

    N2

    (CH3)2N2

    The result for global stoichiometry is based on Eq. 9‐9 that leads to

    index-411_1.png

    index-411_2.png

    index-411_3.png

    402