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8.18: Untitled Page 207

  • Page ID
    18340
  • Chapter 8

    Figure 8.8. Accidental overflow from a stirred tank reactor Section 8.2

    8‐9. Show how Eq. 8‐27 can be used to derive Eq. 8‐28.

    8‐10. A perfectly mixed batch reactor is used to carry out the reversible reaction described by

    k 1

    Chemical kinetic schema:

    A E 

     B

    (1)

    k 2

    and the use of mass action kinetics provides a chemical reaction rate equation given by

    Chemical reaction rate equation:

    R

      k c c

    k c

    (2)

    A

    1 A E

    2

    

    

    B

    second order

    first order

    reaction

    decomposition

    If species E is present in great excess, the concentration c will undergo E

    negligible changes during the course of the process and we can define a pseudo first order rate coefficient by

    k

    k c

    (3)

    1

    1 E

    Given initial conditions of the form

    I.C.

    o

    o

    c

    c ,

    c

    c ,

    t  0

    (4)

    A

    A

    B

    B

    use the pseudo first order rate coefficient to determine the concentration of species A and B as a function of time.

    Transient Material Balances

    387

    8‐11. When molecular species A and B combine to form a product, one often adopts the chemical kinetic schema given by

    k

    A B 

     products

    (1)

    Use of mass action kinetics then leads to a chemical kinetic rate equation of the form

    R

      k c c

    (2)

    A

    A B

    One must always look upon such rate expressions as hypotheses to be tested by experimental studies. For a homogeneous, liquid‐phase reaction, this test can be carried out in a batch reactor which is subject to the initial conditions I.C.1

    o

    c

    c , t  0

    (3)

    A

    A

    I.C.2

    o

    c

    c , t  0

    (4)

    B

    B

    Use the macroscopic mole balances for both species A and B along with the stoichiometric constraint

    R

    R

    (5)

    A

    B

    in order to derive an expression for c as a function of time. In this case one is A

    forced to assume perfect mixing so that  c c  can be replaced by  c   c  .

    A B

    A

    B

    8‐12. A batch reactor illustrated in Figure 8.12 is used to study the irreversible, decomposition reaction

    k

    A 

     products

    (1)

    The proposed chemical kinetic rate equation is

    R

      k c

    (2)

    A

    A

    and this decomposition reaction is catalyzed by sulfuric acid. To initiate the batch process, a small volume of catalyst is placed in the reactor as illustrated in Figure 8.12. At the time, t  0 , the solution of species A is added at a volumetric

    index-397_1.png

    index-397_2.png

    388