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6.20: Untitled Page 143

  • Page ID
    18276
  • Chapter 6

    6‐13. For the molecular species listed in Problem 6‐2, determine the ratio of rates of production given by

    R

    R

    R

    NaOH

    CH Br

    CH OH

    3

    3

    ,

    ,

    R

    R

    R

    NaBr

    NaBr

    NaBr

    6‐14. The production of alumina ( NaAlO ) from bauxite [ Al OH ] requires 2

    3

    sodium hydroxide ( Na OH ) as a reactant and yields water ( H O ) as product.

    2

    For this system, determine the ratio of the rates of production given by R

    R

    R

    Al(OH)

    NaOH

    H O

    3

    2

    ,

    ,

    R

    R

    R

    NaAlO2

    NaAlO2

    NaAlO2

    6‐15. At T  20 C , the rate of disappearance (i.e., the net rate of production) of methyl bromide in the reaction between methyl bromide and sodium hydroxide (see Problems 6‐2 and 6‐12) is

    3

    R

    .

    CH3Br

    0 2 mol/m s

    The molecular species involved in this reaction are sodium hydroxide ( NaOH ), methyl bromide ( CH Br ), methanol ( CH OH ) and sodium bromide ( NaBr ). In 3

    3

    this problem you are asked to

    (a). Determine the rate of production of sodium hydroxide, methanol, and sodium bromide in kmol/m3s.

    (b). Determine the rates of production for all components in kg/m3s.

    (c). Show that mass is neither created nor destroyed by this chemical reaction.

    (d). Verify that atomic species are neither created nor destroyed by this chemical reaction.

    6‐16. Methanol can be synthesized by reacting carbon monoxide and hydrogen over a catalyst. The mass rate of production of methanol at 400 K is 3

    r

    .

    . Determine the rate of production in kmol/m3s for all CH3OH

    0 035 kg/m s

    components of the synthesis reaction.

    6‐17. Given an atomic matrix of the form

    Stoichiometry

    265

    1

    2

    1

    4

    0

    2

    4

    2

    A

     

    0

    1

    5

    4

    0

    1

    3

    2

    indicate how one can obtain a row reduced matrix of the form

    1

    2

    1

    4

    0

    1

    2

    1

    A

     

    0

    0

    1

    1

    0

    0

    0

    0

    6‐18. For the partial oxidation of carbon described in Example 6.3, explore the use of pivot species other than CO and CO . This will lead to five more 2

    possibilities in addition to those given by Eqs. 7 in Example 6.3.

    6‐19. Use elementary row operations to verify that Eq. 4 leads to Eq. 5 in Example 6.4.

    6‐20. Express Eqs. 6 of Example 6.4 in the form of the pivot theorem as illustrated by Eq. 9 in Example 6.3.

    6‐21. Meta‐cresol sulfonic acid is a reddish brown liquid that is used as a pharmaceutical intermediate in the manufacture of disinfectants and in the manufacture of friction dust for disk brakes. This chemical is produced along with water by the sulfonation of meta‐cresol with sulfuric acid. In this problem you are first asked to prove that the rank of the atomic matrix is three. Then show that the net rates of production of meta‐cresol ( C H O ), sulfuric acid 7

    8

    ( H SO ) and meta‐cresol sulfonic acid ( C H O S ) can be expressed in terms of 2

    4

    7

    8

    4

    the net rate of production of water ( H O ).

    2

    6‐22. In Sec. 6.2.6 we illustrated how to construct a column / row partition of a matrix equation, and here you are asked to repeat that type of analysis for a row / row partition of the following matrix equation:

    index-275_1.png

    266