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6.3: Untitled Page 126

  • Page ID
    18259
  • Chapter 6

    atomic species are

    neither created nor

    Axiom II:

    (6‐9)

    destroyed by

     chemical reactions 

    If the process illustrated in Figure 6‐1 is carried out with a stoichiometric mixture of ethane and oxygen, one might find that the product stream contains mostly CO and H O , but one might also find small amounts of CO , CH OH , C H , 2

    2

    3

    2

    4

    etc. and it is not always obvious that these small amounts can be ignored. In fact, we believe that these small amounts should be a matter of constant concern.

    6.1.1 Principle of stoichiometric skepticism

    When a system of the type represented by Figure 6‐1 is encountered, it is appropriate to immediately consider the alternative illustrated in Figure 6‐2. It is always possible that the “other molecular species” suggested in Figure 6‐2 may Figure 6‐2. Incomplete combustion reaction

    be present in amounts small enough so that the schema represented by Eq. 6‐8 is a satisfactory approximation. However, what is meant by small enough may be difficult to determine since the “other molecular species” may consist of biocides or carcinogens or other species that could be damaging to the environment even in small amounts. Under certain circumstances, small amounts may produce major consequences, and we want students to react to any proposed stoichiometric schema in the manner indicated by Figure 6‐2. This idea will be especially important in terms of our studies of reaction kinetics in Chapter 9

    where small amounts of reactive intermediates or Bodenstein products actually control the macroscopic process suggested in Figure 6‐2.

    One can indeed postulate that ethane and oxygen will react to produce carbon dioxide and water, but the postulate needs to be verified by experiment. As an example only, we imagine that the process illustrated in Figure 6‐2 is carried out so that ethane is partially oxidized to produce ethylene oxide, carbon dioxide,

    Stoichiometry

    231

    carbon monoxide and water. Under these circumstances, the stoichiometry of the reaction might be represented by the following undetermined schema:

    ? C H

    + ? O

     ? CO + ? C H O + ? H O + CO

    (6‐10)

    2

    6

    2

    2

    4

    2

    2

    In this case the stoichiometric coefficients could be found by counting atoms to obtain

    2 C H

    + 4O

     CO + C H O + 4 H O + CO

    (6‐11)

    2

    6

    2

    2

    4

    2

    2

    and one could also count atoms to develop a different schema given by 19

    1

    2 C H

    +

    O

     2CO + C H O + 5H O + CO

    (6‐12)

    2

    6

    2

    2

    4

    2

    2

    4

    2

    Here it should be clear that we need more information to treat the case of partial oxidation of ethane, and to organize this additional information efficiently we need a precise mathematical representation of the concept that atomic species are neither created nor destroyed by chemical reactions. It is important to understand that Eqs. 6‐11 and 6‐12 are pictures of the concept that atoms are conserved, and what we need are equations describing the concept that atoms are conserved. In this text we use arrows to represent pictures and equal signs to represent equations.

    .2

    6 Conservation of Atomic Species

    To be precise about the role of omic

    at

    species in chemical reactions, we first

    need to replace the word statement given by Eq. 6‐9 with a word equation that we write as

     the molar rate of production 

    Axiom II:

    per unit volume of J‐type atoms  0 ,

    J  1 , 2 ,...,T (6‐13)

     owing to chemical reactions 

    Here the nomenclature is intended to suggest aTomic species. From this form of Axiom II we need to extract a mathematical equation, and in order to do this we define the number N

    as

    JA

     number of moles of 

    N

      J‐type atoms per mole , J  1 , 2 ,...,T , and A  1 , 2 ,...N

    (6‐14)

    JA

     of molecular species A

    232