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4.3: Untitled Page 58

  • Page ID
    18191
  • Chapter 4

    could avoid this mixed mode nomenclature consisting of both letters and numbers by expressing Eq. 4‐11 in the form;

    Axiom II:

    r

    r r r .... r

     0

    (4‐12)

    A

    B

    C

    D

    N

    however, this approach is rather cumbersome when dealing with N‐component systems.

    The concept that mass is neither created nor destroyed by chemical reactions (as indicated by Eq. 4‐11) is based on the work of Lavoisier (1777) who stated:

    “We observe in the combustion of bodies generally four recurring phenomena which would appear to be invariable laws of nature; while these phenomena are implied in other memoirs which I have presented, I must recall them here in a few words.”

    Lavoisier went on to list four phenomena associated with combustion, the third of which was given by

    Third Phenomenon. In all combustion, pure air in which the combustion takes place is destroyed or decomposed and the burning body increases in weight exactly in proportion to the quantity of air destroyed or decomposed.

    It is this Third Phenomenon, when extended to all reacting systems, that supports Axiom II in the form represented by Eq. 4‐9. The experiments that led to the Third Phenomenon were difficult to perform in the 18th century and those difficulties have been recounted by Toulmin (1957).

    4.1.1 Molar concentration and molecular mass

    When chemical reactions occur, it is generally more convenient to work with the molar form of Eqs. 4‐7 and 4‐11. The appropriate measure of concentration is then the molar concentration defined by

    (4‐13)

    while the appropriate net rate of production for species A is given by (4‐14)

    Multicomponent systems

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    Here MWA represents the molecular mass (see Sec. 2.1.1) of species A that is given explicitly by

    (4‐15)

    The numerical values of the molecular mass are obtained from the atomic masses associated with any particular molecular species, and values for both the atomic mass and the molecular mass are given in Tables A1 and A2 in Appendix A. In those tables we have represented the atomic mass and the molecular mass in terms of grams per mole, thus the definition given by Eq. 4‐15 for water leads to (4‐16)

    In terms of c and R , the two axioms given by Eqs. 4‐7 and 4‐11 take the form A

    A

    Axiom I:

    (4‐17)

    Axiom II:

    (4‐18)

    Here it is important to note that mass is conserved during chemical reactions while moles need not be conserved. For example, the decomposition of calcium carbonate (solid) to calcium oxide (solid) and carbon dioxide (gas) is described by

    (4‐19)

    thus one mole is consumed and two moles are produced by this chemical reaction.

    One must be very careful to understand that the net molar rate of production per unit volume of species A owing to chemical reactions, R , may be the result of many A

    different chemical reactions. For example, in the chemical production system illustrated in Figure 4‐1 carbon dioxide may be created by the oxidation of carbon monoxide, by the complete combustion of methane, or by other chemical reactions taking place within the control volume illustrated in Figure 4‐1. The combination of all these individual chemical reactions is represented by R

    .

    CO2

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