Chemical Thermodynamics
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Chemical Thermodynamics
2.1 Introduction and Definitions We shall often be concerned about the atomic weight and molecular weight of atoms and molecules. For example, relative to the carbon, the number 12 is the number of particles in the nucleus, consisting in this case of six positively charged protons and six neutral neutrons. Carbon 12, being electrically neutral, has six negatively charged electrons, giving it the atomic number 6. The atomic weight or molecular weight of any other atom or molecule is the number of particles in the nucleus: total sum of protons and neutrons in the nucleus. The proton and neutron have almost, but not exactly, the same mass and the electron has a nearly negligible mass compared to the proton (me =mp ffi 0:00054463). The consequence is that almost any atom or molecule will have its atomic or molecular weight very nearly an integer. As an example, the oxygen 16 atom has an atomic weight of 15.995, which is 16 for practical purposes. A common set of elements occurring in combustion problems is the C-H-N-O system. These elements have the atomic weights 12, 1, 14 and 16, respectively. The molecular weight of any compound is merely the sum of the weights of the atomic constituents. For example, the molecular weight of water, H2 O, is 1 þ 1 þ 16 ¼ 18. Similarly, the molecular weight of carbon dioxide, CO2 , is 12 þ 2 16 ¼ 44. The next concept is that of the mole, which is defined as the mass in grams (g) of an element or compound equal to its atomic or molecular weight. For example, 12 g of carbon is one mole of carbon; 44 g of CO2 is one mole of the carbon dioxide. It is clear, since the mole and the mass are synonymous, one mole of a compound or element consists of a fixed number of particles of the substance. This number is Avogadro’s number, given the symbol N0 and having the value N0 ¼ 6:023 1023 particles. Let the number of molecules of each species be denoted by Ni , where i is the species identifier. The concentration of species i, ci , is defined as ci ¼ Ni =N0 V, and has the units of moles per unit volume, where V is the volume. The overall concentration is obtained by summing up the concentrations of the individual components. That is,
M.A. Liberman, Introduction to Physics and Chemistry of Combustion, DOI: 10.1007/978-3-540-78759-4_2, Ó Springer-Verlag Berlin Heidelberg 2008
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2 Chemical Thermodynamics
c¼
M X
ci ¼
i¼1
M N 1 X ¼ Ni ; N0 V N0 V i¼1
(2:1:1)
where M is the total number of species in the volume V. In view of the large magnitude of N0 , it should be clear that even very small volume V contains an enormous number of particles. In fact, V can be shrunk so low that it appears to an observer and to the calculus as a mathematical point, while still containing many particles. This is the continuum limit, where we may speak of concentration at a point, and it may vary from point to point in a flow, for example. This concept we will be using in fluid dynamics. The mole fraction of species i, Xi is defined as Xi ¼ Ni =N ¼ ci =c, where M P Ni . It is obvi
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