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Thermodynamics of mixtures: Functions of mixing and excess functions
1.M. Modell and R. C. Reid, Thermodynamics and its Applications (Prentice–Hall, New Jersey, 1983), 2nd ed., pp. 98–115, 175–213.
2.H. C. Van Ness and M. M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions (McGraw–Hill, New York, 1982).
3.G. S. Rushbrooke, Introduction to Statistical Mechanics (Clarendon, Oxford, 1949), pp. 169–185 and 218–234.
4.J. S. Rowlinson and F. L. Swinton, Liquids and Liquids Mixtures (Butterworths, London, 1982), 3rd ed., pp. 87–129.
5.M. L. McGlashan, Chemical Thermodynamics (Academic, London, 1979), pp. 139–156. See pp. 240–292 for an interesting discussion on experimental methods.
6.G. H. Wannier, Statistical Physics (Wiley, New York, 1966), pp. 135–138.
7.See for example, F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw–Hill, New York, 1965), Sec. 8.7.
8.J. Kestin and J. R. Dorfman, A Course in Statistical Thermodynamics (Academic, New York, 1971), p. 204.
9.The chemical potential per particle is related to the chemical potential per mole, by where is Avogadro’s number. Some textbooks use the notation for the chemical potential per mole.
10.Standard textbooks on classical thermodynamics use the term “partial molar property,” but we are dealing with partial derivatives with respect to the number of particles, not the number of moles. Ref. 3, p. 193 uses the term partial property.
11.See for example, Ref. 7, Section 7.3, Ref. 6, pp. 167–170, and Ref. 3, pp. 169–187.
12.See for example, Ref. 5, pp. 34–35, 69–71.
13.Henry’s model is sometimes considered to be ideal and is useful for very dilute solutions. A discussion of this model may be found in Ref. 6, pp. 366–383. We do not consider this model because it is more difficult than the Lewis–Randall model, and is of interest mainly to chemical engineers and chemists.
14.This definition is the same as that used in Ref. 4, p. 93.
15.The entropy of mixing of a mixture of ideal gases is calculated from statistical thermodynamics in for example, Ref. 8, pp. 263–268, or Ref. 5, p. 227.
16.Mixtures with are called athermal mixtures, and those with regular mixtures. Most real mixtures are neither athermal nor regular. A study of regular solutions can be found in Ref. 3, pp. 287–309.
17.See for example, Ref. 2, pp. 262–400, 424–430, and J. P. Novák, J. Matouš, and J. Pick, Liquid–Liquid Equilibria (Elsevier, Amsterdam, 1987).
18.See for example, Ref. 5, pp. 252–259, or for a more detailed exposition, Ref. 4, Chaps. 7 and 8.
19.See for example Ref. 5, pp. 34–35, 69–71, 242–252, or Ref. 4, pp. 133–190, which also has many experimental results and references.
20.We use “function of mixing” here because it is standard usage. Ref. 6, pp. 109–110 uses “entropy of mixture,” a far better name.
21.See, for example, R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids (McGraw–Hill, New York, 1987), 4th ed., pp. 251–264.
22.Problems 2–4 have been translated (with only small changes) from R. Nieto, J. M. Lacalle, M. C. González, J. Honduvilla, A. Teijeiro, F. Herrero, and J. Turet, Cuestiones de Termodinámica (Sı́ntesis, Madrid, 1998), Chap. 7, and were formerly used in final exams of our course on thermodynamics at E.T.S.I.I.M.
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