Page 307 - Physical Chemistry

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Chapter 9 An ideal solution is one in which the molecules of each species are so similar to
Solutions one another that molecules of one species can replace molecules of another species
without changing the solution’s spatial structure or intermolecular interaction energy.
The thermodynamic definition of an ideal solution is a solution in which the chemical
potential of each species is given by m m*(T, P) RT ln x for all compositions and
i
i
i
a range of T and P. The standard state of an ideal-solution component is the pure sub-
stance at T and P of the solution. For an ideal solution, mix H 0, mix V 0, and
mix S is the same as for an ideal gas mixture. By equating the chemical potentials of i
in the solution and in the vapor (assumed ideal), one finds the partial pressures in the
l
vapor in equilibrium with an ideal solution to be P x P* (Raoult’s law).
i
i
i
An ideally dilute (or ideal-dilute) solution is one so dilute that solute molecules
interact essentially only with solvent molecules (molecular definition). In an ideally
dilute solution, the solute chemical potentials are m m°(T, P) RT ln x and the sol-
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vent chemical potential is m m*(T, P) RT ln x for a small range of composi-
A
A
A
tions with x close to 1 (thermodynamic definition). For an ideally dilute solution,
A
the solute standard state is the fictitious state at T and P of the solution in which the
solute is pure but its molecules experience the same intermolecular forces they expe-
rience when surrounded by solvent molecules in the ideally dilute solution. The sol-
vent standard state is pure A at the T and P of the solution. The solute and solvent
partial pressures in the vapor in equilibrium with an ideally dilute solution are given
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by Henry’s law P K x and by Raoult’s law P x P*, respectively.
i
i i
A
A
A
The following superscripts are used in this chapter: ° standard state, * pure
substance, infinite dilution.
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Important kinds of calculations discussed in this chapter include:
• Calculation of solution mole fractions, molalities, and molar concentrations.
• Calculation of a solution’s volume from its partial molar volumes using V

n V i and similar calculations for other extensive properties.
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• Determination of partial molar volumes relative to the molar volumes of the pure

components (V i V* ) using intercepts of a tangent line to the mix V/n curve,
m,i
and similar determination of other partial molar properties.
• Calculation of mixing quantities for ideal solutions.
• Calculation of vapor partial pressures of ideal solutions using Raoult’s law P
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l
x P*.
i i
• Calculation of vapor partial pressures of ideally dilute solutions using Raoult’s
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and Henry’s laws P x P* and P K x .
A A A i i i
• Use of dilute-solution vapor pressures to find the Henry’s law constant K .
i
• Use of Henry’s law to find gas solubilities in liquids.
FURTHER READING AND DATA SOURCES
McGlashan, secs. 2.7 to 2.11, chaps. 16, 18; de Heer, chaps. 25 and 26; Denbigh,
secs. 2.13 and 2.14, chap. 8; Prigogine and Defay, chaps. 20 and 21.
Mixing quantities: C. P. Hicks in Specialist Periodical Reports, Chemical
Thermodynamics, vol. 2, Chemical Society, London, 1978, chap. 9; Landolt-
Börnstein, New Series, Group IV, vol. 2.
Vapor pressures and vapor compositions of solutions: Landolt-Börnstein, 6th ed.,
vol. II, part 2a, pp. 336–711 and vol. IV, part 4b, pp. 1–120; Landolt-Börnstein, New
Series, Group IV, vol. 3; M. Hirata et al., Computer Aided Data Book of Vapor–Liquid
Equilibria, Elsevier, 1975.
Solubility of gases in liquids: Landolt-Börnstein, vol. II, part 2b and vol. IV, parts
4c1 and 4c2.