Page 257 - Physical Chemistry

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Chapter 7 The Clapeyron equation dP/dT H/(T V)gives the slopes of the lines on a one-
One-Component Phase Equilibrium component P-T phase diagram. The Clapeyron equation tells (a)how the vapor pressure
and Surfaces
of a solid varies with T (line OA in Fig. 7.1a); (b)how the vapor pressure of a liquid
varies with T or, equivalently, how the boiling point of a liquid varies with P (line AC in
Fig. 7.1a); (c)how the melting point of a solid varies with P (line AD in Fig. 7.1a).
For phase equilibrium between a one-component gas and a solid or liquid, neglect
of the volume of the condensed phase and approximation of the gas as ideal converts
2
the Clapeyron equation into d ln P/dT H /RT .
m
Molecules in the interphase region experience different forces and have different
average energies than molecules in either bulk phase. It therefore requires work g d
to reversibly change the area of the interface between two phases by d , where g is
the surface tension.
For a spherically shaped interface, the existence of surface tension leads to a pres-
sure difference between the two bulk phases given by P 2g/R, where R is the ra-
dius of the spherical interface. The phase on the concave side of the interface is at the
higher pressure. Since the liquid–vapor interface in a capillary tube is curved, this
pressure difference will produce a capillary rise of the liquid, given by Eq. (7.37) for
zero contact angle.
A colloidal system contains particles whose dimension in at least one direction is
in the range 1 to 1000 nm.
Important kinds of calculations dealt with in this chapter include:
• Use of the phase rule to find the number of degrees of freedom f.
2
• Use of d ln P/dT H /RT and vapor-pressure data to find H or H
m vap m sub m
of a pure substance.
2
• Use of d ln P/dT H /RT and the vapor pressure at one temperature to find
m
the vapor pressure at another temperature.
2
• Use of d ln P/dT H /RT to find the boiling point at a given pressure from the
m
normal boiling point.
• Use of the Clapeyron equation to find the change in melting point with pressure.
• Use of dG S dT V dP and G° data to find the transition P or T for
m m m f
converting one form of a solid to another.
• Calculation of the pressure difference across a spherical interface from P 2g/R.
• Calculation of the surface tension from the capillary rise using Eq. (7.37).

FURTHER READING AND DATA SOURCES

Denbigh, chap. 5; de Heer, chaps. 18, 21; Zemansky and Dittman, chap. 16; Andrews
(1971), chap. 25; Adamson; Aveyard and Haydon; Defay, Prigogine, Bellemans, and
Everett.
Vapor pressures; enthalpies and entropies of phase transitions. Landolt-Börnstein,
6th ed., vol. II, part 2a, pp. 1–184; vol. II, part 4, pp. 179–430. D. E. Gray (ed.),
American Institute of Physics Handbook, 3d ed., McGraw-Hill, 1972, pp. 4-261 to
4-315; pp. 4-222 to 4-261. Poling, Prausnitz, and O’Connell, Appendix A. I. Barin
and O. Knacke, Thermochemical Properties of Inorganic Substances, Springer-Verlag,
1973. TRC Thermodynamic Tables (see Sec. 5.9 for the full references). O.
Kubaschewski and C. B. Alcock, Metallurgical Thermochemistry, 5th ed., Pergamon,
1979. J. Timmermans, Physico-Chemical Constants of Pure Organic Compounds,
vols. I and II, Elsevier, 1950, 1965. Lide and Kehiaian, sec. 2.1. NIST Chemistry
Webbook at webbook.nist.gov/.
Surface and interfacial tensions: J. J. Jasper, J. Phys. Chem. Ref. Data, 1, 841
(1972); Landolt-Börnstein, vol. II, pt. 3, pp. 420–468.