Chemical Education Today
Letters Boiling Points of the Family of Small Molecules In a recent article (1) Michael Laing claims that if two liquids are made up of molecules that have exactly the same intermolecular cohesive attractions, molecules of both liquids should have the same escape velocities, regardless of mass. His argument is that the process of molecules breaking loose from attractive forces holding them in the liquid is not unlike that of a satellite breaking free of the earth’s gravitational field. While it is true that all satellites have the same escape velocity, independent of mass, it is not true for molecules evaporating from a liquid. For a satellite to escape the earth’s gravitational field, it must have a kinetic energy at least as large in magnitude as its gravitational potential energy at the earth’s surface. The minimum kinetic energy necessary for escape is
suggests that since plots of boiling points versus molecular mass for several groups of halogenated methanes are linear, there must be a causal relationship between the two quantities. However, plots of the number of electrons versus molecular weight for each of the groups of substituted methanes he is considering are also quite linear, so there is an equally good correlation between boiling points and the number of electrons in a molecule. Given the nature of intermolecular forces, it seems far more likely to me that it is the number of electrons in a molecule, rather than its mass, that figures in determining boiling points. Literature Cited 1. Laing, M. J. Chem. Educ. 2001, 78, 1544–1550. Jonathan Mitschele
2 1 2 mve
GMm = RE
Here m is the mass of a satellite, ve its escape velocity, G the universal gravitational constant, M the mass of the earth, and RE the radius of the earth. It follows that the minimum velocity for escape, ve, is given by ve =
2GM RE
and is independent of the mass of the satellite. The potential energy of a molecule leaving a liquid is a function of only its distance from its starting position at or near the surface of the liquid; it is not a function of mass. If we represent this potential energy by the expression U(r), where r is the distance the molecule is from its initial position in the liquid, the minimum kinetic energy a molecule must possess to escape the liquid will be 2 1 2 mve
= U ( 0)
where U(0) is the initial potential energy of the escaping molecule. For such a molecule, the escape velocity, ve, is given by ve =
2U (0) m
This result means that the escape velocity of a molecule does depend on its mass, contrary to what Laing asserts. At the end of his paper, Laing concludes that molecular mass somehow plays a role in determining boiling points. He
Saint Joseph’s College Standish, Maine 04084
[email protected] The author replies I am really pleased that Jonathan Mitschele has taken the trouble to carry out this analysis. His observations emphasise the complexity of the situation, and most importantly that the attractive forces within the liquid are certainly not gravitational in nature. As Ron Rich has so often pointed out, it is the polarizability of the species, in particular of the electron clouds of the exposed atoms, that dictates the boiling point (J. Chem. Educ. 1995, 72, 9–12). However, the behavior of the series CH4, CH3F, CH2F2, CHF3, CF4 shows quite clearly that boiling point is not simply related to any one of these: molecular mass, molar refraction (polarizability), total number of electrons, or number of valence shell electrons. To paraphrase Dr. Johnson: we have found an argument, it is not easy to find an understanding. Literature Cited 1. Rich, R. J. Chem. Educ. 1995, 72, 9–12. Michael Laing 61 Baines Road Durban 4001 Republic of South Africa
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JChemEd.chem.wisc.edu • Vol. 80 No. 4 April 2003 • Journal of Chemical Education
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