Chemical Education Today
Commentary
The Concept of Density by Stephen J. Hawkes
Neanderthals knew no math yet knew that rock has a higher density than wood, and used that knowledge to their advantage. Too many students believe that density is the result of the arithmetic operation of dividing mass by volume. This makes density an abstraction and prevents them from realizing, among other things, that compressing something must increase the density. They have not absorbed the concept that “density” refers to the “denseness” with which mass is packed. End-of-chapter questions about density are almost exclusively exercises in d=m/V. Many students who can use this equation without any difficulty find questions that test the concept of density to be difficult or even unfair. They do not perceive a meaning to the numerical value of a compound’s density. Yet as an aspect of chemistry, the qualitative concept of density is at least as important as its calculation or measurement. We need to teach the following principles and to help students to perceive that the first one implies all the others: • Density is a measure of the denseness with which mass is packed. • The more closely atoms are packed the higher will be the density. • Other things being equal, compounds of atoms with greater atomic mass are denser. • Compression increases density. • Density of an object does not depend on its size or shape. • “Heavier” as applied to a substance is synonymous with “greater density”.
Students who can reason with ratios, which regretfully is less than half of all students (1), will perceive that all the above follow from d=m/V. Most will not perceive this, and will see no connection between m/V and the concept of density as denseness. Teaching and testing these principles is harder than teaching and testing d=m/V. The following questions address this. The answers are not obvious, even though most readers of JCE will find them so. a. Which has the higher density (or are they the same)? Aluminum or steel? Compressed air or regular air (both at 298 K)? Cold steel or hot steel? Liquid water or ice? Helium or air (both at STP)? Argon or xenon (both at STP)? A cubic meter of carbon dioxide or a liter of carbon dioxide (both at STP)? A lump of steel at rest or the same lump in a spinning centrifuge?
14
Journal of Chemical Education
•
A lump of steel in air or the same lump under water? An asteroid at rest or the same asteroid traveling at nearly the velocity of light? Olive oil or water? Regular water or deuterium oxide? As liquids at 300 K? As gases at 800 K? Solid iron at earth’s surface or at a depth of 5000 km? Liquid iron in the earth’s core at a depth of 3000 km or 5000 km? The Statue of Liberty or a souvenir-shop model of it made of the same metal? The nucleus of an atom or the whole atom? The gaseous hexafluoride of U-235 or of U-238 (both at STP)? b. The density of Pluto is 1.1 g cm᎑3. Does this support the belief that it is mostly ice? Does it prove that Pluto is mostly ice? How would the temperature of Pluto affect the density of ice? The density of ice at 273 K is 0.92; at 100 K it is 0.93. Its density at zero K is not reported in chemical reference works. c. If glass beads are poured into a container and the container is then shaken gently making them settle into a smaller volume, does the density of the accumulation of beads increase with the shaking? Does the density of the glass? d. Aragonite and calcite are both calcium carbonate, but aragonite has a higher density. Suggest why this may be. [Another example of this is white phosphorus (d = 1.8 g cm᎑3), red phosphorus (d = 2.2 g cm᎑3) and black phosphorus (d = 2.7 g cm᎑3)]. e. Why does vitreous silica have a lower density (2.2 g cm᎑3) than crystalline silica (2.6 g cm᎑3)? f. Although atoms of calcium and scandium have nearly the same mass, the density of scandium is twice that of calcium. Suggest why. g. Is density mass/volume? Or does that depend on what the definition of “is” is?
Consequences of Density In an electrical conductor, valence electrons are delocalized so that orbitals extend from one end of the conductor to the other (2). This requires that the atoms are close together, that is, at high density (3, 4). This gives rise to the following questions: h. Why, when hydrogen is subjected to extremely high pressure, as on Jupiter, does it become a conductor of electricity although it is a non-conductor at normally attainable pressures? Would this apply to other substances that are non-conductors at STP?
Vol. 81 No. 1 January 2004
•
www.JCE.DivCHED.org
Chemical Education Today
i. Why, when a substance has two forms, does the form that is a conductor of electricity have greater density than the non-conductor? j. Regular tin has density 7.3, but when it is converted to gray tin (in “tin disease”) the density is 5.8. Suggest a possible explanation of why they are different. Suggest which is a better conductor of electricity. Why?
Diffusion is also affected by the density of the medium through which diffusion occurs. The rate of diffusion of benzene through polydimethylsiloxane (“dimethylsilicone”) varies with the molecular weight of the polydimethylsiloxane and is a minimum at about M ⫽ 104, whereas the density has a maximum at nearly the same molecular weight M ⫽ 104.5 (5). The density of this silicone and the rate of diffusion in it are both controlled by the size and number of spaces between the polymer molecules. It has also been shown that in synthetic rubbers (6) the rate of diffusion of hexadecane decreases with increasing density. A similar relation also exists for polyethylene of various densities. We may reasonably assume that this holds generally for polymers with weak intermolecular forces. Exam questions on this concept are hard to write, but… k. Why, when a substance has two forms, do other substances diffuse more quickly through the form with lower density? l. Water beds occasionally need their water to be replenished, because water is lost by diffusion through the polymeric wall of the bed. If the wall is of polyethylene, would the choice of high density or low density polyethylene affect this? Which would be preferable from this perspective? m. Solutions with accurately known concentrations increase in concentration in a few years when stored in plastic bottles, but not when stored in glass (7). Suggest why
www.JCE.DivCHED.org
•
this is so. When several different plastics were tried (8, 9), the lowest penetration was found for high-density polyethylene. Suggest why. If the change is to be minimized, how would this concept affect the choice of the plastic of which the bottle is made?
Density is a formal concept yet only half of students are formal reasoners. They must be led to the formal relation and not be expected to see intuitively that it follows from d=m/ V. The purpose of a university education is often said to be for students to learn to think. Are universities then obligated to train students in ratio reasoning and other basic thinking skills? Do we? Or should taxpayers put money into training pre-college teachers in the necessary techniques for teaching such skills and support the teaching when they undertake it? Literature Cited 1. Arons, Arnold. Teaching Introductory Physics; Wiley: New York, 1997; Part One, p 365. 2. Hawkes, Stephen J. CHEM13 News 2002, 305 (Oct), 4–5. 3. Edwards, P. In The New Chemistry; Hall, N., Ed.; Cambridge University Press: Cambridge, UK, 2000; Ch. 5, pp 85–114. 4. Nellis, W. Scientific American 2000, 282, 84–90. 5. Kong, J. M.; Hawkes, S. J. Macromolecules 1975, 8, 685. 6. Stannett, V. In Diffusion in Polymers; Crank, J., Park, G. S., Eds.; Academic Press: New York, 1968; p 54. 7. Carey, W. M. J. Am. Pharm. Assoc. 1927, 16, 115. 8. Gerstenberger, Heinz. GIT Fachzeitschrift für das Laboratorium 1994, 38, 279–280. 9. Armstrong, Alfred R. Virginia Journal of Science 1969, 20, 58–59.
Stephen J. Hawkes is in the Department of Chemistry, Oregon State University, Corvallis, OR 97330-4003;
[email protected].
Vol. 81 No. 1 January 2004
•
Journal of Chemical Education
15
