Jay A. Young Auburn University Auburn, Alabama 36830 and Robert C. Plumb Worcester Polytechnic Institute Worcester, Massachusetts 01609
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Demonstrating Avogadro's Hypothesis with the Molecular Dynamics Simulator
The Molecular ~ y n a m i c s Simulator1 (MDS), briefly described, consists of a vibrating glass plate, treated to minimize the build-up of static charge, surrounded by a specially contoured circular edge, on which, within the circular area, small objects such as steel balls can move freely. When positioned in the optical path of an overhead projector, the shadows of these balls can be observed on a screen. Because of the particulars of the design, these shadows simulate closely the behaviors predicted by the usual and familiar mathematical descriptions of the kinetic molecular theory. Some of the pedagogical uses of this device have been described by Barnard.% Other uses are clearly possible; one such is the demonstration of Avogadro's Hypothesis (or Theory). The demonstration is most effective when Avogadro's Hypothesis is stated in this form: Two different systems of molecules, differing in mass, which consist of equal numbers of molecules exhibit the same pressure when their temperatures and volumes are the same. This form of statement is required, as will be seen, because of constraints inherent in the device to be used to demonstrate the validity of the statement. To make the demonstration some simple accessories, easily made, are needed: A scale, for use as a reference to locate the position of a "piston"; two chords of a circle, made from acrylic polymer to fit within the circular area of the MDS thus converting the area available to the halls into an approximate rectangle, or "cylinder"; and a "spring loaded piston" made from a piece of used X-ray film. These are described in detail in Figures 1and 2. The chords are affixed temporarily to the glass plate with two lengths of both-sides-sticky transparent tape. The scale is mounted under the triangular frame which supports the glass plate, and the frame together with the scale is secured with the handnuts. However, the tabend of the piston is placed in position under the top hand-nut before it is itself secured into its position, as shown in the figure. Care is taken to level the glass plate, fifty small spheres are counted on to the cylinder area, ajoiuing the piston, and the plate is vibrated. (Time can be saved if the class has learned to trust the professor who has pre-counted the spheres.) Increasing or decreasing the vibration amplitude corresponds to lowering or raising the temperature of the fifty-hall-system. As this is done, the position of the piston on the scale, as seen on
top "lev
scale7
Figure 2.
Adapted from a paper presented at the 163rd meeting of the American Chemical Society, Boston, Mass., April 9-14, 1972. Plumb, R. C., J. CHEM.EDUC.,43, 648-516 (1966). Barnard, R. to appear in NewAids section J. CHEM.EDUC.
The assembly.
the screen, moves appropriately. (One could a t this point determine the "Absolute Zero" of the device if so inclined.) A vibration amplitude is selected which Volume 49, Number 10, October 1972
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causes the piston to reach and maintain a noted position with respect to the reference scale. Then, the vibrator is turned off. When it is restarted the piston will reach its former position within a small discrepancy, since the vibrator amplitude setting has not been changed. By turning the vibrator off, and then on again, a few times, the limits of reproducibility are quickly established. Next, the small balls are removed and replaced with an equal number of larger, more massive, steel halls. When the vibrator is turned on once again, the piston returns to its predicted position within the reproduci-
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bility limits previously established, thus confirming Avogadro's Hypothesis in this simulation. It is useful to call attention, when the small balls are used, to their rather rapid motion and to the pressure that they consequently exert upon the piston. Then, with the larger balls, the motion is noticeably more sluggish but each impact with the piston is also noticeably more effective. This can be discussed quantitatively with appropriate mathematical gyrations or qualitatively, in either case rendering the reasons why Avogadro's Hypothesis does hold more clear to the class.
