WENDELL H. SLABAUGH Kansas State College, Manhattan, Kansas
INAN effort to portray a working model for the kinetic structure of gases, a mechanical system was developed which exhibited a distribution of displacements which was in outward respects similar to the Maxwellian distribution relationships. A quantitative analysis of the model by means of photography revealed a surprising agreement with the classical distribution of velocities. This analysis not only provides a directly visible analogy to the gaseous structure, but offers a classroom demonstration of the distribution character of the linear displacements of gaseous molecules. The model, which involves an extension of that of Woolley and M ~ L a c h l a nwas , ~ constructed of parallel glass sides 1cm. apart and 15 cm. square, mounted in a wooden frame. This glass-enclosed volume contained approximately 200 2-mm. glass beads. Glass beads were found to be superior to metal because of their high degree of elasticity in collisions. Figure 1 shows the
marily in the horizontal plane, where the beads collide rapidly with each other and with the walls of the container. These collisions appear to be elastic and as a result depict in a very effective manner the kinetic structure of gases. This model may be used to demonstrate the effect of temperature on a gas by increasing or decreasing the amplitude of vibrations which is simply controlled by the grip of the hands. The tighter the box is held by both hands the greater the amplitude of the vibrations transmitted to the box. Energy imparted by the vibrating walls of the box to t,he glass beads results in translational motion of the glass beads which is uniformly random and a t an apparent mean velocity which is proportional to the tension with which the box is held. Upon moving the piston and confining the beads to a smaller volume, the translational motions of the beads become greatly increased. This phenomenon parallels in an excellent fashion an adiabatic compression of a gas, wherein the resultant increase in pressure is accompanied by an increase in temperature. Change of state can be dramatically shown by slightly tilting the box so that the beads roll to one side of the box. Slight vibration causes the spherical beads to find their positions in the closest-packed cubic stmcture of a solid. A small amplitude of vibration supplied by the mechanical vibrator causes the beads to oscillate about their lattice positions, whereas larger vibrational energy produces displacements great enough to destroy the lattice formation. The resulting structure is that of a liquid. A further increase of vibrational energy produces an occasional "hot" molecule which breaks away from its neighbors and evaporates, a situation shown in Figure 2. Finally, by increasing the am~litudeof vibration and returnine the box to a horidetails of the model, which includes a piston that is con- zontal position, the liquid becomes completely transtrolled a t one side of the box. On the opposite side of formed to a gas. The velocity distribution of the glass heads was anthe box a rigid extension was provided which served as alyzed by photographing the projected image of the a handle. In operation, this handle is supported by one box on a screen. Figure 3 is a photograph of this type hand to which is fastened a massaging vibrator such as made a t 1/50 second exposure. The velocities of the is commonly available on the market a t present. The beads were determined by measuring the length of the other side of +h,e box is supported by the other hand so blurs of the beads on the photographic image. Measthat the box may be held horizontally a t a distance of 3 urements were based upon 10 units as the diameter of or 4 cm. above the field of a vertical or overhead prothe bead. jector.3 The image which is projected on the screen In the photographic analysis of this model the amconsists of circular shadows of the beads, each exhibitplitude of vibration was varied between the lowest deing a bright center. The motions of the beads are prigree of vibration which produceduniform distribution of Presented a t the 122nd Meeting of the American Chemical motion and the maximum degree of vibration. This Society, Atlantic City, September, 1952. gave a series of photographs from which the velocity "OOLLEY, ROSCOE H., AND DANMCLACHLAN, J. CHEM. distribution data were collected. Two of these curves Envc., 27, 187 (1950). are plotted in Figure 4. The observations are shown SLABAUGH, W. H., J. CAEM.EDUC., 28, 579 (1951).
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FEBRUARY, 1953 Most probable velocity (a)
Figure 2.
N' N
The Process of Evaporation hom a Liquid
as points and the solid curves represent the distribution of velocities calculated from the Maxwell equation for the distribution of velocities in the z dx direction. That is,
+
for four of the systems observed. An arbitraryvalue of E = 11.5 on Figure 4 was selected as the activation energy. The fundamental concept that. a 10- rise in velocity of a given molecule. The two curves in Fig- temperature doubles the reaction rate, the reaction rate ure 4 represent the velocity distributions for systems being primarily dependent upon the number of actiwherein the most probable velocities (the maximum in vated molecules, is substantiated. This model not only provides for the lower-level the curves) are 4 and 5 units, respectively. courses a simple and direct demonstration of some of It is to be noted that the agreement between the obthe fundamentals of gas structure but it is readily served and the calculated values is good. As the temadaptable to upper levels of instruction in the topic of perature (amplitude of vibration) is increased the distribution curve broadens and the number of molecules with the most probable velocity decreases. I t is predicted that a larger number of beads would give better agreement because of the statistical nature of the theory upon which the Maxwell law is established. A comparison of the distribution curves obtained from several different temperatures (amplitudes of vibration) points toward a verification of the Arrhenius equation for the energy of activation. A modified form of this equation is where N' is the number of
Na, is the number of molecules with velocities between z and z dx,N is the total number of molecules in the system, a is the most probable velocity, and x is the
+
activated molecules, N the total number of molecules, E the activation energy, and T the temperature. Since it was not possible to quantitatively observe the temperature (amplitude of vibration), except to note the most. urohable velocitv which v a s based uuon arhitrarv
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kinetic theory. It issuggested that in theselatter courses photographs of this model, such as Figure 3, would provide the necessary information with which to validate the velocity distribution and activation energy rela-
JOURNAL OF CHEMICAL EDUCATION
tionships. This would supply an exercise in which the student could mathematically interpret data which he himself has collected with respect to the kinetic concept of gases.
