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TEACHING THE KINETIC THEORY OF GASES' CREIG S. HOYT Grove City College, Grove City, Pennsylvania
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18 a most unusual fact that substances in the gaseous state behave uniformly when subjected to changes in temperature and pressure. In order to account for such uniformity i t is logical to assume that the structure of all gases is fundamentally the same and to propose such a structure as will best account for the observed behavior. These assumptions together constitute the kinetic theory of gases, one of the m.ost important generalizations from the standpoint of insight into molecular phenomena. From it may he deduced the weight, the velocity, and the energy content of the molecule, affording a basis for the mechanism of reactions. It stresses the characteristics of the molecule as a physical unit rather than as a chemical group, but its importance to the development of chemistry can hardly be overestimated. The kinetic theory of gases presents what is often the first opportunity of indicating to the student the place of theory in the scientific method and under particularly favorable circumstances. Many a. student brings with h i m to the classroom a predisposition to regard atheory as an unsupported guess, the opposite of fact. This has been fostered by the popular attitude that contrasts the practical with the theoretical to the detriment of the latter. The presentation of the kinetic theory must, therefore, make abundantly clear that a theory is a rational explanation of observed facts, mutually
Demonstration of Kinetio Enam of..G
Molecul..
consistent in its various parts and designed not so much to afford the mental satisfaction of having offered an explanation as to permit the prediction of new facts. The ease with which conclusions drawn from the theory may he experimentally verified and the strong substan-
' Presented before the Division of Chemical Education a t the 110th meeting of the American Chemical Society in Chicago, September 9-13,1946.
tiation which this affords make this one of the most important phases in the training of the chemist and afford a valuable impression of the scientific method to those whose interest in chemistry is more casual. The postulates of the kinetic theory are very simple. It is assumed that gases are made up of very small particles, called molecules, separated by spaces relatively large by comparison with the diameter of the particles. These are assumed to be in very rapid motion in straight lines, colliding with each other and the walls of the containing vessel. Molecules of diierent gases differ in mass, but $1 molecules of the same gas have the same mass. By further assuming that the molecules are perfectly elastic and rebound from collision without loss of kinetic energy or momentum, the unending motion of the particles may he explained. All other conclusions from the theory grow out of these fundamental assumptions and are a direct consequence of them. It is well, we believe, to call the attention of the student to the fact that these are common-sense assumptions. He is aware from his own experience that gases offer little opposition to movement through them and that, therefore, the particles composing them must be easily separated. He realizes, when it is called to his attention, that the aura of petfume or the odor of a noxious gas 'quickly spreads from its original source through the atmosphere without any mass movement of the air itself. This requires that the molecules be in
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them. The formal statement of Boyle's Law with its inverse proportion leaves the student with a rather hazy conception of the relation between volume and pressure. A graphical presentation is to be preferred. That volumes become smaller when pressures become larger is in accord with ordinary observation, and the direct relationship is apparent from the graph. But to account for the steady sustained pressure of a confined gas as due to the multitudes of individual impacts requires a new viewpoint. I Two familiar pieces of demonstration equipment will 0 1.0 2.0 LO *OCM assist in giving the necessary conception. In the one, 073 330 224 168 M/SEC a tube, evacuated to increase the mean free path, conTh.or.tic.1 m d Erp.dm.ntd 1nte-ity Dilt.ib"ti0~ h u m i n . Vmpor Composition of 40 Per Cent Bi and 60 Pnr Cent Bi.. tains bits of blue glass resting on a pool of mercury. When the mercury is heated, bringing about vaporimotion in all directions and that the spaces between the zation of the liquid, the impact of the large molecules molecules of the gases in the atmosphere be so large as of mercury is sufficientto drive the glass vigorously in to offer a minimum of resistance to diffusion. The as- chaotic fashion about the interior of the tube. sumption that molecules are perfectly elastic bodies is An even better demonstration is provided by a similar more di5cult hut is preferable to any alternative. tube which uses a pithhall to show the molecular colThe conclusions that can be reached as a consequence lisions. With a suitable rate of heating, the pithball of accepting these simple assumptions regarding the may be supported in space for any period of time. structure of gases are far-reaching. At ordinary pressures, only those molecules next to One of these conclusions is given in Avogadro's Law. the walls are in collision with them. It is apparent That law is merely a special way of stating that, due to that the mean free path is very short and that most of the constant movement of molecules and the consider- the collisions are intermolecular. As the pressure deable spaces between them, uniform distribution is main- creases, the mean free path increases until, a t suffitained, whether one gas or a mixture of gases occupies ciently high vacua, i t may exceed the diameter of the the volume. It follows that a given volume contains containing vessel. A demonstration to illustrate this the same number of molecules under the same con- fact has been described by Smyth and Ufford (I). It reditions of temperature and pressure regardless of what quires two flasks connected to each other by a narrow gas is present. This conclusion is so simple that its im- neck. If solid iodine is placed in the lower flask, i t will port is often missed. A simple and effective demon- vaporize on heating and, after many collisions, some stration to carry through the idea may be made by by- will be distribbted uniformly over the walls of the upper ing liter flasks with various gases and indicating the vessel. If, however, the flasks are evacuated, the only number of molecules to be the same in each case. This is the strategic moment to present the actual number of molecules, to give Avogadro's number a definite meaning. The statement-if a minate opening were to be made in any one of these flasks such that a million molecules could escape each second, nine hundred million years would be required to empty the flask-has the advantage of accuracy and the impact of the startling. A second statement of the same sort is equally-effective. Were the molecules in any one flask to be divided among the approximately two billion people on the earth, each individual share would be fifteen trillion molecules. This type of demonstration has the advantage that i t impresses the student that not only the molar volume but any two equal volumes of gases contain the same number of molecules and that the ratio of the weights of these volumes is also the ratio of the weights of the individual molecules. A conversion a t this point to the molar volume involves only the ratio of the previously assumed molar weight of oxygen to the weight of one liter of oxygen, the familiar 22.4 liters. Another consequence of the kinetic picture of the structure of gases is the conclusion that gas pressure exerted a ~ a i n sthe t walls of the contaiuine vessel is due to the bombardment of the molecules in-collision with B ~ Y I ~L-W . O
188
Diffusion of a G u Through Air at Atmoeph..ic Prassur.'
JOURNAL OF CHEMICAL EDUCATION
Diffusion of a G l u at Raduc-d P-mur.'
molecules in the upper vessel will be those coming through the neck directly, and since these are traveling the entire diameter of the flask in a single flight, the deposit covers only that portion of the flask opposite the neck. One of the original assumptions of the kinetic theory was the perfect elasticity of the molecules. Inasmuch as no perfectly elastic solid is known, there is no basis in emerience for this amum~tion. I n actual solids a
' Material taken with permission from "Matter Motion and Electricity" by Smyth and Ufford, copyrighted 1939 by the McGraw-Hill Book Company, Inc.
part of the kinetic energy of colliding spheres appears as heat due to friction in the deformation of the bodies. But the kinetic theory develops the conception that heat is the energy of molecules in motion. It follows, then, that no energy can be lost as heat in molecular collisions and the body must be perfectly elastic. This matter is receiving careful attention in recent textbooks. Still another conclusion from the kinetio theory r e lates to the effect of temperature on.molecular velocities. Since heat is the kinetic energy of molecular motion, a t any particular temperature the average kinetic energy of all gas molecules is the same. This is true in spite of wide variations in the weight of the molecules. It would follow that a t the absolute zero, the velocity of all molecules would be zero, a conclusion given experimental verification by the experiments of Onnes. Still another conclusion, experimentally tested by Graham, is that the velocity of escape of a gas through a small orifice, a specialized case of diffusion called "effusion," is inversely proportional to the square root of the molecular weight. These velocities are statistical: the velocity of any one molecule may vary from zero at the instant of collision to values considerably above the average. Nevertheless, the kinetic energy on the average is a function of temperature only. Until comparatively recently values of molecular velocities were only computed from the kinetic equation. A number of investigators have proposed methods for the direct determination of molecular velocities. Zartman ( 8 ) employed an apparatus consisting of a furnace for volatilizing bismuth, a series of slits to align a beam of vapor molecules and a rapidly rotating cylinder with a slit in its side to admit the beam b'f bismuth molecules. The whole appiratus was evacuated to give a long mean free path. Were the hollow cylinder to stand still, a spot of condensed metal would be found opposite the slit. When the cylinder rotates, the point of condensation is displaced by an amount which is a function only of the speed of the rotating cylinder rmnd'the molecular velocities. The presence of condensed metal along a section of the periphery is evidence of variation in velocities taken from the same beam. The distribution of velocities is shown on page 187. While this method cannot be demonstrated save as to results, gas effusion apparatus is quite simply made and gives good quantitative results. The molecule race between ammonia and hydrogen chloride devised by Chapin is accurate and interesting, although the results are relative. I n the original assumptions of the theory, no allowance was made for intermolecular attraction. Since the gas laws are usually employed a t moderate pressures, the assumption that the spaces between the molecules are so large as to do away with molecular attractions is usually correct. But the deviations which occur at low temperatures and higher pressures should be presented as normal behavior to be expected as the space between the molecules decreases rather than as a failure in the theory. As a consequence, the phenomena of change of phttse from gas to liquid will be dealt with as
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a particularly effective application of the theory rather than as a failure of the theory to represent adequately the facts. A theory has only one reason for existence: the explanation of the cause of observed fact in such a way = to lead to the discovery of new facts. The final task in the teaching of kinetic theory must always be to check off experimental observations a8 given in the laws of Boyle, Charles, Dalton, Graham, and Avogadro against the explanation offered by the theory. But its usefulness will not end there. Chemical kinetics and the theories of solution will make use of its assumptions.
Much that has been done with the kinetic theory lies outside the scope of general chemistry. But in its presentation to the young chemist, there is a challenge to effectiveteaching, not only for the sake of the task immediately a t hand but for his future development in chemistry. LITERATURE CITED (1) SMYTR,H: D.,AND C. W. UFFORD, "Matter, Motion and Electric~ty,".McGraw-Hill Book Company, Inc., New York, 1939, p. 31. (2) ZLRTMAN, I. F.,Phys. Rm.,37,383 (1931).
