edited by RALPHK. BIRDWHISTELL University of West Florida Pensacola, FL 32504
textbook forum Misuse of Graham's Laws Stephen J. ~ a w k e s ' Oregon State University, Co~allis,OR 97331-4003
A quarter of a century has elapsed since four papers in this Journal ( 1 4 )showed that Graham's laws of diffusion and effusion do not apply to the cases discussed in introductory texts or to most other cases and that the usual demonstrations fail. Yet the errors continue to disgrace these texts and are repeated in successive editions. The original papers were discouragingly erudite, so I will summarize the conclusions that affect the introductory course. Limitations of the Diffusion Law The two gases must be diffusing into each other, not into a third gas. .The pressure must he kept constant with a manostat, not allowing the density of the faster diffusant to decrease or the slower to increase. T h e rates must he specified in molls, not gls.
The first two limitations make the law inapplicable to any situation that a student is likely to meet in professional life, even as a chemist. The third limitation nullifies some of the calculations in introductory texts.
Many texts and one of the current books of demonstrations illustrate Graham's law from the relative rates of diffusion of HCl and N& gases into air. Most have the gases diffusing into the two ends of a tube and meeting a t a line of NH4C1.The text then alleges that the relative rates are
Anyone who does the experiment finds that the ratio is 1.3. The experiment violates the first limitation above. The actual ratio is 'Contribution from the Task Force on the General Chemistry Curriculum.
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Journal of Chemical Education
Shakhashiri's Chemical Demonstrations (5)uses this correctly and provides a good discussion. Limitation of the Effusion Law The flux through a small hole is inversely proportional to M1"only if the hole is so small that the molecules have no opportunity to collide with each other as they pass through the hole. This normally requires that the hole be in a very thin material and that the flux be into a vacuum. Alternatively, a conical hole may be drilled into a thicker material so that it terminates in knife edges. This will make the system behave as if the wall were very thin. Again this is inapplicable to any situation a student is likely to meet. Specifically, it does not apply to leaks from gas tanks.
Balloons Graham's law of effision is invoked in some texts to explain why helium-filled balloons deflate more quickly than air-filled balloons. Actually this is the result of faster diffusion of the small helium atoms through the polymer wall of the balloon. The rate depends on the exponent of the molecular diameter and is not related to the molecular mass. For example, the diffusion rate for helium in butyl rubber (6) is 5.93 x cm2/s a t 25 T,while that of nitrogen is 0.045 x This is a factor of 132 and does not approximate Graham's law. Knudsen's Law and the Separation of Isotopes Isotope separation, especially separation of v35F6and UUsF6,has been achieved using a screen with holes just large enough to allow passage of the molecules one by one (7). The flow through such narrow pores is then governed
by Knudsen's Law (8). This reduces to a proportionality to l/Mmjust a s in Graham's laws. The logic used in textbooks to derive Graham's law of effusion from the kinetic theory will lead in the same way to this reduced form of Knudsen's law. The use of porous materials to separate gases was first suggested by Graham (9),and the history of such separations is discnssed in Partineton's monumental Histow of Chemistry (10).I t has been used to separate isotopes since and V3'Fli the 1920's (11)and was used to sevarate U235F~ in the Manhattan project during world War 11
Conclusion Kirk concludes his paper i n this Journal (2)with the following discussion. It is now appropriate to turn to the question of what might be said on the topic of Graham's Law in the freshman chemistry course. First, we might ask why this topic is discussed at all. The answer to this seems to be that a discussion of effusion illustrates molecular motion very well and that at least one phenomenon depends solely an the molecular velocity. It fwther shows that the speed of molecules is inversely proportional to the square mot of their mass and thus pmvide a very nice confirmation at this level of the statement that all male-
eules at the same temperature have the same average kinetic energy. The experience of the last 25 years is that the price of this illustration is too high. Graham's laws should not be included in i n t r o d u d o ~ c h e m i s t r ybecause students are misled into believing - they- can be applied to problems in their h t e r work. Also, these studentimight gd on to teach this to latergenerations. The law3 should be introduced in physical chemistry courses using the theory discussed in refs 1-4. They can be illustrated with the demonstrations in refs 1 and 4 and in Shakhashiri's book (5)of chemical demonstrations.
Literature Cited 1. Mason, E. A,; Kmnrtsdf, B. J. Chem. E d u . 1981.44.740. Kirk.A.0. ,~~- J. Cham. Educ. 1967.44.745. 3. M a s o n , E . A . J C h m . Educ. 1969.46.358, 4. Evans, R. 6.; Love, L. D.;Mason, E. A. J. Chsm. Edue. 1869.46.423. 5. Shakhsshiti. B.2. Chemled Demonslmtions; UevenitydWiamnsin. 1985:Vol. 2, expetiments 5.15-18. pp 59-74. 6. Stannetf V. Diffusion in Polvmprs: Crank,J.;Park, G. S., Eds; Academic Press, 2. -
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7. Benediet. M.: Pisrord, T N.: Le*. H. W. Nuclsor Chrmicol E"*neWi"#, 2nd d.; McOraw-Hill, 1981; pp 822-823. 8. Koudsen, M.Ann. Phys. 1909,28,75. 9. Graham, T. J. Sci. Art8 1829.27, 74. lo. Partiipton, J. R.AHlsfory of ChmlsLry: Maanillan: landon, 1964;Vol. 4 p 2 6 3 11. Ref 10.p 934.
Volume 70 Number 10 October 1993
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