In the Classroom
Graham’s Law and Perpetuation of Error Stephen J. Hawkes Department of Chemistry, Oregon State University, Corvallis, OR 97331-4003
Errors taught in introductory chemistry are passed on to the student’s students’ students. This is illustrated by two recent contributions (1, 2) to this Journal. Graham’s law of diffusion applies only to gases that are diffusing into each other, so it does not apply to the case in ref 1 comparing the rates of diffusion of HCl and an amine vapor by the relative distances they diffuse in air, paralleling the well-known erroneous demonstration with HCl and NH3. The ratio of the distances they diffuse is (3, 4) 1/2
d HCl Mamine Mair + MHCl = d amine 1/2 MHCl Mair + Mamine
1/2 1/2
(neglecting the correction for unequal cross sections). The quantities in parentheses do not cancel to leave Graham’s ratio unless the molecular weights of the amine and HCl are equal (2). Ammonia fails because its molecular weight, 17, is very different from the 36.5 of HCl, but the two amines used in (1) are closer to 36.5 so that the misinterpretation of Graham’s law is not so obviously disobeyed. As calculated above, the ratios of HCl to methylamine or dimethylamine should be 1.04 or 0.96 compared to 1.09 or 0.90 from misinterpretation of Graham’ s law or to the 1.0 or 0.91 the authors found experimentally (1). When ammonia is used, the ratio is 1.23 calculated as above (or 1.28 if the cross sections are allowed for [2]) instead of the 1.47 from misusing Graham’s law; so the customary demonstra-
tion fails more obviously. I am unable to calculate the cross sections for methylamine–air and dimethylamine–air, but the effect is likely to be smaller than the multiplier 1.04 for ammonia. Graham’s law of effusion applies (4) only to effusion from a hole so small in a material so thin into a gas so dilute that the effusing molecules pass through the hole without touching each other or being hindered by the gas outside the hole, and are not assisted by bulk flow towards the hole. Consequently it cannot apply to the case in ref 2 of gases leaking from holes in balloons into air near atmospheric pressure. It might reasonably be expected that these misunderstandings would have been caught by reviewers, but this underlines the difficulties in the reviewing process. I have no suggestion to offer the editor to help in avoiding the problem. But there is a wider and more important problem. There seems to be no mechanism within our profession to prevent errors from being passed in good faith from generation to generation. Shouldn’t we be doing something about that? Literature Cited 1. Solomon S.; Hur, C.; Lee, A. J. Chem. Educ. l996, 73, 81. 2. Deese, W. C.; Washburn A. M.; Gibbons, J. J. Chem. Educ. 1996, 73, 540. 3. Mason, E. A.; Kronstadt, B. J. Chem. Educ. 1967, 44, 742–744. 4. Kirk, A. D. J. Chem. Educ. 1967, 44, 745–750.
Vol. 74 No. 9 September 1997 • Journal of Chemical Education
1069
