Level: introductory+
Reference: Thomas Graham, "On the Motion of Gases," Philosophical Transactions of the Royal Society of London 136, 573-631 (1846).
Notes: Thomas Graham's (1805-1869) studies of the effusion of gases led to what is now called Graham's law of effusion. This problem asks the student to analyze Graham's data and to arrive at the conclusion Graham actually reached, that the effusion time of a gas is directly proportional to the square root of the its density. Currently, Graham's law of effusion is usually taught as the inverse proportionality of the rate of effusion to the square root of the molar mass of the gas. This formulation follows from Graham's observations and the facts that the rate of effusion is inversely proportional to the time required for effusion and that the density of a gas is proportional to its molar mass.
Note: Effusion and diffusion are distinct but related phenomena of molecular transport. Effusion refers to the passage of a gas through a small hole, as in the experiments summarized in this exercise. Diffusion refers to the spreading of one gas into or through another. For more on the distinction between these phenomena, see Stephen J. Hawkes, "Graham's Law and Perpetuation of Error," J. Chem. Educ. 74 1069ff (1997) and particularly E. A. Mason & Barbara Kronstadt, "Graham's Laws of Diffusion and Effusion," J. Chem. Educ. 44, 740-3 (1967).
Graham's data on diffusion are also the subject of an exercise in Classic Calculations; click here to see it. These data are more extensive and are somewhat higher in quality (at least judging by the approximation of the empirical fit to square root dependence). They were also collected earlier. Effusion is the phenomenon more often encountered in introductory texts, however.
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/grahameff.doc
To download worked spreadsheet, go to:
http://web.lemoyne.edu/giunta/classicalcs/grahameffans.xls
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