Level: introductory+
Reference: Thomas Graham, "On the Law of Diffusion of Gases," Philosophical Magazine 2, 175-190, 269-276, 351-358 (1833)
Notes: Thomas Graham's (1805-1869) studies of the diffusion of gases led to what is now called Graham's law of diffusion. This problem asks the student to analyze Graham's data and to arrive at the conclusion Graham actually reached, that the replacement volume of a gas is inversely proportional to the square root of the its density. Currently, Graham's law is usually taught as the inverse proportionality of the rate of diffusion (or 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 diffusion (or effusion) is directly proportional to the volume of gas diffused (or effused) in a given time and that the density of a gas is proportional to its molar mass.
Note: Diffusion and effusion are distinct but related phenomena of molecular transport. Diffusion refers to the spreading of one gas into or through another, as in the experiments summarized in this exercise. Effusion refers to the passage of a gas through a small hole. 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 effusion are also the subject of an exercise in Classic Calculations; click here to see it. The diffusion 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 gathered earlier. Effusion is the phenomenon more often encountered in introductory texts, however.
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/graham.doc
To download worked spreadsheet, go to:
http://web.lemoyne.edu/giunta/classicalcs/grahamans.xls
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