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Gas_constant_R

# Gas_constant_R - C hemical Education Today Ask the...

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Chemical Education Today JChemEd.chem.wisc.edu Vol. 80 No. 7 July 2003 Journal of Chemical Education 731 Ask the Historian The Universal Gas Constant R by William B. Jensen Question Why is the universal gas constant in PV = nRT represented by the letter R ? Donald R. Paulson Department of Chemistry California State University Los Angeles, CA 90032 Answer This is best answered by tracing the origins of the ideal gas law itself. One of the first persons to combine Boyle’s law (1662) relating volume and pressure and Gay-Lussac’s law (1802) relating volume and temperature in a single equa- tion appears to have been the French engineer, Benoit-Pierre- Émile Clapeyron (1799–1864). In his famous memoir of 1834 on Carnot cycles, he wrote the combined equation as: pv = R (267 + t ) (1) where t is the temperature in degrees centigrade (1). In 1850, the German physicist, Rudolf Clausius (1822–1888), using the experimental data of the French chemist, Henri Victor Regnault (1810–1878), reevaluated the constant inside the parentheses and rewrote the equation (2) as: pv = R (273 + t ) (2) and in 1864 he further simplified it (3) by substituting the absolute temperature T in place of the (273 + t ) term: pv = RT (3) Being French, Clapeyron had attributed the volume- pressure law to the French scientist, Edmé Mariotte (1620– 1684), rather than to Robert Boyle, and Clausius did not question this choice. Indeed, he explicitly proposed that the combined equation be called the Mariotte–Gay-Lussac law or the M–G law for short. Both Clapeyron and Clausius had used the volume per unit mass of gas rather than the volume per mole of gas in their equations. This meant that their gas constant R was not universal for all gases but was rather a specific constant whose value varied from one gas to another and was, as Clausius noted, roughly inversely proportional to the density of the gas in question. In other words, just as the volume per unit

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