Constante r

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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 ofChemistry 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) relatingvolume and pressure and Gay-Lussac's law (1802) relating volume and temperature in a single equation appears to have been the French engineer, Benoit-Pierre- Emile Clapeyron (1799-1864). In his famousmemoir 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)
andin 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 theFrench scientist, Edme 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 theMariotte—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 constantR 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 inquestion. In other words, just as the volume per unit mass and the volume per mole are related by the equation:
v = V/m = (V/n)(n/m) = (V/n)(l/M) (4)
where M = m/n is mass per mole or the...