# La constante universal r

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The Universal Gas Constant
William B. Jensen
Department of Chemistry, University of Cincinnati Cincinnati, OH 45221-0172

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 Angles, CA 90032 Answer This is best answered by tracing the origins of the ideal gas lawitself. 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 equation appears to have been the French engineer, Benoit-Paul Emile Clapeyron (17991864). In his famous memoir of 1834 on the Carnot cycle, he wrote the combined equation as (1): pv = R(267 + t) [1]
Figure 1. Henri Victor Regnault(1810-1878).

where t is the temperature in degrees centigrade. In 1850, the German physicist, Rudolf Clausius (18221888), using the experimental data of the French chemist, Henri Victor Regnault (ﬁgure 1), reevaluated the constant inside the parentheses and rewrote the equation as (2): pv = R(273 + t) [2]

and in 1864 he further simpliﬁed it by substituting the absolute temperature T in place of the(273 + t) term (3): pv = RT [3]

Both Clapeyron and Clausius had used the volume per unit mass of gas (v = V/M) rather than the volume per mole of gas (u = V/N) 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 thedensity (d) of the gas in question (4). The ﬁrst person to convert the speciﬁc constant of Clapeyron and Clausius into a universal gas constant appears to have been Clausius’ student, the German chemist, August F. Horstmann (1842-1929), who rewrote the gas law in 1873 as (5): up = RT [6]

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.

where p and T have their earlier meaning but u is “the volume of a molecular weight [i.e. mole] of the gas” and “R is the constant for the G-M law with regard to the molecular [i.e. molar]volume.”
So why did Clapeyron choose the letter R for the constant in his gas law? The fact is that he doesn’t ex-

J. Chem. Educ., 2003, 80, 731-732

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WILLIAM B. JENSEN plicitly tell us why and we are left with two speculative answers: (a) it was arbitrary or (b) it stood for ratio or one of its French equivalents: raison or rapport, since Clapeyron noted that the value of R for each gaswas obtained by evaluating the constancy of the ratio pv/(267 + t) over a range of pressures and temperatures, a point also emphasized by Clausius using the revised ratio pv/(273 + t).
Given IUPAC’s penchant for naming constants after famous scientists, this suggests that it might not be inappropriate to name R in honor of Regnault whose accurate experimental data was used by Clausius not only tocorrect the conversion factor between the centigrade and absolute temperature scales but also to evaluate the value of R using the above ratio (6). It is also interesting to note that Clausius was aware that Regnault’s data clearly showed that (2): ... the more distant, as regards pressure and temperature, a gas is from its point of condensation the more correct will be the law [i.e. the moreconstant R]. Whilst its accuracy, therefore, for permanent gases in their common state is so great, that in most investigations it may be regarded as perfect, for every gas a limit may be imagined, up to which the law is also perfectly true; and in the following pages, where permanent gases are treated as such, we shall assume the existence of this ideal condition. In 1864 Clausius further...

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