Determinación de la constante universal de los gases 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?

R′= R/m = (R/n)(n/m)
= constant/M = constant′/density

Donald R. Paulson
Department of Chemistry
California State University
Los Angeles, CA 90032
Answer
This is best answered by tracing the originsof 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 equation appears to have been the French engineer, Benoit-PierreÉmile Clapeyron (1799–1864). In his famous memoir of
1834 on Carnot cycles, he wrote the combined equation as:
pv = R(267 + t)

(1)

where tis 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 ofthe (273 + t) term:
pv = RT

(3)

Being French, Clapeyron had attributed the volumepressure 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 thevolume 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
mass and the volumeper mole are related by the equation:
v = V/m = (V/n)(n/m) = (V/n)(1/M)

where M = m/n is mass per mole or the molecular weight, so
the universal gas constant R and the Clapeyron-Clausius’ specific gas constant (designated here as R′ to avoid confusion)
are related by the equation:

(4)

(5)

where by Avogadro’s hypothesis the molecular weight of a
gas at constant PVT is directlyproportional to its density (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 in 1873 rewrote equation
3 as:
up = RT
(6)
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 isthe constant for the G–M law with regard to the molecular
[in other words, molar] volume” (5).
So why did Clapeyron choose the letter R for the constant in his gas law? The fact is that he doesn’t explicitly 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 thatthe
value of R for each gas was 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 datawere used by Clausius not only to correct
the conversion factor between the centigrade and absolute
temperature scales but also to evaluate the values 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...