The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per mole, i.e. the pressure–volume product, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.
The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance. The Boltzmann constant and the Avogadro constant were similarly determined, which separately relate energy to temperature and particle count to amount of substance.
The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB):
R
=
N
A
k
.
{\displaystyle R=N_{\rm {A}}k.}
Since the 2019 redefinition of SI base units, both NA and k are defined with exact numerical values when expressed in SI units. As a consequence, the SI value of the molar gas constant is exactly 8.31446261815324 J⋅K−1⋅mol−1.
Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant. However, the origin of the letter R to represent the constant is elusive. The universal gas constant was apparently introduced independently by Clausius’ student, A.F. Horstmann (1873)
and Dmitri Mendeleev who reported it first on Sep. 12, 1874.
Using his extensive measurements of the properties of gases,
he also calculated it with high precision, within 0.3% of its modern value.
The gas constant occurs in the ideal gas law:
P
V
=
n
R
T
=
m
R
s
p
e
c
i
f
i
c
T
{\displaystyle PV=nRT=mR_{\rm {specific}}T}
where P is the absolute pressure (SI unit pascals), V is the volume of gas (SI unit cubic metres), n is the amount of gas (SI unit moles), m is the mass (SI unit kilograms) contained in V, and T is the thermodynamic temperature (SI unit kelvins). Rspecific is the mass-specific gas constant. The gas constant is expressed in the same units as are molar entropy and molar heat capacity.