Chemistry Definition of Gas Constant (R)

Chemistry and physics equations commonly include "R", which is the symbol for the gas constant, molar gas constant, ideal gas constant, or universal gas constant. It is a proportionality factor that relates energy scales and temperature scales in several equations.

The Gas Constant is the physical constant in the equation for the Ideal Gas Law:

• PV = nRT

P is pressure, V is volume, n is the number of moles, and T is temperature. Rearranging the equation, you can solve for R:

R = PV/nT

The gas constant is also found in the Nernst equation relating the reduction potential of a half-cell to the standard electrode potential:

• E = E⁰ - (RT/nF)lnQ

E is the cell potential, E⁰ is the standard cell potential, R is the gas constant, T is the temperature, n is the number of mole of electrons exchanged, F is Faraday's constant, and Q is the reaction quotient.

The gas constant is equivalent to the Boltzmann constant, just expressed in units of energy per temperature per mole, while the Boltzmann constant is given in terms of energy per temperature per particle. From a physical standpoint, the gas constant is a proportionality constant that related the energy scale to the temperature scale for a mole of particles at a given temperature.

Units for the gas constant vary, depending on other units used in the equation.

Value of the Gas Constant

The value of the gas constant 'R' depends on the units used for pressure, volume and temperature. Prior to 2019, these were common values for the gas constant.

• R = 0.0821 liter·atm/mol·K
• R = 8.3145 J/mol·K
• R = 8.2057 m³·atm/mol·K
• R = 62.3637 L·Torr/mol·K or L·mmHg/mol·K

In 2019, the SI base units were redefined. Both Avogadro's number and the Boltzmann constant were given exact numerical values. As a consequence, the gas constant also now has an exact value: 8.31446261815324 J⋅K⁻¹⋅mol⁻¹.

Because of the relatively recent definition change, use care when comparing calculations prior to 2019 because the values for R are slightly different before and after the redefinition.

Why R Is Used for the Gas Constant

Some people assume the symbol R is used for the gas constant in honor of the French chemist Henri Victor Regnault, who performed experiments that were first used to determine the constant. However, it's unclear whether his name is the true origin of the convention used to denote the constant.

Specific Gas Constant

A related factor is the specific gas constant or individual gas constant. This may be indicated by R or R_gas. It is the universal gas constant divided by the molar mass (M) of a pure gas or mixture. This constant is specific to the particular gas or mixture (hence its name), while the universal gas constant is the same for an ideal gas.

R in the U.S. Standard Atmosphere

The United States government uses a defined value of R, indicated by R*, in its definition of the U.S. Standard Atmosphere. Agencies using R* include NASA, NOAA, and the USAF. By definition, R* is exactly 8.31432×10³ N⋅m⋅kmol⁻¹⋅K⁻¹ or 8.31432 J⋅K⁻¹⋅mol⁻¹.

While this gas constant value is inconsistent with the Boltzmann constant and Avogadro constant, the discrepancy is not huge. It does deviate slightly from the ISO value of R for calculating pressure as a function of altitude.

Sources

• Jensen, William B. (July 2003). "The Universal Gas Constant R". J. Chem. Educ. 80 (7): 731. doi:10.1021/ed080p731..
• Mendeleev, Dmitri I. (September 12, 1874). "An exert from the Proceedings of the Chemical Society's Meeting on Sept. 12, 1874". Journal of Russian Chemical-Physical Society, Chemical Part. VI (7): 208–209.
• Mendeleev, Dmitri I. (March 22, 1877). "Mendeleev's researches on Mariotte's law 1". Nature. 15 (388): 498–500. doi:10.1038/015498a0
• Moran, Michael J.; Shapiro, Howard N. (2000) Fundamentals of Engineering Thermodynamics (4th ed.). Wiley. ISBN 978-0471317135.
• NOAA, NASA, USAF (1976). U.S. Standard Atmosphere. U.S. Government Printing Office, Washington, D.C. NOAA-S/T 76-1562. Part 1, p. 3