constant

gas constant

Universal gas constant relating energy scale to temperature
Value
\(R = 8.314462618\)joule per mole kelvin
16 related articles · 3 formulas

Description

The gas constant (R) is the proportionality constant that links the energy scale of a gas to its temperature in the ideal gas law, PV = nRT. Its value is approximately 8.314 joules per mole per kelvin, meaning that one mole of an ideal gas at 300 K has about 2,500 joules of thermal energy. It appears in thermodynamics, physical chemistry, and statistical mechanics, connecting macroscopic quantities like pressure and volume to microscopic molecular motion. The gas constant is also the product of the Boltzmann constant (k_B) and Avogadro's number (N_A): R = k_B × N_A.

History

The ideal gas law was developed over the 17th–19th centuries by Boyle, Charles, Gay-Lussac, and Avogadro, but the constant R was first explicitly introduced by the French physicist Henri Victor Regnault in the 1840s, who measured it accurately for different gases. The name 'gas constant' became standard in the late 19th century.

How it works

In the ideal gas law, R converts the product of the amount of substance (in moles) and temperature (in kelvin) into an energy, which then appears as pressure times volume (work). For a monatomic ideal gas, the average kinetic energy per molecule is (3/2)k_B T, and summing over a mole gives (3/2)RT. The constant R appears in the entropy change of an ideal gas, in the speed of sound, and in the Nernst equation for electrochemical cells. Its value depends on the units of pressure and volume used, but in SI it is fixed.

In practice

It is used in engineering for calculating the behavior of gases in engines, air conditioning, and chemical reactors, and in meteorology for atmospheric models.

Fun fact

The gas constant is the same for all ideal gases, but real gases deviate from it at high pressures — a fact that helped scientists develop more accurate equations of state like the van der Waals equation.

Concept graph →

Formulas

$$p = \frac{\rho R T}{\mu}$$
Pressure relates to density, temperature, and molar mass.
What is in the formula
pvariablePressure of the gas — pressure pascal
ρvariableMass density of the gas — mass density kilogram per metre cubed
TvariableAbsolute temperature — temperature kelvin
μvariableMean molar mass of the gas mixture — molar mass kilogram per mole
RconstantUniversal gas constant relating energy scale to temperature — gas constant = 8.314462618 joule per mole kelvin
$$\Delta S_{\text{mix}} = -R \sum_i x_i \ln x_i$$
The entropy change when ideal components mix.
What is in the formula
ΔS_mixvariableEntropy change upon mixing — entropy change joule per kelvin
x_ivariableMole fraction of component i — mole fraction
RconstantUniversal gas constant relating energy scale to temperature — gas constant = 8.314462618 joule per mole per kelvin
∑operatorSum over all components i — summation
lnoperatorNatural logarithm — natural logarithm
$$\Delta G = \Delta G^\circ + RT \ln Q$$
Free energy depends on standard state and reaction quotient.
What is in the formula
ΔGvariableChange in Gibbs free energy of the reaction — gibbs free energy change joule
ΔG°variableStandard Gibbs free energy change (at standard conditions) — standard gibbs free energy change joule
TvariableAbsolute temperature — temperature kelvin
QvariableReaction quotient (ratio of product activities to reactant activities) — reaction quotient
RconstantUniversal gas constant relating energy scale to temperature — gas constant = 8.314462618 joule per mole per kelvin
lnoperatorNatural logarithm (base e) — natural logarithm

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