Gas constant

The molar gas constant, R, is the proportionality constant in equations relating a gas’s pressure, volume, temperature, and amount of substance. Its value is exactly 8.314462618… joules per mole per kelvin.

Ideal gas law: The equation PV = nRT relates pressure, volume, temperature, and amount for an ideal gas. R is the proportionality constant connecting these four measurable quantities.
Van 't Hoff equation: An equation describing how an equilibrium constant changes with temperature. R scales the temperature dependence of chemical equilibrium.
Clapeyron equation: A thermodynamic relation connecting pressure, temperature, and molar volume across phase boundaries. Early gas and phase-equilibrium work helped establish the constant’s role in macroscopic equations.
Boltzmann constant: The constant relating temperature to energy per particle, exactly k = R/NA. It expresses the same thermal scale per particle instead of per mole.
Avogadro constant: The number of specified elementary entities in one mole, exactly 6.02214076 × 10²³ mol⁻¹. Multiplying the Boltzmann constant by this constant gives the molar gas constant.
Arrhenius equation: An equation relating a reaction rate constant to temperature and activation energy. R appears in the exponential that governs thermal activation.
Ludwig Boltzmann: An Austrian physicist whose statistical mechanics connected microscopic molecular motion with thermodynamic behavior. His work supplied the microscopic interpretation behind R = NAk.
Specific gas constant: A gas-specific constant equal to the universal gas constant divided by the substance’s molar mass. It replaces molar quantities with mass-specific quantities in engineering equations.
Molar heat capacity: The heat required to raise one mole of a substance by one kelvin under specified conditions. For ideal gases, heat capacities at constant pressure and volume differ by R.
Nernst equation: An equation relating electrode potential to chemical activities and temperature. Its thermal voltage term contains R divided by Faraday’s constant.

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