Gas constant

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Values of R
8.314472 J · K^-1 · mol^-1
0.0820574587 L · atm · K^-1 · mol^-1
8.20574587 x 10^-5 m³ · atm · K^-1 · mol^-1
8.314472 cm³ · MPa · K^-1 · mol^-1
8.314472 L · kPa · K^-1 · mol^-1
8.314472 m³ · Pa · K^-1 · mol^-1
62.3637 L · mmHg · K^-1 · mol^-1
62.3637 L · Torr · K^-1 · mol^-1
83.14472 L · mbar · K^-1 · mol^-1
1.987 cal · K^-1 · mol^-1
6.132439833 lbf · ft · K^-1 · g-mol^-1
10.7316 ft³ · psi · °R^-1 · lbmol^-1

The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. It is another name for the Boltzmann constant, but when used in the ideal gas law it is usually expressed in the more convenient units of energy per kelvin per mole rather than simply energy per kelvin per particle.

The gas constant occurs in the simplest equation of state, the ideal gas law, as follows:

<math>

P = {RT\over{\tilde{V}}} </math> where P is the pressure of an ideal gas, T is its temperature, and <math>\tilde{V}</math> is its molar volume. R also appears in the Nernst equation as well as in the Lorentz-Lorenz formula. Also commonly written as:

<math>\qquad PV=nRT</math>

where P, R and T are all as aforementioned, V is the volume the gas takes up, and n is the moles of gas.

Its value is:

R = 8.314472(15) J · K^-1 · mol^-1

or, dividing by Avogadro's number,

k_B = 1.380 6505(24) × 10⁻²³ joules per kelvin

The two digits between the parentheses denote the uncertainty (standard deviation) in the last two digits of the value.

The US Standard Atmosphere, 1976 (USSA1976) defines the Universal Gas Constant (R) as:

R = 8.31432 x 10^-3 N · m/(kmol · K).

The USSA1976 does recognize, however, that this value is not consistent with the cited values for Avogadro's number and the Boltzmann constant. Still though, the USSA1976 uses this value of R for all the calculations of the standard atmosphere.

The Boltzmann constant k_B (often abbreviated k) may be used in place of the other forms of the ideal gas constant by working in pure particle count rather than number of moles of gas; this simply requires carrying a factor of Avogadro's number. Writing:

One can then express the ideal gas law in direct terms of Boltzmann's constant:

<math>\qquad PV=Nk_BT</math>

with N = nN_A is the actual number of molecules.