The gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i.e. the equation of state of an ideal gas:

Here p is the pressure of gas, V the volume it occupies, n the number of moles of gas, and T its temperature.

It can be shown that R is an universal constant, equal for all gases.   Real gases obey this equation only in an approximation of very diluted gases.

R also appears in the Nernst equation as well as in the Lorentz-Lorenz formula.

Its value is:

R = 8.314472[15] J K^-1 mol^-1

The two digits in brackets signify the uncertainty (standard deviation) in the last two digits of the value.

The Boltzmann constant k_B is defined as a ratio of molar gas constant and the Avogadro's number (Avogadro's number is approximately 6.022 × 10^23 particles/mole):

With it we can write the universal gas equation

with N = n N_A is the actual number of molecules.

Density of gas

At standard temperature and pressure (273.15 K, 101 325 Pa) we get a volume per mole of 8.314472*273.15/101325 = 0.0224 cubic metre, is 22.4 litre.

Conversely, a cubic metre contains 1000/22.4 = 44.6 mole. Thus the density in kg/m³ is 0.0446 times the average molecular mass.

Examples:

• hydrogen: molecular mass is 2, gives density of 0.089 kg/m³
• air: average molecular mass is 29, gives density of 1.23 kg/m³
• radon: molecular mass is 222, gives density of 9.9 kg/m³ (actually it is 9.73)

The small deviation may be because of not being an ideal gas.

The volume of space available per molecule is 37.2 nm³.

Reference

• gas constant CODATA value at NIST