CZ:Featured article/Current

Ideal gas law

by Milton Beychok and Paul Wormer (and Daniel Mietchen and David E. Volk)

---

Values of R	Units
8.314472	J·K-1·mol-1
0.082057	L·atm·K-1·mol-1
8.205745 × 10-5	m3·atm·K-1·mol-1
8.314472	L·kPa·K-1·mol-1
8.314472	m3·Pa·K-1·mol-1
62.36367	L·mmHg·K-1·mol-1
62.36367	L·torr·K-1·mol-1
83.14472	L·mbar·K-1·mol-1
10.7316	ft3·psi· °R-1·lb-mol-1
0.73024	ft3·atm·°R-1·lb-mol-1

The ideal gas law is the equation of state of an ideal gas (also known as a perfect gas) that relates its absolute pressure p to its absolute temperature T. Further parameters that enter the equation are the volume V of the container holding the gas and the amount n (in moles) of gas contained in there. The law reads

$pV=nRT\,$

where R is the molar gas constant, defined as the product of the Boltzmann constant k_B and Avogadro's constant N_A

$R\equiv N_{\mathrm {A} }k_{\mathrm {B} }$

Currently, the most accurate value of R is: 8.314472 ± 0.000015 J·K^-1·mol^-1.

The law applies to ideal gases which are hypothetical gases that consist of molecules that do not interact, i.e., that move through the container independently of each other. In contrast to what is sometimes stated (see, e.g., Ref.) an ideal gas does not necessarily consist of point particles without internal structure, but may be formed by polyatomic molecules with internal rotational, vibrational, and electronic degrees of freedom. The ideal gas law describes the motion of the centers of mass of the molecules and, indeed, mass centers may be seen as structureless point masses. However, for other properties of ideal gases, such as entropy, the internal structure may play a role.

The ideal gas law is a useful approximation for calculating temperatures, volumes, pressures or amount of substance for many gases over a wide range of values, as long as the temperatures and pressures are far from the values where condensation or sublimation occur.

Real gases deviate from ideal gas behavior because the intermolecular attractive and repulsive forces cause the motions of the molecules to be correlated. The deviation is especially significant at low temperatures or high pressures, i.e., close to condensation. A conventional measure for this deviation is the compressibility factor.

There are many equations of state available for use with real gases, the simplest of which is the van der Waals equation.

Historic background

The early work on the behavior of gases began in pre-industrialized Europe in the latter half of the 17th century by Robert Boyle who formulated Boyle's law in 1662 (independently confirmed by Edme Mariotte at about the same time). Their work on air at low pressures established the inverse relationship between pressure and volume, V = constant / p at constant temperature and a fixed amount of air. Boyle's Law is often referred to as the Boyles-Mariotte Law.

.... (read more)

notes