Ideal Gases | Research & Encyclopedia Articles

Ideal Gases

An ideal or perfect gas is one which obeys the equation of state, PV = nRT, where T is the absolute temperature in Kelvin degrees (equal to the temperature in Celsius degrees plus 273 degrees) and R is the universal gas constant (equal to 0.08 when the volume V is in liters, the pressure P is in atmospheres, and n is the number of moles of the gas present; or equivalently, 8.3 joules per degree mole.)

This equation resulted from the examination of the behavior of air by Robert Boyle, Jacques Charles, and Joseph- Louis Gay-Lussac. Based on experimental measurements, Boyle showed that the product of the pressure and the volume of a sample of air, at constant temperature, is always equal to the same value. In other words, when the pressure placed on the sample is doubled, the volume is reduced to half its initial value. The work of Charles in 1787 and of Gay- Lussac in 1808 demonstrated that the volume of a given amount of air is directly proportional to the temperature, if its pressure remains constant; i.e. when the temperature of the sample is doubled the volume will double, if the pressure on the sample is kept constant.

Amadeo Avogadro proposed in 1811 that equal volumes of all gases, at the same pressure and temperature, contain the same number of molecules. In other words, an equal number of molecules (and, therefore an equal number of moles) of all gases occupy the same volume at constant temperature and pressure. This proposal, combined with the relationships discovered by Boyle, Charles, and Gay Lussac led to the equation of state for gases: PV=nRT.

In their work which led to this equation, Boyle, Charles, and Gay- Lussac certainly thought they were deriving quantitative relationships for actual, real gases. However, as subsequent studies were performed on a variety of gases over wide ranges of pressure, volume, and temperature and more precise measurements were made, it was discovered that, although the behavior of real gases generally closely follows the ideal gas equation under circumstances of low pressure and reasonably high temperature, significant deviations from the ideal expectations do occur. Rather than abandon the PV = nRT equation, scientists chose to keep the equation, refer to it as the equation of state for ideal or perfect gases (or, simply, as the ideal gas law), and use it as a first approximation when dealing with gases. They also proceeded to explore the reasons why gases do not always behave ideally and obey this equation. Studies of the departures from ideal behavior by gases have led to a better understanding of atoms and molecules and their interactions in the gaseous state.

This is not an unusual practice in science. In fact, the progress of science depends on the discovery of exceptions to quantitative relationships, such as the ideal gas law, and experimental determination of equations and explanations that fit the observed behavior more consistently. Examples include Newton's laws, which were discovered not to be applicable to atomic and molecular systems. For such systems, quantum mechanics fits the observed phenomena better and is a greater aid to our understanding. The classical mechanics of Newton has not been abandoned, however. Its elegant, simple equations work quite well for macroscopic systems, and the added complexity of quantum mechanics is not needed.

The kinetic-molecular theory of gases was developed by Ludwig Boltzmann, James Clerk Maxwell, and Rudolf Clausius. This theory explains the behavior of ideal gases by assuming that gases are made up of a collection of molecules moving about randomly in the container, colliding randomly and elastically with each other and with the walls of the container. If the molecules are assumed to be point particles with zero volume, the ideal gas equation is derived from this model. The pressure is due to the collision of gas molecules with the container walls, and the temperature is related to the kinetic energy of the molecules. An examination of this ideal kinetic model reveals reasons why real gases should be expected to depart from ideal gas behavior. Gases are not point particles: they occupy space. Collisions between molecules (and with the container wall) are not elastic: they involve the exchange of energy as molecular kinetic translational energy is changed into internal molecular energy such as the vibration of bonds, the rotation of the molecule, and even electronic energy. Although this model provides basic insight into the behavior of gases, a more accurate consideration of the behavior of real gases is needed.

The most widely used modification of the kinetic- molecular theory of gases is that proposed by Johannes van der Waals in 1873. He took into consideration both the attractive forces among the molecules and the space they occupy. The result is an equation of state for gases which is similar in form to the ideal gas equation but in which there is an additional internal pressure term due to the molecular attractions and the space occupied by the molecules is subtracted from the volume term.

Although the van der Waals equation of state was an advance in the understanding of real gases, and it can be used to determine helpful information, it also does not fit the behavior of gases at all values of pressure and temperature. A number of other theoretical and empirical equations of state have been proposed. One of these is the virial equation of state suggested by Heike Kammerlingh-Onnes (1853-1926) in 1901. This equation adds correction terms to the ideal gas equation by multiplying the right side of the equation (nRT) by the mathematical progression (1 + B/V + C/V2 + D/V3 + E/V4 +...), in which the constants A, B, C, etc. are temperature dependent. Computers are used to fit this equation to the experimental data, and the resulting values for the constants are determined for the particular gas. Although this is a purely empirical procedure, there has been some success in using the values of the constants to understand the behavior of gases.