I INTRODUCTION Gases, collective term for one of the three visibly different states of ordinary matter, liquid and solid being the other two. Solids have well-defined shapes and are difficult to compress. Liquids are free-flowing and bounded by self-formed surfaces. Gases expand freely to fill their containers and are much lower in density than liquids and solids.
II THE IDEAL GAS LAW
The atomic theory of matter defines states, or phases, in terms of order. Molecules have a certain freedom of motion in space. These microscopic degrees of freedom are associated with the concept of macroscopic order. Molecules in a solid are arranged in a regular lattice, their freedom restricted to small vibrations about lattice sites. In contrast, there is no macroscopic spatial order in a gas. Molecules move at random, bounded only by the walls of their container.
Empirical laws have been developed that correlate macroscopic variables. For common gases, the macroscopic variables include pressure (P), volume (V), and temperature (T). Boyle's law states that in a gas held at a constant temperature the volume is inversely proportional to the pressure. Charles's law, or Gay-Lussac's law, states that if a gas is held at a constant pressure the volume is directly proportional to the absolute temperature. Combining these laws gives the ideal gas law: PV/T = R (per mole), also known as the equation of state of an ideal gas. The constant R on the right-hand side of the equation is a universal constant, the discovery of which is a cornerstone of modern science.
III THE KINETIC THEORY OF GASES
With the advent of the atomic theory of matter, the above-mentioned empirical laws acquired a microscopic basis. The volume of a gas reflects simply the position distribution of its constituent molecules. More exactly, the macroscopic variable V represents the available amount of space in which a molecule can move. The pressure of a gas, which can be measured with gauges placed on the container walls, registers the average change of momentum experienced by molecules as they collide with, and subsequently rebound from, the walls. The temperature of a gas is proportional to the average kinetic energy of the molecules, or to the square of the average velocity of the molecules. The reduction of these macroscopic measures to such mechanical variables as position, velocity, momentum, and kinetic energy of the molecules, which can be correlated through Newton's laws of mechanics, should yield all the empirical gas laws. This turns out to be generally true.
The physics that relates the properties of gases to classical mechanics is called the kinetic theory of gases. Besides providing a basis for the ideal gas equation of state, the kinetic theory can also be used to predict many other properties of gases, including the statistical distribution of molecular velocities and transport properties such as thermal conductivity, the coefficient of diffusion, and viscosity.
A Van der Waals equation
The ideal gas equation of state is only approximately correct. Real gases do not behave exactly as predicted. In some cases the deviation can be extremely large. For example, ideal gases could never become liquids or solids, no matter how much they were cooled or compressed. Thus, modifications of the ideal gas law, PV = RT, were proposed. Particularly useful and well known is the van der Waals equation of state: (P + a/V2) (V - b) = RT, where a and b are adjustable parameters determined from experimental measurements carried out on actual gases. They are material parameters rather than universal constants, in the sense that their values vary from gas to gas.
The van der Waals equation also has a microscopic interpretation. Molecules interact with one another. The interaction is strongly repulsive in close proximity, becomes mildly attractive at intermediate range, and vanishes at long distance. The ideal gas law must be corrected when attractive and repulsive forces are considered. For example, the mutual repulsion between molecules has the effect of excluding certain territory around each molecule from intrusion by its neighbors. Thus, a fraction of space becomes unavailable to each molecule as it executes random motion. In the equation of state, a volume of exclusion (b) should be subtracted from the volume of the container (V); thus, (V - b).
B Phase Transitions
At low temperatures (reduced molecular motion) and at high pressures or reduced volumes (reduced intermolecular spacing), the molecules in a gas come under the influence of one another's attractive force. Under certain critical conditions, the entire system enters a high-density bound state and acquires a bounding surface. This signifies the onset of the liquid state. The process is known as a phase transition. The van der Waals equation permits such a phase transition. It also describes a two-phase coexistence region that terminates on a critical point, above which no physical distinction can be found between the gas and the liquid phases. These phenomena are consistent with experimental observations. For actual use one has to go to equations that are more sophisticated than the van der Waals equation.
Improved understanding of the properties of gases over the past century has led to large-scale exploitation of the principles of physics, chemistry, and engineering for industrial and consumer applications.
See Atom and Atomic Theory; Matter, States of; Thermodynamics.