GASEOUS STATE

PHYSICAL CHEMISTRY

B.sc First Year

• Introduction

Amongst the three common states of matter, the gaseous state is simplest. The laws of gaseous behaviour are more uniform and are better understood. The well known laws of gaseous behaviour are Boyle’s law, Charle’s law Graham’s law, Dalton’s law and Avogadro’s law. There was no theoretical background to justify them. In the nineteenth century, however, Kronig, Clausius, Maxwell and Boltzmann developed a theory known as kinetic molecular theory of gases, which provided sound theoretical basis for the various gas laws.
As we studied there are two opposite molecular forces, the forces of attraction and the disruptive forces operating between molecules. If the thermal energy is much greater than the forces of attraction, then we have matter in its gaseous state.In contrast with solids and liquids gases occupy the same volume as that of the closed vessel, they are characterized by low density and high compressibility.
The characteristic properties of gases are given below.

1. No definite shape and volume. Gases occupy all available space i.e. the shape and volume of the container in which they are filled.
2. Expansibility. Gases have limitless expansibility. They expand to fill the entire vessel they are placed in.
3. Compressibility. Gases are easily compressed by application of pressure.
4. Diffusibility. Gases can diffuse rapidly through each other to form a homogeneous mixture.
5. Pressure. Gases exert pressure on the walls of the container in all direction. You can site the example of a gas balloon.
6. Effect of heat. When a gas confined in a vessel is heated, its pressure increases.Upon heating in a vessel fitted with a piston, volume of the gas increases.

POSTULATES OF KINETIC THEORY OF GASES
It was earlier observed that the gas laws were based on experimental
observations. The theoretical foundation or mathematical representation was missing. However several workers studied the properties of gases and found that the gases are essentially composed of freely moving molecules. The basic ideas of the workers were mentioned to explain the behaviour of the gases called the kinetic theory of gases. This theory succeeded to attain a rigid mathematical form due to the efforts of Joule, Kronig, Clausius, Maxwell, Boltzmann and many others. The main postulates of kinetic theory of gases may be given as follows.

• Every gas consists of large number of tiny particles called point masses i.e. the actual volume of molecules is negligible when compared to the total volume of the gas. For the same gas, all molecules are of same size and mass.
• The gas molecules are always in a state of rapid zig-zag motion in all directions. These molecules collide with each other and with the walls of the containing vessel.
• A molecule moves in a straight line with uniform velocity between two collisions.
• The molecular collisions are perfectly elastic so that there is no net loss of energy when the gas molecules collide with one another or against the walls of the vessel. Suppose two molecules collide having same mass m. Before collision the velocity of one molecule is ν₁ and velocity of other molecule is ν₂ and after collision the velocity of the molecules changes from ν₁ to ν₁ and from ν2 to ν2 then if the
collisions are elastic there is no loss of kinetic energy. This can be expressed as follows.
Total kinetic energy of two molecules before collision is
½ m1ν12+1/2 m2ν22
And after collision total kinetic energy of both the molecules is
½ m1 ν₁^{`2</sup>+ ½ m<sub>2</sub> ν<sub>2</sub><sup>`2}
  If m₁ ν₁²+1/2 m2 ν₂² = ½ m₁ ν₁`<sup>2</sup>+ ½ m<sub>2</sub> ν<sub>2</sub>`2
  i.e. total kinetic energy before collision is equal to total kinetic energy after collision then the collision is said to be an elastic collision.
• There are no attractive forces operating between molecules or between molecules and the walls of the vessel in which the gas has been contained. The molecule move independently of one another.
• The pressure of the gas is the hits recorded by the molecules on the walls of the container in which the gas is contained.
• The average kinetic energy of gas molecules is directly proportional to absolute temperature. This means that the average kinetic energy of molecules is the same at a given temperature.
  This must be clear to you that all the above postulates are applicable to ideal gases only i.e. the gas which obey Boyle’s and Charle’s law under all conditions of temperature and pressure. These are only approximately valid