The kinetic-molecular theory of gases assumes that ideal gas molecules (1) are constantly moving; (2) have negligible volume; (3) have negligible intermolecular forces; (4) undergo perfectly elastic collisions; and (5) have an average kinetic energy proportional to the ideal gas’s absolute temperature.

The average kinetic energy (KE) of a particle in an ideal gas is given as: ¯¯¯¯¯¯¯¯KE=12m¯¯¯¯¯v2=32kT KE ¯ = 1 2 m v 2 ¯ = 3 2 kT , where k is the Boltzmann’s constant. (See the Atom on “Temperature” in kinetic theory. )

If the temperature is increased, the average speed and kinetic energy of the gas molecules increase. If the volume is held constant, the increased speed of the gas molecules results in more frequent and more forceful collisions with the walls of the container, therefore increasing the pressure (Figure 1).

For a gas to be “ideal” there are four governing assumptions: The gas particles have negligible volume. The gas particles are equally sized and do not have intermolecular forces (attraction or repulsion) with other gas particles. The gas particles move randomly in agreement with Newton’s Laws of Motion.

As the temperature increases, the average kinetic energy increases as does the velocity of the gas particles hitting the walls of the container. The force exerted by the particles per unit of area on the container is the pressure, so as the temperature increases the pressure must also increase.

An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles’ kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them.

V = nRT/p = 40 * 8.3144598 * 250 / 101300 = 0.82 m³ ….Ideal gas law equation

1. p is the pressure of the gas, measured in Pa;
2. V is the volume of the gas, measured in m³;
3. n is the amount of substance, measured in moles;
4. R is the ideal gas constant; and.
5. T is the temperature of the gas, measured in Kelvins.