Deviation from idela gas behaviour

Intermolecular forces
So far molecules of a gas were assumed to be geometric points that exerted no force on each other. In reality molecules are having complicated structure and force between a pair of molecules is of electrical origin which is difficult to express by a simple law. At relatively large separation the intermolecular force is attractive in nature. However, same is repulsive upon collision. Under this situation the electron clouds of both the molecules overlap.
As the separation between the molecules decreases the force of repulsion rises rapidly which can be presented graphically with the solid line on the force-distance (F-r) as sown in Fig. 4.6. Here, or indicates the separation distance between two molecules.

Fig. 4.6 Intermolecular forces of attraction and repulsion

Thus the simplest approximation is to treat the molecules as elastic hard spheres for which the force of repulsion becomes infinite when the surfaces of the spheres come into contact. If a force of attraction is included when the molecules are not in contact, the force law has the form as shown with the dotted lines (Fig. 4.6).

Collision Cross Section and mean free path
Molecules were treated to be mere geometric points for deriving the expression for the pressure exerted by a gas in earlier lecture. These point molecules could fly freely from one wall of the container to the other without colliding with other molecules. Objections were raised in context that if molecules acted this way, a small amount of gas released in a room would spread throughout the room practically instantaneously. However, in reality it does not happen. For example, when a stopper is removed from a bottle of perfume in a room with still air, a considerable time elapses before the scent can be detected even at a point only a few meters away. It was realized that this relatively slow diffusion of one gas in another resulted from molecular collision. A representative figure indicating movement of molecules in irregular, zigzag path is shown in Fig. 4.7.

Fig. 4.7 Mean Free Path

Let us consider the following features:

1. Each molecule is a hard sphere
2. Molecule collided by other molecule is a target molecule
3. Molecule which collides with other molecules is a bullet molecule.
4. Collision between two molecules is only possible if the distance between the two is the molecular diameter.
5. Since it is only the centre-to-centre distance that determines a collision, it does not matter whether the target is large and the bullet is small, or vice-versa. We may consider the bullet molecule to shrink to a point at its centre (a geometric point) and the target molecule to occupy the entire sphere of exclusion, of radius.