Polar molecules

The force F between two polar molecules is directly proportional to the product of the two dipole moments (μ₁ and μ₂) and inversely proportional to the fourth power of the distance between them (r⁴): that is, F varies as μ₁μ₂/r⁴. The equation for this relationship contains a constant of proportionality (F = kμ₁μ₂/r⁴), the sign and magnitude of which depend on the mutual orientation of the two dipoles; if the positive end of one faces the negative end of the other, the constant of proportionality is negative (meaning that an attractive force exists), while it is positive (meaning that a repulsive force exists) when the positive end of one faces the positive end of the other. When polar molecules are free to rotate, they tend to favour those orientations that lead to attractive forces. To a first approximation, the force (averaged over all orientations) is inversely proportional to the temperature and to the seventh power of the distance of separation. Mixtures of polar molecules often exhibit only mild deviations from ideality, but mixtures containing polar and nonpolar molecules are frequently strongly nonideal. Because of the qualitative and quantitative differences in intermolecular forces, the molecules segregate: the polar molecules prefer to be with each other, and so do the nonpolar ones. Only at higher temperatures, such that the thermal energy of the molecules offsets the cohesion between identical molecules, do the two liquids mix in all proportions. In mixtures containing both polar and nonpolar components, deviations from Raoult’s law diminish as temperature rises.

Nonpolar molecules

A nonpolar molecule is one whose charge distribution is spherically symmetric when averaged over time; since the charges oscillate, a temporary dipole moment exists at any given instant in a so-called nonpolar molecule. These temporary dipole moments fluctuate rapidly in magnitude and direction, giving rise to intermolecular forces of attraction called London (or dispersion) forces. All molecules, charged or not, polar or not, interact by London forces. To a first approximation, the London force between two molecules is inversely proportional to the seventh power of the distance of separation; it is therefore short-range, decreasing rapidly as one molecule moves away from the other. The London theory indicates that for simple molecules positive deviations from Raoult’s law may be expected (i.e., the activity coefficient γ_i is greater than 1, as explained previously). Since the London theory suggests that the attractive forces between unlike simple molecules are smaller than those corresponding to an ideal solution, the escaping tendency of the molecules in solution is larger than that calculated by Raoult’s law. As a result, mixing of small nonpolar molecules is endothermic (absorbing heat from the surroundings) and the volume occupied by the liquid solution often exceeds that of the unmixed components—that is, the components expand on mixing.

In addition to the forces listed above, there are so-called induction forces set up when a charged or polar molecule induces a dipole in another molecule: the electric field of the inducing molecule distorts the charge distribution in the other. When a charged molecule induces a dipole in another, the force is always attractive and is inversely proportional to the fifth power of the distance of separation. When a polar molecule induces a dipole in another molecule, the force is also attractive and is inversely proportional to the seventh power of separation. Induction forces are usually small but may make a significant contribution to the energy of a mixture of molecules that are strongly dissimilar.