Kinetic Theory : Liquids

The attractive forces exerted by molecules upon one another are of considerable magnitude when the substance is in the liquid state. In a liquid the molecules are close together, so that there are practically no free paths. The motion is now more analogous to gliding of the particles among and over one another.

Since the actual space occupied by spheres of radius r most densely packed is 0.74 of the total volume, then if we assume that in a liquid the molecules are in contact, we find:

where N₀ is Avogadro's constant and V the molar volume ( = Mol.wt./Density). This equation gives an approximate value of the molecular radius, r, in a liquid.

A molecule in the body of the liquid is attracted equally in all directions, and the resultant force on it is zero. The range of the attractive forces is small; van der Waals calculated it to be of the order of 10^-6 cm. Molecules lying in the surface of the liquid, however, are subjected to a resultant attraction due to the unbalanced forces of the molecules beneath them, and are under a pressure tending inwards towards the body of the liquid.

Fig: Liquid

Diagram indicating the range of molecular forces in a liquid.

This resultant force gives rise to surface tension.

The attractive forces between molecules are not always exerted uniformly in all directions, but may proceed in one or two directions only, as if the molecules were small magnets. The molecules in the surface will then mostly be arranged with the same parts pointing in one direction. Investigations of Rayleigh (1899) indicated that the thinnest oil films on water were unimolecular in thickness, and the formation of unimolecular films has been proved in many cases, notably byLangmuir (1917) and Harkins (from 1917). A drop of a solution of fatty acid or other insoluble substance in benzene is brought on a perfectly clean surface of water. The solvent evaporates, leaving an isolated patch of the film. By bringing a strip of paraffined paper across the surface of the water so as to enclose the film between it and the sides of the trough, no resistance is encountered until the edges of the film touch the sides of the trough and the strip of paper. A resistance is now observed. The area of the film is then equal to the area A between the paper strip and the sides of the trough and since the weight, w, of the film is known, the area, a, occupied by a single molecule in the unimolecular film is given by:

A = AM/wN₀

where M is the molecular weight of the substance in the film and N₀, Avogadro's constant. The thickness t of the film can be calculated on the assumption that the density is the same as that of the substance in bulk, δ:

δAt = w.

It is found that for fatty acids a is practically the same with varying lengths of chains of carbon atoms, so that it is assumed that the molecule is orientated vertically on the water surface with the carboxyl group, COOH, of the acid immersed in the water and the carbon chain outside.

Some molecules in a liquid possess more kinetic energy than the average. Such molecules, approaching the surface, will have sufficient energy to break away from the attractive forces, and will proceed outwards into the space above the liquid. This is the phenomenon of evaporation.

Escape of molecules of higher kinetic energy than the average will reduce the mean energy of the liquid, which becomes cooler. To maintain the temperature constant, heat must be added from outside; this is the latent heat of evaporation.

Molecules in the vapour approaching the liquid will be attracted when they come near the surface, will describe curved orbits, and in many cases will be caught by the surface and dragged into the liquid. They experience an acceleration in the field of attraction, and pass into the liquid with increased kinetic energy. Heat is therefore given out on condensation. Eventually, as many molecules leave the liquid as pass back again per second; this is a condition corresponding with the saturation vapour pressure; it is a kinetic equilibrium, due to two opposite processes going on simultaneously at equal rates.

If the forces acting on liquid molecules are as shown in Figure, the work done in bringing a molecule from the interior of the liquid to the surface will be half that required to remove it altogether from the liquid to the vapour space, the latter being measured by the latent heat of evaporation (Stefan, 1886). The translational kinetic energy of the molecule is the same in the liquid and vapour, since it depends only on the temperature.

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