Kinetic Theory : Molecular Weights Of Liquids

Since the particles in a liquid move about as individuals, they possess definite molecular weights. Molecules of more than one kind may, of course, be present: those formed by the combination of simple molecules are called associated molecules e.g., (H₂O)_x.

Attempts have been made to determine the molecular weights of liquids by measurements of surface tension. The product

where σ = surface tension, V - molecular volume = M/D (D = density), is proportional to the surface energy of 1 mol of liquid in the form of a sphere, and was called by Eötvös and by Ramsay and Shields the molecular surface energy. This decreases with temperature, t° C., according to the equation:

where k is a constant and t_c is the critical temperature. For most liquids k is approximately 2.12, but in some cases, as with water, alcohol, and acetic acid, it is smaller.

For bromine, σ =44 at 13° C., t_c = 302.2; M= 16o(Br2), D = 3.12;

Since this is very nearly 2.12, bromine can be assumed to be normal. For water, σ = 73 at 15° C., t_c = 370, M = 18, D = 1, hence

k =73 x (18)^2/3/(370 - 15 - 6) = 1.497.

This is smaller than the normal value, 2.12. If we assume the molecular weight of water to be x*18, where x = degree of association, we may expect to get the normal value of k (since 18x is the true molecular weight), hence by division:

X^2/3 = 2.12/1.497; x = 1.69.

This result indicates that liquid water is associated.

In some cases (e.g., fused metals) the method leads to values of x smaller than 1, which are difficult to interpret.

Another method which indicates association is the value of the Trouton coefficient, ML_e/T₀, where L_e is the latent heat of evaporation, and T₀ the boiling point in degrees Abs. For normal liquids this is about 21, for associated liquids it is larger, e.g., 26.9 for alcohol and 25.9 for water.

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