Molecular Weight Of Substances In Solutions : Relations Between Different Methods For The Determination Of Molecular Weights Of Dissolved Substances

At first sight it would seem that no two sets of phenomena could be less related than the osmotic pressure and the freezing point, or vapour pressure, of solutions. A little consideration will show, however, that they must be connected. The osmotic pressure is a mechanical measure of the tendency of liquid solvent to mix with a solution and so dilute it. Since the vapour pressure of a solution is lower than that of the pure solvent, the same tendency for solvent to pass over to solution and dilute it is manifested by isothermal distillation. The relation between freezing point lowering and the lowering of vapour pressure has already been explained. In all cases, it is theoretically possible to obtain work by diluting the solution with pure solvent, but of course the two must not simply be allowed to mix. This statement is most evidently true in the case of osmotic pressure, but the difference of vapour pressures could also produce work in a turbine or other suitable engine. In 1886 van't Hoff was able to show that the osmotic pressure, vapour pressure, and freezing point of a solution are closely connected, so that if one is given the others may be calculated without knowing anything beyond the properties of the pure solvent. The three methods are interconnected, and necessarily give the same results.

Let solution be contained in a tube A,

Fig: Osmotic and vapour pressure

closed at the lower end by a semipermeable membrane in contact with solvent in C. In the tube a column of solution ab will be supported by the osmotic pressure. The apparatus is enclosed in a vessel B, which contains only the vapour of the solvent. The vapour pressure is greater at a than at b by the weight of the column ab of vapour. The vapour pressure at a is that, f₀, of the pure solvent in C, whilst the vapour pressure at 6 is that, f, of the solution in A. Hence f₀ - f, the lowering of vapour pressure, increases with the height ab, i.e., with the osmotic pressure, and for small osmotic pressures will be proportional to the latter, i.e., to the concentration of the solution.

The lowering of vapour pressure has been shown to be proportional to the depression of freezing point, hence the latter is proportional to the osmotic pressure, and therefore to the concentration.

Let one molecule of electrolyte on complete ionisation yield x ions. If n gm. mols. are dissolved in 1 kgm. of water, and if α is the degree of ionisation, the solution will contain n(1 - α) gm. mols. of un-ionised substance and nxα gm. mols. of ions, or n [1 + (x - 1) α] gm. mols. of solute in all. If D is the observed depression of freezing point, elevation of boiling point, or osmotic pressure, and A the corresponding normal value (for α = 0), then:

D : Δ = 1 + (x - 1) α : 1;

α = (D - Δ) / Δ (x - 1),

from which the value of a may be calculated for a dilute solution.

On the other hand, the conductivity would, on Arrhenius's theory, be an entirely independent method of finding the ionisation, and the agreement between the value so found and that found by any or all of the other three methods would afford a valuable confirmation of the ionisation hypothesis. The following table shows that there is approximate agreement only.

Substance	Concentration gm. mol./litre.	Ionisation from conductivity %	Ionisation from freezing point %
NaCl	0.001	98.0	98.4
	0.01	93.5	90.5
	0.1	84.1	84.1
K₂SO₄	0.001	92.3	94.2
	0.005	85.8	88.7
	0.05	70.1	72.6
HCl	0.002	100.0	98.4
	0.01	98.9	95.8
	0.1	93.9	88.6

Protein crystallography
Chemistry guide
Molecular Weight Of Substances In Solutions
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