EXTENSION OF THE GAS LAWS TO EMULSIONS It should be borne in mind in the first place how, thanks to Van't Hoff, the Gas laws, and especially Avogadro's law, became recognized as applicable to dilute solutions. The pressure exerted by a gas on its containing walls becomes, in the case of a dissolved substance, the osmotic pressure exerted on semi-permeable walls which allow the solvent to pass, but stop the solute. A membrane of copper ferrocyanide separating aqueous sugar solution from pure water is an example.
Pfeffer's measurements show that equilibrium exists only when a definite excess pressure is established on the side where the sugar is, and Van't Hoff has pointed out that the amount of this excess pressure (osmotic pressure) is precisely the same as the pressure which would be exerted, in accordance with Avogadro's law, on the walls of the vessel containing the sugar solution, if the sugar contained therein could alone occupy the vessel in the gas eous state. Hence it is probable that the same thing will apply to any dissolved substance; and there is no need even to cite the thermodynamical arguments by which Van't Hoff supported this generalization, nor to make any other measurements of osmotic pressure, for Arrhenius showed that any substance which, in solu tion, obeys the well-known laws of Raoult as regards its freezing point and vapour pressure, will, as a necessary consequence, exert the pressure predicted by Van't Hoff on any boundary-wall which stops it without stopping its solvent. In short, Raoult's laws, which are founded on a very large number of measurements, are logically equivalent to Van't Hoff's laws; the latter embodies the extension of Avogadro's law to solutions, and we can now say : equal numbers of molecules, of any kind whatever, either in the gaseous state or dissolved, exert (at the same temperature and in equal volumes) equal pressures on the walls which confine them.
This law applies to heavy and to light molecules indiscrimi nately ; thus the quinine molecule, which contains over i oo atoms, produces neither more nor less effect when it impinges against the walls than the light hydrogen molecule which contains only two atoms. Perrin suggests that this law may also apply to even the visible particles in stable emulsions, with the result that each of the particles agitated by Brownian movement may count as a molecule when it happens to strike a confining wall.
Let us then assume that we can measure the osmotic pressure exerted as a result of their Brownian movement by particles of equal size on any surface element which stops them but allows water to pass, e.g., blotting paper. Suppose, also, that we can count the number of particles per unit volume in the immediate vicinity of the surface element, so as to know their concentration. This number, n, also designates the concentration of molecules in any gas (let us say hydrogen) which would exert the same pres sure on the walls of the vessel in which it was contained. If, for instance, the osmotic pressure thus measured is the ioo-millionth of a dyne per square centimetre, we know that, under normal conditions (when the pressure is one million dynes per square centimetre), one cubic centimetre of hydrogen will contain ioo million million times n molecules (i . Also, one gram-mole cule (22,412 cu.cm. in the gaseous state at N.T.P.) will contain 22,412 times this number of molecules; the product will be Avo gadro's Number. This is quite simple; but how are we to measure the extremely minute osmotic pressure exerted by an emulsion? As a matter of fact, this will not be necessary, any more (as we have just explained) than it is to measure the osmotic pres sure of a solution in order to make sure that the solution obeys the gas laws. It will be quite sufficient to demonstrate, in the case of emulsions, some property which can be treated experimentally, and which is the logical outcome of these laws. Jean Perrin found such a property (1908) when he extended to certain emulsions the well-known law that in a vertical column of gas in equilibrium the density decreases as altitude increases.