exposed to an electric field. The credit of having put forward a plausible and consistent theory is due to Arrhenius; his memoir1 constitutes one of the most important steps in the history of electro-chemistry.

A solution is always capable of producing what is known as osmotic pressure, and which may, perhaps, best be regarded as a tendency to draw to itself more solvent, and so expand. This phenomenon is most clearly seen in the apparatus known as an osmometer. A porous earthenware jar is filled with copper sulphate solution and placed in a beaker of potassium ferrocyanide; a membranous precipitate of copper ferrocyanide is thus formed in the pores of the earthenware, which is found to possess the peculiar property of allowing water to flow through, but stopping the particles of dissolved substances, such as sugar; it is therefore called a semipermeable partition. The porous jar is now filled with a solution, say of sugar in water, tightly closed by an indiarubber stopper, through which passes the tube of a pressure-gauge, and the whole immersed in water. Since, then, water can enter the jar, but sugar cannot leave, it will be found that water enters, and so raises the pressure. The rise of pressure is an indication of the work that can be done by the sugar when expanding into a larger volume of water, and it will continue till the excess of pressure inside the apparatus just balances that tendency to expansion; then the work required to force more water in against the excess pressure is as great as that which can be done by the expansion, and the action stops. This excess pressure is described as measuring the osmotic pressure of the solution.

The resistance of a dissolved substance to diminution of the volume open to it is shown in other ways. Thus if a solution (say for simplicity aqueous) is frozen, water separates out, leaving the dissolved substance occupying a smaller space than before: the osmotic pressure accordingly opposes such a process, and it is found that the temperature must be lowered more to cause ice to crystallize out of a solution than out of pure water.

Again, if a solution is boiled, it is the solvent that goes away 1 Zeitschr. phys. Chem., 1. 631 (1887).

in form of vapour, leaving the residue more concentrated; this is resisted by osmotic pressure, and the boiling-point consequently raised.

In these ways many measurements of osmotic pressure have been obtained, and van't Hoff was enabled to make the very important and far-reaching generalisation that a solution behaves like a gas. That is, just as gas molecules, being free from each other's action, tend to fly in all directions, and so produce a pressure on the walls of a containing vessel; so molecules of dissolved substance, being practically free to move in all directions where there is any solvent, tend to occupy more and more of the solvent and so produce osmotic pressure on any semipermeable boundary. Van't Hoff followed out this conception in detail by showing that the laws of gases-known as Boyle's, Charles' or Gay-Lussac's, and Avogadro's-are applicable in many instances to solutions.

There are, however, exceptions; these may conveniently be expressed by the ratio (van't Hoff's factor)

i =

observed osmotic pressure

osmotic pressure calculated according to laws of gases

It was found that many common aqueous solutions gave values of i considerably greater than unity.

Arrhenius pointed out that the solutions which gave too high values of i were all electrolytes, and offered this explanation. The osmotic pressure of a solution-say of KC-is calculated according to Avogadro's law on the assumption that the dissolved molecules of salt have the composition indicated by the ordinary chemical formula. If, however, they break up into ions K and Cl', the number of free particles in the solution, is increased, and so, according to Avogadro's law, the osmotic pressure should be. E.g., if out of 100 molecules 86 are dissociated at any time, the total number of particles is 14 undissociated molecules + 86 cations + 86 anions = 186. The osmotic pressure would in this case be 86 per cent. greater than if no dissociation occurred, or i = 1.86.

More generally, if y is the fraction of molecules dissociated (degree of dissociation), and each molecule forms two ions,

i = 1+ y

if each molecule forms three ions Ca(NO3), ZnCl2, Na,CO, etc., i = 1 + 2y

if four (FeCl3, tricarboxylic acids, etc.),

We have, then, a method of calculating the quantity y which enters into our equations, but so far has been unknown. Let us apply the values so obtained to the data arrived at by conductivity measurements. A set of numbers calculated by Jahn from the freezing-points of Loomis and conductivities of Kohlrausch will serve—

The first column gives the concentration in gram molecules per litre; the second, y, as calculated from the freezing-point; the third, the equivalent conductivity; the fourth column serves to show how closely y and A are proportional to each other.

A

we see that if A is proportional to y, U▲ and Uc must be constant; i.e. the actual velocity with which any ion moves must be the same whatever the concentration of the ions. This result may, at least provisionally, be accepted as true, for the resistance to which a moving ion is exposed is due to collision with surrounding molecules, and these, unless the solution is exceptionally concentrated, will be nearly all water; we may expect, therefore, that the mobility will be little influenced by concentration, and the experimental numbers confirm this view.

If, then, A may be taken as a measure of y, it must attain its greatest possible value when the dissociation is complete, i.e. when y = 1. Reverting to the illustration given on p. 59, it is clear that if all the salt molecules are broken up into ions, the conduction due to the quantity (one equivalent) between the plates is the maximum. We have here an explanation of the tendency noted in the previous section, for the molecular conductivity to approach a maximum for very great dilution. It is, in fact, in accordance with what we know of ordinary gaseous dissociation that it should become complete when an indefinitely great volume is occupied by the dissociating substance. It is what may be expected, for dissociation of a molecule may occur spontaneously, but recombination requires the separated parts first to meet; if, then, the parts are so widely scattered that they practically never meet, there will be no recombination, and eventually all the substance will become dissociated.

We shall therefore use the symbol A-i.e. the equivalent conductivity at indefinitely great dilution-for this limiting, maximum value, due to complete dissociation.

A∞ = 96600 (Ua + Uc)

Then

Arrhenius in establishing this formula gives (loc. cit.) a table in which the value of van't Hoff's factor as measured by two osmotic-pressure methods (plasmolysis and freezing-point)

is compared with 1 + (n − 1)y as determined by the conductivity. The table is as follows:

The agreement is not so good as in the previous table for potassium chloride, because there were not such exact data available at the time of Arrhenius' paper. The table, however, brings out very plainly the general relation. Cane sugar is not a conductor at all; it accordingly, in solution, follows the ordinary laws of gases, and give the osmotic pressure calculated from its formula C12H22O11. Acetic acid is a very poor conductor; it becomes considerably dissociated only when extremely dilute (p. 59). The other substances are all strong electrolytes, and give values for van't Hoff's factor very different from unity; and it may be noted that while the binary electrolytes never exceed two, the ternary (Ca(NO3)2,SrCl) approach three, and K,FeC,N, which breaks up into the group FeC,N," and four Kions, exceeds three.

It should be remarked that the simple laws of dilute solutions are not exact when the concentration much exceeds those in the above tables, i.e. when it approaches or exceeds normality. In particular, the conductivity is then an unsafe guide to the degree of dissociation, for the ionic mobilities are then probably different from those in very dilute solution. How great the discrepancy is, it is not at present possible to say. This point is, however, further considered below.

Since the equivalent conductivity is in any case the sum of two terms depending on the cation and anion respectively, particular importance attaches to the limiting values of the ionic conductivities.