In a paper submitted to the Swedish Academy of Sciences, on the 14th of October, 1895, [sic. I think it was 1885, but I need to check. 11/13/96 by John Park] Van't Hoff proved experimentally, as well as theoretically, the following unusually significant generalization of Avogadro's law:

"The pressure which a gas exerts at a given temperature, if a definite number of molecules is contained in a definite volume, is equal to the osmotic pressure which is produced by most substances under the same conditions, if they are dissolved in any given liquid."

Van't Hoff has provd this law in a manner which scarcely leaves any doubt as to its absolute correctness. But a difficulty which still remains to be overcome, is that the law in question holds only for "most substances"; a very considerable number of the aqueous solutions investigated furnishing exceptions, and in the sense that they exert a much greater osmotic pressure than would be required from the law referred to.

If a gas shows such a deviation from the law of Avogadro, it is explained by assuming that the gas is in a state of dissociation. The conduct of chlorine, bromine, and iodine, at higher temperatures is a very well-known example. We regard these substances under such conditions as broken down into simple atoms.

The same expedient may, of course, be made use of to explain the exceptions to Van't Hoff's law; but it has no been put forward up to the present, probably on account of the newness of the subject, the many exceptions known, and the vigourous objections which would be raised from the chemical side to such an explanation. The purpose of the following lines is to show that such an assumption, of the dissociation of certain substances dissolved in water, is strongly supported by the conclusions drawn from the electrical properties of the same substances, and that also the objections to it from the chemical side are diminished on more careful examination.

In order to explain the electrical phenomena, we must assume with Clausius that some of the molecules of an electrolyte are dissociated into their ions, which move independently of one another....If, then, we could calculate what fraction of the molecules of and electrolyte is dissociated into ions, we should be able to calculate the osmotic pressure from Van't Hoff's law.

In former communication "On the Electrical Conductivity of Electrolytes," I have designated those molecules whose ions are independent of one another in their movements, as active; the remaining molecules, whose ions are firmly combined with one another, as inactive. I have also maintained it as probable, that in extreme dilution all the inactive molecules of an electrolyte are transformed into active. This assumption I will make the basis of the calculations now to be carried out. I have designated the relation between the number of active molecules and the sum of the active and inactive molecules, as the activity coefficient. The activity coefficient of an electrolyte at infinite dilution is therefore taken as unity. For smaller dilution it is less than one, and , from the principles established in my work already cited, it can be regarded as equal to the ratio of the actual molecular conductivity of the solution to the maximum limiting value which the molecular conductivity of the same solution approaches with increasing dilution. This obtains for solutions which are not too concentrated (i.e., for solutions in which disturbing conditions, such as internal friction, etc., can be disregarded).

If this activity coefficient ([alpha]) is known, we can calculate as follows the value of the coefficient i tabulated by Van't Hoff. i is the relation between the osmotic pressure actually exerted by a substance and the osomotic pressure which it would exert if it consisted only of inactive (undissociated) molecules. i is evidently equal to the sum of the number of inactive molecules, plus the number of ions, divided by the sum of the inactive and active molecules. If, then, m represents the number of inactive, into which every active molecule dissociates (e.g., k = 2 for KCl, i.e., K and Cl; k = 3 for BaCl₂ and K₂SO₄, i.e. Ba, Cl, Cl, and K, K, SO₄) then we have:

i = (m + kn) / (m + n)

But snce the activity coefficient [alpha] can evidently be written

n / (m + n)

we obtain

i = 1 + (k - 1) [alpha]

Part of the figures below (those in the last column) were calculated from this formula.

On the other hand, i can be calculated from the results of Raoult's experiments on the freezing points of solutions, making use of the principles stated by Van't Hoff. The lowering of the freezing point of water (in degrees Celsius) produced by dissolving a gram-molecule of the given substance in one litre of water is divided by 18.5. The values of i thus calculated are recorded in the next to last column. All the figures given below are calculated on the assumption that one gram of the substance to be investigated was dissolved in one litre of water as was done in the experiments of Raoult.

An especially marked parallelism appears, beyond doubt, on comparing the figures in the last two columns. This shows, a posteriori, that in all probability the assumptions on which I have based the calculation of these figures are, in the main, correct. These assumptions were:

1. That Van't Hoff's law holds not only for most, but for all substances, even for those which have hitherto been regarded as exceptions (electrolytes in aqueous solution).
2. That every electrolyte (in aqueous solution), consists partly of active (in electrical and chemical relation), and partly of inactive molecules, the latter passing into active molecules on increasing the dilution, so that in infinitely dilute solutions only active molecules exist.

The objections which can probably be raised from the chemical side are essentially the same which have been brought forward against the hypothesis of Clausius, and which I have earlier sought to show, were completely untenable. A repetition of these objections would, then, be almost superfluous. I will call attention to only one point. Although the dissolved substance exercises an osmotic pressure against the wall of the vessel, just as if it were partly dissociated into its ions, yet the dissociation with which we are here dealing is not exactly the same as that which exists when, e.g., and ammonium salt is decomposed at a higher temperature. The products of dissociation in the first case, the ions, are charged with very large quantities of electricity of opposite kind, whence certain conditions appear (the incompressibility of electricity), from which it follows that the ions cannot be separated from one another to any great extent without a large expenditure of energy. On the contrary, in ordinary dissociation where no such conditions exist, the products of dissociation can, in general, be separated from one another.

The above two assumptions are of the very widest significance, not only in their theoretical relation...but also, to the highest degree, in a practical sense. If it could, for instance, be shown that the law of Van't Hoff is generally applicable--which I have tried to show is highly probable--the chemist would have at his disposal an extraordinarily convenient means of determining the molecular weight of every substance soluble in a liquid.