Similar relations are found to obtain for other solvents, with the single exception of water.

Making use of this observation, Raoult has been able to extend this law and express it in the following terms:

If the molecular weight of any compound be dissolved in one hundred times the molecular weight of any liquid, then the freezing point of this liquid will be depressed by about 0°-62 C.

The majority of inorganic acids and salts when dissolved in water form exceptions to this law.

The molecular weights of other bodies, then, can be determined by aid of Raoult's law in the following manner:

A weight P of the substance is dissolved in a large excess (a quantity L) of a solvent having the molecular weight M, and the reduction in the freezing point E is then determined. If m is the molecular weight to be found, then we have, approximately,

The value of m so obtained is then to be corrected by the stœchiometric composition of the substance in question. It is, as a rule, more convenient to take, instead of m, the smallest quantity q, which represents a whole number of atoms and to calculate the reduction e brought about by this quantity in its solution in 100 M, thus:

Then to try with what whole number x, the value of e, must be multiplied so that the product approximates as nearly as possible to 0°.62; the required molecular weight m is then equal

to x q.

§ 79. Exceptions to Raoult's Law. The exceptions to this law already mentioned are of two kinds. In the first place there are those substances, one molecular weight of which dissolved in 100 molecular weights of water (in round numbers 1800, or more exactly 1796 parts of water) does not give the normal depression of 0°.62, but one which is about 1° C. In order to bring the freezing point to 0°.62 it is necessary to add more water, some 2700 to 3000 parts, or 150 to 160 molecular weights to one molecular weight of the body dissolved. So water behaves as though its molecular weight were greater than the weight represented by the formula H2O. One may imagine in fact that in water near its freezing point molecular aggregates exist, some of the formula H2O, or

2

the formula H6O3, and so on. The existence of such aggregates

would explain the abnormal expansion below 4° C.

Cold water, therefore, may be looked upon as a solution of ice in water, and indeed in the light of a mixture consisting of one molecular weight, H2O2, with one of the molecular weight H2O, or one molecular weight, HO,, to three molecules of the formula H2O.

The second class of exceptions is formed of many acids and salts, the smallest amount of which represented by the stœchiometric formula depresses the freezing point of water much more than the molecular weight of any indifferent organic substance, in some cases the depression being twice as great. According to the above table, for instance, a solution of 58.37 grammes of common salt in a litre of water freezes at-3°.5, whereas a solution containing 341.2 grammes of cane sugar (C12H22O11) would freeze at -1°85. Common salt, therefore, behaves as though it were composed, not of an amount represented by the formula NaCl, but by an amount almost equivalent to two molecules. To explain these facts S. Arrhenius has suggested that the greater portion of the salt exists in solution dissociated into sodium and chlorine. A somewhat similar proposal was formerly made by Clausius to explain the decomposition of its solution in electrolysis (compare §§ 12 and 99). Improbable as this hypothesis may at first sight appear, very weighty arguments have been advanced in support of it.

§ 80. Diffusion.-If the composition of a solution is different in different parts, then even when the temperature throughout is

the same there arises without any external cause a gradual adjustment, inasmuch as all the constituents of the solution are gradually and uniformly distributed throughout the mass.

The movement by which this uniform distribution is effected was styled 'diffusion' by Graham. This diffusion takes place slowly and consequently the substances mixing with one another may often take weeks and perhaps months in passing through a distance of a few decimetres only. Inasmuch as this admixture takes place spontaneously, it must result from the motion of the particles in the liquid state, and must also take place in perfectly homogeneous and uniformly mixed liquids.

The difference between this case and that in which the mixture is not uniform is to be found in the fact that as each of the particles in any given position moves in one direction, an equal number of particles will move in the opposite direction; whereas in the case of mixtures lacking this uniformity, then from that portion of the liquid containing a larger number of particles in a given space, more particles will come in consequence of this excess, assuming that the temperature, and consequently the velocity of the particles on both sides, is equal. The uniform distribution of the concentration will therefore occur the more readily the greater the difference in the contents of the two layers of liquids in contact with each other.

From the considerable amount of heat which is rendered latent in the passage from the solid into the liquid state, one may conclude that the liquid particles have considerable motion imparted to them. That these particles, despite this motion, only move slowly from one position to another may arise from the fact that they interfere with one another's free movement, and consequently only with great difficulty and very slowly are they able to force their way through the crowd of surrounding particles.

The velocity with which a substance diffuses depends, not only upon its nature, but also upon the nature of the solvent, and further upon the temperature. These phenomena have been chiefly investigated for aqueous solutions. One might at first be inclined to believe that the smaller and lighter particles would diffuse more rapidly than the larger and heavier particles. Whilst this frequently is the case, it does not obtain universally,

and especially is this found not to be so with bodies which are very nearly allied to one another. In illustration of this, a comparison may be made by taking an equal number of molecular weights of different substances dissolved in an equal volume of the same solvent. For instance, if the weight in grammes of potassium chloride, 74-4, represented by the formula KCl, of common salt the amount 58.37, of lithium chloride the amount 42.38, represented by their respective formulæ, be dissolved in a litre of water, and the several solutions brought in contact with pure water, then by determining the quantities of each which pass in equal times under otherwise similar conditions into the water we obtain values for the diffusion of these different substances which may be compared with one another. Experiments of this character conducted by J. H. Long have shown that the number of molecular weights of each of these bodies which diffuse in equal times are represented by the values given under d in the following table :

These examples show that potassium salts, despite their greater molecular weights, diffuse more readily than the corresponding sodium compounds, and these latter more readily than the corresponding compounds of lithium. Such examples, which might be considerably increased, show that frequently the large molecules diffuse more readily than the small ones; still, on the other hand, there are substances having very large molecular weights, more especially complicated organic compounds, which diffuse with extraordinary slowness. The substances mentioned

in the foregoing section diffuse at a comparatively rapid rate, and these bodies, according to the hypothesis advanced by Arrhenius, must be supposed to exist in their solutions in a state of dissociation.

§ 81. Osmosis and Dialysis.—If two liquids capable of diffusing into one another are brought, not into immediate contact, but are separated by a septum which is permeable to one or other of the

OSMOSIS AND DIALYSIS

141

constituents and not the other, or only permeable to a lesser degree, then we have produced that remarkable phenomenon to which Dutrochet has applied the term osmosis, from wouós, an impulse. As this term implies, the liquid to which the septum is permeable is driven through in such a way that a considerable inequality of pressure on each side of the separating wall is produced. Substances which swell up when moistened (compare § 72) are the best adapted for such septa. Animal or vegetable membranes, parchment paper, gelatinous precipitates, such as copper ferrocyanide or tanned gelatine, and also caoutchouc and other bodies, are examples of the materials which may be used for such septa; still there are also many substances which act in a similar manner, although they do not swell up when moistened. But what may and what may not pass through such septa is determined by the nature of the septum itself and also of the liquid. The cuticle of plants and animals and also many membranes which are produced from aqueous solutions are permeable by water, but are impermeable to many substances easily or only slightly soluble in water. Caoutchouc does not allow water to pass through it, although many organic substances diffuse readily through this material. The most remarkable fact observed in connection with the phenomenon of osmosis is that the portion of the liquid by which the wall is permeated will force its way through the membrane, despite the greater pressure existing on the opposite side. For instance, supposing an aqueous solution of salt be separated from pure water by a membrane permeable only to water; still, as has been shown by Nollet in 1748, and later by Fisher, Magnus, Dutrochet, and others, the water passes through the membrane to the salt, so that on the salt side an increased pressure is produced. The water therefore moves in opposition to the pressure which has been produced by its own movements. As soon, however, as the pressure reaches a certain amount, then this increase in volume ceases. This maximum pressure, the so-called 'osmotic pressure,' has been studied and measured for different substances by W. Pfeffer, and in many cases has been found to be very considerable and to be proportional to the concentration of the solution. At one time it was believed that this pressure was due to the attraction of the salt or other dissolved solid for the