François-Marie Raoult (1830-1901)

General Law of the Freezing of Solutions

If A is the lowering of the freezing point due to the presence of 1 gram of a substance dissolved in 100 grams of solvent; M the molecular weight of the dissolved substance, supposedly anhydrous, calculated according to the atomic formula H = 1, O = 16 ...; T its molecular lowering of the freezing point (that is, the lowering of the freezing point caused by one molecule dissolved in 100 gram of liquid), then, if the solutions are dilute,
MA = T.

My previous studies have shown that, in the same liquid, the molecular lowering, T, is a nearly constant number for very numerous groups of compounds of the same type. Since then I have made new experiments using as solvents the following compounds whose freezing points can always be determined with extreme precision.

	Freezing Point,		Freezing Point,
	Degrees		Degrees
Water	0.00	Ethylene dibromide	7.92
Benzene	4.96	Formic Acid	8.52
Nitrobenzene	5.28	Acetic acid	16.75

All these liquids except water contract when solidifying.

Lack of space prevents me from giving details here of the extremely numerous experiments made with these solvents. I will limit myself to giving a summary. Nevertheless, it is possible to judge of the number and variety of dissolved compounds as well as the degree of concordance of the results from the table of 60 analogous experiments made on solutions of organic compounds in water and in benzene published in the Comptes Rendus of the Academy (June 5 and July 24, 1882). My new studies confirm the former and permit the formulation of the law of freezing of solvents in a general and complete manner.

Acetic acid.--[1] The experiments done with this solvent involved more than 60 compounds of all kinds. All the organic substances without exception and, in addition, potassium acetate, the acetates of ammonia, aniline, quinine, strychnine, brucine, codeine, the protochloride of sulfur[2], the chloride of arsenic, the bichloride of tin[3], hydrogen sulfide, and sulfurous acid, produce in acetic acid a molecular lowering of freezing point all between 36 and 40, most often near 39. Only some compounds, all mineral in nature, produce in acetic acid a different molecular lowering; these are sulfuric and hydrochloric acid, calcium nitrate, and magnesium acetate. For these bodies, the molecular lowering is near 19; it is, thus, equal to half of the preceding.

Formic acid, used as a solvent, yields completely similar results.

In the great majority of cases, the molecular lowering is near 28 and, in exceptional instances, it approaches 14.

Benzene.-- All the organic substances (with the exception of some alcohols and acids) and all the metalloidal chlorides produce in benzene molecular lowerings all between 47 and 51; mean 49. As for methyl and ethyl alcohol and formic, acetic, valerianic, and benzoic acids, they produce molecular lowerings which varied from 28 to 27 and whose mean is 25 [sic]: this is half of the normal lowering.

In nitrobenzene and ethylene dibromide, used as solvents, all the molecular lowerings equally approach two values, one of which is twice the other; and they are produced by the same bodies as in benzene. These values are: for nitrobenzene, 68 and 34, and for ethylene dibromide, 117 and 58.

Water used as a solvent.-- The results presented by the solutions made with water are less consistent than those observed with the other solvents, at least with respect to alkali and alkaline-earth salts; they produce a molecular lowering between 33 and 43. The chlorides of barium and strontium, by contrast, give about 50. The great majority of results obtained with more than 60 mineral species approaches 37.

On the other hand, the sulfates of magnesium, meta-phosphoric, hydrogen sulfide, and all the organic materials, without exception, produce a molecular lowering much more constant, between 17 and 20; mean, 18.5.

Here too, then, one of the lowerings, is twice the other.

Conclusions. These experiments, in which more than two hundred compounds have been dissolved in six different liquids, are very numerous and agree in establishing the following:

All bodies, on dissolving in a definite liquid compound which can solidify, lower the freezing point.

In all liquids, the molecular lowering of the freeing point due to the different compounds approaches two values, invariable for each liquid, of which one is double the other. The larger is more often found and constitutes the normal molecular lowering. The lesser corresponds to the case where the molecules of the dissolved body are joined two to two.

The normal molecular lowering of the freezing point varies with the nature of the solvent: it is 37 for water, 28 for formic acid, 39 for acetic acid, 49 for benzene, 70.5 for nitrobenzene, and 117 for ethylene dibromide. If each of these numbers is divided by the molecular weight of the solvent to which it relates (which is equivalent to reducing the results to the case where one molecule of dissolved body will be contained in 100 molecules of the solvent), the quotients differ little from each other, except for water. Thus

Water	37:18 = 2.050	Benzene	49:78 = 0.628
Formic acid	28:46 = 0.608	Nitrobenzene	70.5:123 = 0.600
Acetic acid	39:60 = 0.650	Ethylene dibromide	117:188 = 0.623

To make water agree with the general rule, it is enough to admit that the physical molecules which compose it are formed from three chemical molecules joined together, at least near the freezing point. Then, indeed, this solvent gives 37:18 x [sic] 3 = 0.685, a number which does not differ much from 0.622 degrees, the mean of the five others. The following law can then be formulated:

One molecule of any compound dissolved in 100 molecules of any liquid of a different nature lowers the freezing point of this liquid by a nearly constant quantity, close to 0.62 degrees.

This statement is altogether general if we admit that the physical molecules which act here can be formed of two, and exceptionally, three, chemical molecules.

[2][The protochloride of sulfur is probably S₂Cl₂, the sulfur chloride with the lowest Cl:S ratio. --CJG]

[3][The "bichloride" of tin is probably SnCl₄ (the tin chloride with the higher Cl:Sn ratio), not SnCl₂ (tin dichloride). --CJG]