[48] This amount is usually expressed by the weight of the substance dissolved per 100 parts by weight of water. Probably it would be better to express it by the quantity of the substance in a definite volume of the solution—for instance, in a litre—or by the ratios of the number of molecules of water and of the substance dissolved.
[49] The variation of the vapour tension of solutions has been investigated by many. The best known researches are those of Wüllner in Germany (1858–1860) and of Tamman in Russia (1887). The researches on the temperature of the formation of ice from various solutions are also very numerous; Blagden (1788), Rüdorff (1861), and De Coppet (1871) established the beginning, but this kind of investigation takes its chief interest from the work of Raoult, begun in 1882 on aqueous solutions, and afterwards continued for solutions in various other easily frozen liquids—for instance, benzene, C6H6 (melts at 4·96°), acetic acid, C2H4O2 (16·75°), and others. An especially important interest is attached to these cryoscopic investigations of Raoult in France on the depression of the freezing point, because he took solutions of many well-known carbon-compounds and discovered a simple relation between the molecular weight of the substances and the temperature of crystallisation of the solvent, which enabled this kind of research to be applied to the investigation of the nature of substances. We shall meet with the application of this method later on (see also Chapter [VII].), and at present will only cite the deduction arrived at from these results. The solution of one-hundredth part of that molecular gram weight which corresponds with the formula of a substance dissolved (for example, NaCl = 58·5, C2H6O = 46, &c.) in 100 parts of a solvent lowers the freezing point of its solution in water 0·185°, in benzene 0·49°, and in acetic acid O·39°, or twice as much as with water. And as in weak solutions the depression or fall of freezing point is proportional to the amount of the substance dissolved, it follows that the fall of freezing point for all other solutions may be calculated from this rule. So, for instance, the weight which corresponds with the formula of acetone, C3H6O is 58; a solution containing 2·42, 6·22, and 12·35 grams of acetone per 100 grams of water, forms ice (according to the determinations of Beckmann) at 0·770°, 1·930°, and 3·820°, and these figures show that with a solution containing 0·58 gram of acetone per 100 of water the fall of the temperature of the formation of ice will be 0·185°, 0·180°, and 0·179°. It must be remarked that the law of proportionality between the fall of temperature of the formation of ice, and the composition of a solution, is in general only approximate, and is only applicable to weak solutions (Pickering and others).
We will here remark that the theoretical interest of this subject was strengthened on the discovery of the connection existing between the fall of tension, the fall of the temperature of the formation of ice, of osmotic pressure (Van't Hoff, Note [19]), and of the electrical conductivity of solutions, and we will therefore supplement what we have already said on the subject by some short remarks on the method of cryoscopic investigations, although the details of the subject form the subject of more special works on physical chemistry (such as Ostwald's Lehrbuch der allgemeinen Chemie, 1891–1894, 2 vols.)
In order to determine the temperature of the formation of ice (or of crystallisation of other solvents), a solution of known strength is prepared and poured into a cylindrical vessel surrounded by a second similar vessel, leaving a layer of air between the two, which, being a bad conductor, prevents any rapid change of temperature. The bulb of a sensitive and corrected thermometer is immersed in the solution, and also a bent platinum wire for stirring the solution; the whole is then cooled (by immersing the apparatus in a freezing mixture), and the temperature at which ice begins to separate observed. If the temperature at first falls slightly lower, it nevertheless becomes constant when ice begins to form. By then allowing the liquid to get just warm, and again observing the temperature of the formation of ice, an exact determination may be arrived at. It is still better to take a large mass of solution, and induce the formation of the first crystals by dropping a small lump of ice into the solution already partially over-cooled. This only imperceptibly changes the composition of the solution. The observation should be made at the point of formation of only a very small amount of crystals, as otherwise the composition of the solution will become altered from their separation. Every precaution must be taken to prevent the access of moisture to the interior of the apparatus, which might also alter the composition of the solution or properties of the solvent (for instance, when using acetic acid).
With respect to the depression of dilute solutions it is known—(1) That the depression increases in almost direct proportion to the amount of the substance in solution (always per 100 parts of water), for example, for KCl when the solution contains 1 part of salt (per 100 parts of water) the depression = 0·45°, when the solution contains 2 parts of salt = 0·90°, with 10 parts of salt = 4·4°. (2) The greater the molecular weight expressed by the formula (see Chapter [VII].), and designated by M, the less, under other similar conditions, will be the depression d, and therefore if the concentration of a solution (the amount by weight of substance dissolved per 100 parts of water) be designated by p, then the fraction M d / p or the molecular depression for a given class of substances will be a constant quantity; for example, in the case of methyl alcohol in water 17·3, for acetone about 18·0, for sugar about 18·5. (3) In general the molecular depression for substances whose solutions do not conduct an electric current is about 18·5, while for acids, salts, and such like substances whose solutions do conduct electricity, it is i times greater; for instance, for HCl, KI, HNO3, KHO, &c., about 36 (i is nearly 2), for borax about 66, and so on where i varies in the same manner as it does in the case of the osmotic pressure of solutions (Note [19]). (4) Different solvents (water, acetic acid, benzene, &c.) have each their corresponding constants of molecular depression (which have a certain remote connection with their molecular weight); for example, for acetic acid the molecular depression is about 39 and not 19 (as it is for water), for benzene 49, for methyl alcohol about 17, &c. (5) If the molecular weight M of a substance be unknown, then in the case of non-conductors of electricity or for a given group, it may be found by determining the depression, d, for a given concentration, p; for example, in the case of peroxide of hydrogen, which is a non-conductor of electricity, the molecular weight, M, was found to be nearly 34, i.e. equal to H2O2.
Similar results have also been found for the fall in the vapour tension of solutions (Note [51]), and for the rise of their boiling points (hence these data may also serve for determining the molecular weight of a substance in solution, as is shortly described in Chapter VII., Note [27 bis]). And as these conclusions are also applicable in the case of osmotic pressure (Note [19]), and a variation in the magnitude of i, in passing from solutions which do not conduct an electric current to those which do conduct electricity is everywhere remarked, so it was natural to here seek that causal connection which Arrhenius (1888), Ostwald, and others expected to find in the supposition that a portion of the substance of the electrolyte is already decomposed in the very act of solution, into its ions (for example, NaCl into Na and Cl), or into the atoms of those individual substances which make their appearance in electrolysis, and in this way to explain the fact that i is greater for those bodies which conduct an electric current. We will not consider here this supposition, known as the hypothesis of ‘electrolytic dissociation,’ not only because it wholly belongs to that special branch—physical chemistry, and gives scarcely any help towards explaining the chemical relations of solutions (particularly their passage into definite compounds, their reactions, and their very formation), but also because—(1) all the above data (for constant depression, osmotic pressure, &c.) only refer to dilute solutions, and are not applicable to strong solutions; whilst the chemical interest in strong solutions is not less than in dilute solutions, and the transition from the former into the latter is consecutive and inevitable; (2) because in all homogeneous bodies (although it may be insoluble and not an electrolyte) a portion of the atoms may he supposed (Clausius) to be passing from one particle to another (Chapter X., Note [28]), and as it were dissociated, but there are no reasons for believing that such a phenomenon is proper to the solutions of electrolytes only; (3) because no essential mark of difference is observed between the solution of electrolytes and non-conductors, although it might be expected there would be according to Arrhenius' hypothesis; (4) because it is most reasonable to suppose the formation of new, more complex, but unstable and easily dissociated compounds in the act of solution, than a decomposition, even partial, of the substances taken; (5) because if Arrhenius' hypothesis be accepted it becomes necessary to admit the existence in solutions of free ions, like the atoms Cl or Na, without any apparent expenditure of the energy necessary for their disruption, and if in this case it can be explained why i then = 2, it is not at all clear why solutions of MgSO4 give i = 1, although the solution does conduct an electric current; (6) because in dilute solutions, the approximative proportionality between the depression and concentration may be recognised, while admitting the formation of hydrates, with as much right as in admitting the solution of anhydrous substances, and if the formation of hydrates be recognised it is easier to admit that a portion of these hydrates is decomposed than to accept the breaking-up into ions; (7) because the best conductors of electricity are solutions like the sulphates in which it is necessary to recognise the formation of associated systems or hydrates; (8) because the cause of electro-conductivity can be sooner looked for in this affinity and this combination of the substance dissolved with the solvent, as is seen from the fact, that (D. P. Konovaloff) neither aniline nor acetic acid alone conduct an electric current, a solution of aniline in water conducts it badly (and here the affinity is very small), while a solution of aniline in acetic acid forms a good electrolyte, in which, without doubt, chemical forces are acting, bringing aniline, like ammonia, into combination with the acetic acid; which is evident from the researches made by Prof. Konovaloff upon mixtures (solutions) of aniline and other amines; and, lastly, (9) because I, together with many of the chemists of the present day, cannot regard the hypothesis of electrolytic dissociation in the form given to it up to now by Arrhenius and Ostwald, as answering to the sum total of the chemical data respecting solutions and dissociation in general. Thus, although I consider it superfluous to discuss further the evolution of the above theory of solutions, still I think that it would he most useful for students of chemistry to consider all the data referring to this subject, which can be found in the Zeitschrift für physikalische Chemie, 1888–1894.
[50] This fact, which was established by Gay-Lussac, Pierson, and v. Babo, is confirmed by the latest observations, and enables us to express not only the fall of tension (p - p′) itself, but its ratio to the tension of water ( p - p′ / p ). It is to be remarked that in the absence of any chemical action, the fall of pressure is either very small, or does not exist at all (note [33]), and is not proportional to the quantity of the substance added. As a rule, the tension is then equal, according to the law of Dalton, to the sum of the tensions of the substances taken. Hence liquids which are insoluble in each other (for example, water and chloride of carbon) present a tension equal to the sum of their individual tensions, and therefore such a mixture boils at a lower temperature than the more volatile liquid (Magnus, Regnault).
[51] If, in the example of common salt, the fall of tension be divided by the tension of water, a figure is obtained which is nearly 105 times less than the magnitude of the fall of temperature of formation of ice. This correlation was theoretically deduced by Goldberg, on the basis of the application of the mechanical theory of heat, and is repeated by many investigated solutions.
[52] Fritzsche showed that solutions of certain colouring matters yield colourless ice, which clearly proves the passage of water only into a solid state, without any intermixture of the substance dissolved, although the possibility of the admixture in certain other cases cannot be denied.
[53] As the solubility of certain substances (for example, coniine, cerium sulphate, and others) decreases with a rise of temperature (between certain limits—see, for example, note 24), so these substances do not separate from their saturated solutions on cooling but on heating. Thus a solution of manganese sulphate, saturated at 70°, becomes cloudy on further heating. The point at which a substance separates from its solution with a change of temperature gives an easy means of determining the co-efficient of solubility, and this was taken advantage of by Prof. Alexéeff for determining the solubility of many substances. The phenomenon and method of observation are here essentially the same as in the determination of the temperature of formation of ice. If a solution of a substance which separates out on heating be taken (for example, the sulphate of calcium or manganese), then at a certain fall of temperature ice will separate out from it, and at a certain rise of temperature the salt will separate out. From this example, and from general considerations, it is clear that the separation of a substance dissolved from a solution should present a certain analogy to the separation of ice from a solution. In both cases, a heterogeneous system of a solid and a liquid is formed from a homogeneous (liquid) system.