Blagden, in 1788, showed that the freezing point of a salt solution is lower than that of pure water by an amount which is nearly pro portional to the concentration of the solution, so long as the solution does not approach too nearly to saturation. Other investigators have examined this subject from time to time, and especially Raoult (1882), who worked with many different solutes, and with several sol vents. Raoult's general conclusion was, that in any given solvent the freezing point is low ered by the same amount, by the presence of one gram-molecule of any dissolved substance whatever. This law is somewhat too general, as it has exceptions which cannot be here dis cussed; but it is sufficiently general and suffi ciently accurate to be of material service in the determination of the molecular weights of sub stances whose percentage compositions are known by other methods. Raoult found also that the boiling point of a solvent is raised by the presence of a dissolved substance, the elevation being here also proportional to the concentration of the solution, and being, for any one solvent, independent of the nature of the solute, so long as the same number of gram-molecules of the solute are present in every case. This law is also subject to exceptions; but, like the freezing point law, it is very useful. In the determina tion of molecular weights by either of these methods, it must be remembered that the molec ular weight of a substance may be (and indeed often is) different when the substance is con sidered in different physical states. Beckmann, for example, found that the boiling point of carbon disulphide is raised by sulphur by an amount which indicates that the molecule of sulphur contains eight atoms, when that element is dissolved in carbon disulphide; previous ex periments on the vapor density of sulphur indi cating that in the vaporous condition its mole cule contains six atoms.
In a general way, the ultimate nature of the process of solution is explained by the molecu lar theory of matter (see MOLECULAR THEORY) ; but the molecular theory still leaves much to be desired on this score. We are to think of the solid solute as composed of a system of mole cules, held together by the inter-molecular at tractive forces that cause the parts of solids to cohere to one another. When the solute is placed in the solvent, the external attractive force of the solvent upon the superficial molec ular layers of the solute partially neutralizei the internal forces by which these molecules are held in position, and more or less of the mole cules of the solid escape into the solvent. As the concentration of the solution increases, an increasing number of the dissolved molecules will again come within the range of attraction of the undissolved portion of the solute, in such a way as to be caught by the solute, and tem porarily retained as a part of it. Saturation occurs when the number of molecules regained by the solute in this way in any given time be comes equal to the number lost by it in the same time. Saturation being thus determined by the equality of the molecular exchanges that take place in a given time at the surface of the undissolved solute, it is evident that when no free solid is present there can be no such equality of exchanges. Hence the possibility of a "supersaturated" solution. Indefinite super saturation cannot be experimentally realized, however, for in the ceaseless rearrangement of molecules that takes place in a liquid, it occa sionally happens that a certain number of mole cules of the dissolved substance fortuitously come together in such a way as to serve as a nucleus for the deposition of the solid; and when this occurs, the supersaturated solution spontaneously deposits the excess of solute that it contains.
The molecular condition of the dissolved portion of the solute has been made the subject of much study. When a solute dissolves, its dissolution is almost invariably accompanied by thermal changes, the solution becoming either cooled or heated. By reason of these thermal changes, the phenomena of solutions may be discussed by the aid of the general laws of thermodynamics (q.v.), without making any special hypotheses as to the ultimate molecular nature of the solution. This plan was carried out with great power by Gibbs, in his celebrated paper entitled On the Equilibrium of Hetero geneous Substances) (Transactions of the Con necticut Academy of Sciences, October 1875). His paper is so exceedingly general, and so entirely mathematical, that it is very difficult to read; and hence his methods are not stood, even yet, as widely as they should be. Van't Hoff and Arrhenius, attracted more to the purely physical side of the question, and desir ing to form (if possible) some sort of a mental image of the actual processes that are going on, have developed a theory regarding the nature of the dissolved solute, which is known as the "ionic theory," or as the "electrolytic dissocia• tion theory"; and it is this theory which is most widely accepted at the present time. It has at least the merit of being suggestive, as well as fruitful in its practical results. There is also a so-called "hydrate theory° of solutions, in which the solute, in aqueous solutions, is supposed to form a series of definite hydrates with the sol.' vent; analogous compounds being also formed in non-aqueous solutions. This theory has had many distinguished supporters, among whom the great Russian chemist Mendeleeff may be specially mentioned. In recent years its most devoted apostle is perhaps S. U. Pickering, who has defended it with ingenuity and power. The literature of the hydrate theory is not extensive, however, when compared with that of the ionic theory; and the ionic theory has the decided preference among physical chemists at the pres ent time. A general presentation of the hydrate theory, written by Mr. Pickering, will be found in Watts' Dictionary of Chemistry,' article . "Solutions II." According to the ionic theory of Van't Hoff and Arrhenius, the solute, in a solution, is dis sociated more or less completely into little bodies called "ions"; the dissociation being slight or even zero in some cases, and very ex tensive in others. In a solution (such as that of sugar in water) which does not conduct electricity electrolytically, there is little or no "ionization," or dissociation of the solute mole cules into ions; while in a salt solution, which does conduct electrolytically, the dissociation is large, and may even be almost complete, when the solution is very dilute. The ions are not necessarily identical with the atoms, although they may be so in certain cases. When sulphuric acid and water compose the solution, the sul phuric acid is supposed to be partially disso ciated into hydrogen and "sulphion" (SO4); sulphion being a hypothetical "ion," supposed to be present in the solution, but being admit tedly incapable of existence in the free state. In the same way, sodium chloride, NaC1, when dissolved, is supposed to be more _or less corn pletely dissociated into the ions Na and Cl. It will be observed, however, that the ions are here atoms of sodium and chlorine, and not mole cules; the molecules of these substances having the respective formula Na, and Cl,, and being, therefore, composed, in each case, of two ions joined together. Here, as in the case of sul phion, the ions are seen to be incapable of free existence; because when the sodium and the chlorine are set free, by electrolysis or other wise, it is a molecular aggregate that is ob tained, and not a collection of the free ions. The completeness of the ionization of a solute is affected by various circumstances, but most notably by the degree of concentration of the solution; and the nroportion of the solute mole cules that are dissociated in any given solution may be numerically determined by various methods, for which the special works on solu tions must be consulted. It is important to observe that ions are entirely different things from aelectrons,( the electrons being the ulti mate particles of which the atoms are supposed to be built up, while the ions are either the atoms themselves, or else larger systems com posed of the atoms. (See Exacriton THEORY).
The dissociated ions in a solution are supposed to be endowed with electric charges, the two ions into which any given molecule is separatedbe ing charged oppositely. In the case of sodium chloride, for example, the sodium ion is charged positively and the chlorine ion negatively. Upon the evaporation of the solvent, these ions recombine, their electric charges then neutraliz ing each other, so that the molecule, as a whole, is not electrified. There is no immediate evi dence, in a solution, of the existence, within it, of electrified particles, or but if an elec trical stress is excited across the solution, by inserting the electrodes of a galvanic battery at opposite sides of the containing vessel, the pos tively electrified ions are urged one way, and the negatively electrified ones the other way. Eventually the ions, thus urged along, come in contact with the electrodes themselves, and here the ions discharge their electricities, becoming thereby capable of existing in the free state again, and being, in fact, deposited upon the electrodes, unless prevented by some secondary action within the cell. It will be observed that electrical conduction through an electrolyte is entirely different (according to the ionic theory) from conduction through solid con ductors like metallic wires. The ions in a solu tion transport their charges bodily and pour them out upon the electrodes. The charge of an ion is supposed to be perfectly definite in mag nitude; and hence Faraday's law, that electro lytic decomposition is accurately proportional to the total quantity of electricity passing through the electrolyte, is easily understood. It might be even better to state it in the inverse form; namely, that the quantity of electricity conveyed across an electrolytic solution, under a given electric stress, is accurately proportional to the total quantity of matter set free upon the electrodes. In a solution which does not con duct electricity, the reason that it does not conduct is supposed to be, that the molecules of the solute are not dissociated into ions to any important extent, so that they are incapable of being electrically charged, and are, therefore, in capable of acting as conveyors of electricity. - single example may be given of the appli cation of the molecular theory of solutions to the explanation of chemical equilibrium and mass action. Suppose that m gram-molecules of ethyl alcohol, one gram-molecule of acetic acid and n gram-molecules of water are mixed and the solution is allowed to stand indefinitely. The acetic acid H.C.Fla02, combines with the alcohol, C,H,.OH, to form ethyl acetate, C,H..C.H.02, and water, H20, in accordance with the equation: C,Hs.C21110.+Hz0. But the reaction proceeds very slowly, so that several days elapse before a state of approximate equilibrium is attained; and even then the solution will contain free acetic acid and free alcohol, the amounts of these that remain uncombined depending upon the relative quantities of the several constitu ents that were present in the original solution; — that is, upon m and n. (It is this dependence upon the relative quantities of the reacting sub stances that is understood when we speak of the of mass' in chemical reactions; or, more briefly, of amass Suppose, now, that after a certain time, there have been x gram molecules of ethyl acetate formed in the course of the reaction. This implies that there have also been x gram-molecules of water formed at the same time, and x gram-molecules, each, of acetic acid and of alcohol destroyed. At the instant cantettplated, the number of gram molecules of each of the several substances present in thEl solution will, therefore, be as follows : Of alcohol, ('m—x) ; of acetic acid, (1—x) ; of ethyl acetate, x; and of water, (n+xl. The number of actual molecules of alcohol: and of acetic acid present in the solu tion aj this time will, therefore, be proportional to (m—x) and to (1—x), respectively; and hence the number of chance encounters, during one second, between a molecule or acetic acid and one of alcohol will be proportional to the prod uct of these quantities, or to (m—x) (l—x). We may assume that the number of actual com binations taking place under these circum stances will be proportional to this number of encounters, and to a certain (as yet unknown) coefficient of "affinity' between the two sub stances, which coefficient we will denote by k. The total number of gram-molecules of ethyl acetate formed during the next following sec ond may, therefore, be taken as k(m—x) (1—x). Now if we had started our experiment by mixing ethyl acetate with pure water, we should have found that the water and the ethyl acetate would combine to form alcohol and free acetic acid, as indicated by reading the foregoing chemical equation from right to left; the reaction, in that case also, proceeding only to a definite point, and then ceasing. In the actual case we must conceive of both of these reactions as going on simultaneously. There being x gram-molecules of ethyl acetate pres ent at the proposed instant, and (n+x) gram molecules of water, and the affinity' of water for ethyl acetate being supposed to be measured by a new coefficient, k', we con clude, by a process of reasoning entirely anal ogous to that just explained, that in the next following second the number of gram-mole cules of ethyl acetate that will be decomposed will be 10 (n-i-x)x. When equilibrium is finally established, so that ethyl acetate is no longer formed or decomposed (that is, when it is formed and decomposed with equal rapidity), we have the equation k(m—x) (1—x).= By trying the experiment with known initial quantities of acetic acid, alcohol and water, we could ascertain, directly, the value of x, which now represents the number of gram-molecules of ethyl acetate present when equilibrium is attained; and substitution in the foregoing equation would then give us the ratio of k to k ,— that is, it would give us the ratio of the actual chemical affinities that are involved in this reaction. It has been found, in this way, that if we make (initially) ni=1 and n then when equilibrium is attained, the resulting value of x is M. Substituting this for x, and putting 1 for m and 0 for n, we easily find that With this value of the ratio of k to k', we may write the foregoing equa tion in the form 3xl--(4-1-4m-i-n)x+4m. This is a quadratic equation, and in order to find the final state of equilibrium for any pro portion of alcohol and water to acetic acid in the original solution, we have merely to substitute for m and n their values as given for the primi tive solution, and then solve for x. The equa tion, being a quadratic, has two roots; but no trouble need be had on that account, since it is plain that we must accept that root which would give x-0 when we set The results ob tained from this equation by calculation have been compared with the direct results of ex periment, and the agreement has been found to be quite satisfactory. Many other similar prob lems have also been worked out from theoretical principles and the results verified by direct obser vation, and by the introduction of the methods of the differential and integral calculus it has even been found to be possible to follow the course of such reactions from stage to stage, so that the composition of the solution can be known at every instant, and not merely for the state of final equilibrium.
Arrhenius, 'Theories of Solutions); Jones, The Freezing-Point, Boil ing-Point and Conductivity Methods,' and 'The Nature of Solution' ; Lehfeldt, 'Text-book of Physical Chemistry' ; Nernst, 'Theoretical Chemistry' ; Ostwald, 'Solutions' ; Whetham, 'Solution and Electrolysis.'