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action is much simplified in the case in which the reaction-velocity is enormously great, when practically an instantaneous adjustment of the equilibrium results. Only in this case can the state of the system, which pertains after mixing the different components, be determined merely from knowledge of the equilibrium-constant. This case is realized in the reactions between gases at very high temperatures, which have, however, been little investigated, and especially by the reactions between electrolytes, the so-called ion-reactions. In this latter case, which has been thoroughly studied on account of its fundamental importance for inorganic qualitative and quantitative analysis, the degrees of dissociation of the various electrolytes (acids, bases and salts) are for the most part easily determined by the aid of the freezing-point apparatus, or of measurements of the electric conductivity; and from these data the equilibrium-constant K may be calculated. Moreover, it can be shown that the state of the system can be determined when the equilibrium constants of all the electrolytes which are present in the common solution are known. If this be coupled with the law that the solubility of solid substances, as with vapour-pressures, is independent of the presence of other electrolytes, it is sufficient to know the solubilities of the electrolytes in question, in order to be able to determine which substances must participate in the equilibrium in the solid state, i.e. we arrive at the theory of the formation and solution of precipitates.

As an illustration of the application of these principles, we shall deal with a problem of the doctrine of affinity, namely, that of the relative strengths of acids and bases. It Strength of acids and bases. was quite an early and often repeated observation that the various acids and bases take part with very varying intensity or avidity in those reactions in which their acid or basic nature comes into play. No success attended the early attempts at giving numerical expression to the strengths of acids and bases, i.e. of finding a numerical coefficient for each acid and base, which should be the quantitative expression of the degree of its participation in those specific reactions characteristic of acids and bases respectively. Julius Thomsen and W. Ostwald attacked the problem in a far-seeing and comprehensive manner, and arrived at indisputable proof that the property of acids and bases of exerting their effects according to definite numerical coefficients finds expression not only in salt-formation but also in a large number of other, and indeed very miscellaneous, reactions.

When Ostwald compared the order of the strengths of acids deduced from their competition for the same base, as determined by Thomsen’s thermo-chemical or his own volumetric method, with that order in which the acids arrange themselves according to their capacity to bring calcium oxalate into solution, or to convert acetamide into ammonium acetate, or to split up methyl acetate into methyl alcohol and acetic acid catalytically, or to invert cane-sugar, or to accelerate the mutual action of hydriodic on bromic acid, he found that in all these well-investigated and very miscellaneous cases the same succession of acids in the order of their strengths is obtained, whichever one of the above chemical processes be chosen as measure of these strengths. It is to be noticed that all these chemical changes cited took place in dilute aqueous solution, consequently the above order of acids refers only to the power to react under these circumstances. The order of acids proved to be fairly independent of temperature. While therefore the above investigations afforded a definite qualitative solution of the order of acids according to strengths, the determination of the quantitative relations offered great difficulties, and the numerical coefficients, determined from the separate reactions, often displayed great variations, though occasionally also surprising agreement. Especially great were the variations of the coefficients with the concentration, and in those cases in which the concentration of the acid changed considerably during the reaction, the calculation was naturally quite uncertain. Similar relations were found in the investigation of bases, the scope of which, however, was much more limited.

These apparently rather complicated relations were now cleared up at one stroke, by the application of the law of chemical mass-action on the lines indicated by S. Arrhenius in 1887, when he put forward the theory of electrolytic dissociation to explain that peculiar behaviour of substances in aqueous solution first recognized by van’t Hoff in 1885. The formulae which must be made use of here in the calculation of the equilibrium-relations follow naturally by simple application of the law of mass-action to the corresponding ion-concentrations.

The peculiarities which the behaviour of acids and bases presents, and, according to the theory of Arrhenius, must present—peculiarities which found expression in the very early distinction between neutral solutions on the one hand, and acid or basic ones on the other, as well as in the belief in a polar antithesis between the two last—must now, in the light of the theory of electrolytic dissociation, be conceived as follows:—

The reactions characteristic of acids in aqueous solution, which are common to and can only be brought about by acids, find their explanation in the fact that this class of bodies gives rise on dissociation to a common molecular species, namely, the positively charged hydrogen-ion (H+). The specific chemical actions peculiar to acids are therefore to be attributed to the hydrogen-ion just as the actions common to all chlorides are to be regarded as those of the free chlorine-ions. In like manner, the reactions characteristic of bases in solution are to be attributed to the negatively charged hydroxyl-ions (OH), which result from the dissociation of this class of bodies.

A solution has an acid reaction when it contains an excess of hydrogen-ions, and a basic reaction when it contains an excess of hydroxyl-ions. If an acid and an alkaline solution be brought together mutual neutralization must result, since the positive H-ions and the negative OH-ions cannot exist together in view of the extremely weak conductivity of pure water and its consequent slight electrolytic dissociation, and therefore they must at once combine to form electrically neutral molecules, in the sense of the equation

 +    −
 H + OH= H2O.

In this lies the simple explanation of the “polar” difference between acid and basic solutions. This rests essentially upon the fact that the ion peculiar to acids and the ion peculiar to bases form the two constituents of water, i.e. of that solvent in which we usually study the course of the reaction. The idea of the “strength” of an acid or base at once arises. If we compare equivalent solutions of various acids, the intensity of those actions characteristic of them will be the greater the more free hydrogen-ions they contain; this is an immediate consequence of the law of chemical mass-action. The degree of electrolytic dissociation determines, therefore, the strength of acids, and a similar consideration leads to the same result for bases.

Now the degree of electrolytic dissociation changes with concentration in a regular manner, which is given by the law of mass-action. For if C denote the concentration of the electrolyte and a its degree of dissociation, the above law states that

a²/C(1−a) = Ca²/(1−a) = K.

At very great dilutions the dissociation is complete, and equivalent solutions of the most various acids then contain the same number of hydrogen-ions, or, in other words, are equally strong; and the same is true of the hydroxyl-ions of bases. The dissociation also decreases with increasing concentration, but at different rates for different substances, and the relative “strengths” of acids and bases must hence change with concentration, as was indeed found experimentally. The dissociation-constant K is the measure of the variation of the degree of dissociation with concentration, and must therefore be regarded as the measure of the strengths of acids and bases. So that in this special case we are again brought to the result which was stated in general terms above, viz. that the dissociation-coefficient forms the measure of the reactivity of a dissolved electrolyte. Ostwald’s series of acids, based upon the investigation of the most various reactions, should therefore correspond with the order of their dissociation-constants, and further with the