Barium sulphate, BaSO4, which is insoluble in water, when fused with sodium carbonate, Na2CO3, gives, but not completely, barium carbonate, BaCO3, (also insoluble), and sodium sulphate, Na2SO4. If a solution of sodium carbonate acts on precipitated barium sulphate, the same decomposition is also effected (Dulong, Rose), but it is restricted by a limit and requires time. A mixture of sodium carbonate and sulphate is obtained in the solution and a mixture of barium carbonate and sulphate in the precipitate. If the solution be decanted off and a fresh solution of sodium carbonate be poured over the precipitate, then a fresh portion of the barium sulphate passes into barium carbonate, and so by increasing the mass of sodium carbonate it is possible to entirely convert the barium sulphate into barium carbonate. If a definite quantity of sodium sulphate be added to the solution of sodium carbonate, then the latter will have no action whatever on the barium sulphate, because then a system in equilibrium determined by the reverse action of the sodium sulphate on the barium carbonate and by the presence of both sodium carbonate and sulphate in the solution, is at once arrived at. On the other hand, if the mass of the sodium sulphate in the solution be great, then the barium carbonate is reconverted into sulphate until a definite state of equilibrium is attained between the two opposite reactions, producing barium carbonate by the action of the sodium carbonate and barium sulphate by the action of the sodium sulphate.
Another most important principle of Berthollet's teaching is the existence of a limit of exchange decomposition, or the attainment of a state of equilibrium. In this respect the determinations of Malaguti (1857) are historically the most important. He took a mixture of solutions of equivalent quantities of two salts, MX and NY, and judged the amount of the resulting exchange from the composition of the precipitate produced by the addition of alcohol. When, for example, zinc sulphate and sodium chloride (ZnSO4 and 2NaCl) were taken, there were produced by exchange sodium sulphate and zinc chloride. A mixture of zinc sulphate and sodium sulphate was precipitated by an excess of alcohol, and it appeared from the composition of the precipitate that 72 per cent. of the salts taken had been decomposed. When, however, a mixture of solutions of sodium sulphate and zinc chloride was taken, the precipitate presented the same composition as before—that is, about 28 per cent. of the salts taken had been subjected to decomposition. In a similar experiment with a mixture of sodium chloride and magnesium sulphate, 2NaCl + MgSO4 or MgCl2 + Na2SO4, about half of the metals underwent the decomposition, which may be expressed by the equation 4NaCl + 2MgSO4 = 2NaCl + MgSO4 + Na2SO4 + MgCl2 = 2Na2SO4 + 2MgCl2. A no less clear limit expressed itself in another of Malaguti's researches when he investigated the above-mentioned reversible reactions of the insoluble salts of barium. When, for example, barium carbonate and sodium sulphate (BaCO3 + Na2SO4) were taken, then about 72 per cent. of the salts were decomposed, that is, were converted into barium sulphate and sodium carbonate. But when the two latter salts were taken, then about 19 per cent. of them passed into barium carbonate and sodium sulphate. Probably the end of the reaction was not reached in either case, because this would require a considerable time and a uniformity of conditions attainable with difficulty.
Gladstone (1855) took advantage of the colour of solutions of different ferric salts for determining the measure of exchange between metals. Thus a solution of ferric thiocyanate has a most intense red colour, and by making a comparison between the colour of the resulting solutions and the colour of solutions of known strength it was possible to judge to a certain degree the quantity of the thiocyanate formed. This colorimetric method of determination has an important significance as being the first in which a method was applied for determining the composition of a solution without the removal of any of its component parts. When Gladstone took equivalent quantities of ferric nitrate and potassium thiocyanate—Fe(NO3)3 + 3KCNS—only 13 per cent. of the salts underwent decomposition. On increasing the mass of the latter salt the quantity of ferric thiocyanate formed increased, but even when more than 300 equivalents of potassium thiocyanate were taken a portion of the iron still remained as nitrate. It is evident that the affinity acting between Fe and NO3 and between K and CNS on the one hand, is greater than the affinity acting between Fe and CNS, together with the affinity of K for NO3, on the other hand. The investigation of the variation of the fluorescence of quinine sulphate, as well as the variation of the rotation of the plane of polarisation of nicotine, gave in the hands of Gladstone many proofs of the entire applicability of Berthollet's doctrine, and in particular demonstrated the influence of mass which forms the chief distinctive feature of the teaching of Berthollet, teaching little appreciated in his own time.
At the beginning of the year 1860, the doctrine of the limit of reaction and of the influence of mass on the process of chemical transformations received a very important support in the researches of Berthelot and P. de Saint-Gilles on the formation of the ethereal salts RX from the alcohols ROH and acids HX, when water is also formed. This conversion is essentially very similar to the formation of salts, but differs in that it proceeds slowly at the ordinary temperature, extending over whole years, and is not complete—that is, it has a distinct limit determined by a reverse reaction; thus an ethereal salt RX with water gives an alcohol ROH and an acid HX—up to that limit generally corresponding with two-thirds of the alcohol taken, if the action proceed between molecular quantities of alcohol and acid. Thus common alcohol, C2H5OH, with acetic acid, HC2H3O2, gives the following system rapidly when heated, or slowly at the ordinary temperature, ROH + HX + 2RX + 2H2O, whether we start from 3RHO + 3HX or from 3RX + 3H2O. The process and completion of the reaction in this instance are very easily observed, because the quantity of free acid is easily determined from the amount of alkali requisite for its saturation, as neither alcohol nor ethereal salt acts on litmus or other reagent for acids. Under the influence of an increased mass of alcohol the reaction proceeds further. If two molecules of alcohol, RHO, be taken for every one molecule of acetic acid, HX, then instead of 66 p.c., 83 p.c. of the acid passes into ethereal salt, and with fifty molecules of RHO nearly all the acid is etherised. The researches of Menschutkin in their details touched on many important aspects of the same subject, such as the influence of the composition of the alcohol and acid on the limit and rate of exchange—but these, as well as other details, must be looked for in special treatises on organic and theoretical chemistry. In any case the study of etherification has supplied chemical mechanics with clear and valuable data, which directly confirm the two fundamental propositions of Berthollet; the influence of mass, and the limit of reaction—that is, the equilibrium between opposite reactions. The study of numerous instances of dissociation which we have already touched on, and shall again meet with on several occasions, gave the same results. With respect to double saline decompositions, it is also necessary to mention the researches of Wiedemann on the decomposing action of a mass of water on the ferric salts, which could be determined by measuring the magnetism of the solutions, because the ferric oxide (soluble colloid) set free by the water is less magnetic than the ferric salts.
A very important epoch in the history of Berthollet's doctrine was attained when, in 1867, the Norwegian chemists, Guldberg and Waage, expressed it as an algebraical formula. They defined the active mass as the number of molecules contained in a given volume, and assumed, as follows from the spirit of Berthollet's teaching, that the action between the substances was equal to the product of the masses of the reacting substances. Hence if the salts MX and NY be taken in equivalent quantities (m = 1 and n = 1) and the salts MY and NX are not added to the mixture but proceed from it, then if k represent the coefficient of the rate of the action of MX on NY and if k′ represent the same coefficient for the pair MY and NX, then we shall have at the moment when the decomposition equals x a measure of action for the first pair: k(1 - x)(1 - x) and for the second pair k′xx, and a state of equilibrium or limit will be reached when k(1 - x)2 = k′x2, whence the ratio k/k′ = [x/(1 - x)]2. Therefore in the case of the action of alcohol on an acid, when x = ⅔, the magnitude k/k′ = 4, that is, the reaction of the alcohol on the acid is four times as fast as that of the ethereal salt on water. If the ratio k/k′ be known, then the influence of mass may be easily determined from it. Thus if instead of one molecule of alcohol two be taken, then the equation will be k(2 - x)(1 - x) = k′xx, whence x = 0·85 or 85 percent., which is close to the result of experiment. If 300 molecules of alcohol be taken, then x proves to be approximately 100 per cent., which is also found to be the case by experiment.[26]
But it is impossible to subject the formation of salts to any process directly analogous to that which is so conveniently effected in etherification. Many efforts have, however, been made to solve the problem of the measure of reaction in this case also. Thus, for example, Khichinsky (1866), Petrieff (1885), and many others investigated the distribution of metals and haloid groups in the case of one metal and several haloids taken in excess, as acids; or conversely with an excess of bases, the distribution of these bases with relation to an acid; in cases where a portion of the substances forms a precipitate and a portion remains in solution. But such complex cases, although they in general confirm Berthollet's teaching (for instance, a solution of silver nitrate gives some silver oxide with lead oxide, and a solution of nitrate of lead precipitates some lead oxide under the action of silver oxide, as Petrieff demonstrated), still, owing to the complexity of the phenomena (for instance, the formation of basic and double salts), they cannot give simple results. But much more instructive and complete are researches like those made by Pattison Muir (1876), who took the simple case of the precipitation of calcium carbonate, CaCO3, from the mixture of solutions of calcium chloride and sodium or potassium carbonate, and found in this case that not only was the rate of action (for example, in the case of CaCl2 + Na2CO3, 75 per cent. of CaCO3 was precipitated in five minutes, 85 per cent. in thirty minutes, and 94 per cent. in two days) determined by the temperature, relative mass, and amount of water (a large mass of water decreases the rate), but that the limit of decomposition was also dependent on these influences. However, even in researches of this kind the conditions of reaction are complicated by the non-uniformity of the media, inasmuch as a portion of the substance is obtained or remains in the form of a precipitate, so that the system is heterogeneous. The investigation of double saline decompositions offers many difficulties which cannot be considered as yet entirely overcome. Although many efforts have long since been made, the majority of the researches were carried on in aqueous solutions, and as water is itself a saline compound and able to combine with salts and enter into double decomposition with them, such reactions taking place in solutions in reality present very complex cases.[27] In this sense the reaction between alcohols and acids is much more simple, and therefore its significance in confirmation of Berthollet's doctrine is of particular importance. The only cases which can be compared with these reactions for simplicity are those exchange decompositions investigated by G. G. Gustavson, which take place between CCl4 and RBrn on the one hand, and CBr4 and RCln on the other. This case is convenient for investigation inasmuch as the RCln and RBrn taken (such as BCl3, SiCl4, TiCl4, POCl3, and SnCl4) belong to those substances which are decomposed by water, whilst CCl4 and CBr4 are not decomposed by water; and therefore, by heating, for instance, a mixture of CCl4 + SiBr4 it is possible to arrive at a conclusion as to the amount of interchange by treating the product with water, which decomposes the SiBr4 left unchanged and the SiCl4 formed by the exchange, and therefore by determining the composition of the product acted on by the water it is possible to form a conclusion as to the amount of decomposition. The mixture was always formed with equivalent quantities—for instance, 4BCl3 + 3CBr4. It appeared that there was no exchange whatever on simple intermixture, but that it proceeded slowly, when the mixture was heated (for example, with the mixture above mentioned at 123° 4·86 per cent. of Cl was replaced by Br after 14 days' heating, and 6·83 per cent. after 28 days, and 10·12 per cent. when heated at 150° for 60 days). A limit was always reached which corresponded with that of the complemental system; in the given instance the system 4BBr3 + 3CCl4. In this last 89·97 per cent. of bromine in the BBr3 was replaced by chlorine; that is, there were obtained 89·97 molecules of BCl3 and there remained 10·02 molecules of BBr3, and therefore the same state of equilibrium was reached as that given by the system 4BCl3 + 3CBr4. Both systems gave one and the same state of equilibrium at the limit, which is in agreement with Berthollet's doctrine.[28]
Thus we now find ample confirmation from various quarters for the following rules of Berthollet, applying them to double saline decompositions: 1. From two salts MX and NY containing different haloids and metals there result from their reaction two others, MY and NX, but such a substitution will not proceed to the end unless one product passes from the sphere of action. 2. This reaction is limited by the existence of an equilibrium between MX, NY, MY, and NX, because a reverse reaction is quite as possible as the direct reaction. 3. This limit is determined both by the measure of the active affinities and by the relative masses of the substances as measured by the number of the reacting molecules. 4. Other conditions being constant, the chemical action is proportional to the product of the chemical masses in action.[29]