[26] From the above it follows that an excess of acid should influence the reaction like an excess of alcohol. It is in fact shown by experiment that if two molecules of acetic acid be taken to one molecule of alcohol, 84 p.c. of alcohol is etherified. If with a large preponderance of acid or of alcohol certain discrepancies are observed, their cause must be looked for in the incomplete correspondence of the conditions and external influences.
[27] As an example two methods may be mentioned, Thomsen's and Ostwald's. Thomsen (1869) applied a thermochemical method to exceedingly dilute solutions without taking the water into further consideration. He took solutions of caustic soda containing 100H2O per NaHO, and sulphuric acid containing ½H2SO4 + 100H2O. In order that these solutions may be mixed in such quantities that atomic proportions of acid and alkali would act, for forty grams of caustic soda (which answers to its equivalent) there should be employed 49 grams of sulphuric acid, and then +15,689 heat units would be evolved. If the normal sodium sulphate so formed be mixed with n equivalents of sulphuric acid, a certain amount of heat is absorbed, namely a quantity equal to n.1650 / (n + 0·8) heat units. An equivalent of caustic soda, in combining with an equivalent of nitric acid, evolves +13,617 units of heat, and the augmentation of the amount of nitric acid entails an absorption of heat for each equivalent equal to -27 units; so also in combining with hydrochloric acids +13,740 heat units are absorbed, and for each equivalent of hydrochloric acid beyond this amount there are absorbed -32 heat units. Thomsen mixed each one of three neutral salts, sodium sulphate, sodium chloride and sodium nitrate, with an acid which is not contained in it; for instance, he mixed a solution of sodium sulphate with a solution of nitric acid and determined the number of heat units then absorbed. An absorption of heat ensued because a normal salt was taken in the first instance, and the mixture of all the above normal salts with acid produces an absorption of heat. The amount of heat absorbed enabled him to obtain an insight into the process taking place in this mixture, for sulphuric acid added to sodium sulphate absorbs a considerable quantity of heat, whilst hydrochloric and nitric acids absorb a very small amount of heat in this case. By mixing an equivalent of sodium sulphate with various numbers of equivalents of nitric acid, Thomsen observed that the amount of heat absorbed increased more and more as the amount of nitric acid was increased; thus when HNO3 was taken per ½Na2SO4, 1,752 heat units were absorbed per equivalent of soda contained in the sodium sulphate. When twice as much nitric acid was taken, 2,026 heat units, and when three times as much, 2,050 heat units were absorbed. Had the double decomposition been complete in the case where one equivalent of nitric acid was taken per equivalent of Na2SO4 then according to calculation from similar data there should have been absorbed -2,989 units of heat, while in reality only -1,752 units were absorbed. Hence Thomsen concluded that a displacement of only about two-thirds of the sulphuric acid had taken place—that is, the ratio k : k′ for the reaction ½Na2SO4 + HNO3 and NaNO3 + ½H2SO4 is equal, as for ethereal salts, to 4. By taking this figure and admitting the above supposition, Thomsen found that for all mixtures of soda with nitric acid, and of sodium nitrate with sulphuric acid, the amounts of heat followed Guldberg and Waage's law; that is, the limit of decomposition reached was greater the greater the mass of acid added. The relation of hydrochloric to sulphuric acid gave the same results. Therefore the researches of Thomsen fully confirm the hypotheses of Guldberg and Waage and the doctrine of Berthollet.
Thomsen concludes his investigation with the words: (a) ‘When equivalent quantities of NaHO, HNO3 (or HCl) and ½H2SO4 react on one another in an aqueous solution, then two-thirds of the soda combines with the nitric and one-third with the sulphuric acid; (b) this subdivision repeats itself, whether the soda be taken combined with nitric or with sulphuric acid; (c) and therefore nitric acid has double the tendency to combine with the base that sulphuric acid has, and hence in an aqueous solution it is a stronger acid than the latter.’
‘It is therefore necessary,’ Thomsen afterwards remarks, ‘to have an expression indicating the tendency of an acid for the saturation of bases. This idea cannot be expressed by the word affinity, because by this term is most often understood that force which it is necessary to overcome in order to decompose a substance into its component parts. This force should therefore be measured by the amount of work or heat employed for the decomposition of the substance. The above-mentioned phenomenon is of an entirely different nature,’ and Thomsen introduces the term avidity, by which he designates the tendency of acids for neutralisation. ‘Therefore the avidity of nitric acid with respect to soda is twice as great as the avidity of sulphuric acid. An exactly similar result is obtained with hydrochloric acid, so that its avidity with respect to soda is also double the avidity of sulphuric acid. Experiments conducted with other acids showed that not one of the acids investigated had so great an avidity as nitric acid; some had a greater avidity than sulphuric acid, others less, and in some instances the avidity = 0.’ The reader will naturally see clearly that the path chosen by Thomsen deserves to be worked out, for his results concern important questions of chemistry, but great faith cannot be placed in the deductions he has already arrived at, because great complexity of relations is to be seen in the very method of his investigation. It is especially important to turn attention to the fact that all the reactions investigated are reactions of double decomposition. In them A and B do not combine with C and distribute themselves according to their affinity or avidity for combination, but reversible reactions are induced. MX and NY give MY and NX, and conversely; therefore the affinity or avidity for combination is not here directly determined, but only the difference or relation of the affinities or avidities. The affinity of nitric acid not only for the water of constitution, but also for that serving for solution, is much less than that of sulphuric acid. This is seen from thermal data. The reaction N2O5 + H2O gives +3,600 heat units, and the solution of the resultant hydrate, 2NHO3, in a large excess of water evolves +14,986 heat units. The formation of SO3 + H2O evolves +21,308 heat units, and the solution of H2SO4 in an excess of water 17,860—that is, sulphuric acid gives more heat in both cases. The interchange between Na2SO4 and 2HNO3 is not only accomplished at the expense of the production of NaNO3, but also at the expense of the formation of H2SO4, hence the affinity of sulphuric acid for water plays its part in the phenomena of displacement. Therefore in determinations like those made by Thomsen the water does not form a medium which is present without participating in the process; it also takes part in the reaction. (Compare Chapter IX., Note [14].)
Whilst retaining essentially the methods of Thomsen, Ostwald (1876) determined the variation of the sp. gr. (and afterwards of volume), proceeding in the same dilute solutions, on the saturation of acids by bases, and in the decomposition of the salts of one acid by the other, and arrived at conclusions of just the same nature as Thomsen's. Ostwald's method will be clearly understood from an example. A solution of caustic soda containing an almost molecular (40 grams) weight per litre had a specific gravity of 1·04051. The specific gravities of solutions of equal volume and equivalent composition of sulphuric and nitric acids were 1·02970 and 1·03084 respectively. On mixing the solutions of NaHO and H2SO4 there was formed a solution of Na2SO4 of sp. gr. 1·02959; hence there ensued a decrease of specific gravity which we will term Q, equal to 1·04051 + 1·02970 - 2(1·02959) = 0·01103. So also the specific gravity after mixture of the solutions of NaHO and HNO3 was 1·02633, and therefore Q = 0·01869. When one volume of the solution of nitric acid was added to two volumes of the solution of sodium sulphate, a solution of sp. gr. 1·02781 was obtained, and therefore the resultant decrease of sp. gr.
Q1 = 2(1·02959) + 1·03084 - 3(1·02781) = 0·00659.
Had there been no chemical reaction between the salts, then according to Ostwald's reasoning the specific gravity of the solutions would not have changed, and if the nitric acid had entirely displaced the sulphuric acid Q2 would be = 0·01869 - 0·01103 = 0·00766. It is evident that a portion of the sulphuric acid was displaced by the nitric acid. But the measure of displacement is not equal to the ratio between Q1 and Q2, because a decrease of sp. gr. also occurs on mixing the solution of sodium sulphate with sulphuric acid, whilst the mixing of the solutions of sodium nitrate and nitric acid only produces a slight variation of sp. gr. which falls within the limits of experimental error. Ostwald deduces from similar data the same conclusions as Thomsen, and thus reconfirms the formula deduced by Guldberg and Waage, and the teaching of Berthollet.
The participation of water is seen still more clearly in the methods adopted by Ostwald than in those of Thomsen, because in the saturation of solutions of acids by alkalis (which Kremers, Reinhold, and others had previously studied) there is observed, not a contraction, as might have been expected from the quantity of heat which is then evolved, but an expansion, of volume (a decrease of specific gravity, if we calculate as Ostwald did in his first investigations). Thus by mixing 1,880 grams of a solution of sulphuric acid of the composition SO3 + 100H2O, occupying a volume of 1,815 c.c., with a corresponding quantity of a solution 2(NaHO + 5H2O), whose volume = 1,793 c.c., we obtain not 3,608 but 3,633 c.c., an expansion of 25 c.c. per gram molecule of the resulting salt, Na2SO4. It is the same in other cases. Nitric and hydrochloric acids give a still greater expansion than sulphuric acid, and potassium hydroxide than sodium hydroxide, whilst a solution of ammonia gives a contraction. The relation to water must be considered as the cause of these phenomena. When sodium hydroxide and sulphuric acid dissolve in water they develop heat and give a vigorous contraction; the water is separated from such solutions with great difficulty. After mutual saturation they form the salt Na2SO4, which retains the water but feebly and evolves but little heat with it, i.e., in other words, has little affinity for water. In the saturation of sulphuric acid by soda the water is, so to say, displaced from a stable combination and passes into an unstable combination; hence an expansion (decrease of sp. gr.) takes place. It is not the reaction of the acid on the alkali, but the reaction of water, that produces the phenomenon by which Ostwald desires to measure the degree of salt formation. The water, which escaped attention, itself has affinity, and influences those phenomena which are being investigated. Furthermore, in the given instance its influence is very great because its mass is large. When it is not present, or only present in small quantities, the attraction of the base to the acid leads to contraction, and not expansion. Na2O has a sp. gr. 2·8, hence its molecular volume = 22; the sp. gr. of SO3 is 1·9 and volume 41, hence the sum of their volumes is 63; for Na2SO4 the sp. gr. is 2·65 and volume 53·6, consequently there is a contraction of 10 c.c. per gram-molecule of salt. The volume of H2SO4 = 53·3, that of 2NaHO = 37·4; there is produced 2H2O, volume = 36, + Na2SO4, volume = 53·6. There react 90·7 c.c., and on saturation there result 89·6 c.c.; consequently contraction again ensues, although less, and although this reaction is one of substitution and not of combination. Consequently the phenomena studied by Ostwald depend but little on the measure of the reaction of the salts, and more on the relations of the dissolved substances to water. In substitutions, for instance 2NaNO3 + H2SO4 = 2HNO3 + Na2SO4, the volumes vary but slightly: in the above example they are 2(38·8) + 53·3 and 2(41·2) + 53·6; hence 131 volumes act, and 136 volumes are produced. It may be concluded, therefore, on the basis of what has been said, that on taking water into consideration the phenomena studied by Thomsen and Ostwald are much more complex than they at first appear, and that this method can scarcely lead to a correct interpretation as to the distribution of acids between bases. We may add that P. D. Chroustcheff (1890) introduced a new method for this class of research, by investigating the electro-conductivity of solutions and their mixtures, and obtained remarkable results (for example, that hydrochloric acid almost entirely displaces formic acid and only ⅔ of sulphuric acid), but details of these methods must be looked for in text-books of theoretical chemistry.
[28] G. G. Gustavson's researches, which were conducted in the laboratory of the St. Petersburg University in 1871–72, are among the first in which the measure of the affinity of the elements for the halogens is recognised with perfect clearness in the limit of substitution and in the rate of reaction. The researches conducted by A. L. Potilitzin (of which mention will be made in Chapter XI., Note [66]) in the same laboratory touch on another aspect of the same problem which has not yet made much progress, notwithstanding its importance and the fact that the theoretical side of the subject (thanks especially to Guldberg and Van't Hoff) has since been rapidly pushed forward. If the researches of Gustavson took account of the influence of mass, and were more fully supplied with data concerning velocities and temperatures, they would be very important, because of the great significance which the case considered has for the understanding of double saline decompositions in the absence of water.
Furthermore, Gustavson showed that the greater the atomic weight of the element (B, Si, Ti, As, Sn) combined with chlorine the greater the amount of chlorine replaced by bromine by the action of CBr4, and consequently the less the amount of bromine replaced by chlorine by the action of CCl4 on bromine compounds. For instance, for chlorine compounds the percentage of substitution (at the limit) is—