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of them are removed from the sphere of interaction almost as quickly as they are formed. The typical normal case of chemical change, according to Berthollet's view, is one wherein every member of the system is free to interact with all the other members throughout the whole of the change; those changes wherein a final distribution of the interacting substances is quickly established by the formation of solid precipitates or the evolution of gases are special limiting cases.

Berthollet's law of mass has been developed in recent years 247 chiefly by the researches of Guldberg and Waage and of Ostwald. Guldberg and Waage formulate the law of mass thus chemical action is proportional to the active mass of each substance taking part in the change. By active mass is meant that quantity of a substance measured in equivalent weights which is present in unit volume of the chemical system.

The expression equivalent weights will be explained more fully hereafter (s. Chap. XVII.). We know that the amounts of potash and soda which severally neutralise 36.5 parts by weight of hydrochloric acid (HCl = 36.5) are those expressed by the formulae KOH (56) and NaOH (40), respectively. We also know that to neutralise a reacting weight of sulphuric acid (H SO,=98) 112 parts by weight of potash (2KOH) or 80 of soda (2NaOH) are required. So far as neutralising by alkali is concerned, the quantities expressed by the formulae 2HCl (or H,01) and H.SO, are equivalent; so far as neutralising by acid is concerned the quantities KOH and NaOH (or 2KOH and 2NaOH) are equivalent.

Suppose that a solution of 112 parts by weight of potash (2KOH), 73 parts by weight of hydrochloric acid (2HCĪ), and 98 parts by weight of sulphuric acid (H SO.), is diluted with water to a specified volume; then the active masses of potash, hydrochloric acid, and sulphuric acid, respectively, in this solution are one equivalent of each, provided that by one equivalent is meant the quantity expressed by the formulae 2KOH (or KO,H), 2NaOH (or Nao,H_), and H,80, respectively.

The law of mass-action has been experimentally proved in many different reactions; it probably holds good in all chemical changes.

The principle of the coexistence of reactions states that 248 when several reactions occur simultaneously, each proceeds as if it alone took place. No direct experimental investigation of this principle has been made; but it has been largely M. E. c.

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applied in work on 'chemical affinity, and numerous results have been obtained in keeping with the principle.

Assuming the law of mass-action, and the principle of the coexistence of reactions, let us briefly examine a fairly simple chemical change. Let equivalent quantities of the alkali caustic potash, and the acids hydrochloric and sulphuric, be mixed in dilute aqueous solution; let the substances be present in the ratio KO,H, : HCl, : H Soc. The possible products of the interactions are potassium sulphate (K,SO.), potassium-hydrogen sulphate (KHSO.), potassium chloride (KCI), and water (HO). But these substances may interact to reproduce the original substances. We have then certain direct changes and certain reverse changes possible. Chemical equilibrium will result when the velocities of the opposite reactions have become equal, that is, when the quantities of the substances formed in the direct change are equal to the quantities of the substances formed in the reverse change, in unit of time. But we say that each change, the direct and the reverse, is proportional to the affinities, and the masses, of the reacting substances. Now we can measure the mass of each substance present at the beginning of the change, and we can also measure the mass of each substance present when equilibrium is established; hence we can deduce numerical values for the affinities of the reacting substances. Guldberg and Waage, Ostwald, van 't Hoff, and others, have deduced the necessary equations from the fundamental statements already made.

But there is another method by which values for the relative affinities of the substances taking part in a chemical change may be deduced from experimental data. The change may be allowed to proceed to a certain extent only, but not until the system has settled down into equilibrium; the quantity of each substance present in the system may then be measured, and the velocity of the change may thus be determined. Then, assuming that the change which has occurred is proportional to the affinities and the masses of the interacting substances, we may deduce relative values for these affinities from our meaşurements of the masses. The necessary equations have been deduced by Guldberg and Waage, Ostwald, and others.

One of the great difficulties in applying these methods is to find reactions which are sufficiently simple, Very many chemical changes which appear to be simple are complicated

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by the occurrence of secondary reactions among the products of the primary change.

Another difficulty is to measure the masses of the substances present when equilibrium is established. Suppose, for instance, that potash and sulphuric and nitric acids have been mixed in the ratio K,0,H,: H.NO.: H. SO, in dilute aqueous solution; how are we to determine how much potassium nitrate, and how much potassium sulphate, is actually present in the solution ? The ordinary methods of analysis are useless here, because they are based on the use of reagents other than the substances in the solution ; but the addition of any reagent is forbidden because the equilibrium of the system would thereby be destroyed. We cannot here go into the methods adopted; many of them consist in measuring some definite physical change and using this as an index of the chemical change which has occurred.

In the case of the two acids, nitric and sulphuric, reacting 251 with potash in equivalent quantities it has been shewn, with a very high degree of probability, that about 10 parts of potash combine with the nitric acid to form potassium nitrate, for each 7 parts which combine with the sulphuric acid to form potassium sulphate, when the system is in equilibrium. Hence it is concluded that the ratio of the affinities for potash of nitric and sulphuric acids is approximately 10 : 7. When the acids are nitric and hydrochloric, and the base is potash, the potash divides itself almost equally between the two acids; that is one half of the potash reacts with the nitric acid to produce potassium nitrate, and one half with the hydrochloric acid to produce potassium chloride. Hence the affinities of hydrochloric and nitric acids for potash are approximately equal. When the acids are hydrochloric and acetic almost the whole of the potash reacts with the hydrochloric acid ; only about '4 parts of potash react to produce potassium acetate for each 100 parts which react to produce potassium chloride. Hence the ratio of the affinities for potash of hydrochloric and acetic acids is approximately 100 : 4.

It is very important to observe what is the exact meaning we are now giving to such a statement as this the relative affinity for potash of nitric acid is to that of hydrochloric acid as 1 : 1,' or as this the ratio of the affinities for potash of hydrochloric and acetic acids is 100 : •4. When these statements are amplified they assert, (1) that if equivalent masses of caustic potash (KOH), hydrochloric acid (HCI), and nitric

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acid (HNO3), are allowed to interact freely in dilute aqueous solution, one half of the potash combines with each acid to produce potassium chloride and potassium nitrate, respectively; (2) that if equivalent masses of caustic potash, hydrochloric acid, and acetic acid (C,H,02), are allowed to interact freely in dilute aqueous solution, then for every 100 parts of potash which are changed to potassium chloride only '4 parts of potash are changed to potassium acetate.

If these statements are correct, it is evident that when equilibrium results the solution contains in the first case, potassium chloride and nitrate and also hydrochloric and nitric acids; and in the second case, much potassium chloride, a little potassium acetate, a little hydrochloric acid, and much acetic acid.

The experiments of Ostwald and Thomsen have shewn that the relative affinities of acids are almost, if not quite, independent of the nature of the base; in other words that if equivalent masses of, say, hydrochloric and nitric acids, are mixed in dilute aqueous solution with an equivalent mass of caustic potash (KOH), or soda (NaOH), or ammonia (NH,OH), or caustic lime (CaO H), or caustic baryta (BaO H.), &c. one half of the base combines with each acid.

Ostwald's experiments have also rendered it very probable that the ratio of the affinities for bases of any two acids is independent of the temperature, at least within such a range as 0° to 60°.

There are many chemical changes brought about by acids other than those which take place between acids and bases. Some of these changes have been examined with the object of determining whether they are quantitatively conditioned by the same values as have been found to condition the reactions between acids and bases. Thus Ostwald made a number of measurements of the effects of different acids on the velocity of the change of acetamide into ammonium acetate. This change may be represented thus

CH,CONH, Aq+H,0 = CH COONH, Aq.

(acetamide) (ammonium acetate) The change occurs more or less quickly in the presence of acids; each acid increases the amount of change in unit time to a certain definite extent. The equations deduced from the fundamental statement, that chemical action is proportional to the relative affinities and the active masses of the interacting

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substances, shew that the ratio of the affinities in such a change as that under consideration is equal to that of the square roots of the velocities of the reactions. Ostwald measured the velocities of the reaction for various acids, and hence deduced the relative affinities of these acids. The numbers obtained agree well with those found by the examination of the reactions between the same acids and potash, soda, and other bases. Among other chemical changes examined were, the change of methylic acetate in presence of water and an acid into methylic alcohol and acetic acid

(CH_COOCH Aq + H,0 = CH OHAq+CH COOHAq); and the change of cane sugar in presence of water and an acid into glucose (C, H, O, Aq+HO = 2C,HAq). In each case the velocity of the change was determined for various acids; the ratios of the square roots of the velocities were taken (as indicated by theory) as the ratios of the relative affinities of the acids. The numbers agree as well as could be expected among themselves, and also with the numbers found by the study of the reactions between acids and bases.

The electrical conductivities of solutions of acids are pro- 254 portional to the velocities of the chemical changes produced by these acids. Hence measurements of the electrical conductivities of acids in aqueous solutions of various concentrations give data from which the relative affinities of these acids may be deduced. Many measurements have been made of the electrical conductivities of acids in aqueous solutions, chiefly by Ostwald ; the values of the relative affinities deduced from these results agree very well with those found by more strictly chemical methods.

The outcome of the work which has been done in recent 255 years on the subject of the affinities of acids is to establish the conclusion that it is possible to determine for each acid a specific affinity-constant which quantitatively conditions all the reactions brought about by this acid.

Of course when it is said that this or that reaction is brought about by an acid, the reaction is regarded as being more simple than it really is. The reaction is brought about by all the substances which form the chemically changing system. But it seems that we may regard the complete change as made up of various parts each of which occurs in accordance with its own laws. The more completely a specified change is dependent on the character of the acids which take

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