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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+H,0 = 2C 1,0 Aq). 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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part in that change the more suitable is it for deducing values.
for the relative affinities of these acids.
The interactions of acids and bases in dilute

aqueous

solutions are conditioned only by the characters of the acids and the bases. The results of measurements of these changes render it very probable that each acid has a specific affinityconstant which is independent of the nature of the base interacting with the acid, and that each base has a specific affinityconstant which is independent of the nature of the acid interacting with the base.

The results of measurements of many other reactions which occur only in the presence of acids, and which may justly be said to be caused by these acids, render it very probable that the amount of change occurring in a specified time, or the amount of change which has occurred when the system has settled down into equilibrium, is conditioned by the values of the same specific affinity-constants which condition the interactions between these acids and bases in dilute aqueous. solutions.

If these conclusions are granted—and they rest on a large body of carefully verified facts—it follows that measurements of the specific affinity-constants of the acids are of the utmost importance.

Of the various methods hitherto employed for making these measurements the most promising seems to be that based the proportionality between the electrical conductivities and the velocities of the chemical reactions brought about by acids. This method presents no great experimental difficulties, and it is free, or nearly free, from the disturbing influence of secondary reactions. Most, if not all, purely chemical methods are open to the objection that the primary change to be measured is complicated and modified by the occurrence of other changes, and that the influence of these secondary changes can scarcely be eliminated by any experimental arrangements. Many measurements of the electrical conductivities of aqueous solutions of acids have been made, and data have thus been accumulated for comparing the relative affinities of many acids. We shall shortly consider some of these data when we have learned more about the composition of acids (s. Chap. XVII.)

Acids with large affinity-values are called strong acids; those with small affinity-values are called weak acids.

Answers can then be given to the questions propounded at

on

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the close of Chap. XII.; we have learnt that a number can be found for each acid, and each base, which expresses the amount of chemical change which this acid, or base, is capable of producing under defined conditions.

It is probable that, as investigation proceeds, specific affinity-constants will be determined for the members of other classes of compounds besides acids and bases.

We have now learnt something about chemical composition 258 and chemical classification. We have also found that many, and probably all, chemical reactions brought about by the compounds classed together as acids are quantitatively conditioned by the affinity-constants of these acids.

We ought now to inquire into the connexions between the compositions of acids and the values of their affinity-constants. But we are not yet ready for this inquiry; we must learn more regarding chemical composition. (s. Chap. XVII.)

No attempt has been made in this chapter to analyse the 259 meaning of the term affinity; we have not asked why this body chemically interacts with that; we have not inquired as to the nature of chemical affinity. We have been content to call affinity that property of elements and compounds by virtue of which they interact to produce new combinations. We have found it possible to assign quantitative values to this property in the cases of acids and bases.

Before proceeding to consider in some detail the generally accepted theory regarding the mechanism of chemical change, we shall briefly glance at the relations between chemical changes and the changes of energy which invariably accompany them.

CHAPTER XIV.

RELATIONS BETWEEN CHEMICAL CHANGES AND CHANGES

OF ENERGY *.

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EVERY chemical change consists of two parts, a change in the form of combination of the matter of the system, and a change in the total quantity, or in the form, or in both the quantity and form, of the energy of the system.

Energy is the power of doing work. Work is the "act of producing a change of configuration in a system in opposition to a force which resists that change.”

If one system does work on another system, one loses and the other gains energy; and the energy lost by one is equal to the energy gained by the other. If both systems are included in a larger, the total energy of this system is unchanged. If one part of a system does work on another part, the total energy of the system is unchanged, although one part has gained and another part has lost energy.

The principle of the conservation of energy affirms that ;

The total energy of any material system is a quantity which can neither be increased nor diminished by any action between the parts of the system, though it may be transformed into any of the forms of which energy is susceptible.” (Clerk Maxwell.)

The energies of actually existing material systems depend upon the states of these systems at any moment. The state of a system is conditioned by many variables; among the more important are chemical composition, pressure, temperature, and volume.

If we wish to connect changes of energy with changes of chemical composition we must start with chemical systems of

* The subject of energy is treated very shortly. The student should refer to a book on Physical principles, e.g. to Clerk Maxwell's Matter and Motion.

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definite and defined composition, in definite and defined states, and we must cause these to change to other definite and defined states; we must then determine the compositions of the resulting systems, and we must measure the changes of energy which have accompanied these changes of composition and of state.

Of two equal quantities of energy one may be more 262 available for doing work than the other. Thus, in order to cause thermal energy to do work it is necessary to allow it to pass from a body at a higher to a body at a lower temperature. A certain body may be at a very low temperature and yet contain thermal energy; but it may be impossible to cause this energy to do work, because of the impossibility of framing an engine consisting of the cold body and another system at a lower temperature than the cold body. A quantity of heat as it exists in a hot body is more available for doing work than the same quantity of heat as it exists in a colder body.

When energy passes from a more available, or higher, to a 263 less available, or lower, form it is said to be degraded. All forms of energy can be directly or indirectly transformed into heat. A given quantity of heat-energy cannot be wholly transformed into one of the higher forms of energy. Every transformation of energy involves the degradation of a portion of the energy. But every chemical change is accompanied by a transformation of energy from the form of chemical energy to other forms of which thermal energy is usually one; every chemical change therefore is accompanied by a degradation of energy. It is not asserted that the whole of the energy which changes form during a chemical change is necessarily degraded.

The chemical system represented by the symbols 2H+0 264 contains more energy than the system represented by the symbol H,0. In the passage from one of these systems to the other energy is lost by the changing system ; the energy so lost by the system is gained by neighbouring systems, by the vessel in which the change is accomplished, the surrounding air, &c. But although there is no destruction, there is degradation, of energy. If 2H represents 2 grams of hydrogen,

represents 16 grams of oxygen, and HO represents 18 grams of liquid water, all measured at normal

pressure and at about 15°—16°, then the change 2H +0= H,O is accompanied by the production of 68,360 gram-units of heat. If we assume that the whole of the energy which changes form during the chemical change 2H +0=1,0 appears as heat, then 68,360

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