CIIEMICAL) , it is well known empirically that a relatively small rise of temperature often causes reactions to take place with great rapid ity—sometiines with explosive violence. Usu ally a rise of 10° C. doubles or even trebles the velocity. In a perfectly general manner, how ever, the dependence of the velocity on tempera ture cannot as yet be formulated. As far as chemical knowledge goes at present, it seems probable that a law analogous to Ohm's law in electricity will motile time be found to express the relation between the reaction-velocity, the chemical force causing the reaction, and the 'chemical resistance.' If chemists should suc ceed in working out a clear conception of the latter, in measuring it, and expressing quanti tatively its variation with the temperature, then the problem of the dependence of reaction velocity on temperature would be solved. But all this remains to be done; and chemists realize that it is not by any means an easy matter to do it; for 'chemical resistance,' and hence also the velocity of reactions, depend, besides the tem perature, on a number of more or less accidental factors—on the accelerating influence of certain `catalytic agents' (see CATALYTIC ACTION), on the retarding influence of certain other sub stances, indeed sometimes on the material of the vessel in which the reaction takes place. Under such circumstances, the field for the mathematical application of thermodynamical principles is naturally very limited. Neverthe less, Van 't Hoff has succeeded in showing that in many cases the dependence of reaction-velocity 011 the temperature can be expressed by simple equations of the following form: A log1 —c B, an equation established by him by combining the principles of thermodynamics with experimental observations. In this equation k stands for the velocity at the instant when the product of the active masses equals unit; T stands for the absolute temperature (i.e. the centigrade tem perature plus 273 degrees) ; and A and B are constants whose numerical values depend on the nature of the substances taking part in the re action. If k is actually measured at only two different temperatures. and its two corresponding values (say k, and k,), together with the two temperature numbers (say T, and T,), are sub stituted in the above eqimtion, we get: A log — B, A log B, two equations with two unknowns, A and B. Solving these equations, and substituting the resulting numerical values of A and B in the general equation given above, we obtain a gen eral relation between k and T for the given re action. In other words,. we can readily calculate what may be termed 'the standard velocity' for any temperature whatever—the 'standard veloc ity' being the velocity at the instant the concen trations of the reacting substances are such that the product of their active masses equals unit. The law of chemical mass-action then permits of calculating the reaction-velocity for all other possible concentrations.
With reference to chemical equilibrium (see REACTION, CHEMICAL) , thermodynamics, as Van 't Hoff has shown, permits of foreseeing the equilibrium of a reaction at some temperature T,. if the equilibrium at some given temperature and the average of the energy-changes (heats given of or taken up by the reaction) at the two temperatures are known. In this manner it is possible to calculate, for instance, the degree of dissociation of ammonium chloride (see DECOM POSITION ; DiSsocIATION) at different tempera tures, if the degree of dissociation at some one temperature, and the heat of dissociation, are known.
In connection with the influence of changes of temperature on chemical equilibrium, it is necessary to mention Gibbs's phase rule, which is of great importance in classifying the phenomena of equilibrium in material systems. By the 'phases' of a chemical system Gibbs means its several homogeneous parts that can be separated from one another mechanically. For instance,
let water be shaken up in a bottle with ordinary ether, and three layers will form—a solution of ether in water, a solution of water in ether, and, over the liquid, a mixture of the vapors of water and ether; the three homogeneous layers can be separated by mechanical means, and hence they constitute the three 'phases' of the system. Since all gases and vapors form homogeneous mixtures, it is evident that no system can contain more than one gaseous phase. According to Gibbs's phase rule, a phases in equilibrium with one an other cannot possibly be made up by less than a —2 independent chemical substances, or, what is the same, n-2 independent chemical sub stances cannot possibly form more than a phases in equilibrium with one another. When a-2 independent substances do form n phases, then the slightest change of temperature destroys the equilibrium, a transformation takes place, and one of the phases disappears. For instance, let n-2 = 1, and therefore a = 3, as is the case at the melting-point of ice, when ice, liquid water, and water vapor may form three phases made up of a single chemical substance—water. As long as the temperature is constant, the three phases remain iu equilibrium; let the tempera ture rise, and all the ice will have melted away; let the temperature fall, and all the water will have frozen. The melting-point of water is sometimes referred to as its triple point, because of the three phases which may exist in equilib rium at that point. Above and below that point, in the regions of the simultaneous existence of only two phases (liquid water and its vapor, or ice and its vapor), a change in temperature causes a corresponding change in the equilibrium. the vapor-tension, and hence the concentration of the gaseous phase varying with the temperature; but none of the phases necessarily disappears, i.e. the equilibrium of the several phases is not necessarily destroyed. In the case of ether and water forming three phases (see above), the number of independent substances being only one less than the number of phases, a change in temperature would likewise cause a change in equilibrium; but ordinarily none of the phases would necessarily disappear, i.e. again, the equi librium would not necessarily he destroyed. If, however, the temperature should fall to the point at which water would begin to freeze out of the aqueous solution of ether, then a fourth phase (ice) would be added to the three phases of the system; the number of phases (4) would then exceed by two the number of independent sub stances (2, ether and water) composing them, and the equilibrium that would then ensue would be destroyed by the slightest variation of tem perature from that 'quadruple point' (i.e. the point of four phases)of the system. Tempera tures like the triple point of water and the quad ruple point of water and ether are referred to genera lly as the multiple points of chemical sys tems. The above examples, involving physical transformations alone ( melting, freezing, evapo ration, solution), have been considered here for simplicity's sake. But the phase rule is equally applicable to systems in which very complex chemical phenomena may be taking place, and its value lies largely in the fact that it likens very complex phenomena of chemical equilibrium to the simple phenomenon of the physical equi librium between water and ice. It further, evi dently, permits of classifying the phenomena of chemical equilibrium with reference to the num ber of substances taking part in them, and thus possesses considerable didactic importance. Final ly. it can serve as a guide to the discovery of new substances (for instance, new hydrates of inorganic salts) that may appear as phases in chemical systems in equilibrium and thus render service to certain branches of purely experimen tal research.