THERMO-CHEMISTRY. 211 THERMO-CHEMISTRY. that if carbon, hydrogen, and oxygen combined to form ordinary alcohol, an amount of heat would be formed equal to the heat of combustion of the isolated elements of alcohol minus the heat of combustion of alcohol itself; 6, the heat of combustion of two atoms (i.e. twice 12 grams) of carbons^ is found to be 94,300 X 2 = 188.600 calories; c, the heat of combustion of three molecules (i.e. 3X2 grams) of hydrogen, is found to be 67.500X3 = 202.500 calories; finally, a, the heat of combustion of one molecule (46 grams) of alcohol, is found to be 340.000 calories. Hence, 6+c — a, the heat of forma- tion of alcohol, is 18S.0OO + 202,500 — 340,000 — 51,100 calories. See Combu.stion. Theoretical Therjio-Chemistry. This, as already stated above, consists in the application of the principles of thermodynamics to chemi- cal phenomena. The subject, if not very diffi- cult, requires a working knowledge of the higher mathematics and thermodynamics, and can there- fore be discussed here only in its more elemen- tary aspects. The principal questions to which thermodynamics have been applied concern: (1) the influence of temperature upon the total energy-change {Wariiictonuiig) of reactions, i.e. heat given off or absorbed, no mechanical work being performed ; ( 2 ) the influence of tempera- ture upon the velocity of reactions (see Re- action, Chemical) ; (3) the influence of tem- perature on chemical equilibrium; (4) the de- termination of the maximum mechanical work that can be performed by the chemical energy of reactions. We will briefly consider these ques- tions in their consecutive order. With reference to the dependence of the energ^'changc of a reaction upon the tempera- ture, the verdict of thermodynamics is, first of all, that in case the heat-capacity of the reacting substances is the same as that of the products of the reaction, the energy-change of the reaction does not vary w-ith the temperature. This is generally the case when the reacting substances and the products of the reaction are all solids. Thus the combination of silver and solid iodine into silver iodide sets free practically the same amount of heat (about 14.000 calories), no matter at what temperature the combination is caused to take place. On the other hand, if a given reaction does cause a change in the heat- capacity, then, if t denotes the difference be- tween two temperatures at which the reaction may take place, «, — u, the difference between the energy-change at the first and that at the second temperature, and c the difference between the heat-capacity of the reacting substances and that of the products of the reaction, «, — «j = ct. By measuring calorimetrically the heat-capaci- ties in question and the energy-change of the reaction at some one temperature, it is therefore easy to calculate the energy-change of the re- action at any other temperature — a result of con- siderable importance, because direct calorimetrie measurements of the energy-change can by no means be readily carried out at any desirable temperature. As to the velocity of reactions (see T?eaction, Chemical), it is well known empirically that a relatively small rise of temperature often causes reactions to take place with great rapid- ity — sometimes 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 some 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 on the temperature can be expressed by simple equations of the following form : A log t = — Tj, -I- 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 Jc is actually measured at only two different temperatures, and its two corresponding values (say l and A-.), together with the two temperature numbers ( say T, and T,) , are sub- stituted in the above equation, we get: log A-, = — ^ + B, A l0g^2 = — 7p -fB, 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 wh.it may be termed 'the standard vglocity' 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
