RICHARDS. — ENERGY OF PHYSICO-CHEMICAL REACTION. 475 



shall call this newly defined exponent N'. Mathematically, the inspec- 

 tion of the equations (4) and (5) shows that the expression 



(where ^ is the total number of grara-molecules in the initial reacting 

 mixture, and Pi and P2 the initial and final total pressures respectively) 

 is true either for constant pressure or constant volume. Whether this 

 still holds true for the ill-defined cases where neither volume nor pressure 

 is constant, we shall not at present determine. In constant volume, 

 according to this definition, N' = N ; under constant pressure, likewise 

 according to this definition, N' = 0. With the help of this new defini- 

 tion, together with the use of the symbol Q to signify in general the 

 actually observed latent heat of the reaction, it becomes possible to com- 

 bine the reactions-isochor and isobar into one equation, from which either 

 may be logically obtained again, according to the circumstances attending 

 the reaction. Thus, we may write : — 



which is a general expression for the temperature coefficient of the equi- 

 librium ratio * of dilute reactions. 



If the total osmotic or gas pressure is kept constant, N' = 0, hence 

 T''' — 1, and disappears, and Q = X = NRT — U. This is the reac- 

 tion isobar. If, on the other hand, the volume is kept constant, T''' rep- 

 resents the increase in pressure which at constant pressure would have 

 represented work, and — Q ^ U. This is the reaction isochor. If ^' 

 is 0, and — Q = U, the equation is both isochor and isobar. 



For the general expression (6) which defines the temperature-coeffi- 

 cient of the equilibrium ratio I propose the name "reaction metatherm" 

 (fieTOL, between). The chief advantage which it possesses over the con- 

 centration equation is the fact that its term — ^ is always the heat 

 actually evolved, whether work is done or not, as well as the fact that it 

 deals with the more rational dimension, — pressure. 



Since Q is the heat really observed, it is clear that the expression 

 must be the analytical statement of the theorem of Maupertuis or Le 



* This satisfactory name is due to Lewis. " Mass law constant " is less satisfac- 

 tory, because the quantity is not constant, and the law seems to be due to pressure 

 rather than to mass. 



