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 ifl is the total number of gram-molecules in the initial reacting 

 mixture, and P x and P 2 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: — 



dT ln p^pY*--- ~ RT 1 ' w 



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, W = 0, hence 

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

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

 resents the increase in pressure which at constant pressure would have 

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

 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" 

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

 centration equation is the fact that its term — Q 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. 



