RICHARDS. ENERGY OF PHYSICO-CHEMICAL REACTION. 477 



ing pressure is in the denomiuator, and vice versa. The reasoning may 

 be stated in the form of an equation : — 



rt «i rt' «'i ■r >h 9-' "'2 



This equation is simply a definition of the vahies z, which are made 

 logarithmic from analogy to the other pressures. One must bear in 

 mind, however, that this z, or •' physico-chemical potential," need not be 

 the reciprocal of p ; for the condition of equilibrium demands only that the 

 total sum of the logarithms on each side must be equal, and not that the 

 individual opposites are immediate functions of one another. The p 

 values depend of course upon the amount of substance present ; while 

 the z values are constant for any given temperature, because they are 

 by definition the constant factors of a constant. Any constant tendencies, 

 not given by the differential equation, may hence be included among the 

 z values. 



Transposing the second member, we obtain 



In ;^i-;>i;---^i--i ••• ^ o. (7) 



This expression may be written 

 «i In i^pi 2i) + n\ 1q {p'\ z'l) — «2 111 {p^'^i) — ^'2 lo (,p'2. ^'2) . . . = 0. 



Except for its logarithmic form and the substitution of pressure for 

 mass, this equation reminds one of Berthollet's old statement concerning 

 chemical action. It is a fundamental equation of chemical equilibrium in 

 dilute or ideal mixtures. 



Stated in words, the equation reads : Each molecule taking part in a 

 reaction may be said to possess at any given temperature a reacting ten- 

 dency which is the logarithm of the product of its constant physico-chemical 

 potential and variable observed pressure. Obviously the logarithmic 

 arrangement is so convenient as almost to demand its adoption, although 

 the same idea might have been expressed otherwise. One may say, for 

 example, that in equilibrium the algebraic sum of the opposing energies 

 concerned is zero, — almost an axiom. The logarithmic equation is a 

 plausible hypothesis which is concordant with the well known Nernst 

 equation, and with many other natural tendencies. 



The substitution of the new value for k instead of its pressure equiva- 

 lent in the equation gives us a less inverted view of the theorem of 

 Maupertuis : — 



