Reaction before Complete Equilibrium. 53 



follows : — Hie 'potential for each component substance must be 

 constant throughout the whole mass " *. 



These are the general conditions deduced by Gibbs as 

 necessary and sufficient for thermal, mechanical, and chemical 

 equilibrium in heterogeneous systems. There is also another 

 region of phenomena not touched upon in Gibbs's work on 

 equilibrium, namely, the region of thermal, mechanical, and 

 chemical reaction which takes place when the system is not in 

 equilibrium. This region of phenomena is of the deepest 

 interest not only because the state of equilibrium of a system 

 is never actually reached in nature, and reaction is the only 

 real phenomenon in nature, but also because the true con- 

 ception of one region is so very deeply connected with the 

 conception of the other. 



The above generalizations of Gibbs' s give evidently also, 

 although indirectly, the general condition which is necessary in 

 order that reaction should take place in a system : there is no 

 thermal, or mechanical, or chemical equilibrium in the hetero- 

 geneous system; there is a thermal, or a mechanical, or a 

 chemical reaction going on in the system when the temperature 

 or pressure or the chemical potential is in the different parts 

 of the heterogeneous system different. It is also evident that 

 not only in the different parts o£ the heterogeneous system, 

 but also in each of the homogeneous parts of the system, the 

 condition of the thermal, mechanical, and chemical equilibrium 

 is that temperature, pressure, and chemical potential should 

 be everywhere the same. It can be shown that this is not 

 restricted to homogeneous systems when they form parts 

 of a heterogeneous system. If we divide a homogeneous 

 system into Aery thin layers, and assume at first that de or 

 tdrj—pdv + pd m . . . + p n d 'n i n is in different layers different we 

 get, since the condition of equilibrium will be that 'Zde^O for 

 all variations for which *$dr} = 0, Sdn = 0, 5^/^ = . . . 

 %dm n =0, that at equilibrium t, p, p, . . . p n must be constant 

 through the whole system. We may formulate the same from 

 another aspect: at equilibrium the state of the homogeneous 

 system in respect to its thermal, mechanical, and chemical energy 

 is everywhere the same. So also in homogeneous parts or 

 systems tJw general condition for thermal, mechanical, and 

 chemical reaction is that the tempered u re, pressure, and chemical 

 potential are not everywhere the same. 



In a more general form the last-mentioned principle was 



* It should be noted that this does not explicitly cover the case of 

 superficial tension, external forces such as gravity, and other causes that 

 would make pressure different in different places. 



