380 KEYES 



ART. J 





where v represents the coefficients, for example — 1, 1/2 and 1 in 

 the decomposition of water. Here the minus sign signifies that 

 a component vanishes while the positive sign signifies the 

 appearance of components formed from those having the 

 minus sign. Assume also that the heat capacities Ci, c^, ... 

 are not constants but functions of the temperature. Starting 

 with equations [265] and [283] there is finally obtained 



2^= S'^i / ^1*^^ + ^n,Ex -h^n, Rt -Y^Uit \ 



J to J to 



- ^niRtlog—^ - ^nitHi, 



whence 



f r dt Rt 



Ml = / ci*dt +E^-t \ c*-r -Rt\og-- + Rt- H,t. (113) 



The equivalent of equation (2) [300] may now be easily formed, 

 and on rearrangement there results 



2jVi log pxi = - + Zj""' ^°S Rt - 



^ 



Rt ' Z-V—-^"" Rt 



't 



^U'^*^'^' S^^^^-S^^^ 



+ -^ + -]f^ (114) [309] 



This equation is perfectly general within the limits of appli- 

 cability of the perfect gas laws, and [282] and [283] apply. The 

 energy constants and the entropy constants may be adjusted to 

 suit practical convenience, but this has already been referred to 

 earlier and need not detain us here. 



The case of the dissociation of water vapor and of the decom- 

 position of hydriodic acid will illustrate in detail the points 

 raised by Gibbs. For the former we have 



H2O =^02 + H2, 



1 



Vz = —\, J/2 = 2' "1 ^ -^• 



(115) 



