HETEROGENEOUS EQUILIBRIUM 243 



for a two-component system, composition was expressed as the 

 total mass rrii and wi of the substances present, and volume and 

 entropy as total volume and total entropy. For some purposes 

 this is the most convenient form, but for our present discussion 

 it is more convenient to express composition as weight per cent 

 potassium nitrate. Since we have Wi + Wj grams of the two 

 components water and potassium nitrate, respectively, if we 

 divide through hy rtii -{- rrh we shall get 



dp = ; dt + 1 dfjLi + ; dfn. 



nil -{- nh mi + m2 rui -\- rUi mi + mj 



The coefficient of the first term, the total volume divided by 

 the total number of grams of material, is evidently the specific 

 volume of the phase. Similarly, the coefficient of the second 

 term is the specific entropy. The fractions 



mi rtii 



and 



mi -\- nh mi + ma 



are the weight fractions of the components H2O and KNO3, 

 respectively, and if we represent the weight fraction of KNO3 

 by X, that of H2O will be (1 — x). The equation now is 



vdp = rjdt + (1 — x)dni + xdm, (7) 



in which v and rj are specific volume and specific entropy. We 

 will have three such equations, one for the vapor, denoted by 

 the superscript v, one for the liquid, denoted by the superscript /, 

 and one for the solid, denoted by the superscript s. From these 

 equations we may eliminate dfxi and d^a by the usual methods of 

 cross-multiplication, giving the equation 



x" — a;' 



dt , ^ x" — x\ 



(y' - rO - ; {v' - v^) 



x' — x 



(8) 



6. The Equilibrium, KNO3 + Solution -\- Vapor* At the 



* The data for the system, HjO-KNOj, are taken in part from Lan- 

 dolt-Bornstein, Physikalisch-chemische Tahellen, 1912; in part from 

 unpublished data by F. C. Kracek and G. W. Morey. 



