242 MOREY ART. G 



which may be regarded as the projections of the sohd p-t-x 

 model on the p-x, p-t, and t-x planes, respectively. It 

 should be noted that in referring to these projections, and to the 

 similar ones in the following figures, their conventional designa- 

 tion in chemical literature has been followed, instead of the 

 convention in mathematics that the symbols shall be in the 

 order abscissa, ordinate; a:, y. The system, H2O-KNO3,* does 

 not show liquid immiscibility, nor are solid hydrates formed, so 

 there are four possible phases in the system; one vapor phase, 

 one liquid phase and two solids, ice and solid KNO3. Co- 

 existence of four phases in a two-component system gives us 

 four equations of the type of (1) [97] between the four un- 

 knowns, pressure, temperature, and the two chemical poten- 

 tials, so the system is completely determined. The four phases 

 can only coexist at one temperature and one pressure, that is, at 

 the invariant point, often called the cryohydrate when one 

 component is water. The invariant point can be considered 

 as the intersection of four curves representing univariant 

 equilibria, each of which equilibria will contain three of the 

 phases which coexisted at the invariant point. We can have the 

 four combinations: ice + solution + vapor, ice + potassium 

 nitrate -f vapor, ice + potassium nitrate -\- solution, and potas- 

 sium nitrate + solution -{- vapor. Consider each of these curves 

 in detail, starting with the last, the solubihty curve of potas- 

 sium nitrate in water. 



5. Application of Equation [97] to a System in Which No Com- 

 pounds Are Formed. H2O-KNO3. In the univariant equilib- 

 rium, potassium nitrate + solution + vapor, there is only 

 one phase of variable composition, the solution. Since potassium 

 nitrate is not volatile at temperatures we are considering, the 

 vapor phase is pure water; since potassium nitrate forms 

 neither hydrates nor solid solutions with water, the solid phase 

 is pure potassium nitrate. Let us now apply equation (1) [97] 

 to this univariant equilibrium. In the derivation of equation 

 (1) [97], 



Vdp = Udt + midfxi + WgC^Ma 



* The circumstance that an inversion takes place in KNOj at 127.8° is 

 ignored, as not being pertinent to the points under consideration. 



