262 MOREY ART. G 



the compound disappearing, the solution was a eutectic, and the 

 compound had a congruent melting point. The solution at 

 this invariant point contains 56.4 per cent CaCl2, while the 

 tetrahydrate contains 60.6 per cent CaCl2; substitution of these 

 values in equation (8) gives 



dp _ (v" - V) + 0.606 - 0.564 ^^' ~ ^^ 

 dt (t;" - I'O 4- 13.4 (v - v') 



The positive entropy of vaporization is larger than the negative 

 entropy of fusion multiplied by its coefficient, dp/dt is still 

 positive, and both temperature and pressure are increasing 

 along the solubility curve of the tetrahydrate at the invariant 

 point. This solubility curve differs from the preceding in that 

 solid and liquid do not have the same composition at any point ; 

 calcium chloride tetrahydrate has an incongruent melting point 

 and the invariant point is not a eutectic but a transition point. 

 Pure hexahydrate, when heated, melts to form a liquid of its 

 own composition ; pure tetrahydrate decomposes into dihydrate 

 and saturated solution of the composition of the solution at the 

 invariant point. 



From this invariant point three other univariant equilibria 

 can be obtained. One of them is the condensed system, whose 

 p-t curve is almost vertical; a second is the dissociation- 

 pressure curve of the tetrahydrate, the univariant equilibrium, 

 tetrahydrate + dihydrate + vapor; the third is the solubility 

 curve of the dihydrate. The curves representing these equilib- 

 ria are shown in Fig. 3. 



22. Types of Invariant Points and Univariant Systems. 

 While the preceding discussion has dealt primarily with the 

 application of the Phase Rule to simple systems having only 

 one phase of variable composition, with especial reference to 

 the direct application of equation (1) [97], the modifications 

 necessary to include additional phases of variable composition 

 have been indicated. In a binary system, coexistence of three 

 phases constitutes a univariant system, of four phases, an 

 invariant system, and the possible types of such equilibria are 

 the possible permutations of solid, liquid, and vapor, with the 



