HETEROGENEOUS EQUILIBRIUM 261 



rium requires the presence of both soUd phases, calcium 

 chloride hexahydrate and calcium chloride tetrahydrate, which, 

 together with the vapor, make three phases, hence three 

 equations. The common name, dissociation-pressure curve 

 of the hexahydrate, is misleading; it is the univariant equilib- 

 rium involving all three phases. The invariant point is the 

 high temperature termination of the stable portion of this 

 curve ; when a mixture of these two solids, together with vapor, 

 is heated, at the invariant point some solution is formed; some 

 of the solid melts to form the eutectic liquid. 



20. The Equilibrium, Two Solids -\- Liquid. A second uni- 

 variant equilibrium is that formed by the disappearance of 

 vapor. This is the condensed system composed of the two 

 hydrates and the eutectic liquid ; the composition of the eutectic 

 liquid and the eutectic temperature both change as the pressure 

 is increased, but the change is small, and will not be considered 

 further. 



SI . The Equilibrium, Solid -\- Solution -\- Vapor. Two univari- 

 ant equilibria between solid, liquid, and vapor can be formed, the 

 solubility curves of the hexahydrate and the tetrahydrate. The 

 first of these, the equilibrium vapor + solution -t- CaCl2 • 6H2O, 

 has already been considered; both temperature and pres- 

 sure increase from the invariant point with increase in water 

 content of the solution. At the minimum melting point solid 

 hexahydrate melts to form a liquid of the same composition; 

 this is called a congruent melting point. 



The other equilibrium between solid, liquid, and vapor is 

 the solubility curve of the tetrahydrate. Application of 

 equation (8) to this brings out no novel features; temperature and 

 pressure both increase as the solution becomes richer in CaCl2, 

 and this portion of the y-t curve is concave downward over 

 its entire course. It differs from the preceding, however, 

 because of the circumstance that, before the point at which 

 the y-t curve has a horizontal tangent, a new solid phase 

 appears, calcium chloride dihydrate. This gives rise to 

 another invariant point, at which the four phases are tetra- 

 hydrate, dihydrate, solution, and vapor. In the case of the 

 hexahydrate the invariant solution was richer in CaCl2 than 



