HETEROGENEOUS EQUILIBRIUM 259 



second term predominates, the numerator is negative, and 

 dijdx^ is positive; as {x* — x^) approaches zero, the numerator 

 first approaches zero, and both the p-t and t-x curves show a 

 point of maximum temperature. The numerator remains 

 positive when x* = x^, at the minimum melting point, which is 

 no special point on the i-x curve except when dealing with 

 condensed systems, in which the vapor phase is absent. In the 

 case in which Av''^ is positive, the numerator is still negative, 

 hence dt/dx^ still positive, when x* = x^, and at the point of 

 maximum temperature x' < xK In systems in which both 

 components are volatile, complications arise from the varying 

 composition of the vapor phase, and interesting special cases 

 arise when the vapor-pressure curve of the liquid shows either 

 maximum or minimum points, and also in connection with 

 the location of the maximum sublimation temperature, es- 

 pecially with dissociating compounds.* 



19. The Equilibrium between a Dissociating Hydrate and Its 

 Products of Dissociation. From the invariant point, CaCl2 • 6H2O 

 + CaCl2 -41120 + solution + vapor (Fig. 3), four uni- 

 variant equilibria are obtained by the disappearance of each, 

 separately, of these four phases. If the liquid phase dis- 

 appears we have the three phases, hexahydrate, tetrahydrate, 

 and vapor; since all of these phases are of constant composition 

 the pressure is a function of the temperature only; there is no 

 concomitant change in composition of one of the phases. Our 

 equation becomes 



^ ^ ("• - "') - t^S^' - "•[ 



dt , ^ x" — x\ ^ 



{v" — v') — — -iv'' — v') 



x'' — x' 



in which the superscripts h and t represent the hexahydrate and 

 the tetrahydrate, respectively. Substituting the numerical 



values of X', ^tetrahydrate ^^^ ^hexahydrate^ q^ O.QOQS, and 0.5066, 



* J. D. van der Waals, Verslag. Akad. Wetenschappen Amsterdam, 6, 

 482 (1897). A. Smits, Z. physik. Chem., 64, 5 (1906). 



