HETEROGENEOUS EQUILIBRIUM 257 



increase in the CaCl2 content the slope of the y-t curve becomes 

 negative, and the pressure falls with increasing temperature. 

 1 7. The Minimum Melting Point of a Dissociating Compound. 

 It will be remembered that in the discussion of the system, 

 H2O-KNO3, it was stated that when the liquid phase was very- 

 close in composition to the solid phase, the coefficient of the 

 second term would become large enough for the small negative 

 volume difference (solid — liquid), multiplied by the large coeffi- 

 cient, to equal the very much larger and positive volume 

 difference (vapor — liquid), but that the effect would be difficult 

 to detect in such a system. When that is the case, the denomi- 

 nator approaches zero, the slope* of the p-t curve, dp/dt, 

 becomes infinite, the curve has a vertical tangent, and hence a 

 point of maximum temperature. This is shown clearly in this 

 system. On further increase in the CaCl2 content of the solu- 

 tion, a maximum temperature is found, after which both tem- 

 perature and pressure fall. Two effects take place very close 

 together here; first, the liquid approaches the solid so closely 

 that the denominator becomes zero, then the two compositions 

 become identical. When the two phases, solid and liquid, have 

 the same composition, the equation of the p-t curve becomes 



dp ri' — 17' 

 dt V' — v^ 



which is the equation of the melting-point curve of the hexa- 

 hydrate. The condensed system, liquid CaCl2-6H20 + solid 

 CaCla -61120, is one of the great majority of cases where melting 

 causes expansion; both the specific entropy and the specific 

 volume of the liquid are greater than those of the solid phase. 

 This melting point of the hydrate is called the "minimum 

 melting point" because it is the lowest temperature at which 

 solid and liquid of the same composition can exist together in 

 equilibrium; a whole series of such melting points can be 

 obtained at higher pressures in the absence of vapor along the 

 melting-point curve of the hydrate, the curve of the condensed 



* Cf . footnote on page 251 ; t is represented by the axis of x, p by 



. tiy . . dp 



the axis of y, hence ~ is equivalent to -j-. 



