HETEROGENEOUS EQUILIBRIUM 265 



liquid immiscible with the first and containing about 36 per 

 cent of phenol, and a vapor phase containing so small an 

 amount of phenol that we may consider it as pure water. 

 Four uni variant equilibria proceed from this invariant point. 

 The equilibrium, solid phenol + solution + vapor, the solubil- 

 ity curve of solid phenol; and the equilibrium, solid phenol + 

 two liquids, a condensed system giving the change with pressure 

 in the composition of the two layers in equilibrium with solid; 

 present no new features, and will not be considered. The 

 equilibrium between vapor, the water-rich liquid, and the 

 phenol-rich liquid is of greater interest. At the invariant 

 point equation (8) becomes 



dp _ rc'^ — x'' 



(^« — v^^) — (y'^ — v^') 



x^' — x^' 



Substituting the values 0, 0.018 and 0.36 for the composition of 

 the vapor, the water-rich hquid and the phenol-rich hquid, 

 respectively, gives us 



(t?" - tjO - W'-v^') 



dp ^ 0.36 - 0.018 



dt (v'' - v^) - 0.053 (y'^ - i;'') 



and in this case also the entropy and volume of the water are the 

 dominating factors. The p-f curve accordingly is concave 

 upward. As the temperature is increased, the two liquids 

 approach each other in composition, the water-rich layer chang- 

 ing less than the phenol-rich layer. But at the same time their 

 specific entropies and specific volumes approach each other, 

 since both are liquids composed of the same components and 

 increasingly close to each other in composition. For this reason 

 the increasing value of the coefficient of the second term is 

 offset by the decrease in the second term itself, and no maximum 

 pressure is found. Finally, the two phases becomiC identical in 

 composition and properties. At the same time that the differ- 

 ence in composition becomes zero the difference in entropy and 



