HETEROGENEOUS EQUILIBRIUM 

 It is easy to show that 



1 x' y' 



269 



1 X y 



1 x^^'y'"' 



1 x' y' 

 1 x" y" 

 1 x"'y"' 



or, expressed in areas, that 



A234 + ^124 = -4i34 + -4i23. 



Hence we can ehminate any one of the above coefficients,* and 

 cast the equation into the form 



dp 

 dt 



(V" -ri'n + 



iv^ , ^' (,' _ ,-) _ 4^^ (," - ,-) 



^23 



-123 



iv'" -v")-\- 



IV^ , 4!i4(j;' 



v'") - 4^' iv" - v'") 



.(16) 



1-123 



■123 



S6. Equilibrium, KiO-SiOi-^H^O + Solution + Vapor. A 

 systematic apphcation of this equation to the numerous types of 

 equihbria that may arise in ternary systems will not be possible, 

 and the discussion will be confined to one system, the ternary 

 system, H20-K20-Si02-Si02,t which contains examples of 

 several common types of uni variant equilibria. The experi- 

 mental details are given in the first of the papers just cited; the 

 phase relationships are shown in Figs. 5 to 8. Figure 5 shows 

 the isothermal polybaric saturation curves; Fig. 6, the boundary 

 curves and invariant points ;t Fig. 7, the experimentally deter- 



* In a 2-component system the corresponding determinant coefficients 

 represent the lengths of lines; in a 4-component system, volumes of 

 solids; in an n-component system, the supervolumes of n-dimensional 

 supersolids. 



t G. W. Morey and C. N. Fenner, /. Am. Chem. Soc, 39, 1173 (1917). 

 G. W. Morey and E. D. Williamson, /. Am. Chem. Soc, 40, 59 (1918). 

 F. C. Kracek, N. L. Bowen and G. W. Morey, /, Phys. Chem., 33, 1857 

 (1929). 



t In the original, a eutectic between K2O -28102 and Si02 is indicated, 

 but later studies (Kracek, Bowen and Morey, op. cit.) have shown that 

 K2O -48102 is formed, and the compound, K2O- 48102 -H2O, may be con- 

 sidered as a hydrate of the former. The necessary changes in the 

 diagrams have been made. 



