HETEROGENEOUS EQUILIBRIUM 289 



contains H2O only. The presence of K2O in the vapor has been 

 detected,* but the amount was very small. The boundary 

 curves show the change in composition of the liquid phase in 

 the univariant equilibria, S' + S" + L + V, as we pass from 

 quintuple point to quintuple point, or from quintuple point to 

 quadruple point, in the limiting binary systems. The com- 

 position of the liquid phase at each quintuple point is given by 

 the point of intersection of three boundary curves; these points 

 are designated by the letters Qi, Q2, etc. The p-t curves 

 experimentally determined are shown in Fig. 7. Figure 8 is a 

 diagrammatic representation of the jp-t curves, which is 

 easier to follow. 



At quintuple point Qi we have the three solid phases, K2O • Si02, 

 K2O • Si02 • ^H20, and K2O -28102, the liquid phase whose com- 

 position is given by the point Qi, and the vapor phase, whose com- 

 position is given by the H2O apex of the component triangle (Figs, 

 5, 6) . Since K2O • SiOa, K2O • SiOa • IH2O and V lie on a straight 

 line, the curves, K2O • 2Si02 + K2O • SiOs + K2O • Si02 • ^H20 + V 

 (curve 10a) t and K20-Si02 + KaO-SiOz- h^20 + L + V (curve 

 106), will coincide; metastably, since the phases, K2O -28102 and 

 L, lie on the same side of the Hne, V-K20-8i02. These two 

 curves also coincide with the dissociation-pressure curve of 

 K2O • 8i02 • IH2O in the binary system, H20-K20-8i02 (curve 

 10a + 106), Fig. 7, hence their position is as shown. 



If the compositions of the phases were such that V, L, and 

 K2O - 28102 lay on a straight line, the y-t curves of the univariant 

 equilibrium, KaO-SiOa + KgO- 28102 + L + V (curve 6d), would 

 coincide, metastably, with the y-t curve, K20-8i02-^H20 + 

 K2O- 28102 + L + V (curve 6c); if the phases V, L, KgO-SiOg 

 lay on a straight line, the curve, K2O • 8102 + K2O - 28102 + L 

 + V (curve 6d), would coincide, stably, with the curve, 

 KjO-SiOa + K20-8i02-^H20 + L -f- V (curve 106). Hence 

 curve, K20-8i02 + K2O- 28102 4- L -|- V {<6d), must lie be- 



* Consult the discussion of this point on p. 1210 of the paper: G. W. 

 Morey and C. N. Fenner, J. Am. Chem. Soc, 39, 1173 (1917). 



t The curves are numbered as in Figs. 5, 6, 7, and 8. In Fig. 6 only 

 curves of the type S' + S" + L + V are shown. In Fig. 8 the p-t curves 

 of the condensed systems are not numbered; their position is obvious. 



