HETEROGENEOUS EQUILIBRIUM 277 



curve of K20-2Si02-H20- Hence, as we saw before, the p-t 

 curves of the equUibrium, K2O • 2Si02 • H2O + K2O -28102 + 

 L + V, coincide with the dissociation-pressure curve of 

 K2O • 2Si02 • H2O, The slope of this curve will remain positive as 

 we go along the boundary curve, K20-2Si02-K20 -28102 -1120, 

 and will not show anything special until the liquid phase falls on 

 the line, V-K2O-28IO2. But here the two triangles A234 and 

 A 134 become zero at the same time, and the equation becomes 

 meaningless. This point corresponds to the termination of 

 the curve at the quadruple point, K20- 28102 + K2O - 28102 • H2O 

 •f L + V in the binary system, H2O-K2O • 28IO2. When the 

 liquid has crossed the line, H2O-K2O • 28102 the areas of all the 

 triangles change sign, hence dp/dt remains positive, and with 

 decreasing temperature we retrace the same p-t curve to the 

 quintuple point Q4. This portion of the curve also corre- 

 sponds to the equilibrium, K2O - 4SIO2 • H2O + K2O -28102 + 

 K20-28102-H20 -f V. 



In the first equihbrium considered, the univariant equilib- 

 rium, K20-8i02-^H20 -\- K2O-8IO2 + L + V, the assumption 

 that the vapor phase is pure H2O was practically without 

 Influence; the vapor phase might contain appreciable quantities 

 of either K2O or SIO2 or both without appreciably affecting the 

 course of the p-t curve. The only effect would be a slight 

 diminution of the areas Auv and A21V, the coefficients of (77" — 77O 

 and (v" — v^), and of {-q' - v^) and {v' - v^), respectively. In 

 the second case, however, the assumption is of Importance; 

 only in the Improbable case that the ratio of 8102 /K2O in the 

 vapor is the same as in the solid, i.e., 2/1, would it still be true 

 that the equilibrium, K2O -28102 + K2O • 28IO2 - H2O + L -f V, 

 coincides with the equilibria K2O-28IO2 + K2O - 28IO2 - H2O + 

 K20-8i02-|H20 + V and K2O -28102 + K2O • 28102 • H2O ■\- 

 K2O- 48102 -1120 + V, and with the dissociation-pressure curve 

 of K2O -28102-1120. In case the vapor contained a small 

 amount of K2O, the curve, K2O-2SIO2 + K2O • 28IO2 - H2O + L 

 -f V, would consist of two parts, one on one side, the other 

 on the other side, of the dissociation-pressure curve, and the 

 two parts would join at the top in a smooth curve, whose point 

 of maximum temperature would be found at the point where 



