418 On Freezing* points. Boiling-points* and Solubilities. 



concentration C y (belonging to T y ) and continuing up to the 

 solution having the concentration C //y (belonging to Ty//)- 



C. Only within T T y T y/y T r T a/itZ o>i T abs., and 

 not beyond the same, is real equilibrium possible, as may be 

 seen from the above figures (2 and 3) . The system which is in 

 equilibrium at T, (fig. 2) cannot be in equilibrium at any point 

 on aT r say (5), since the solution will have to contain more salt 

 than it possibly can below T y (this quantity is given by (5') 

 on /3T ; ) : it cannot be in equilibrium at any point on /3T y , say 

 on (6), because solutions containing the amount of salt of (6) 

 can only be in equilibrium with ice at a higher temperature, 

 corresponding to (6') on the freezing-point curve. In the 

 same way the system which is in equilibrium at T //y cannot 

 be in equilibrium at anv point on yT //y , say at (7), since for 

 this a concentration higher than that which the system can 

 dissolve at this temperature (given by [V) on 8T yyy ) will be 

 necessary ; it cannot be in equilibrium at any point on ST yy/ , 

 say at (8). because solutions having the concentration of (8) 

 can be in equilibrium with their vapour at the given atmo- 

 spheric pressure only at (8') on yT //r i. e. at a lower tempe- 

 rature. That systems cannot be in equilibrium beyond the 

 lines T T /5 T,T y// , T y// T</, To'T , T o abs.. has been already 

 generally shown in another place*, when the effect of cooling 

 or heating by the surrounding medium was considered. 

 Though it has been shown in the above papers that the 

 equilibrium of the systems represented by the above diagrams 

 are never in reality reached in nature, the above diagrams lose 

 nevertheless nothing of their meaning and theoretical content. 

 The observed equilibria of systems are always more or less 

 removed from the real points of equilibrium, and the apparent 

 points of equilibrium often fall outside the region of 

 T^T^T/Tq, T o abs., but apparent equilibrium is not real 

 equilibrium, but only a state of the system, when a reaction is 

 still going on in the same. At apparent equilibrium one or 

 more parts of the system may even completely disappear 

 and the system may be transformed into another one, quite in 

 conformity with the meaning of Gibbs' " Rule of Phases." 



The region included in T J/T^T/T, is further most in- 

 teresting on account of the fact that we can here describe any 

 amount of reversible cycle processes, starting from any point 

 and returning to the same in different ways, e.g. starting at T /yy 

 we can pass along the solubility curve, then along the freezing- 

 point curve, then along the curve of pure water or of an 



* See " On real and apparent Freezinff-points, Boiling-points, 

 bilities/' Phil. Mag. xlv. p. 204 (1898), and August 1902, p. 270. 



Solu- 



