6 4 



ISOMORPHISM AND THERMAL PROPERTIES OF FELDSPARS. 



in an exceptionally favorable case showed still closer identity of 

 composition. 



It appears altogether improbable that the laws of solutions can 

 apply in the face of so extreme a controverting case. 



If it has proved difficult to bring the isomorphous mixture within 

 the general laws of solutions, a most satisfactory theoretical deriva- 

 tion of the conditions of equilibrium in such mixtures has been 

 developed by Roozeboom. No other principle is required than the 

 second law of thermodynamics as applied to solutions by Gibbs: 

 A system of substances will be in equilibrium for a particular pres- 

 sure when the thermodynamic potential (C-function) of the system 

 is a minimum. The scheme of representation is the graphical one 

 proposed by Van Ryn Van Alkemade,* and is itself a powerful 

 instrument of analysis in this field. 



P, T constant 



*Zeitschr. f. Phys. Chem., n, p. 289, 1893. 



Except for the suggestions of Vogt to which reference has been made, this 

 method seems not to have been utilized for the study of mineral solutions before. 

 A brief outline of it will, therefore, be given here. 



In a system of rectilinear coordinates (fig. 17) the ordinates may represent the 

 potential of a particular system (Gibbs' ^-function, not directly measurable) and 



the abscissas the number of gram-mole- 

 cules of solvent (water for example) 

 supposed to contain 1 gr. mol. of solute. 

 In other words, every point of the curve 

 represents a solution of which the x 

 coordinate is concentration and the y 

 coordinate the potential. The condi- 

 tions of pressure and temperature are 

 assumed constant for a particular dia- 

 gram. 



Every such curve for substances solu- 

 ble in all proportions will be convex 

 downward, otherwise there would be some particular point on the curve which 

 would not represent a minimum potential for a particular composition and the 

 solution would tend to separate into two, the mean potential of which would be 

 lower. 



The condition for equilibrium between such a solution and its solid phase (pure 

 salt) may now be readily found. Lay off on the ^-axis a distance equal to the 

 potential of the solid salt and from the point so obtained draw a tangent to the 

 curve. This tangent is the locus of minimum potential (stable systems) for any 

 composition. At the point a, for example, we have a saturated solution contain- 

 ing the number of gr. mol. of solvent indicated by the corresponding abscissa and 



etc 

 the proportion -7 of salt, the balance of the salt remaining in solid phase. At b 



we have the saturated solution with all the salt included ; to the left of b upon the 

 curve, supersaturated solution; and to the right unsaturated solution. With 

 increase of temperature the form of the curve changes and c approaches d, the 

 melting point of the salt. 



Concentration 



Fig. 17. 



