The Phase Rule and Its Applications

by Alexander Findlay

2FeCl3,12H2O	HCl,3H2O	2FeCl3,2HCl,12H2O
2FeCl3,7H2O	HCl,2H2O	2FeCl3,2HCl,8H2O
2FeCl3,5H2O	HCl,H2O	2FeCl3,2HCl,4H2O
2FeCl3,4H2O
FeCl3

From this it will be readily understood that the complete study of the conditions of temperature and concentration under which solutions can exist, either with one solid phase or with two or three solid phases, are exceedingly complicated; and, as a matter of fact, only a few of the possible equilibria have been investigated. We shall attempt here only a brief description of the most important of these.[^[368]]

If we again employ rectangular co-ordinates for the graphic

representation of the results, we have the two planes XOT and YOT (Fig. 115): the concentration of ferric chloride being measured along the X-axis, the concentration of hydrogen chloride along the Y-axis, and the temperature along the T-axis. The curve ABCDEFGHJK is, therefore, the solubility curve of ferric chloride in water (p. [152]), and the curve A′B′C′D′E′F′ the solubility curve of hydrogen chloride and its hydrates. B′ and D′ are the melting points of the hydrates HCl,3H₂O and HCl,2H₂O. In the space between these two planes are represented those systems in which all three components are present. As already stated, only a few of the possible ternary systems have been investigated, and these are represented in Fig. 116. The figure shows the model resting on the XOT-plane, so that the lower edge represents the solubility curve of ferric chloride, the concentration increasing from right to left. The concentration of hydrogen chloride is measured upwards, and the temperature forwards. The further end of the model represents the isothermal surface for -30°. The surface of the model on the left does not correspond with the plane YOT in Fig. 115, but with a parallel plane which cuts the concentration axis for ferric chloride at a point representing 65 gm.-molecules FeCl₃ in 100 gm.-molecules of water. The upper surface corresponds with a plane parallel to the axis XOT, at a distance corresponding with the concentration of 50 gm.-molecules HCl in 100 gm.-molecules of water.

Ternary Systems.—We pass over the binary system FeCl₃—H₂O, which has already been discussed (p. [152]), and the similar system HCl—H₂O (see Fig. 115), and turn to the discussion of some of the ternary systems represented by

points on the surface of the model between the planes XOT and YOT. As in the case of carnallite, a plane represents the conditions of concentration of solution and temperature under which a ternary solution can be in equilibrium with a single solid phase (bivariant systems), a line represents the conditions for the coexistence of a solution with two solid phases (univariant systems), and a point the conditions for equilibrium with three solid phases (invariant systems).

In the case of a binary system, in which 2FeCl₃,12H₂O is in equilibrium with a solution of the same composition, addition of hydrogen chloride must evidently lower the temperature at which equilibrium can exist; and the same holds, of course,

for all other binary solutions in equilibrium with this solid phase. In this way we obtain the surface I., which represents the temperatures and concentrations of solutions in which 2FeCl₃,12H₂O can be in equilibrium with a ternary solution containing ferric chloride, hydrogen chloride, and water. This surface is analogous to the curved surface K₁K₂k₄k₃ in Fig. 97 (p. [256]). Similarly, the surfaces II., III., IV., and V. represent the conditions for equilibrium between the solid phases 2FeCl₃,7H₂O; 2FeCl₃,5H₂O; 2FeCl₃,4H₂O; FeCl₃ and ternary solutions respectively. The lines CL, EM, GN, and IO on the model represent univariant systems in which a ternary solution is in equilibrium with two solid phases, viz. with those represented by the adjoining fields. These lines correspond with the ternary eutectic curves k₃K₁ and k₄K₂ in Fig. 97. Besides the surfaces already mentioned, there are still three others, VI., VII., and VIII., which also represent the conditions for equilibrium between one solid phase and a ternary solution; but in these cases, the solid phase is not a binary compound or an anhydrous salt, but a ternary compound containing all three components. The solid phases which are in equilibrium with the ternary solutions represented by the surfaces VI., VII., and VIII., are 2FeCl₃,2HCl,4H₂O; 2FeCl₃,2HCl,8H₂O; and 2FeCl₃,2HCl,12H₂O respectively.