If the double salt is anhydrous, the point S lies at infinity, and the lines ef and gh are parallel to each other.

The same result is arrived at by means of the triangular method of representation.[[377]] If we start with the three components in known amounts, and represent the initial composition of the whole by a point in the triangle, and then ascertain the final composition of the solution in equilibrium with the solid phase at a definite temperature, the line joining the points representing the initial and end concentration passes through the point representing the composition of the solid phase. If two determinations are made with solutions having different initial and final concentrations in equilibrium with the same solid phase, then the point of intersection of the two lines so obtained gives the composition of the solid phase.

CHAPTER XVII

ABSENCE OF A LIQUID PHASE

In the preceding chapters dealing with equilibria in three-component systems, our attention was directed only to those cases in which liquid solutions formed one or more phases. Mention must, however, be made of certain systems which contain no liquid phase, and in which only solids and gases are in equilibrium. Since, in all cases, there can be but one gas phase, four solid phases will be necessary in order to form an invariant system. When only three solid phases are present, the system is univariant; and when only two solid phases coexist with gas, it is bivariant. If, however, we make the restriction that the gas pressure is constant, we diminish the variability by one.

On account of their great industrial importance, we shall describe briefly some of the systems belonging to this class.

Iron, Carbon Monoxide, Carbon Dioxide.—Some of the most important systems of three components in which equilibrium exists between solid and gas phases are those formed by the three components—iron, carbon monoxide, and carbon dioxide—and they are of importance especially for the study of the processes occurring in the blast furnace.

If carbon monoxide is passed over reduced iron powder at a temperature of about 600°, the iron is oxidized and the carbon monoxide reduced with separation of carbon in accordance with the equation