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 Fe + CO = FeO + C This reaction is succeeded by the two reactions FeO + CO = Fe + CO_{2} CO_{2} + C = 2CO {305} [Illustration: FIG. 121.] The former of these reactions is not complete, but leads to a definite equilibrium. The result of the different reactions is therefore an equilibrium between the three solid phases, carbon, iron, and ferrous oxide, and the gas phase consisting of carbon monoxide and dioxide. We have here four phases; and if the total pressure is maintained constant, equilibrium can occur only at a definite temperature. Since, under certain conditions, we can also have the reaction Fe_{3}O_{4} + CO = 3FeO + CO_{2} {306} a second series of equilibria can be obtained of a character similar to the former. These various equilibria have been investigated by Baur and Glaessner,[378] and the following is a short account of the results of their work. Mixtures of the solid phases in equilibrium with carbon monoxide and dioxide were heated in a porcelain tube at a definite temperature until equilibrium was produced, and the gas was then pumped off and analyzed. The results which were obtained are given in the following tables, and represented graphically in Fig. 121. SOLID PHASES: Fe_{3}O_{4}; FeO.