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

Fe + CO = FeO + C

This reaction is succeeded by the two reactions

FeO + CO = Fe + CO₂
CO₂ + C = 2CO

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

Fe₃O₄ + CO = 3FeO + CO₂

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: Fe₃O₄; FeO.

No.	Tube filled with	Duration of the experiment in hours.	Temperature.	Percentage of
No.	Tube filled with	Duration of the experiment in hours.	Temperature.	CO₂	CO
1	CO	14	600°	59.3	40.7
2	CO	15	590°	54.7	45.3
3	CO₂	16	590°	64.6	35.4
4	CO	24	590°	58.4	41.6
5	CO	22	730°	67.7	32.3
6	CO₂	22	730°	86.1	31.9
7	CO	22	750°	68.4	31.6
8	CO₂	22	610°	64.9	35.1
9	CO	23	420°	56.0	44.0
10	CO	47	350°	65.6	34.4
11	CO₂	46	350°	72.8	27.2
12	CO	53	350°	64.0	36.0
13	CO	18	570°	53.4	46.6
14	CO	19	680°	60.5	39.5
15	CO₂	24	540°	55.5	44.5
16	CO	21	630°	57.5	42.5
17	CO₂	17	690°	65.5	34.5
18	CO₂	17	670°	67.0	33.0
19	CO₂	24	410°	58.5	41.5
20	CO	24	490°	51.7	48.8
21	CO₂	23	590°	54.4	45.6
22	CO₂	4	950°	77.0	23.0
23	CO₂	15	850°	73.4	26.6
24	CO	8	800°	71.2	28.8
25	CO₂	24	540°	56.7	43.3

Solid Phases: FeO; Fe.

No.	Tube filled with	Duration of the experiment in hours.	Temperature.	Percentage of
No.	Tube filled with	Duration of the experiment in hours.	Temperature.	CO₂	CO
I.	CO	15	800°	35.2	64.8
II.	CO	18	530°	29.1	70.9
III.	CO	13	880°	30.2	69.6
IV.	CO₂	24	870°	32.3	67.7
V.	CO	18	760°	36.9	63.1
VI.	CO₂	16	820°	34.7	65.3
VII.	CO₂	18	730°	41.1	58.9
VIII.	CO	18	630°	34.9	65.1
IX.	CO₂	17	630°	61.6	58.4
X.	CO	18	540°	25.0	75.0
XI.	CO₂	25	540°	36.5	63.5

As is evident from the above tables and from the curves in Fig. 121, the curve of equilibrium in the case of the reaction

Fe₃O₄ + CO = 3FeO + CO₂

exhibits a maximum for the ratio CO : CO₂, at 490°, while, for the reaction

FeO + CO = Fe + CO₂

this ratio has a minimum value at 680°. From these curves can be derived the conditions under which the different solid phases can exist in contact with gas. Thus, for example, at a temperature of 690°, FeO and Fe₃O₄ can coexist with a mixture of 65.5 per cent. of CO₂ and 34.5 per cent. of CO. If the partial pressure of CO₂ is increased, there occurs the reaction

3FeO + CO₂ = Fe₃O₄ + CO

and if carbon dioxide is added in sufficient amount, the ferrous oxide finally disappears completely. If, on the other hand, the partial pressure of CO is increased, there occurs the reaction

Fe₃O₄ + CO = 3FeO + CO₂

and all the ferric oxide can be made to disappear. We see, therefore, that Fe₃O₄ can only exist at temperatures and in

contact with mixtures of carbon monoxide and dioxide, represented by the area which lies below the under curve in Fig. 121. Similarly, the region of existence of FeO is that represented by the area between the two curves; while metallic iron can exist under the conditions of temperature and composition of gas phase represented by the area above the upper curve in Fig. 121. If, therefore, ferric oxide or metallic iron is heated for a sufficiently long time at temperatures above 700° (to the right of the dotted line; vide infra), complete transformation to ferrous oxide finally occurs.

In another series of equilibria which can be obtained, carbon is one of the solid phases. In Fig. 121 the equilibria between carbon, carbon monoxide, and carbon dioxide under pressures of one and of a quarter atmosphere, are represented by dotted lines.[^[379]]

If we consider only the dotted line on the right, representing the equilibria under atmospheric pressure, we see that the points in which the dotted line cuts the other two curves must represent systems in which carbon monoxide and carbon dioxide are in equilibrium with FeO + Fe₃O₄ + C, on the one hand, and with Fe + FeO + C on the other. These systems can only exist at one definite temperature, if we make the restriction that the pressure is maintained constant (atmospheric pressure). Starting, therefore, with the equilibrium FeO + Fe₃O₄ + CO + CO₂ at a temperature of about 670°, and then add carbon to the system, the reaction

C + CO₂ = 2CO

will occur, because the concentration of CO₂ is greater than what corresponds with the system FeO + Fe₃O₄ + C in equilibrium with carbon monoxide and dioxide. In consequence of this reaction, the equilibrium between FeO + Fe₃O₄ and the gas phase is disturbed, and the change in the composition of the gas phase is opposed by the reaction Fe₃O₄ + CO = 3FeO + CO₂, which continues until either all the carbon

or all the ferric oxide is used up. If the ferric oxide first disappears, the equilibrium corresponds with a point on the dotted line in the middle area of Fig. 121, which represents equilibria between FeO + C as solid phases, and a mixture of carbon monoxide and dioxide as gas phase. If the temperature is higher than 685°, at which temperature the curve for C—CO—CO₂ cuts that for Fe—FeO—CO—CO₂; then, when all the ferric oxide has disappeared, the concentration of CO₂ is still too great for the coexistence of FeO and C. Consequently, there occurs the reaction C + CO₂ = 2CO, and the composition of the gas phase alters until a point on the upper curve is reached. A further increase in the concentration of CO is opposed by the reaction FeO + CO = Fe + CO₂, and the pressure remains constant until all the ferrous oxide is reduced and only iron and carbon remain in equilibrium with gas. If the quantities of the substances have been rightly chosen, we ultimately reach a point on the dotted curve in the upper part of Fig. 121.

Fig. 121 shows us, also, what are the conditions under which the reduction of ferric to ferrous oxide by carbon can occur. Let us suppose, for example, that we start with a mixture of carbon monoxide and dioxide at about 600° (the lowest point on the dotted line), and maintain the total pressure constant and equal to one atmosphere. If the temperature is increased, the concentration of the carbon dioxide will diminish, owing to the reaction C + CO₂ = 2CO, but the ferric oxide will undergo no change until the temperature reaches 647°, the point of intersection of the dotted curve with the curve for FeO and Fe₃O₄. At this point further increase in the concentration of carbon monoxide is opposed by the reduction of ferric oxide in accordance with the equation Fe₃O₄ + CO = 3FeO + CO₂. The pressure, therefore, remains constant until all the ferric oxide has disappeared. If the temperature is still further raised, we again obtain a univariant system, FeO + C, in equilibrium with gas (univariant because the total pressure is constant); and if the temperature is raised the composition of the gas must undergo change. This is effected by the reaction C + CO₂ = 2CO. When the

temperature rises to 685°, at which the dotted curve cuts the curve for Fe—FeO, further change is prevented by the reaction FeO + CO = Fe + CO₂. When all the ferrous oxide is used up, we obtain the system Fe + C in equilibrium with gas. If the temperature is now raised, the composition of the gas undergoes change, as shown by the dotted line. The two temperatures, 647° and 685°, give, evidently, the limits within which ferric or ferrous oxide can be reduced directly by carbon.

It is further evident that at any temperature to the right of the dotted line, carbon is unstable in presence of iron or its oxides; while at temperatures lower than those represented by the dotted line, it is stable. In the blast furnace, therefore, separation of carbon can occur only at lower temperatures, and the carbon must disappear on raising the temperature.

Finally, it may be remarked that the equilibrium curves show that ferrous oxide is most easily reduced at 680°, since the concentration of the carbon monoxide required at this temperature is a minimum. On the other hand, ferric oxide is reduced with greatest difficulty at 490°, since at this temperature the requisite concentration of carbon monoxide is a maximum.

Other equilibria between solid and gas phases are: Equilibrium between iron, ferric oxide, water vapour, and hydrogen,[^[380]] and the equilibria between carbon, carbon monoxide, carbon dioxide, water vapour, and hydrogen,[^[381]] which is of importance for the manufacture of water gas.