The Phase Rule and Its Applications Part 27

SOLID PHASES: Fe_{3}O_{4}; FeO.

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

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SOLID PHASES: FeO; Fe.

------+-------------+-------------+--------------+--------------- Duration of Percentage of No. Tube filled experiment Temperature. with in hours. CO_{2} 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. CO_{2} 24 870 32.3 67.7 V. CO 18 760 36.9 63.1 VI. CO_{2} 16 820 34.7 65.3 VII. CO_{2} 18 730 41.1 58.9 VIII. CO 18 630 34.9 65.1 IX. CO_{2} 17 630 61.6 58.4 X. CO 18 540 25.0 75.0 XI. CO_{2} 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

Fe_{3}O_{4} + CO = 3FeO + CO_{2}

exhibits a maximum for the ratio CO : CO_{2}, at 490, while, for the reaction

FeO + CO = Fe + CO_{2}

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 Fe_{3}O_{4} can coexist with a mixture of 65.5 per cent. of CO_{2} and 34.5 per cent.

of CO. If the partial pressure of CO_{2} is increased, there occurs the reaction

3FeO + CO_{2} = Fe_{3}O_{4} + 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

Fe_{3}O_{4} + CO = 3FeO + CO_{2}

and all the ferric oxide can be made to disappear. We see, therefore, that Fe_{3}O_{4} can only exist at temperatures and in {308} 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 + Fe_{3}O_{4} + 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 + Fe_{3}O_{4} + CO + CO_{2} at a temperature of about 670, and then add carbon to the system, the reaction

C + CO_{2} = 2CO

will occur, because the concentration of CO_{2} is greater than what corresponds with the system FeO + Fe_{3}O_{4} + C in equilibrium with carbon monoxide and dioxide. In consequence of this reaction, the equilibrium between FeO + Fe_{3}O_{4} and the gas phase is disturbed, and the change in the composition of the gas phase is opposed by the reaction Fe_{3}O_{4} + CO = 3FeO + CO_{2}, which continues until either all the carbon {309} 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--CO_{2} cuts that for Fe--FeO--CO--CO_{2}; then, when all the ferric oxide has disappeared, the concentration of CO_{2} is still too great for the coexistence of FeO and C. Consequently, there occurs the reaction C + CO_{2} = 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 + CO_{2}, and the pressure remains constant until all the ferrous oxide is reduced and only iron and carbon remain in equilibrium with gas. If the quant.i.ties 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 + CO_{2} = 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 Fe_{3}O_{4}. At this point further increase in the concentration of carbon monoxide is opposed by the reduction of ferric oxide in accordance with the equation Fe_{3}O_{4} + CO = 3FeO + CO_{2}. 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 + CO_{2} = 2CO. When the {310} 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 + CO_{2}. 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.

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CHAPTER XVIII

SYSTEMS OF FOUR COMPONENTS

In the systems which have so far been studied, we have met with cases where two or three components could enter into combination; but in no case did we find double decomposition occurring. The reason of this is that in the systems previously studied, in which double decomposition might have been possible, namely in those systems in which two salts acted as components, the restriction was imposed that either the basic or the acid const.i.tuent of these salts must be the same; a restriction imposed, indeed, for the very purpose of excluding double decomposition. Now, however, we shall allow this restriction to fall, thereby extending the range of study.

Hitherto, in connection with four-component systems, the attention has been directed solely to the study of aqueous solutions of salts, and more especially of the salts which occur in sea-water, _i.e._ chiefly, the sulphates and chlorides of magnesium, pota.s.sium, and sodium. The importance of these investigations will be recognized when one recollects that by the evaporation of sea-water there have been formed the enormous salt-beds at Sta.s.sfurt, which const.i.tute at present the chief source of the sulphates and chlorides of magnesium and pota.s.sium. The investigations, therefore, are not only of great geological interest as tending to elucidate the conditions under which these salt-beds have been formed, but are of no less importance for the industrial working of the deposits.

It is, however, not the intention to enter here into any detailed description of the different systems which have so far been studied, and of the sometimes very complex relations.h.i.+ps {312} met with, but merely to refer briefly to some points of more general import in connection with these systems.[382]

Reciprocal Salt-Pairs. Choice of Components.--When two salts undergo double decomposition, the interaction can be expressed by an equation such as

NH_{4}Cl + NaNO_{3} = NaCl + NH_{4}NO_{3}

Since one pair of salts--NaCl + NH_{4}NO_{3}--is formed from the other pair--NH_{4}Cl + NaNO_{3}--by double decomposition, the two pairs of salts are known as _reciprocal salt-pairs_.[383] It is with systems in which the component salts form reciprocal salt-pairs that we have to deal here.

It must be noted, however, that the four salts formed by two reciprocal salt-pairs do not const.i.tute a system of four, but only of _three_ components. This will be understood if it is recalled that only so many const.i.tuents are taken as components as are necessary to _express_ the composition of all the phases present (p. 12). It will be seen, now, that the composition of each of the four salts which can be present together can be expressed in terms of three of them. Thus, for example, in the case of NH_{4}Cl, NaNO_{3}, NH_{4}NO_{3}, NaCl, we can express the composition of NH_{4}Cl by NH_{4}NO_{3} + NaCl - NaNO_{3}; or of NaNO_{3} by NH_{4}NO_{3} + NaCl - NH_{4}Cl. In all these cases it will be seen that negative quant.i.ties of one of the components must be employed; but that we have seen to be quite permissible (p. 12). The number of components is, therefore, three; but any three of the four salts can be chosen.

Since, then, two reciprocal salt-pairs const.i.tute only three {313} components or independently variable const.i.tuents, another component is necessary in order to obtain a four-component system. As such, we shall choose water.

Transition Point.--In the case of the formation of double salts from two single salts, we saw that there was a point--the _quintuple point_--at which five phases could coexist. This point we also saw to be a transition point, on one side of which the double salt, on the other side the two single salts in contact with solution, were found to be the stable system.

A similar behaviour is found in the case of reciprocal salt-pairs. The four-component system, two reciprocal salt-pairs and water, can give rise to an invariant system in which the six phases, four salts, solution, vapour, can coexist; the temperature at which this is possible const.i.tutes a _s.e.xtuple point_. Now, this s.e.xtuple point is also a transition point, on the one side of which the one salt-pair, on the other side the reciprocal salt-pair, is stable in contact with solution.

The s.e.xtuple point is the point of intersection of the curves of six univariant systems, viz. four solubility curves with three solid phases each, a vapour-pressure curve for the system: two reciprocal salt-pairs--vapour; and a transition curve for the condensed system: two reciprocal salt-pairs--solution. If we omit the vapour phase and work under atmospheric pressure (in open vessels), we find that the transition point is the point of intersection of four solubility curves.

Just as in the case of three-component systems we saw that the presence of one of the single salts along with the double salt was necessary in order to give a univariant system, so in the four-component systems the presence of a third salt is necessary as solid phase along with one of the salt-pairs. In the case of the reciprocal salt-pairs mentioned above, the transition point would be the point of intersection of the solubility curves of the systems with the following groups of salts as solid phases: Below the transition point: NH_{4}Cl + NaNO_{3} + NaCl; NH_{4}Cl + NaNO_{3} + NH_{4}NO_{3}; above the transition point: NaCl + NH_{4}NO_{3} + NaNO_{3}; NaCl + NH_{4}NO_{3} + NH_{4}Cl. From this we see that the two salts NH_{4}Cl and NaNO_{3} would be able to exist together with solution below the transition point, but not above it. This transition point has not been determined. {314}

Formation of Double Salts.--In all cases of four-component systems so far studied, the transition points have not been points at which one salt-pair pa.s.sed into its reciprocal, but at which a double salt was formed. Thus, at 4.4 Glauber's salt and pota.s.sium chloride form glaserite and sodium chloride, according to the equation

2Na_{2}SO_{4},10H_{2}O + 3KCl = K_{3}Na(SO_{4})_{2} + 3NaCl + 20H_{2}O

Above the transition point, therefore, there would be K_{3}Na(SO_{4})_{2}, NaCl and KCl; and it may be considered that at a higher temperature the double salt would interact with the pota.s.sium chloride according to the equation

K_{3}Na(SO_{4})_{2} + KCl = 2K_{2}SO_{4} + NaCl

thus giving the reciprocal of the original salt-pair. This point has, however, not been experimentally realized.[384]

Transition Interval.--A double salt, we learned (p. 277), when brought in contact with water at the transition point undergoes partial decomposition with separation of one of the const.i.tuent salts; and only after a certain range of temperature (transition interval) has been pa.s.sed, can a pure saturated solution be obtained. A similar behaviour is also found in the case of reciprocal salt-pairs. If one of the salt-pairs is brought in contact with water at the transition point, interaction will occur and one of the salts of the reciprocal salt-pair will be deposited; and this will be the case throughout a certain range of temperature, after which it will be possible to prepare a solution saturated only for the one salt-pair. In the case of ammonium chloride and sodium nitrate the lower limit of the transition interval is 5.5, so that above this temperature and up to that of the transition point (unknown), ammonium chloride and sodium nitrate in contact with water would give rise to a third salt by double decomposition, in this case to sodium chloride.[385]

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Graphic Representation.--For the graphic representation of systems of four components, four axes may be chosen intersecting at a point like the edges of a regular octahedron (Fig. 122).[386] Along these different axes the equivalent molecular amounts of the different salts are measured.

[Ill.u.s.tration: FIG. 122.]

[Ill.u.s.tration: FIG. 123.]

To represent a given system consisting of _x_B, _y_C, and _z_D in a given amount of water (where B, C, and D represent equivalent molecular amounts of the salts), measure off on OB and OC lengths equal to _x_ and _y_ respectively. The point of intersection _a_ (Fig. 122) represents a solution containing _x_B and _y_C (_ab_ = _x_; _ac_ = _y_). From _a_ a line _a_P is drawn parallel to OD and equal to _z_. P then represents the solution of the above composition.