Fig. 115Fig.115.
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 bypoints 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 asinglesolid 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).
Fig. 116Fig.116.
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 K1K2k4k3in 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; FeCl3and 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 curvesk3K1andk4K2in 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.
The model for FeCl3—HCl—H2O exhibits certain other peculiarities not found in the case of MgCl2—KCl—H2O. On examining the model more closely, it is found that the field of the ternary compound 2FeCl3,2HCl,8H2O (VII.) resembles the surface of a sugar cone, and has a projecting point, the end of which corresponds with a higher temperature than does any other point of the surface. At the point of maximum temperature the composition of the liquid phase is the same as that of the solid. This point, therefore, represents the melting point of the double salt of the above composition.
The curves representing univariant systems are of two kinds. In the one case, the two solid phases present are both binary compounds; or one is a binary compound and the other is one of the components. In the other case, either one or both solid phases are ternary compounds. Curves belongingto the former class (so-calledborder curves) start from binary eutectic points, and their course is always towards lower temperatures,e.g.CL, EM, GN, IO. Curves belonging to the latter class (so-calledmedial curves) would, in a triangular diagram, lie entirely within the triangle. Such curves are YV, WV, VL, LM, MV, NS, ST, SO, OZ. These curves do not always run from higher to lower temperatures, but may even exhibit a point of maximum temperature. Such maxima are found, for example, at U (Fig. 116), and also on the curves ST and LV.
Finally, whereas all the other ternary univariant curves run in valleys between the adjoining surfaces, we find at the point X a similar appearance to that found in the case of carnallite, as the univariant curve here rises above the surrounding surface. The point X, therefore, does not correspond with a eutectic point, but with a transition point. At this point the ternary compound 2FeCl3,2HCl,12H2O melts with separation of 2FeCl3,12H2O, just as carnallite melts at 168° with separation of potassium chloride.
The Isothermal Curves.—A deeper insight into the behaviour of the system FeCl3—HCl—H2O is obtained from a study of the isothermal curves, the complete series of which, so far as they have been studied, is given in Fig. 117.[369]In this figure the lightly drawn curves represent isothermal solubility curves, the particular temperature being printed beside the curve.[370]The dark lines give the composition of the univariant systems at different temperatures. The point of intersection of a dark with a light curve gives the composition of the univariant solution at the temperature represented by the light curve; and the point of intersection of two dark lines gives the composition of the invariant solution in equilibrium with three solid phases. The dotted lines represent metastable systems, and the points P, Q, and R represent solutions ofthe composition of the ternary salts, 2FeCl3,2HCl,4H2O; 2FeCl3,2HCl,8H2O; and 2FeCl3,2HCl,12H2O.
Fig. 117Fig.117.
The farther end of the model (Fig. 116) corresponds, as already mentioned, to the temperature -30°, so that the outline evidently represents the isothermal curve for that temperature. Fig. 117 does not show this. We can, however, follow the isothermal for -20°, which is the extreme curve on the right in Fig. 117. Point A represents the solubility of 2FeCl3,12H2O in water. If hydrogen chloride is added, the concentration of ferric chloride in the solution first decreases and then increases, until at point 34 the ternary double salt 2FeCl3,2HCl,12H2O is formed. If the addition of hydrogen chloride is continued, the ferric chloride disappears ultimately, and only the ternary double salt remains. This salt can coexist with solutions of the composition represented by the curve which passes through the points 173, 174, 175. At the last-mentioned point, the ternary salt with 8H2O is formed. The composition of the solutions with which this salt is in equilibrium at -20° is represented by the curve which passes through a point of maximal concentration with respect to HCl, and cuts the curve SN at the point 112, at which the solution is in equilibrium with the two solid phases 2FeCl3,4H2O and 2FeCl3,2HCl,8H2O. The succeeding portion of the isotherm represents the solubility curve at -20° of 2FeCl3,4H2O, which cuts the dark line OS at point 113, at which the solution is in equilibrium with the two solid phases 2FeCl3,4H2O and 2FeCl3,2HCl,4H2O. Thereafter comes the solubility curve of the latter compound.
The other isothermal curves can be followed in a similar manner. If the temperature is raised, the region of existence of the ternary double salts becomes smaller and smaller, and at temperatures above 30° the ternary salts with 12H2O and 8H2O are no longer capable of existing. If the temperature is raised above 46°, only the binary compounds of ferric chloride and water and the anhydrous salt can exist as solid phases. The isothermal curve for 0° represents the solubility curve for 2FeCl3,12H2O; 2FeCl3,7H2O; 2FeCl3,5H2O; and 2FeCl3,4H2O.
Finally, in the case of the system FeCl3—HCl—H2O, we findclosedisothermal curves. Since, as already stated, the salt 2FeCl3,2HCl,8H2O has a definite melting point, the temperature of which is therefore higher than that at which this compound is in equilibrium with solutions of other composition, it follows that the line of intersection of an isothermal plane corresponding with a temperature immediately below the melting point of the salt with the cone-shaped surface of its region of existence, will form a closed curve. This is shown by the isotherm for -4.5°, which surrounds the point Q, the melting point of the ternary salt.
The following table gives some of the numerical data from which the curves and the model have been constructed:—
Basic Salts.—Another class of systems in the study ofwhich the Phase Rule has performed exceptional service, is that of the basic salts. In many cases it is impossible, by the ordinary methods of analysis, to decide whether one is dealing with a definite chemical individual or with a mixture. The question whether a solid phase is a chemical individual can, however, be answered, in most cases, with the help of the principles which we have already learnt. Let us consider, for example, the formation of basic salts from bismuth nitrate, and water. In this case we can choose as components Bi2O3, N2O5, and H2O; since all the systems consist of these in varying amounts. If we are dealing with a condition of equilibrium at constant temperature between liquid and solid phases, three cases can be distinguished,[371]viz.—
1. The solutions in different experiments have the same composition, but the composition of the precipitate alters. In this case there must be two solid phases.
2. The solutions in different experiments can have varying composition, while the composition of the precipitate remains unchanged. In this case only one solid phase exists, a definite compound.
3. The composition both of the solution and of the precipitate varies. In this case the solid phase is a solid solution or a mixed crystal.
In order, therefore, to decide what is the nature of a precipitate produced by the hydrolysis of a normal salt, it is only necessary to ascertain whether and how the composition of the precipitate alters with alteration in the composition of the solution. If the composition of the solution is represented by abscissæ, and the composition of the precipitate by ordinates, the form of the curves obtained would enable us to answer our question; for vertical lines would indicate the presence of two solid phases (1st case), horizontal lines the presence of only one solid phase (2nd case), and slanting lines the presence of mixed crystals (3rd case). This method of representation cannot, however, be carried out in most cases. It is, however,generally possible to find one pair or several pairs of components, therelative amountsof which in the solution or in the precipitate undergo change when, and only when, the composition of the solution or of the precipitate changes. Thus, in the case of bismuth, nitrate, and water, we can represent the ratio of Bi2O3: N2O5in the precipitate as ordinates, and N2O5: H2O in the solution as abscissæ. A horizontal line then indicates a single solid phase, and a vertical line two solid phases. An example of this is given in Fig. 118.[372]
Fig. 118Fig.118.
Bi2O3—N2O5—H2O.—Although various systems have been studied in which there is formation of basic salts,[373]we shall content ourselves here with the description of some of the conditions for the formation of basic salts of bismuth nitrate, and for their equilibrium in contact with solutions.[374]
Three normal salts of bismuth oxide and nitric acid are known, viz. Bi2O3,3N2O5,10H2O(S10); Bi2O3,3N2O5,4H2O(S4); and Bi2O3,3N2O5,3H2O(S3). Besides these normal salts, there are the following basic salts:—
Probably some others also exist. The problem now is to find the conditions under which these different normal and basic salts can be in equilibrium with solutions of varying concentration of the three components. Having determined the equilibrium conditions for the different salts, it is then possible to construct a model similar to that for MgCl2—KCl—H2O or for FeCl3—HCl—H2O, from which it will be possible to determine the limits of stability of the different salts, and to predict what will occur when we bring the salts in contact with solutions of nitric acid of different concentrations and at different temperatures.
For our present purpose it is sufficient to pick out only some of the equilibria which have been studied, and which are represented in the model (Fig. 119). In this case use has been made of the triangular method of representation, so that the surface of the model lies within the prism.
Fig. 119Fig.119.
This model shows the three surfaces, A, B, and C, which represent the conditions for the stable existence of the salts B1-1-1, S10, and S3in contact with solution at differenttemperatures. The front surface of the model represents the temperature 9°, and the farther end the temperature 75.5°. The dotted curve represents the isotherm for 20°. The prominences between the surfaces represent, of course, solutions which are saturated in respect of two solid phases. Thus, for example,pabcrepresents solutions in equilibrium with B1-1-1and S10; and the ridgeqdc, solutions in equilibrium with S10and S3. The pointb, which lies at 75.5°, is the point of maximum temperature for S10. If the temperature is raised above this point, S10decomposes into the basic salt B1-1-1and solution. This point is therefore analogous to the point M in the carnallite model, at which this salt decomposes into potassium chloride and solution (p.284); or to the point at which the salt 2FeCl3,2HCl,12H2O decomposes into 2FeCl3,12H2O and solution (p.294). The curvepabhas been followed to the temperature of 72° (pointc). The end of the model is incomplete, but it is probable that in the neighbourhood of the pointcthere exists a quintuple point at which the basic salt B1-2-2appears. In the neighbourhood ofealso there probably exists another quintuple point at which S4is formed. These systems have, however, not been studied.
The following tables give some of the numerical data:—
Isotherm for 20°.
Systems in Equilibrium with B1-1-1and S10(Curvepabc).
Systems in Equilibrium with S10and S3(Curveqde).
Basic Mercury Salts.—The Phase Rule has also been applied by A. J. Cox[375]in an investigation of the basic salts of mercury, the result of which has been to show that, of the salts mentioned in text-books, quite a number are incorrectly stated to be chemical compounds or chemical individuals (p.92). The investigation, which was carried out essentially in the manner described above, included the salts mentioned in the following table; and of the basic salts said to be derived from them, only those mentioned really exist. In the following table, the numbers in the second column give the minimum values of the concentration of the acid, expressed in equivalent normality, necessary for the existence of thecorresponding salts in contact with solution at the temperature given in the third column:—
Mercuric fluoride does not form any basic salt.
Since two succeeding members of a series can coexist only in contact with a solution of definite concentration, we can prepare acid solutions of definite concentration by bringing an excess of two such salts in contact with water.
Indirect Determination of the Composition of the Solid Phase.—It has already been shown (p.228) how the composition of the solid phase in a system of two components can be determined without analysis, and we shall now describe how this can be done in a system of three components.[376]
We shall assume that we are dealing with the aqueous solution of two salts which can give rise to a double salt, in which case we can represent the solubility relations in a system of rectangular co-ordinates. In this case we should obtain, as before (Fig. 120), the isothermadcb, if we express thecomposition of the solution in gram-molecules of A or of B to 100 gram-molecules of water.
Fig. 120Fig. 120.
Let us suppose, now, that the double salt is in equilibrium with the solution at a definite temperature, and that the composition of the solution is represented by the pointe. The greater part of the solution is now separated from the solid phase, and the latter,together with the adhering mother liquor, is analyzed. The composition (expressed, as before, in gram-molecules of A and B to 100 gram molecules of water) will be represented by a point (e.g.f) on the lineeS, where S represents the composition of the double salt. That this is so will be evident when one considers that the composition of the whole mass must lie between the composition of the solution and that of the double salt, no matter what the relative amounts of the solid phase and the mother liquor.
If, in a similar manner, we analyze a solution of a different composition in equilibrium with the same double salt (not necessarily at the same temperature as before), and also the mixture of solid phase and solution, we shall obtain two other points, as, for example,gandh, and the line joining these must likewise pass through S. The method of finding thecomposition of an unknown double salt consists, therefore, in finding, in the manner just described, the position of two lines such asefandgh. The point of intersection of these lines then gives the composition of the double salt.
If the double salt is anhydrous, the point S lies at infinity, and the linesefandghare 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.
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 + CO2CO2+ C = 2CO
Fig. 121Fig. 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
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.
Solid Phases: FeO; Fe.
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 Fe3O4can coexist with a mixture of 65.5 per cent. of CO2and 34.5 per cent. of CO. If the partial pressure of CO2is 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 Fe3O4can only exist at temperatures and incontact 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 + CO2at a temperature of about 670°, and then add carbon to the system, the reaction
C + CO2= 2CO
will occur, because the concentration of CO2is 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 + Fe3O4and 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 carbonor 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—CO2cuts that for Fe—FeO—CO—CO2; then, when all the ferric oxide has disappeared, the concentration of CO2is 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 thetemperature 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.