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 constituent 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, potassium, 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 Stassfurt, which constitute at present the chief source of the sulphates and chlorides of magnesium and potassium. 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 relationshipsmet 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
NH4Cl + NaNO3= NaCl + NH4NO3
Since one pair of salts—NaCl + NH4NO3—is formed from the other pair—NH4Cl + NaNO3—by double decomposition, the two pairs of salts are known asreciprocal 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 constitute a system of four, but only ofthreecomponents. This will be understood if it is recalled that only so many constituents are taken as components as are necessary toexpressthe 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 NH4Cl, NaNO3, NH4NO3, NaCl, we can express the composition of NH4Cl by NH4NO3+ NaCl - NaNO3; or of NaNO3by NH4NO3+ NaCl - NH4Cl. In all these cases it will be seen that negative quantities 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 constitute only threecomponents or independently variable constituents, 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—thequintuple 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 constitutes asextuple point. Now, this sextuple 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 sextuple 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: NH4Cl + NaNO3+ NaCl; NH4Cl + NaNO3+ NH4NO3; above the transition point: NaCl + NH4NO3+ NaNO3; NaCl + NH4NO3+ NH4Cl. From this we see that the two salts NH4Cl and NaNO3would be able to exist together with solution below the transition point, but not above it. This transition point has not been determined.
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 passed into its reciprocal, but at which a double salt was formed. Thus, at 4.4° Glauber's salt and potassium chloride form glaserite and sodium chloride, according to the equation
2Na2SO4,10H2O + 3KCl = K3Na(SO4)2+ 3NaCl + 20H2O
Above the transition point, therefore, there would be K3Na(SO4)2, NaCl and KCl; and it may be considered that at a higher temperature the double salt would interact with the potassium chloride according to the equation
K3Na(SO4)2+ KCl = 2K2SO4+ 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 constituent salts; and only after a certain range of temperature (transition interval) has been passed, 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]
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.
Fig. 123Fig.123.
Fig. 122Fig.122.
To represent a given system consisting ofxB,yC, andzD 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 toxandyrespectively. The point of intersectiona(Fig. 122) represents a solution containingxB andyC (ab=x;ac=y). Fromaa lineaP is drawn parallel to OD and equal toz. P then represents the solution of the above composition.
It is usual, however, not to employ the three-dimensional figure, but its horizontal and vertical projections. Fig. 122, if projected on the base of the octahedron, would yield a diagram such as is shown in Fig. 123. The projection of the edges of the octahedron form two axes at right angles and give rise to four quadrants similar to those employed for the representation of ternary solutions (p.273). Here, the pointarepresents a ternary solution saturated with respect to B and C; andaP, quaternary solutions in equilibrium with the same two salts as solid phases. Such a diagram represents the conditions of equilibrium only for one definite temperature, and corresponds, therefore, to the isothermal diagrams for ternary systems (p.273). In such a diagram, since the temperature andpressure are constant (vessels open to the air), a surface will represent a solution in equilibrium with only one solid phase; a line, a solution with two solid phases, and a point, one in equilibrium with three solid phases.
Fig. 124Fig.124.
Example.—As an example of the complete isothermal diagram, there may be given one representing the equilibria in the system composed of water and the reciprocal salt-pair sodium sulphate—potassium chloride for the temperature 0° (Fig. 124).[387]The amounts of the different salts are measured along the four axes, and the composition of the solution isexpressed in equivalent gram-molecules per 1000 gram-molecules of water.[388]
The outline of this figure represents four ternary solutions in which the component salts have a common acid or basic constituent; viz. sodium chloride—sodium sulphate, sodium sulphate—potassium sulphate, potassium sulphate—potassium chloride, potassium chloride—sodium chloride. These four sets of curves are therefore similar to those discussed in the previous chapter. In the case of sodium and potassium sulphate, a double salt,glaserite[K3Na(SO4)2] is formed. Whether glaserite is really a definite compound or not is still a matter of doubt, since isomorphic mixtures of Na2SO4and K2SO4have been obtained. According to van't Hoff and Barscholl,[389]glaserite is an isomorphous mixture; but Gossner[390]considers it to be a definite compound having the formula K3Na(SO4)2. Points VIII. and IX. represent solutions saturated with respect to glaserite and sodium sulphate, and glaserite and potassium sulphate respectively.
The lines which pass inwards from these boundary curves represent solutions containing three salts, but in contact with only two solid phases; and the points where three lines meet, or where three fields meet, represent solutions in equilibrium with three solid phases; with the phases, namely, belonging to the three concurrent fields.
If it is desired to represent a solution containing the salts say in the proportions, 51Na2Cl2, 9.5K2Cl2, 3.5K2SO4, the difficulty is met with that two of the salts, sodium chloride and potassium sulphate, lie on opposite axes. To overcome this difficulty the difference 51 - 3.5 = 47.5 is taken and measured off along the sodium chloride axis; and the solution is therefore represented by the point 47.5Na2Cl2, 9.5K2Cl2. In order, therefore, to find the amount of potassium sulphate presentfrom such a diagram, it is necessary to know the total number of salt molecules in the solution. When this is known, it is only necessary to subtract from it the sum of the molecules of sodium and potassium chloride, and the result is equal to twice the number of potassium sulphate molecules. Thus, in the above example, the total number of salt molecules is 64. The number of molecules of sodium and potassium chloride is 57; 64 - 57 = 7, and therefore the number of potassium sulphate molecules is 3.5.
Another method of representation employed is to indicate the amounts of only two of the salts in a plane diagram, and to measure off the total number of molecules along a vertical axis. In this way a solid model is obtained.
The numerical data from which Fig. 124 was constructed are contained in the following table, which gives the composition of the different solutions at 0°:—[391]
From the aspect of these diagrams the conditions under which the salts can coexist can be read at a glance. Thus,for example, Fig. 124 shows that at 0° Glauber's salt and potassium chloride can exist together with solution; namely, in contact with solutions having the composition X—XI. This temperature must therefore be below the transition point of this salt-pair (p.314). On raising the temperature to 4.4°, it is found that the curve VIII.—XI. moves so that the point XI. coincides with point X. At this point, therefore, there will befourconcurrent fields, viz. Glauber's salt, potassium chloride, glaserite, and sodium chloride. But these four salts can coexist with solution only at the transition point; so that 4.4° is the transition temperature of the salt-pair: Glauber's salt—potassium chloride. At higher temperatures the line VIII.—XI. moves still further to the left, so that the field for Glauber's salt becomes entirely separated from the field for potassium chloride. This shows that at temperatures above the transition point the salt-pair Glauber's salt—potassium chloride cannot coexist in presence of solution.
Fig. 125Fig.125.
If it is only desired to indicate the mutual relationships of the different components and the conditions for their coexistence (paragenesis), a simpler diagram than Fig. 124 can be employed. Thus if the boundary curves of Fig. 124 are so drawn that they cut one another at right angles, a figure such as Fig. 125 is obtained, the Roman numerals here corresponding with those in Fig. 124.
Ammonia-Soda Process.—One of the most important applications of the Phase Rule to systems of four components with reciprocal salt-pairs has recently been made by Fedotieff[392]in his investigations of the conditions for the formation of sodium carbonate by the so-called ammonia-soda (Solvay)process.[393]This process consists, as is well known, in passing carbon dioxide through a solution of common salt saturated with ammonia.
Whatever differences of detail there may be in the process as carried out in different manufactories, the reaction which forms the basis of the process is that represented by the equation
NaCl + NH4HCO3= NaHCO3+ NH4Cl
We are dealing here, therefore, with reciprocal salt-pairs, the behaviour of which has just been discussed in the preceding pages. The present case is, however, simpler than that of the salt-pair Na2SO4.10H2O + KCl, inasmuch as under the conditions of experiment neither hydrates nor double salts are formed. Since the study of the reaction is rendered more difficult on account of the fact that ammonium bicarbonate in solution, when under atmospheric pressure, undergoes decomposition at temperatures above 15°, this temperature was the one chosen for the detailed investigation of the conditions of equilibrium. Since, further, it has been shown by Bodländer[394]that the bicarbonates possess a definite solubility only when the pressure of carbon dioxide in the solution has a definite value, the measurements were carried out in solutions saturated with this gas. This, however, does not constitute another component, because we have made the restriction that the sum of the partial pressures of carbon dioxide and water vapour is equal to 1 atmosphere. The concentration of the carbon dioxide is, therefore, not independently variable (p.10).
Fig. 126Fig.126.
In order to obtain the data necessary for a discussion of the conditions of soda formation by the ammonia-soda process, solubility determinations with the four salts, NaCl, NH4Cl, NH4HCO3, and NaHCO3were made, first with the single salts and thenwith the salts in pairs. The results obtained are represented graphically in Fig. 126, which is an isothermal diagram similar to that given by Fig. 124. The points I., II., III., IV., represent the composition of solutions in equilibrium with two solid salts. We have, however, seen (p.314) that the transition point, when the experiment is carried out under constant pressure (atmospheric pressure), is the point of intersection of four solubility curves, each of which represents the composition of solutions in equilibrium with three salts, viz. one of the reciprocal salt-pairs along with a third salt. Since, now, it was found that the stable salt-pair at temperatures between 0° and 30° is sodium bicarbonate and ammonium chloride, determinations were made of the composition of solutions in equilibrium with NaHCO3+ NH4Cl + NH4HCO3and with NaHCO3+ NH4Cl + NaCl as solid phases. Under theconditions of experiment (temperature = 15°) sodium chloride and ammonium bicarbonate cannot coexist in contact with solution. These determinations gave the data necessary for the construction of the complete isothermal diagram (Fig. 127). The most important of these data are given in the following table (temperature, 15°):—
With reference to the solution represented by the point P1, it may be remarked that it is an incongruently saturated solution (p.279). If sodium chloride is added to this solution, the composition of the latter undergoes change; and if a sufficient amount of the salt is added, the solution P2is obtained.
Turning now to the practical application of the data so obtained, consider first what is the influence of concentration on the yield of soda. Since the reaction consists essentially in a double decomposition between sodium chloride and ammonium bicarbonate, then, after the deposition of the sodium bicarbonate, we obtain a solution containing sodium chloride, ammonium chloride, and sodium bicarbonate. In order to ascertain to what extent the sodium chloride has been converted into solid sodium bicarbonate, it is necessary to examine the composition of the solution which is obtainedwith definite amounts of sodium chloride and ammonium bicarbonate.
Fig. 127Fig.127.
Consider, in the first place, the solutions represented by the curve P2P1. With the help of this curve we can state the conditions under which a solution, saturated for ammonium chloride, is obtained, after deposition of sodium bicarbonate. In the following table the composition of the solutions is given which are obtained with different initial amounts of sodium chloride and ammonium bicarbonate. The last two columns give the percentage amount of the sodium used, which is deposited as solid sodium bicarbonate (UNa); and likewise the percentage amount of ammonium bicarbonate which is usefully converted into sodium bicarbonate, that is to say, the amount of the radical HCO3deposited (UNH4):—
This table shows that the greater the excess of sodium chloride, the greater is the percentage utilization of ammonia (Point P2); and the more the amount of sodium chloride decreases, the greater is the percentage amount of sodium chloride converted into bicarbonate. In the latter case, however, the percentage utilization of the ammonium bicarbonate decreases; that is to say, less sodium bicarbonate is deposited, or more of it remains in solution.
Consider, in the same manner, the relations for solutions represented by the curve P2IV, which gives the composition of solutions saturated with respect to sodium bicarbonate and ammonium bicarbonate. In this case we obtain the following results:—
As is evident from this table, diminution in the relative amount of sodium chloride exercises only a slight influenceon the utilization of this salt, but is accompanied by a rapid diminution of the effective transformation of the ammonium bicarbonate. So far as the efficient conversion of the sodium is concerned, we see that it reaches its maximum at the point P1, and that it decreases both with increase and with decrease of the relative amount of sodium chloride employed; and faster, indeed, in the former than in the latter case. On the other hand, the effective transformation of the ammonium bicarbonate reaches its maximum at the point P2, and diminishes with increase in the relative amount of ammonium bicarbonate employed. Since sodium chloride is, in comparison with ammonia—even when this is regenerated—a cheap material, it is evidently more advantageous to work with solutions which are relatively rich in sodium chloride (solutions represented by the curve P1P2). This fact has also been established empirically.
When, as is the case in industrial practice, we are dealing with solutions which are saturated not for two salts but only for sodium bicarbonate, it is evident that we have then to do with solutions the composition of which is represented by points in the area P1P2I,IV. Since in the commercial manufacture, the aim must be to obtain as complete a utilization of the materials as possible, the solutions employed industrially must lie in the neighbourhood of the curves P2P1IV, as is indicated by the shaded portion in Fig. 127. The best results, from the manufacturer's standpoint, will be obtained, as already stated, when the composition of the solutions approaches that given by a point on the curve P2P1. Considered from the chemical standpoint, the results of the experiments lead to the conclusion that the Solvay process,i.e.passage of carbon dioxide through a solution of sodium chloride saturated with ammonia, is not so good as the newer method of Schlösing, which consists in bringing together sodium chloride and ammonium bicarbonate with water.[395]
Preparation of Barium Nitrite.—Mention may also be made here of the preparation of barium nitrite by double decomposition of barium chloride and sodium nitrite.[396]
The reaction with which we are dealing here is represented by the equation
BaCl2+ 2NaNO2= 2NaCl + Ba(NO2)2
It was found that at the ordinary temperature NaCl and Ba(NO2)2form the stable salt-pair. If, therefore, barium chloride and sodium nitrite are brought together with an amount of water insufficient for complete solution, transformation to the stable salt-pair occurs, and sodium chloride and barium nitrite are deposited. When, however, a stable salt-pair is in its transition interval (p.315), a third salt—in this case barium chloride—will be deposited, as we have already learned. On bringing barium chloride and sodium nitrite together with water, therefore, three solid phases are obtained, viz. BaCl2, NaCl, Ba(NO2)2. These three phases, together with solution and vapour, constitute a univariant system, so that at each temperature the composition of the solution must be constant.
Witt and Ludwig found that the presence of solid barium chloride can be prevented by adding an excess of sodium nitrite, as can be readily foreseen from what has been said. Since the solution in presence of the three solid phases must have a definite composition at a definite temperature, the addition of sodium nitrite to the solution must have, as its consequence, the solution of an equivalent amount of barium chloride, and the deposition of an equivalent amount of sodium chloride and barium nitrite. By sufficient addition of sodium nitrite, the complete disappearance of the solid barium chloride can be effected, and there will remain only the stable salt-pair sodium chloride and barium nitrite. As was pointed out by Meyerhoffer, however, the disappearance of the barium chloride is effected, not by a change in thecomposition of the solution, but by the necessity for the composition of the solution remaining constant.