CHAPTER V

SYSTEMS OF TWO COMPONENTS—PHENOMENA OF DISSOCIATION

In the preceding pages we have studied the behaviour of systems consisting of only one component, or systems in which all the phases, whether solid, liquid, or vapour, had the same chemical composition (p. [13]). In some cases, as, for example, in the case of phosphorus and sulphur, the component was an elementary substance; in other cases, however, e.g. water, the component was a compound. The systems which we now proceed to study are characterized by the fact that the different phases have no longer all the same chemical composition, and cannot, therefore, according to definition, be considered as one-component systems.

In most cases, little or no difficulty will be experienced in deciding as to the number of the components, if the rules given on pp. [12] and [13] are borne in mind. If the composition of all the phases, each regarded as a whole, is the same, the system is to be regarded as of the first order, or a one-component system; if the composition of the different phases varies, the system must contain more than one component. If, in order to express the composition of all the phases present when the system is in equilibrium, two of the constituents participating in the equilibrium are necessary and sufficient, the system is one of two components. Which two of the possible substances are to be regarded as components will, however, be to a certain extent a matter of arbitrary choice.

The principles affecting the choice of components will best be learned by a study of the examples to be discussed in the sequel.

Different Systems of Two Components.—Applying the Phase Rule

P + F = C + 2

to systems of two components, we see that in order that the system may be invariant, there must be four phases in equilibrium together; two components in three phases constitute a univariant, two components in two phases a bivariant system. In the case of systems of one component, the highest degree of variability found was two (one component in one phase); but, as is evident from the formula, there is a higher degree of freedom possible in the case of two-component systems. Two components existing in only one phase constitute a tervariant system, or a system with three degrees of freedom. In addition to the pressure and temperature, therefore, a third variable factor must be chosen, and as such there is taken the concentration of the components. In systems of two components, therefore, not only may there be change of pressure and temperature, as in the case of one-component systems, but the concentration of the components in the different phases may also alter; a variation which did not require to be considered in the case of one-component systems.

Since a two-component system may undergo three possible

independent variations, we should require for the graphic representation of all the possible conditions of equilibrium a system of three co-ordinates in space, three axes being chosen, say, at right angles to one another, and representing the three variables—pressure, temperature, and concentration of components (Fig. 18). A curve (e.g. AB) in the plane containing the pressure and temperature axes would then represent the change of pressure with the temperature, the concentration remaining unaltered (pt-diagram); one in the plane containing the pressure and concentration axes (e.g. AF or DF), the change of pressure with the concentration, the temperature remaining constant (pc-diagram), while in the plane containing the concentration and the temperature axes, the simultaneous change of these two factors at constant pressure would be represented (tc-diagram). If the points on these three curves are joined together, a surface, ABDE, will be formed, and any line on that surface (e.g. FG, or GH, or GI) would represent the simultaneous variation of the three factors—pressure, temperature, concentration. Although we shall at a later point make some use of these solid figures, we shall for the present employ the more readily intelligible plane diagram.

The number of different systems which can be formed from two components, as well as the number of the different phenomena which can there be observed, is much greater than in the case of one component. In the case of no two substances, however, have all the possible relationships been studied; so that for the purpose of gaining an insight into the very varied behaviour of two-component systems, a number of different examples will be discussed, each of which will serve to give a picture of some of the relationships.

Although the strict classification of the different systems according to the Phase Rule would be based on the variability of the systems, the study of the many different phenomena, and the correlation of the comparatively large number of different systems, will probably be rendered easiest by grouping these different phenomena into classes, each of these classes being studied with the help of one or more typical examples. The order of treatment adopted here is, of course, quite arbitrary;

but has been selected from considerations of simplicity and clearness.

Phenomena of Dissociation.

Bivariant Systems.—As the first examples of the equilibria between a substance and its products of dissociation, we shall consider very briefly those cases in which there is one solid phase in equilibrium with vapour. Reference has already been made to such systems in the case of ammonium chloride. On being heated, ammonium chloride dissociates into ammonia and hydrogen chloride. Since, however, in that case the vapour phase has the same total composition as the solid phase, viz. NH₃ + HCl = NH₄Cl, the system consists of only one component existing in two phases; it is therefore univariant, and to each temperature there will correspond a definite vapour pressure (dissociation pressure).[^[146]]

If, however, excess of one of the products of dissociation be added, the system becomes one of two components.

In the first place, analysis of each of the two phases yields as the composition of each, solid: NH₄Cl (= NH₃ + HCl); vapour: mNH₃ + nHCl. Obviously the smallest number of substances by which the composition of the two phases can be expressed is two; that is, the number of components is two. What, then, are the components? The choice lies between NH₃ + HCl, NH₄Cl + NH₃, and NH₄Cl + HCl; for the three substances, ammonium chloride, ammonia, hydrogen chloride, are the only ones taking part in the equilibrium of the system.

Of these three pairs of components, we should obviously choose as the most simple NH₃ and HCl, for we can then represent the composition of the two phases as the sum of the two components. If one of the other two possible pairs of components be chosen, we should have to introduce negative quantities of one of the components, in order to represent the composition of the vapour phase. Although it must be allowed that the introduction of negative quantities of a component in such cases is quite permissible, still it will be

better to adopt the simpler and more direct choice, whereby the composition of each of the phases is represented as a sum of two components in varying proportions (p. [12]).

If, therefore, we have a solid substance, such as ammonium chloride, which dissociates on volatilization, and if the products of dissociation are added in varying amounts to the system, we shall have, in the sense of the Phase Rule, a two-component system existing in two phases. Such a system will possess two degrees of freedom. At any given temperature, not only the pressure, but also the composition, of the vapour-phase, i.e. the concentration of the components, can vary. Only after one of these independent variables, pressure or composition, has been arbitrarily fixed does the system become univariant, and exhibit a definite, constant pressure at a given temperature.

Now, although the Phase Rule informs us that at a given temperature change of composition of the vapour phase will be accompanied by change of pressure, it does not cast any light on the relation between these two variables. This relationship, however, can be calculated theoretically by means of the Law of Mass Action.[^[147]] From this we learn that in the case of a substance which dissociates into equivalent quantities of two gases, the product of the partial pressures of the gases is constant at a given temperature.

This has been proved experimentally in the case of ammonium hydrosulphide, ammonium cyanide, phosphonium bromide, and other substances.[^[148]]

Univariant Systems.—In order that a system of two components shall possess only one degree of freedom, three phases must be present. Of such systems, there are seven possible, viz. S-S-S, S-S-L, S-S-V, L-L-L, S-L-L, L-L-V, S-L-V; S denoting solid, L liquid, and V vapour. In the present chapter we shall consider only the systems S-S-V, i.e. those systems in which there are two solid phases and a vapour phase present.

As an example of this, we may first consider the well-known case of the dissociation of calcium carbonate. This substance on being heated dissociates into calcium oxide, or quick-lime, and carbon dioxide, as shown by the equation CaCO₃

The dissociation pressure of calcium carbonate was first studied by Debray,[^[149]] but more exact measurements have been made by Le Chatelier,[^[150]] who found the following corresponding values of temperature and pressure:—

Temperature.	Pressure in cm. mercury.
547°	2.7
610°	4.6
625°	5.6
740°	25.5
745°	28.9
810°	67.8
812°	76.3
865°	133.3

From this table we see that it is only at a temperature of about 812° that the pressure of the carbon dioxide becomes equal to atmospheric pressure. In a vessel open to

the air, therefore, the complete decomposition of the calcium carbonate would not take place below this temperature by the mere heating of the carbonate. If, however, the carbon dioxide is removed as quickly as it is formed, say by a current of air, then the entire decomposition can be made to take place at a much lower temperature. For the dissociation equilibrium of the carbonate depends only on the partial pressure of the carbon dioxide, and if this is kept small, then the decomposition can proceed, even at a temperature below that at which the pressure of the carbon dioxide is less than atmospheric pressure.

Ammonia Compounds of Metal Chlorides.—Ammonia possesses the property of combining with various substances, chiefly the halides of metals, to form compounds which again yield up the ammonia on being heated. Thus, for example, on passing ammonia over silver chloride, absorption of the gas takes place with formation of the substances AgCl,3NH₃ and 2AgCl,3NH₃, according to the conditions of the experiment. These were the first known substances belonging to this class, and were employed by Faraday in his experiments on the liquefaction of ammonia. Similar compounds have also been obtained by the action of ammonia on silver bromide, iodide, cyanide, and nitrate; and with the halogen compounds of calcium, zinc, and magnesium, as well as with other salts. The behaviour of the ammonia compounds of silver chloride is typical for the compounds of this class, and may be briefly considered here.

It was found by Isambert[^[151]] that at temperatures below 15°, silver chloride combined with ammonia to form the compound AgCl,3NH₃, while at temperatures above 20° the compound 2AgCl,3NH₃ was produced. On heating these substances, ammonia was evolved, and the pressure of this gas was found in the case of both compounds to be constant at a given temperature, but was greater in the case of the former than in the case of the latter substance; the pressure, further, was independent of the amount decomposed. The behaviour of these two substances is, therefore, exactly analogous to that shown by calcium carbonate, and the explanation is also similar.

Regarded from the point of view of the Phase Rule, we see that we are here dealing with two components, AgCl and NH₃. On being heated, the compounds decompose according to the equations:—

2(AgCl,3NH₃)

There are, therefore, three phases, viz. AgCl,3NH₃; 2AgCl,3NH₃, and NH₃, in the one case; and 2AgCl,3NH₃; AgCl, and NH₃ in the other. These two systems are therefore univariant, and to each temperature there must correspond a definite pressure of dissociation, quite irrespective of the amounts of the phases present. Similarly, if, at constant temperature, the volume is increased (or if the ammonia which is evolved is pumped off), the pressure will remain constant so long as two solid phases, AgCl,3NH₃ and 2AgCl,3NH₃, are present, i.e. until the compound richer in ammonia is completely decomposed, when there will be a sudden fall in the pressure to the value corresponding to the system 2AgCl,3NH₃—AgCl—NH₃. The pressure will again remain constant at constant temperature, until all the ammonia has been pumped off, when there will again be a sudden fall in the pressure to that of the system formed by solid silver chloride in contact with its vapour.

The reverse changes take place when the pressure of the ammonia is gradually increased. If the volume is continuously diminished, the pressure will first increase until it has reached a certain value; the compound 2AgCl,3NH₃ can then be formed, and the pressure will now remain constant until all the silver chloride has disappeared. The pressure will again rise, until it has reached the value at which the compound AgCl,3NH₃ can be formed, when it will again remain constant until the complete disappearance of the lower compound. There is no gradual change of pressure on passing from one system to another; but the changes are abrupt, as is demanded by the Phase Rule, and as experiment has conclusively proved.[^[152]]

The dissociation pressures of the two compounds of silver

chloride and ammonia, as determined by Isambert,[^[153]] are given in the following table:—

AgCl,3NH₃.		2AgCl,3NH₃.
Temperature.	Pressure.	Temperature.	Pressure.
0°	29.3 cm.	20.0°	9.3 cm.
10.6°	50.5 ,,	31.0°	12.5 ,,
17.5°	65.5 ,,	47.0°	26.8 ,,
24.0°	93.7 ,,	58.5°	52.8 ,,
28.0°	135.5 ,,	69.0°	78.6 ,,
34.2°	171.3 ,,	71.5°	94.6 ,,
48.5°	241.4 ,,	77.5°	119.8 ,,
51.5°	413.2 ,,	83.5°	159.3 ,,
54.0°	464.1 ,,	86.1°	181.3 ,,
		88.5°	201.3 ,,

The conditions for the formation of these two compounds, by passing ammonia over silver chloride, to which reference has already been made, will be readily understood from the above tables. In the case of the triammonia mono-chloride, the dissociation pressure becomes equal to atmospheric pressure at a temperature of about 20°; above this temperature, therefore, it cannot be formed by the action of ammonia at atmospheric pressure on silver chloride. The triammonia dichloride can, however, be formed, for its dissociation pressure at this temperature amounts to only 9 cm., and becomes equal to the atmospheric pressure only at a temperature of about 68°; and this temperature, therefore, constitutes the limit above which no combination can take place between silver chloride and ammonia under atmospheric pressure.

Attention may be here drawn to the fact, to which reference will also be made later, that two solid phases are necessary in order that the dissociation pressure at a given temperature shall be definite; and for the exact definition of this pressure it is necessary to know, not merely what is the substance undergoing dissociation, but also what is the solid product of dissociation formed. For the definition of the equilibrium, the latter is as important as the former. We shall presently find proof of this in the case

of an analogous class of phenomena, viz. the dissociation of salt hydrates.

Salts with Water of Crystallization.—In the case of the dehydration of crystalline salts containing water of crystallization, we meet with phenomena which are in all respects similar to those just studied. A salt hydrate on being heated dissociates into a lower hydrate (or anhydrous salt) and water vapour. Since we are dealing with two components—salt and water[^[154]]—in three phases, viz. hydrate a, hydrate b (or anhydrous salt), and vapour, the system is univariant, and to each temperature there will correspond a certain, definite vapour pressure (the dissociation pressure), which will be independent of the relative or absolute amounts of the phases, i.e. of the amount of hydrate which has already undergone dissociation or dehydration.

The constancy of the dissociation pressure had been proved experimentally by several investigators[^[155]] a number of years before the theoretical basis for its necessity had been given. In the case of salts capable of forming more than one hydrate, we should obtain a series of dissociation curves (pt-curves), as in the case of the different hydrates of copper sulphate. In Fig. 19 there are represented diagrammatically the vapour-pressure curves of the following univariant systems of copper sulphate and water:—

Curve OA: CuSO₄,5H₂O

Curve OB: CuSO₄,3H₂O

Curve OC: CuSO₄,H₂O

Let us now follow the changes which take place on

increasing the pressure of the aqueous vapour in contact with anhydrous copper sulphate, the temperature being meanwhile maintained constant. If, starting from the point D, we slowly add water vapour to the system, the pressure will gradually rise, without formation of hydrate taking place; for at pressures below the curve OC only the anhydrous salt can exist. At E, however, the hydrate CuSO₄,H₂O will be formed, and as there are now three phases present, viz. CuSO₄, CuSO₄,H₂O, and vapour, the system becomes univariant; and since the temperature is constant, the pressure must also be constant. Continued addition of vapour will result merely in an increase in the amount of the hydrate, and a decrease in the amount of the anhydrous salt. When the latter has entirely disappeared, i.e. has passed into hydrated salt, the system again becomes bivariant, and passes along the line EF; the pressure gradually increases, therefore, until at F the hydrate 3H₂O is formed, and the system again becomes univariant; the three phases present are CuSO₄,H₂O, CuSO₄,3H₂O, vapour. The pressure will remain constant, therefore, until the hydrate 1H₂O has disappeared, when it will again increase till G is reached; here the hydrate 5H₂O is formed, and the pressure once more remains constant until the complete disappearance of the hydrate 3H₂O has taken place.

Conversely, on dehydrating CuSO₄,5H₂O at constant temperature, we should find that the pressure would maintain the value corresponding to the dissociation pressure of the system CuSO₄,5H₂O—CuSO₄,3H₂O—vapour, until all the hydrate 5H₂O had disappeared; further removal of water would then cause the pressure to fall abruptly to the pressure of the system CuSO₄,3H₂O—CuSO₄,H₂O—vapour, at which value it would again remain constant until the tri-hydrate had passed into the monohydrate, when a further sudden diminution of the pressure would occur. This behaviour is represented diagrammatically in Fig. 20, the values of the pressure being those at 50°.

Efflorescence.—From Fig. 19 we are enabled to predict the conditions under which a given hydrated salt will effloresce when exposed to the air. We have just learned that copper

sulphate pentahydrate, for example, will not be formed unless the pressure of the aqueous vapour reaches a certain value; and that conversely, if the vapour pressure falls below the dissociation pressure of the pentahydrate, this salt will undergo dehydration. From this, then, it is evident that a crystalline salt hydrate will effloresce when exposed to the air, if the partial pressure of the water vapour in the air is lower than the dissociation pressure of the hydrate. At the ordinary temperature the dissociation pressure of copper sulphate is less than the pressure of water vapour in the air, and therefore copper sulphate does not effloresce. In the case of sodium sulphate decahydrate, however, the dissociation pressure is greater than the normal vapour pressure in a room, and this salt therefore effloresces.

Indefiniteness of the Vapour Pressure of a Hydrate.—Reference has already been made (p. [84]), in the case of the ammonia compounds of the metal chlorides, to the importance of the solid product of dissociation for the definition of the dissociation pressure. Similarly also in the case of a hydrated salt. A salt hydrate in contact with vapour constitutes only a bivariant system, and can exist therefore at different values of temperature and pressure of vapour, as is seen from the diagram, Fig. 19. Anhydrous copper sulphate can exist in contact with water vapour at all values of temperature and pressure lying in the field below the curve OC; and the hydrate CuSO₄,H₂O can exist in contact with vapour at all values of temperature and pressure in the field BOC. Similarly, each of the other hydrates can exist in contact with vapour at different values of temperature and pressure.

From the Phase Rule, however, we learn that, in order that at a given temperature the pressure of a two-component system

may be constant, there must be three phases present. Strictly, therefore, we can speak only of the vapour pressure of a system; and since, in the cases under discussion, the hydrates dissociate into a solid and a vapour, any statement as to the vapour pressure of a hydrate has a definite meaning only when the second solid phase produced by the dissociation is given. The everyday custom of speaking of the vapour pressure of a hydrated salt acquires a meaning only through the assumption, tacitly made, that the second solid phase, or the solid produced by the dehydration of the hydrate, is the next lower hydrate, where more hydrates than one exist. That a hydrate always dissociates in such a way that the next lower hydrate is formed is, however, by no means certain; indeed, cases have been met with where apparently the anhydrous salt, and not the lower hydrate (the existence of which was possible), was produced by the dissociation of the higher hydrate.[^[156]]

That a salt hydrate can exhibit different vapour pressures according to the solid product of dissociation, can not only be proved theoretically, but it has also been shown experimentally to be a fact. Thus CaCl₂,6H₂O can dissociate into water vapour and either of two lower hydrates, each containing four molecules of water of crystallization, and designated respectively as CaCl₂,4H₂Oα, and CaCl₂,4H₂Oβ. Roozeboom[^[157]] has shown that the vapour pressure which is obtained differs according to which of these two hydrates is formed, as can be seen from the following figures:—

Temperature.	Pressure of System.
Temperature.	CaCl₂,6H₂O; CaCl₂, 4H₂Oα; vapour.	CaCl₂,6H₂O; CaCl₂, 4H₂Oβ; vapour.
-15°	0.027 cm.	0.022 cm.
0	0.092 ,,	0.076 ,,
+10	0.192 ,,	0.162 ,,
20	0.378 ,,	0.315 ,,
25	0.508 ,,	0.432 ,,
29.2	—	0.567 ,,
29.8	0.680 ,,	—

By reason of the non-recognition of the importance of the solid dissociation product for the definition of the dissociation pressure of a salt hydrate, many of the older determinations lose much of their value.

Suspended Transformation.—Just as in systems of one component we found that a new phase was not necessarily formed when the conditions for its existence were established, so also we find that even when the vapour pressure is lowered below the dissociation pressure of a system, dissociation does not necessarily occur. This is well known in the case of Glauber's salt, first observed by Faraday. Undamaged crystals of Na₂SO₄,10H₂O could be kept unchanged in the open air, although the vapour pressure of the system Na₂SO₄,10H₂O—Na₂SO₄—vapour is greater than the ordinary pressure of aqueous vapour in the air. That is to say, the possibility of the formation of the new phase Na₂SO₄ was given; nevertheless this new phase did not appear, and the system therefore became metastable, or unstable with respect to the anhydrous salt. When, however, a trace of the new phase—the anhydrous salt—was brought in contact with the hydrate, transformation occurred; the hydrate effloresced.

The possibility of suspended transformation or the non-formation of the new phases must also be granted in the case where the vapour pressure is raised above that corresponding to the system hydrate—anhydrous salt (or lower hydrate)—vapour; in this case the formation of the higher hydrate becomes a possibility, but not a certainty. Although there is no example of this known in the case of hydrated salts, the suspension of the transformation has been observed in the case of the compounds of ammonia with the metal chlorides (p. [82]). Horstmann,[^[158]] for example, found that the pressure of ammonia in contact with 2AgCl,3NH₃ could be raised to a value higher than the dissociation pressure of AgCl,3NH₃ without this compound being formed. We see, therefore, that even when the existence of the higher compound in contact with the lower became possible, the higher compound was not immediately formed.

Range of Existence of Hydrates.—In Fig. 19 the vapour

pressure curves of the different hydrates of copper sulphate are represented as maintaining their relative positions throughout the whole range of temperatures. But this is not necessarily the case. It is possible that at some temperature the vapour pressure curve of a lower hydrate may cut that of a higher hydrate. At temperatures above the point of intersection, the lower hydrate would have a higher vapour pressure than the higher hydrate, and would therefore be metastable with respect to the latter. The range of stable existence of the lower hydrate would therefore end at the point of intersection. This appears to be the case with the two hydrates of sodium sulphate, to which reference will be made later.[^[159]]

Constancy of Vapour Pressure and the Formation of Compounds.—We have seen in the case of the salt hydrates that the continued addition of the vapour phase to the system caused an increase in the pressure until at a definite value of the pressure a hydrate is formed; the pressure then becomes constant, and remains so, until one of the solid phases has disappeared. Conversely, on withdrawing the vapour phase, the pressure remained constant so long as any of the dissociating compound was present, independently of the degree of the decomposition (p. [86]). This behaviour, now, has been employed for the purpose of determining whether or not definite chemical compounds are formed. Should compounds be formed between the vapour phase and the solid, then, on continued addition or withdrawal of the vapour phase, it will be found that the vapour pressure remains constant for a certain time, and will then suddenly assume a new value, at which it will again remain constant. By this method, Ramsay[^[160]] found that no definite hydrates were formed in the case of ferric and aluminium oxides, but that two are formed in the case of lead oxide, viz. 2PbO,H₂O and 3PbO,H₂O.

The method has also been applied to the investigation of the so-called palladium hydride,[^[161]] and the results obtained appear to show that no compound is formed. Reference will, however, be made to this case later (Chap. X.).

Measurement of the Vapour Pressure of Hydrates.—For the purpose of measuring the small pressures exerted by the vapour of salt hydrates, use is very generally made of a differential manometer called the Bremer-Frowein tensimeter.[^[162]]

This apparatus has the form shown in Fig. 21. It consists of a U-tube, the limbs of which are bent close together, and placed in front of a millimetre scale. The bend of the tube is filled with oil or other suitable liquid, e.g. bromonaphthalene. If it is desired to measure the dissociation pressure of, say, a salt hydrate, concentrated sulphuric acid is placed in the flask e, and a quantity of the hydrate, well dried and powdered,[^[163]] in the bulb d. The necks of the bulbs d and e are then sealed off. Since, as we have learned, suspended transformation may occur, it is advisable to first partially dehydrate the salt, in order to ensure the presence of the second solid product of dissociation; the value of the dissociation pressure being independent of the degree of dissociation of the hydrate (p. [86]). The small bulbs d and e having been filled, the apparatus is placed on its side, so as to allow the liquid to run from the bend of the tube into the bulbs a and b; it is then exhausted through f by means of a mercury pump, and sealed off. The apparatus is now placed in a perpendicular position in a thermostat, and kept at constant temperature until equilibrium is established. Since the vapour pressure on the side containing the sulphuric acid may be regarded as zero, the difference in level of the two surfaces of liquid in the U-tube gives directly the dissociation pressure of the hydrate in terms of the particular liquid employed; if the density of the latter is known, the pressure can then be calculated to cm. of mercury.