CHAPTER VI
SOLUTIONS
Definition.—In all the cases which have been considered in the preceding pages, the different phases—with the exception of the vapour phase—consisted of a single substance of definite composition, or were definite chemical individuals.[[164]] But this invariability of the composition is by no means imposed by the Phase Rule; on the contrary, we shall find in the examples which we now proceed to study, that the participation of phases of variable composition in the equilibrium of a system is in no way excluded. To such phases of variable composition there is applied the term solution. A solution, therefore, is to be defined as a homogeneous mixture, the composition of which can undergo continuous variation within certain limits; the limits, namely, of its existence.[[165]]
From this definition we see that the term solution is not restricted to any particular physical state of substances, but includes within its range not only the liquid, but also the gaseous and solid states. We may therefore have solutions of gases in liquids, and of gases in solids; of liquids in liquids or in solids; of solids in liquids, or of solids in solids. Solutions of gases in gases are, of course, also possible; since, however, gas solutions never give rise to more than one phase, their
treatment does not come within the scope of the Phase Rule, which deals with heterogeneous equilibria.
It should also be emphasized that the definition of solution given above, neither creates nor recognizes any distinction between solvent and dissolved substance (solute); and, indeed, a too persistent use of these terms and the attempt to permanently label the one or other of two components as the solvent or the solute, can only obscure the true relationships and aggravate the difficulty of their interpretation. In all cases it should be remembered that we are dealing with equilibria between two components (we confine our attention in the first instance to such), the solution being constituted of these components in variable and varying amounts. The change from the case where the one component is in great excess (ordinarily called the solvent) to that in which the other component predominates, may be quite gradual, so that it is difficult or impossible to say at what point the one component ceases to be the solvent and becomes the solute. The adoption of this standpoint need not, however, preclude one from employing the conventional terms solvent and solute in ordinary language, especially when reference is made only to some particular condition of equilibrium of the system, when the concentration of the two components in the solution is widely different.
Solutions of Gases in Liquids.
As the first class of solutions to which we shall turn our attention, there may be chosen the solutions of gases in liquids, or the equilibria between a liquid and a gas. These equilibria really constitute a part of the equilibria to be studied more fully in Chapter VIII.; but since the two-phase systems formed by the solutions of gases in liquids are among the best-known of the two-component systems, a short section may be here allotted to their treatment.
When a gas is passed into a liquid, absorption takes place to a greater or less extent, and a point is at length reached when the liquid absorbs no more of the gas; a condition of equilibrium is attained, and the liquid is said to be saturated
with the gas. In the light of the Phase Rule, now, such a system is bivariant (two components in two phases); and two of the variable factors, pressure, temperature, and concentration of the components, must therefore be chosen in order that the condition of the system may be defined. If the concentration and the temperature are fixed, then the pressure is also defined; or under given conditions of temperature and pressure, the concentration of the gas in the solution must have a definite value. If, however, the temperature alone is fixed, the concentration and the pressure can alter; a fact so well known that it does not require to be further insisted on.
As to the way in which the solubility of a gas in a liquid varies with the pressure, the Phase Rule of course does not state; but guidance on this point is again yielded by the theorem of van't Hoff and Le Chatelier. Since the absorption of a gas is in all cases accompanied by a diminution of the total volume, this process must take place with increase of pressure. This, indeed, is stated in a quantitative manner in the law of Henry, according to which the amount of a gas absorbed is proportional to the pressure. But this law must be modified in the case of gases which are very readily absorbed; the direction of change of concentration with the pressure will, however, still be in accordance with the theorem of Le Chatelier.
If, on the other hand, the pressure is fixed, then the concentration will vary with the temperature; and since the absorption of gases is in all cases accompanied by the evolution of heat, the solubility is found, in accordance with the theorem of Le Chatelier, to diminish with rise of temperature.
In considering the changes of pressure accompanying changes of concentration and temperature, a distinction must be drawn between the total pressure and the partial pressure of the dissolved gas, in cases where the solvent is volatile. In these cases, the law of Henry applies not to the total pressure of the vapour, but only to the partial pressure of the dissolved gas.
Solutions of Liquids in Liquids.
When mercury and water are brought together, the two liquids remain side by side without mixing. Strictly speaking, mercury undoubtedly dissolves to a certain extent in the water, and water no doubt dissolves, although to a less extent, in the mercury; the amount of substance passing into solution is, however, so minute, that it may, for all practical purposes, be left out of account, so long as the temperature does not rise much above the ordinary.[[166]] On the other hand, if alcohol and water be brought together, complete miscibility takes place, and one homogeneous solution is obtained. Whether water be added in increasing quantities to pure alcohol, or pure alcohol be added in increasing amount to water, at no point, at no degree of concentration, is a system obtained containing more than one liquid phase. At the ordinary temperature, water and alcohol can form only two phases, liquid and vapour. If, however, water be added to ether, or if ether be added to water, solution will not occur to an indefinite extent; but a point will be reached when the water or the ether will no longer dissolve more of the other component, and a further addition of water on the one hand, or ether on the other, will cause the formation of two liquid layers, one containing excess of water, the other excess of ether. We shall, therefore, expect to find all grades of miscibility, from almost perfect immiscibility to perfect miscibility, or miscibility in all proportions. In cases of perfect immiscibility, the components do not affect one another, and the system therefore remains unchanged. Such cases do not call for treatment here. We have to concern ourselves here only with the second and third cases, viz. with cases of complete and of partial miscibility. There is no essential difference between the two classes, for, as we shall see,
the one passes into the other with change of temperature. The formal separation into two groups is based on the miscibility relations at ordinary temperatures.
Partial or Limited Miscibility.—In accordance with the Phase Rule, a pure liquid in contact with its vapour constitutes a univariant system. If, however, a small quantity of a second substance is added, which is capable of dissolving in the first, a bivariant system will be obtained; for there are now two components and, as before, only two phases—the homogeneous liquid solution and the vapour. At constant temperature, therefore, both the composition of the solution and the pressure of the vapour can undergo change; or, if the composition of the solution remains unchanged, the pressure and the temperature can alter. If the second (liquid) component is added in increasing amount, the liquid will at first remain homogeneous, and its composition and pressure will undergo a continuous change; when, however, the concentration has reached a definite value, solution no longer takes place; two liquid phases are produced. Since there are now three phases present, two liquids and vapour, the system is univariant; at a given temperature, therefore, the concentration of the components in the two liquid phases, as well as the vapour pressure, must have definite values. Addition of one of the components, therefore, cannot alter the concentrations or the pressure, but can only cause a change in the relative amounts of the phases.
The two liquid phases can be regarded, the one as a solution of the component I. in component II., the other as a solution of component II. in component I. If the pressure is maintained constant, then to each temperature there will correspond a definite concentration of the components in the two liquid phases; and addition of excess of one will merely alter the relative amounts of the two solutions. As the temperature changes, the composition of the two solutions will change, and there will therefore be obtained two solubility curves, one showing the solubility of component I. in component II., the other showing the solubility of component II. in component I. Since heat may be either evolved or absorbed when one liquid dissolves in another, the solubility may diminish or increase
with rise of temperature. The two solutions which at a given temperature correspond to one another are known as conjugate solutions.
The solubility relations of partially miscible liquids have been studied by Guthrie,[[167]] and more especially by Alexejeff[[168]] and by Rothmund.[[169]] A considerable variety of curves have been obtained, and we shall therefore discuss only a few of the different cases which may be taken as typical of the rest.
Phenol and Water.—When phenol is added to water at the ordinary temperature, solution takes place, and a homogeneous liquid is produced. When, however, the concentration of the phenol in the solution has risen to about 8 per cent., phenol ceases to be dissolved; and a further addition of it causes the formation of a second liquid phase, which consists of excess of phenol and a small quantity of water. In ordinary language it may be called a solution of water in phenol. If now the temperature is raised, this second liquid phase will disappear, and a further amount of phenol must be added in order to produce a separation of the liquid into two layers. In this way, by increasing the amount of phenol and noting the temperature at which the two layers disappear, the so-called solubility curve of phenol in water can be obtained. By noting the change of the solubility with the temperature in this manner, it is found that at all temperatures below 68.4°, the addition of more than a certain amount of phenol causes the formation of two layers; at temperatures above this, however, two layers cannot be formed, no matter how much phenol is added. At temperatures above 68.4°, therefore, water and phenol are miscible in all proportions.
On the other hand, if water is added to phenol at the ordinary temperature, a liquid is produced which consists chiefly of phenol, and on increasing the amount of water beyond a certain point, two layers are formed. On raising the temperature these two layers disappear, and a homogeneous solution is again obtained. The phenomena are exactly analogous to those already described. Since, now, in the second
case the concentration of the phenol in the solution gradually decreases, while in the former case it gradually increases, a point must at length be reached at which the composition of the two solutions becomes the same. On mixing the two solutions, therefore, one homogeneous liquid will be obtained. But the point at which two phases become identical is called a critical point, so that, in accordance with this definition, the temperature at which the two solutions of phenol and water become identical may be called the critical solution temperature, and the concentration at this point may be called the critical concentration.
From what has been said above, it will be seen that at any temperature below the critical solution temperature, two conjugate solutions containing water and phenol in different concentration can exist together, one containing excess of water, the other excess of phenol. The following table gives the composition of the two layers, and the values are represented graphically in Fig. 22.[[170]]
Phenol and Water.
C1 is the percentage amount of phenol in the first layer.
C2 ,, ,, ,, second layer.
| Temperature. | C1. | C2. |
| 20° | 8.5 | 72.2 |
| 30° | 8.7 | 69.9 |
| 40° | 9.7 | 66.8 |
| 50° | 12.0 | 62.7 |
| 55° | 14.2 | 60.0 |
| 60° | 17.5 | 56.2 |
| 65° | 22.7 | 49.7 |
| 68.4° | 36.1 | 36.1 |
The critical solution temperature for phenol and water is 68.4°, the critical concentration 36.1 per cent. of phenol. At all temperatures above 68.4°, only homogeneous solutions of phenol and water can be obtained; water and phenol are then miscible in all proportions.
At the critical solution point the system exists in only two phases—liquid and vapour. It ought, therefore, to possess two degrees of freedom. The restriction is, however, imposed that the composition of the two liquid phases, coexisting at a point infinitely near to the critical point, becomes the same, and this disposes of one of the degrees of freedom. The system is therefore univariant; and at a given temperature the pressure will have a definite value. Conversely, if the pressure is fixed (as is the case when the system is under the pressure of its own vapour), then the temperature will also be fixed; that is, the critical solution temperature has a definite value depending only on the substances. If the vapour phase is omitted, the temperature will alter with the pressure; in this case, however, as in the case of other condensed systems, the effect of pressure is slight.
From Fig. 22 it is easy to predict the effect of bringing together water and phenol in any given quantities at any temperature. Start with a solution of phenol and water having the composition represented by the point x. If to this solution phenol is added at constant temperature, it will dissolve, and the composition of the solution will gradually change, as shown by the dotted line xy. When, however, the concentration has reached the value represented by the point y, two liquid layers will be formed, the one solution having the composition represented by y, the other that represented by y′. The system is now univariant, and on further addition of phenol, the composition of the two liquid phases will remain unchanged, but their relative amounts will alter. The phase richer in phenol will increase in amount; that richer in water will decrease, and ultimately disappear, and there will remain the solution y′. Continued addition of phenol will then lead to the point x′, there being now only one liquid phase present.
Since the critical solution point represents the highest temperature at which two liquid phases consisting of phenol and
water can exist together, these two substances can be brought together in any amount whatever at temperatures higher than 68.4°, without the formation of two layers. It will therefore be possible to pass from a system represented by x to one represented by x′, without at any time two liquid phases appearing. Starting with x, the temperature is first raised above the critical solution temperature; phenol is then added until the concentration reaches the point x2. On allowing the temperature to fall, the system will then pass into the condition represented by x′.
Methylethylketone and Water.—In the case just described, the solubility of each component in the other increased continuously with the temperature. There are, however, cases where a maximum or minimum of solubility is found, e.g. methylethylketone and water. The curve which represents the equilibria between these two substances is given in Fig. 23, the concentration values being contained in the following table:[[171]]—
Methylethylketone and Water.
| Temperature. | C1 per cent. | C2 per cent. |
| -10° | 34.5 | 89.7 |
| +10° | 26.1 | 90.0 |
| 30° | 21.9 | 89.9 |
| 50° | 17.5 | 89.0 |
| 70° | 16.2 | 85.7 |
| 90° | 16.1 | 84.8 |
| 110° | 17.7 | 80.0 |
| 130° | 21.8 | 71.9 |
| 140° | 26.0 | 64.0 |
| 151.8° | 44.2 | 44.2 |
These numbers and Fig. 23 show clearly the occurrence of a minimum in the solubility of the ketone in water, and also a minimum (at about 10°) in the solubility of water in methylethylketone. Minima of solubility have also been found in other cases.
Triethylamine and Water.—Although in most of the cases studied the solubility of one liquid in another increases with rise of temperature, this is not so in all cases. Thus, at temperatures below 18°, triethylamine and water mix together in all proportions; but, on raising the temperature, the homogeneous solution becomes turbid and separates into two layers. In this case, therefore, the critical solution temperature is found in the direction of lower temperature, not in the direction of higher.[[172]] This behaviour is clearly shown by the graphic representation in Fig. 24, and also by the numbers in the following table:—
Triethylamine and Water.
| Temperature. | C1 per cent. | C2 per cent. |
| 70° | 1.6 | — |
| 50° | 2.9 | — |
| 30° | 5.6 | 96 |
| 25° | 7.3 | 95.5 |
| 20° | 15.5 | 73 |
| ±18.5° | ±30 | ±30 |
General Form of Concentration-Temperature Curve.—From the preceding figures it will be seen that the general
form of the solubility curve is somewhat parabolic in shape; in the case of triethylamine and water, the closed end of the curve is very flat. Since for all liquids there is a point (critical point) at which the liquid and gaseous states become identical, and since all gases are miscible in all proportions, it follows that there must be some temperature at which the liquids become perfectly miscible. In the case of triethylamine and water, which has just been considered, there must therefore be an upper critical solution temperature, so that the complete solubility relations would be represented by a closed curve of an ellipsoidal aspect. An example of such a curve is furnished by nicotine and water. At temperatures below 60° and above 210°, nicotine and water mix in all proportions.[[173]] Although it is possible that this is the general form of the curve for all pairs of liquids, there are as yet insufficient data to prove it.
With regard to the closed end of the curve it may be said that it is continuous; the critical solution point is not the intersection of two curves, for such a break in the continuity of the curve could occur only if there were some discontinuity in one of the phases. No such discontinuity exists. The curve is, therefore, not to be considered as two solubility curves cutting at a point; it is a curve of equilibrium between two components, and so long as the phases undergo continuous change, the curve representing the equilibrium must also be continuous. As has already been emphasized, a distinction between solvent and solute is merely conventional (p. [93]).
Pressure-Concentration Diagram.—In considering the pressure-concentration diagram of a system of two liquid components, a distinction must be drawn between the total pressure of the system and the partial pressures of the components. On studying the total pressure of a system, it is found that two cases can be obtained.[[174]]
So long as there is only one liquid phase, the system is bivariant. The pressure therefore can change with the concentration and the temperature. If the temperature is maintained
constant, the pressure will vary only with the concentration, and this variation can therefore be represented by a curve. If, however, two liquid phases are formed, the system becomes univariant: and if one of the variables, say the temperature, is arbitrarily fixed, the system no longer possesses any degree of freedom. When two liquid phases are formed, therefore, the concentrations and the vapour pressure have definite values, which are maintained so long as the two liquid phases are present; the temperature being supposed constant.
In Fig. 25 is given a diagrammatic representation of the two kinds of pressure-concentration curves which have so far been obtained. In the one case, the vapour pressure of the invariant system (at constant temperature) lies higher than the vapour pressure of either of the pure components; a phenomenon which is very generally found in the case of partially miscible liquids, e.g. ether and water.[[175]] Accordingly, by the addition of water to ether, or of ether to water, there is an increase in the total vapour pressure of the system.
With regard to the second type, the vapour pressure of the systems with two liquid phases lies between that of the two single components. An example of this is found in sulphur dioxide and water.[[176]] On adding sulphur dioxide to water there is an increase of the total vapour pressure; but on adding water to liquid sulphur dioxide, the total vapour pressure is diminished.
The case that the vapour pressure of the system with two
liquid phases is less than that of each of the components is not possible.
With regard to the partial pressure of the components, the behaviour is more uniform. The partial pressure of one component is in all cases lowered by the addition of the other component, the diminution being approximately proportional to the amount added. If two liquid phases are present, the partial pressure of the components, as well as the total pressure, is constant, and is the same for both phases. That is to say, in the case of the two liquids, saturated solution of water in ether, and of ether in water, the partial pressure of the ether in the vapour in contact with the one solution is the same as that in the vapour over the other solution.[[177]]
Complete Miscibility.—Although the phenomena of complete miscibility are here treated under a separate heading, it must not be thought that there is any essential difference between those cases where the liquids exhibit limited miscibility and those in which only one homogeneous solution is formed. As has been already pointed out, the solubility relations alter with the temperature; and liquids which at one temperature can dissolve in one another only to a limited extent, are found at some other temperature to possess the property of complete miscibility. Conversely, we may expect that liquids which at one temperature, say at the ordinary temperature, are miscible in all proportions, will be found at some other temperature to be only partially miscible. Thus, for example, it was found by Guthrie that ethyl alcohol and carbon disulphide, which are miscible in all proportions at the ordinary temperature, possess only limited miscibility at temperatures below -14.4°.[[178]] Nevertheless, it is doubtful if the critical solution temperature is in all cases experimentally realizable.
Pressure-Concentration Diagram.—Since, in the cases of complete miscibility of two liquid components, there are never more than two phases present, the system must always be bivariant; and two of the variables pressure, temperature or concentration of the components, must be arbitrarily chosen
before the system becomes defined. For this reason the Phase Rule affords only a slight guidance in the study of such equilibria; and we shall therefore not enter in detail into the behaviour of these homogeneous mixtures. All that the Phase Rule can tell us in connection with these solutions, is that at constant temperature the vapour pressure of the solution varies with the composition of the liquid phase; and if the composition of the liquid phase remains unchanged, the pressure also must remain unchanged. This constancy of composition is exhibited not only by pure liquids, but also by liquid solutions in all cases where the vapour pressure of the solution reaches a maximum or minimum value. This is the case, for example, with mixtures of constant boiling point.[[179]]