Fig. 22Fig. 22.
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.
C1is the percentage amount of phenol in the first layer.C2,, ,, ,, second layer.
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 pointx. 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 linexy. When, however, the concentration has reached the value represented by the pointy, two liquid layers will be formed, the one solution having the composition represented byy, the other that represented byy′. 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 solutiony′. Continued addition of phenol will then lead to the pointx′, 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 andwater 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 byxto one represented byx′, without at any time two liquid phases appearing. Starting withx, the temperature is first raised above the critical solution temperature; phenol is then added until the concentration reaches the pointx2. On allowing the temperature to fall, the system will then pass into the condition represented byx′.
Fig. 23Fig. 23.
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.
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.
Fig. 24Fig. 24.
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.
General Form of Concentration-Temperature Curve.—From the preceding figures it will be seen that the generalform 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 maintainedconstant, 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 thetotalvapour pressure of the system.
Fig. 25Fig. 25.
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 twoliquid phases islessthan that of each of the components is not possible.
With regard to thepartial pressureof 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 chosenbefore 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]
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE
General.—When a solid is brought into contact with a liquid in which it can dissolve, a certain amount of it passes into solution; and the process continues until the concentration reaches a definite value independent of the amount of solid present. A condition of equilibrium is established between the solid and the solution; the solution becomessaturated. Since the number of components is two, and the number of phases three, viz. solid, liquid solution, vapour, the system is univariant. If, therefore, one of the factors, pressure, temperature, or concentration of the components (in the solution[180]), is arbitrarily fixed, the state of the system becomes perfectly defined. Thus, at any given temperature, the vapour pressure of the system and the concentration of the components have a definite value. If the temperature is altered, the vapour pressure and also, in general, the concentration will undergo change. Likewise, if the pressure varies, while the system is isolated so that no heat can pass between it and its surroundings, the concentration and the temperature must also undergo variation until they attain values corresponding to the particular pressure.
That the temperature has an influence, sometimes a very considerable influence, on the amount of substance passing into solution, is sufficiently well known; the effect of pressure, although less apparent, is no less certain. If at any given temperature the volume of the vapour phase is diminished,vapour will condense to liquid, in order that the pressure may remain constant, and so much of the solid will pass into solution that the concentration may remain unchanged; for, so long as the three phases are present, the state of the system cannot alter. If, however, one of the phases,e.g.the vapour phase, disappears, the system becomes bivariant; at any given temperature, therefore, there may be different values of concentration and pressure.
The direction in which change of concentration will occur with change of pressure can be predicted by means of the theorem of Le Chatelier, if it is known whether solution is accompanied by increase or diminution of the total volume. If diminution of the total volume of the system occurs on solution, increase of pressure will increase the solubility; in the reverse case, increase of pressure will diminish the solubility.
This conclusion has also been verified by experiment, as is shown by the following figures.[181]
As can be seen, a large increase of the pressure brings about a no more than appreciable alteration of the solubility; a result which is due, as in the case of the alteration of the fusion point with the pressure, to the small change in volume accompanying solution or increase of pressure. For all practical purposes, therefore, the solubility as determined under atmospheric pressure may be taken as equal to the truesolubility, that is, the solubility when the system is under the pressure of its own vapour.
The Saturated Solution.—From what has been said above, it will be seen that the condition of saturation of a solution can be defined only with respect to a certain solid phase; if no solid is present, the system is undefined, for it then consists of only two phases, and is therefore bivariant. Under such circumstances not only can there be at one given temperature solutions of different concentration, all containing less of one of the components than when that component is present in the solid form, but there can also exist solutions containing more of that component than corresponds to the equilibrium when the solid is present. In the former case the solutions areunsaturated, in the latter case they aresupersaturated with respect to a certain solid phase; in themselves, the solutions are stable, and are neither unsaturated nor supersaturated. Further, if the solid substance can exist in different allotropic modifications, the particular form of the substance which is in equilibrium with the solution must be known, in order that the statement of the solubility may be definite; for each form has its own solubility, and, as we shall see presently, the less stable form has the greater solubility (cf. p.47). In all determinations of the solubility, therefore, not only must the concentration of the components in the solution be determined, but equal importance should be attached to the characterisation of the solid phase present.
In this connection, also, one other point may be emphasised. For the production of the equilibrium between a solid and a liquid, time is necessary, and this time not only varies with the state of division of the solid and the efficiency of the stirring, but is also dependent on the nature of the substance.[182]Considerable care must therefore be taken that sufficient time is allowed for equilibrium to be established. Such care is more especially needful when changes may occur in the solid phase, and neglect of it has greatly diminished the value of many of the older determinations of solubility.
Form of the Solubility Curve.—The solubility curve—thatis, the curve representing the change of concentration of the components in the solution with the temperature—differs markedly from the curve of vapour pressure (p.63), in that it possesses no general form, but may vary in the most diverse manner. Not only may the curve have an almost straight and horizontal course, or slope or curve upwards at varying angles; but it may even slope downwards, corresponding to a decrease in the solubility with rise of temperature; may exhibit maxima or minima of solubility, or may, as in the case of some hydrated salts, pass through a point of maximum temperature. In the latter case the salt may possess two values of solubility at the same temperature. We shall consider these cases in the following chapter.
Fig. 26Fig.26.
The great variety of form shown by solubility curves is at once apparent from Fig. 26, in which the solubility curves of various substances (not, however, drawn to scale) are reproduced.[183]
Varied as is the form of the solubility curve, itsdirection, nevertheless, can be predicted by means of the theorem of van't Hoff and Le Chatelier; for in accordance with that theorem (p.57) increase of solubility with the temperature must occur in those cases where the process of solution is accompanied by anabsorptionof heat; and a decrease in the solubility with rise of temperature will be found in cases where solution occurs withevolutionof heat. Where there is no heat effect accompanying solution,change of temperature will be without influence on the solubility; and if the sign of the heat of solution changes, the direction of the solubility curve must also change,i.e.must show a maximum or minimum point. This has in all cases been verified by experiment.[184]
In applying the theorem of Le Chatelier to the course of the solubility curve, it should be noted that by heat of solution there is meant, not the heat effect produced on dissolving the salt in a large amount of solvent (which is the usual signification of the expression), but the heat which is absorbed or evolved when the salt is dissolved in the almost saturated solution (the so-called last heat of solution). Not only does the heat effect in the two cases have a different value, but it may even have a different sign. A striking example of this is afforded by cupric chloride, as the following figures show:[185]—
In the above table the positive sign indicates evolution of heat, the negative sign, absorption of heat; and the values of the heat effect are expressed in centuple calories. Judging from the heat effect produced on dissolving cupric chloride in a large bulk of water, we should predict that the solubility of that salt would diminish with rise of temperature; as a matter of fact, it increases. This is in accordance with the fact thatthe last heat of solution isnegative(as expressed above),i.e.solution of the salt in the almost saturated solution is accompanied by absorption of heat. We are led to expect this from the fact that the heat of solution changes sign from positive to negative as the concentration increases; experiment also showed it to be the case.
Despite its many forms, it should be particularly noted that the solubility curve of any substance iscontinuous, so long as the solid phase, or solid substance in contact with the solution, remains unchanged. If any "break" or discontinuous change in the direction of the curve occurs, it is a sign that thesolid phase has undergone alteration. Conversely, if it is known that a change takes place in the solid phase, a break in the solubility curve can be predicted. We shall presently meet with examples of this.[186]
A.—Anhydrous Salt and Water.
The Solubility Curve.—In studying the equilibria in those systems of two components in which the liquid phase is a solution or phase of varying composition, we shall in the present chapter limit the discussion to those cases where no compounds are formed, but where the components crystallise out in the pure state. Since some of the best-known examples of such systems are yielded by the solutions of anhydrous salts in water, we shall first of all briefly consider some of the results which have been obtained with them.
For the most part the solubility curves have been studied only at temperatures lying between 0° and 100°, the solid phase in contact with the solution being the anhydrous salt. For the representation of these equilibria, the concentration-temperaturediagram is employed, the concentration being expressed as the number of grams of the salt dissolved in 100 grams of water, or as the number of gram-molecules of salt in 100 gram-molecules of water. The curves thus obtained exhibit the different forms to which reference has already been made. So long as the salt remains unchanged the curve will be continuous, but if the salt alters its form, then the solubility curve will show a break.
Fig. 27Fig.27.
Now, we have already seen in Chapter III. that certain substances are capable of existing in various crystalline forms, and these forms are so related to one another that at a given temperature the relative stability of each pair of polymorphic forms undergoes change. Since each crystalline variety of a substance must have its own solubility, there must be a break in the solubility curve at the temperature of transition of the two enantiotropic forms. At this point the two solubility curves must cut, for since the two forms are in equilibrium with respect to their vapour, they must also be in equilibrium with respect to their solutions. From the table on p.63it is seen that potassium nitrate, ammonium nitrate, silver nitrate, thallium nitrate, thallium picrate, are capable of existing in two or more different enantiotropic crystalline forms, the range of stability of these forms being limited by definite temperatures (transition temperature). Since the transition point is not altered by a solvent (provided the latter is not absorbed by the solid phase), we should find on studying the solubility of these substances in water that the solubility curve would exhibit a change in direction at the temperature of transition. As a matter of fact this has been verified, more especially in the case of ammonium nitrate[187]and thallium picrate.[188]The following table contains the values of the solubility of ammonium nitrate obtained by Müller and Kaufmann, the solubility being expressed in gram-molecules NH4NO3in 100 gram-molecules of water. In Fig. 27 these results are represented graphically. The equilibrium point was approached both from the side of unsaturation and of supersaturation, and the condition of equilibrium was controlled by determinations of the density of the solution.
Solubility of Ammonium Nitrate.
From the graphic representation of the solubility given in Fig. 27, there is seen to be a distinct change in the direction of the curve at a temperature of 32°; and this break in the curve corresponds to the transition of theβ-rhombic into theα-rhombic form of ammonium nitrate (p.63).
Suspended Transformation and Supersaturation.—As has already been learned, the transformation of the one crystalline form into the other does not necessarily take place immediately the transition point has been passed; and it has therefore been found possible in a number of cases to follow the solubility curve of a given crystalline form beyond the point at which it ceases to be the most stable modification. Now, it will be readily seen from Fig. 27 that if the two solubility curves be prolonged beyond the point of intersection, the solubility of the less stable form is greater than that of the more stable. A solution, therefore, which is saturated with respect to the less stable form,i.e.which is in equilibrium with that form, issupersaturated with respect to the more stable modification. If,therefore, a small quantity of the more stable form is introduced into the solution, the latter must deposit such an amount of the more stable form that the concentration of the solution corresponds to the solubility of the stable form at the particular temperature. Since, however, the solution is nowunsaturatedwith respect to the less stable variety, the latter, if present, must pass into solution; and the two processes, deposition of the stable and solution of the metastable form, must go on until the latter form has entirely disappeared and a saturated solution of the stable form is obtained. There will thus be a conversion, through the medium of the solvent, of the less stable into the more stable modification. This behaviour is of practical importance in the determination of transition points (v.Appendix).
From the above discussion it will be seen how important is the statement of the solid phase for the definition of saturation and supersaturation.[189]
Solubility Curve at Higher Temperatures.—On passing to the consideration of the solubility curves at higher temperatures, two chief cases must be distinguished.
(1) The two components in the fused state can mix in all proportions.(2) The two components in the fused state cannot mix in all proportions.
(1) The two components in the fused state can mix in all proportions.
(2) The two components in the fused state cannot mix in all proportions.
1.Complete Miscibility of the Fused Components.
Fig. 28Fig.28.
The best example of this which has been studied, so far as anhydrous salts and water are concerned, is that of silver nitrate and water. The solubility of this salt at temperaturesabove 100° has been studied chiefly by Etard[190]and by Tilden and Shenstone.[191]The values obtained by Etard are given in the following table, and represented graphically in Fig. 28.
Solubility of Silver Nitrate.
In this figure the composition of the solution is expressed in parts of silver nitrate in 100 parts by weight of the solution, so that 100 per cent. represents pure silver nitrate. As can be seen, the solubility increases with the temperature. At a temperature of about 160° there should be a break in the curve due to change of crystalline form (p.63). Such a change in the direction of the solubility curve, however, does not in any way alter the essential nature of the relationships discussed here, and may for the present be left out of account. On following the solubility curve of silver nitrate to higher temperatures, therefore, the concentration of silver nitrate in the solution gradually increases, until at last, at a temperature of 208°,[192]the melting point of pure silver nitrate is reached, and the concentration of the water has become zero. The curve throughout its whole extent represents the equilibrium between silver nitrate, solution, and vapour. Conversely, starting with pure silver nitrate in contact with the fused salt, addition of water will lower the melting point,i.e.will lower the temperature at which the solid salt can exist in contact with the liquid;and the depression will be all the greater the larger the amount of water added. As the concentration of the water in the liquid phase is increased, therefore, the system will pass back along the curve from higher to lower temperatures, and from greater to smaller concentrations of silver nitrate in the liquid phase. The curve in Fig. 28 may, therefore, be regarded either as the solubility curve of silver nitrate in water, or as the freezing point curve for silver nitrate in contact with a solution consisting of that salt and water.
As the temperature of the saturated solution falls, silver nitrate is deposited, and on lowering the temperature sufficiently a point will at last be reached at which ice also begins to separate out. Since there are now four phases co-existing, viz. silver nitrate, ice, solution, vapour, the system is invariant, and the point is aquadruple point. This quadruple point, therefore, forms the lower limit of the solubility curve of silver nitrate. Below this point the solution becomes metastable.
Ice as Solid Phase.—Ice melts or is in equilibrium with water at a temperature of 0°. The melting point, will, however, be lowered by the solution of silver nitrate in the water; and the greater the concentration of the salt in the solution the greater will be the depression of the temperature of equilibrium. On continuing the addition of silver nitrate, a point will at length be reached at which the salt is no longer dissolved, but remains in the solid form along with the ice. We again obtain, therefore, the invariant system ice—salt—solution—vapour. The temperature at which this invariant system can exist has been found by Middelberg[193]to be -7.3°, the solution at this point containing 47.1 per cent. of silver nitrate.
The same general behaviour will be found in the case of all other systems of two components belonging to this class; that is, in the case of systems from which the components crystallise out in the pure state, and in which the fused components are miscible in all proportions. In all such cases, therefore, the solubility curves (curves of equilibrium) can be represented diagrammatically as in Fig. 29. In this figure OA represents the solubility curve of the salt, and OB the freezingpoint curve of ice. O is the quadruple point at which the invariant system exists, and may be regarded as the point of intersection of the solubility curve with the freezing-point curve. Since this point is fixed, the condition of the system as regards temperature, vapour pressure, and concentration of the components (or composition of the solution), is perfectly definite. From the way, also, in which the condition is attained, it is evident that the quadruple point is the lowest temperature that can be obtained with mixtures of the two components in presence of vapour. It is known as thecryohydric point, or, generally, theeutectic point.[194]