The Phase Rule and Its Applications Part 13

(_The name placed at the head of each table is the solid phase._)

ICE.

--------------------------- Temperature. Composition.

--------------------------- -55 2.75 -40 2.37 -27.5 1.90 -20.5 1.64 -10 1.00 0 0 ---------------------------

Fe_{2}Cl_{6},12H_{2}O.

--------------------------- Temperature. Composition.

--------------------------- -55 2.75 -41 2.81 -27 2.98 0 4.13 10 4.54 20 5.10 30 5.93 35 6.78 36.5 7.93 37 8.33 36 9.29 33 10.45 30 11.20 274 12.15 20 12.83 10 13.20 8 13.70 ---------------------------

Fe_{2}Cl_{6},7H_{2}O.

--------------------------- Temperature. Composition.

--------------------------- 20 11.35 274 12.15 32 13.55 32.5 14.29 30 15.12 25 15.54 ---------------------------

Fe_{2}Cl_{6},5H_{2}O.

--------------------------- Temperature. Composition.

--------------------------- 20 11.35 12 12.87 20 13.95 27 14.85 30 15.12 35 15.64 50 17.50 55 19.15 56 20.00 55 20.32 ---------------------------

Fe_{2}Cl_{6},4H_{2}O --------------------------- Temperature. Composition.

--------------------------- 20 11.35 50 19.96 55 20.32 60 20.70 69 21.53 72.5 23.35 73.5 25.00 72.5 26.15 70 27.90 66 29.20 ---------------------------

Fe_{2}Cl_{6} (ANHYDROUS).

--------------------------- Temperature. Composition.

--------------------------- 20 11.35 66 29.20 70 29.42 75 28.92 80 29.20 100 29.75 ---------------------------

The lowest portion of the curve, AB, represents the equilibria between ice and solutions containing ferric chloride. It represents, in other words, the lowering of the fusion point of ice by addition of ferric chloride. At the point B (-55), the cryohydric point (p. 117) is reached, at which the solution is in equilibrium with ice and ferric chloride dodecahydrate. As {154} has already been shown, such a point represents an invariant system; and the liquid phase will, therefore, solidify to a mixture of ice and hydrate without change of temperature. If heat is added, ice will melt and the system will pa.s.s to the curve BCDN, which is the solubility curve of the dodecahydrate. At C (37), the point of maximum temperature, the hydrate melts completely. The retroflex portion of this curve can be followed backwards to a temperature of 8, but below 27.4 (D), the solutions are supersaturated with respect to the heptahydrate; point D is the eutectic point for dodecahydrate and heptahydrate. The curve DEF is the solubility curve of the heptahydrate, E being the melting point, 32.5. On further increasing the quant.i.ty of ferric chloride, the temperature of equilibrium is lowered until at F (30) another eutectic point is reached, at which the heptahydrate and pentahydrate can co-exist with solution. Then follow the solubility curves for the pentahydrate, the tetrahydrate, and the anhydrous salt; G (56) is the melting point of the former hydrate, J (73.5) the melting point of the latter. H and K, the points at which the curves intersect, represent eutectic points; the temperature of the former is 55, that of the latter 66. The dotted portions of the curves represent metastable equilibria.

As is seen from the diagram, a remarkable series of solubility curves is obtained, each pa.s.sing through a point of maximum temperature, the whole series of curves forming an undulating "festoon." To the right of the series of curves the diagram represents unsaturated solutions; to the left, supersaturated.

If an unsaturated solution, the composition of which is represented by a point in the field to the right of the solubility curves, is cooled down, the result obtained will differ according as the composition of the solution is the same as that of a cryohydric point, or of a melting point, or has an intermediate value. Thus, if a solution represented by _x__{1} is cooled down, the composition will remain unchanged as indicated by the horizontal dotted line, until the point D is reached. At this point, dodecahydrate and heptahydrate will separate out, and the liquid will ultimately solidify completely to a mixture or "conglomerate" of these two hydrates; the temperature of {155} the system remaining constant until complete solidification has taken place. If, on the other hand, a solution of the composition _x__{3} is cooled down, ferric chloride dodecahydrate will be formed when the temperature has fallen to that represented by C, and the solution will completely solidify, without alteration of temperature, with formation of this hydrate. In both these cases, therefore, a point is reached at which complete solidification occurs without change of temperature.

Somewhat different, however, is the result when the solution has an intermediate composition, as represented by _x__{2} or _x__{4}. In the former case the dodecahydrate will first of all separate out, but on further withdrawal of heat the temperature will fall, the solution will become relatively richer in ferric chloride, owing to separation of the hydrate, and ultimately the eutectic point D will be reached, at which complete solidification will occur. Similarly with the second solution.

Ferric chloride dodecahydrate will first be formed, and the temperature will gradually fall, the composition of the solution following the curve CB until the cryohydric point B is reached, when the whole will solidify to a conglomerate of ice and dodecahydrate.

Suspended Transformation.--Not only can the upper branch of the solubility curve of the dodecahydrate be followed backwards to a temperature of 8, or about 19 below the temperature of transition to the heptahydrate; but suspended transformation has also been observed in the case of the heptahydrate and the pentahydrate. To such an extent is this the case that the solubility curve of the latter hydrate has been followed downwards to its point of intersection with the curve for the dodecahydrate. This point of intersection, represented in Fig. 39 by M, lies at a temperature of about 15; and at this temperature, therefore, it is possible for the two solid phases dodecahydrate and pentahydrate to coexist, so that M is a eutectic point for the dodecahydrate and the pentahydrate. It is, however, a metastable eutectic point, for it lies in the region of supersaturation with respect to the heptahydrate; and it can be realized only because of the fact that the latter hydrate is not readily formed.

Evaporation of Solutions at Constant Temperature.--On {156} evaporating dilute solutions of ferric chloride at constant temperature, a remarkable series of changes is observed, which, however, will be understood with the help of Fig. 40. Suppose an unsaturated solution, the composition of which is represented by the point _x__{1}, is evaporated at a temperature of about 17 - 18. As water pa.s.ses off, the composition of the solution will follow the dotted line of constant temperature, until at the point where it cuts the curve BC the solid hydrate Fe_{2}Cl_{6},12H_{2}O separates out. As water continues to be removed, the hydrate must be deposited (in order that the solution shall remain saturated), until finally the solution dries up to the hydrate. As dehydration proceeds, the heptahydrate can be formed, and the dodecahydrate will finally pa.s.s into the heptahydrate; and this, in turn, into the pentahydrate.

[Ill.u.s.tration: FIG. 40.]

But the heptahydrate is not always formed by the dehydration of the dodecahydrate, and the behaviour on evaporation is therefore somewhat perplexing at first sight. After the solution has dried to the dodecahydrate, as explained above, further removal of water causes liquefaction, and the system is now represented by the point of intersection at _a_; at this point the solid hydrate is in equilibrium with a solution containing relatively more ferric chloride. If, therefore, evaporation is continued, the solid hydrate must _pa.s.s into solution_ in order that the composition of the latter may remain unchanged, so that ultimately a liquid will again be obtained. A very slight further dehydration will bring the solution into the state represented by _b_, at which the pentahydrate is formed, and the solution will at last disappear and leave this hydrate alone.

Without the information to be obtained from the curves in Figs. 39 and 40, the phenomena which would be observed on carrying out the evaporation at a temperature of about 31 - 32 {157} would be still more bewildering. The composition of the different solutions formed will be represented by the perpendicular line _x__{2}12345. Evaporation will first cause the separation of the dodecahydrate, and then total disappearance of the liquid phase. Then liquefaction will occur, and the system will now be represented by the point 2, in which condition it will remain until the solid hydrate has disappeared. Following this there will be deposition of the heptahydrate (point 3), with subsequent disappearance of the liquid phase.

Further dehydration will again cause liquefaction, when the concentration of the solution will be represented by the point 4; the heptahydrate will ultimately disappear, and then will ensue the deposition of the pentahydrate, and complete solidification will result. On evaporating a solution, therefore, of the composition _x__{2}, the following series of phenomena will be observed: solidification to dodecahydrate; liquefaction; solidification to heptahydrate; liquefaction; solidification to pentahydrate.[233]

Although ferric chloride and water form the largest and best-studied series of hydrates possessing definite melting points, examples of similar hydrates are not few in number; and more careful investigation is constantly adding to the list.[234] In all these cases the solubility curve will show a point of maximum temperature, at which the hydrate melts, and will end, above and below, in a cryohydric point. Conversely, if such a curve is found in a system of two components, we can argue that a definite compound of the components possessing a definite melting point is formed.

Inevaporable Solutions.--If a saturated solution in contact with two hydrates, or with a hydrate and anhydrous salt is heated, the temperature and composition of the solution will, of course, remain unchanged so long as the two solid phases are present, for such a system is invariant. In addition to this, however, the _quant.i.ty_ of the solution will also remain unchanged, the water which evaporates being supplied by the higher hydrate.

The same phenomenon is also observed in the case of cryohydric points when ice is a solid phase; so long as the latter is present, evaporation will be accompanied {158} by fusion of the ice, and the quant.i.ty of solution will remain constant. Such solutions are called _inevaporable_.[235]

[Ill.u.s.tration: FIG. 41.]

Ill.u.s.tration.--In order to ill.u.s.trate the application of the principles of the Phase Rule to the study of systems formed by a volatile and a non-volatile component, a brief description may be given of the behaviour of sulphur dioxide and pota.s.sium iodide, which has formed the subject of a recent investigation. After it had been found[236] that liquid sulphur dioxide has the property of dissolving pota.s.sium iodide, and that the solutions thus obtained present certain peculiarities of behaviour, the question arose as to whether or not compounds are formed between the sulphur dioxide and the pota.s.sium iodide, and if so, what these compounds are. To find an answer to this question, Walden and Centnerszwer[237] made a complete investigation of the solubility curves (equilibrium curves) of these two components, the investigation extending from the freezing point to the critical point of sulphur dioxide. For convenience of reference, the results which they obtained are represented diagrammatically in Fig. 41.

The freezing point (A) of pure sulphur dioxide was found to be -72.7.

Addition of pota.s.sium iodide lowered the freezing point, but the maximum depression obtained was very small, and was reached when the concentration of the pota.s.sium iodide in the solution was only 0.336 mols. per cent.

Beyond this point, an increase in the concentration of the iodide was accompanied by an elevation of the freezing point, the change of the freezing point with the concentration being represented by the curve BC.

The solid {159} which separated from the solutions represented by BC was a bright _yellow_ crystalline substance. At the point C (-23.4) a temperature-maximum was reached; and as the concentration of the pota.s.sium iodide was continuously increased, the temperature of equilibrium first fell and then slowly rose, until at +0.26 (E) a second temperature-maximum was registered. On pa.s.sing the point D, the solid which was deposited from the solution was a _red_ crystalline substance. On withdrawing sulphur dioxide from the system, the solution became turbid, and the temperature remained constant. The investigation was not pursued farther at this point, the attention being then directed to the equilibria at higher temperatures.

When a solution of pota.s.sium iodide in liquid sulphur dioxide containing 1.49 per cent. of pota.s.sium iodide was heated, solid (pota.s.sium iodide) was deposited at a temperature of 96.4. Solutions containing more than about 3 per cent. of the iodide separated, on being heated, into two layers, and the temperature at which the liquid became heterogeneous fell as the concentration was increased; a temperature-minimum being obtained with solutions containing 12 per cent. of pota.s.sium iodide. On the other hand, solutions containing 30.9 per cent. of the iodide, on being heated, deposited pota.s.sium iodide; while a solution containing 24.5 per cent. of the salt first separated into two layers at 89.3, and then, on cooling, solid was deposited and one of the liquid layers disappeared.

Such are, in brief, the results of experiment; their interpretation in the light of the Phase Rule is the following:--

The curve AB is the freezing-point curve of solid sulphur dioxide in contact with solutions of pota.s.sium iodide. BCD is the solubility curve of the yellow crystalline solid which is deposited from the solutions. C, the temperature-maximum, is the melting point of this _yellow_ solid, and the composition of the latter must be the same as that of the solution at this point (p. 145), which was found to be that represented by the formula KI,14SO_{2}. B is therefore the eutectic point, at which solid sulphur dioxide and the compound KI,14SO_{2} can exist together in equilibrium with solution and vapour. The curve DE is the solubility curve of the _red_ crystalline solid, and the {160} point E, at which the composition of solution and solid is the same, is the melting point of the solid. The composition of this substance was found to be KI,4SO_{2}.[238] D is, therefore, the eutectic point at which the compounds KI,14SO_{2} and KI,4SO_{2} can coexist in equilibrium with solution and vapour. The curve DE does not exhibit a retroflex portion; on the contrary, on attempting to obtain more concentrated solutions in equilibrium with the compound KI,4SO_{2}, a new solid phase (probably pota.s.sium iodide) was formed. Since at this point there are four phases in equilibrium, viz. the compound KI,4SO_{2}, pota.s.sium iodide, solution, and vapour, the system is invariant. E is, therefore, the _transition point_ for KI,4SO_{2} and KI.

Pa.s.sing to higher temperatures, FG is the solubility curve of pota.s.sium iodide in sulphur dioxide; at G two liquid phases are formed, and the system therefore becomes invariant (cf. p. 121). The curve GHK is the solubility curve for two partially miscible liquids; and since complete miscibility occurs on _lowering_ the temperature, the curve is similar to that obtained with triethylamine and water (p. 101). K is also an invariant point at which pota.s.sium iodide is in equilibrium with two liquid phases and vapour.

The complete investigation of the equilibria between sulphur dioxide and pota.s.sium iodide, therefore, shows that these two components form the compounds KI,14SO_{2} and KI,4SO_{2}; and that when solutions having a concentration between those represented by the points G and K are heated, separation into two layers occurs. The temperatures and concentrations of the different characteristic points are as follows:--

------------------------------------------------------------- Composition of Point. Temperature. the solution per cent. KI.

------------------------------------------------------------- A (m.p. of SO_{2}) -72.7 -- B (eutectic point) -- 0.86 C (m.p. of KI,14SO_{2}) -23.4 17.63 E (m.p. of KI,4SO_{2}) +0.26 39.33 G (KI + two liquid phases) (about) 88 24.0 H (critical solution point) 77.3 12 K (KI + two liquid phases) (about) 88 2.7 -------------------------------------------------------------

{161}

CHAPTER IX

EQUILIBRIA BETWEEN TWO VOLATILE COMPONENTS

General.--In the two preceding chapters certain restrictions were imposed on the discussion of the equilibria between two components; but in the present chapter the restriction that only one of the components is volatile will be allowed to fall, and the general behaviour of two volatile[239]

components, each of which is capable of forming a liquid solution with the other, will be studied. As we shall see, however, the removal of the previous restriction produces no alteration in the general aspect of the equilibrium curves for concentration and temperature, but changes to some extent the appearance of the pressure-temperature diagram. The latter would become still more complicated if account were taken not only of the total pressure but also of the partial pressures of the two components in the vapour phase; this complication, however, will not be introduced in the present discussion.[240] In this chapter we shall consider the systems formed by the two components iodine and chlorine, and sulphur dioxide and water.

Iodine and Chlorine.--The different systems furnished by iodine and chlorine, rendered cla.s.sical by the studies of Stortenbeker,[241] form a very complete example of equilibria in a two-component system. We shall first of all consider the {162} relations between concentration and temperature, with the help of the accompanying diagram, Fig. 42.

[Ill.u.s.tration: FIG. 42.]

Concentration-Temperature Diagram.--In this diagram the temperatures are taken as the abscissae, and the composition of the solution, expressed in atoms of chlorine to one atom of iodine,[242] is represented by the ordinates. In the diagram, A represents the melting point of pure iodine, 114. If chlorine is added to the system, a solution of chlorine in liquid iodine is obtained, and the temperature at which solid iodine is in equilibrium with the liquid solution will be all the lower the greater the concentration of the chlorine. We therefore obtain the curve ABF, which represents the composition of the solution {163} with which solid iodine is in equilibrium at different temperatures. This curve can be followed down to 0, but at temperatures below 7.9 (B) it represents metastable equilibria. At B iodine monochloride can be formed, and if present the system becomes invariant; B is therefore a quadruple point at which the four phases, iodine, iodine monochloride, solution, and vapour, can coexist. Continued withdrawal of heat at this point will therefore lead to the complete solidification of the solution to a mixture or conglomerate of iodine and iodine monochloride, while the temperature remains constant during the process. B is the eutectic point for iodine and iodine monochloride.

Just as we found in the case of aqueous salt solutions that at temperatures above the cryohydric or eutectic point, two different solutions could exist, one in equilibrium with ice, the other in equilibrium with the salt (or salt hydrate), so in the case of iodine and chlorine there can be two solutions above the eutectic point B, one containing a lower proportion of chlorine in equilibrium with iodine, the other containing a higher proportion of chlorine in equilibrium with iodine monochloride. The composition of the latter solution is represented by the curve BCD. As the concentration of chlorine is increased, the temperature at which there is equilibrium between iodine monochloride and solution rises until a point is reached at which the composition of the solution is the same as that of the solid. At this point (C), iodine monochloride melts. Addition of one of the components will lower the temperature of fusion, and a continuous curve,[243] exhibiting a retroflex portion as in the case of CaCl_{2},6H_{2}O, will be obtained. At temperatures below its melting point, therefore, iodine monochloride can be in equilibrium with two different solutions.

The upper portion of this curve, CD, can be followed downwards to a temperature of 22.7. At this temperature iodine trichloride can separate out, and a second quadruple {164} point (D) is obtained. This is the eutectic point for iodine monochloride and iodine trichloride.

By addition of heat and increase in the amount of chlorine, the iodine monochloride disappears, and the system pa.s.ses along the curve DE, which represents the composition of the solutions in equilibrium with solid iodine trichloride. The concentration of chlorine in the solution increases as the temperature is raised, until at the point E, where the solution has the same composition as the solid, the maximum temperature is reached; the iodine trichloride melts. On increasing still further the concentration of chlorine in the solution, the temperature of equilibrium falls, and a continuous curve, similar to that for the monochloride, is obtained. The upper branch of this curve has been followed down to a temperature of 30, the solution at this point containing 99.6 per cent. of chlorine.[244] The very rounded form of the curve is due to the trichloride being largely dissociated in the liquid state.

One curve still remains to be considered. As has already been mentioned, iodine monochloride can exist in two crystalline forms, only one of which, however, is stable at temperatures below the melting point; the two forms are _monotropic_ (p. 44). The stable form which melts at 27.2, is called the [alpha]-form, while the less stable variety, melting at 13.9, is known as the [beta]-form. If, now, the presence of [alpha]-ICl is excluded, it is possible to obtain the [beta]-form, and to study the conditions of equilibrium between it and solutions of iodine and chlorine, from the eutectic point F to the melting point G. As the [beta]-ICl becomes less stable in presence of excess of chlorine, it has not been possible to study the retroflex portion of the curve represented by the dotted continuation of FG.

The following table gives some of the numerical data from which Fig. 42 was constructed.[245]