The Phase Rule and Its Applications

he concentration reaches a definite value independent of the amount of solid present. A condition of equilibrium is established between the solid and the solution;

pour 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

ure 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

f it is known whether solution is accompanied by increase or diminution of the total volume. If diminution of the total volume of the system

rified by experiment, as is show

Chan

ume

lving

alt

ura

bility (at 18°

of so

es

tm. P

00

ride -0.07

loride +0.1

.067 0.

400

tion 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 solubi

nt 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 are unsaturated, in the latter case they are supersaturated 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

ion 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

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

g.

apparent from Fig. 26, in which the solubility curves of vario

s where the process of solution is accompanied by an absorption of heat; and a decrease in the solubility with rise of temperature will be found in cases where solution occurs with evolution of heat. Where there is no heat effect accompanying solution, change o

nt 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

gram-mol

2O dissol

es of water.

+3

2 +

+10

+11

+11

+91

8 -

6 -

5 -1

k 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 that the last heat of solution is negative (as expressed above), i.e. solution of

ith the solution, remains unchanged. If any "break" or discontinuous change in the direction of the curve occurs, it is a sign that the solid phase has undergone alteration.

ous Salt

resent 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 exa

entration-temperature diagram 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 curve

g.

ilibrium with respect to their solutions. From the table on p. 63 it 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 a

of Ammoni

ubility. Tempera

4.50 32

3.30 34

8.19 35.

1.86 36

4.40 37

4.61 38

7.20 39

7.60 40

ct change in the direction of the curve at a temperature of 32°; and this break in the curve cor

ility 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, is supersaturated 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, howeve

rtant is the statement of the solid phase for the

o the consideration of the solubility curves at highe

in the fused state can

n the fused state cannot

ibility of the F

g.

ate and water. The solubility of this salt at temperatures above 100° has been studied chiefly by Etard[190] and by Tilden

y of Silv

arts of dry sa

olut

°

°

°

°

°

5°

°

° 9

° 9

ty 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 sal

h 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

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 ag

atically as in Fig. 29. In this figure OA represents the solubility curve of the salt, and OB the freezing point 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

g.

f temperature. A similar behaviour was found by Guthrie in the case of a large number of other salts, a temperature below that of the melting point of ice being reached at which on continued withdrawal of heat, the solution solidified at a constant temperature. When the system had attained this minimum temperatur

mperat

ication

ce

to -2

2° 2

2° 2

3° 2

3° 2

3° 2

n 2

that the solid which was deposited was crystalline, and that the same constant temperature was attained, no matter with what proportions of water and salt one started, led Guthrie to the belief that the solids which thus separated at constant temperature were d

hydr

c point. Percen

the cryo

romide -

hloride

iodide -

trate -17

sulphate

chloride

odide -1

bromide

chloride -

sulphate

nitrate

ulphate

definite chemical compounds, but of mixtures; the arguments given being that the heat of solution and the specific volume are the same for the cryohydrate as for a mixture of ice and salt of the same composition; and it was further shown

ase, but with two solid phases, ice and salt; the cryohydric point, therefore

ke place immediately the cryohydric point is reached. It will, therefore, be possible to follow the curves BO and AO beyond the quadruple point,[200] which is thereby clearly seen to be the point

Le Chatelier; and, after what was said in Chap. IV., need only be briefly referred to here. In the first place, addition of heat will cause ice to melt, and the concentration of the solution will be thereby altered; salt must therefore dissolve until the original concentration is reached, and the heat of fusion of ice will be counteracted by the heat of solution of the salt. Changes of volume of the solid and liquid phases must also be taken into account; an alteration in the volume of these phases being compensated by condensation or evaporation. All four phases will therefore be involved in the change, and the final state of the system will be depen

point must be at length reached, for it is only at this temperature that the four phases ice-salt-solution-vapour can coexist. Or, on the other hand, if salt is added to the system ice-solution-vapour, the concentration of the solution will increase, ice must melt, and the temperature must thereby fall; and this process also will go on until the cryohydric point is reached. In both cases ice melts and there is a

the temperature falls, the more rapid does the radiation become; and the rate at which the temperature sinks decreases as the amount of solution increases. Both these factors counteract the effect of the latent heat of fusion and the heat of solution, so that a point is reached (which may lie considerably above the cryohydric point) at which the two opposing influences balance. The absorption of heat by the soluti

ibility of the

d that the relationships are not quite so simple as in the case of silver nitrate and water. In the latter case, only one liquid phase was possible; in the cases now to be studied, two

ve, therefore, the phenomenon of melting under the solvent. This melting point will, of course, be lower than the melting point of the pure substance, because the solid is now in contact with a solution, and, as we have already seen, addition of a foreign substance lowers the melting point.

g.

en the concentration of the nitrile in the solution has increased to 2.5 molecules per cent., the nitrile melts and two liquid phases are formed; the concentration of the nitrile in these two phases is given by the points c and c′. As there are now four phases present, viz. solid nitrile, solution of fused nitrile in water, solution of water in fused nitrile, and vapour, the system is invariant. Since at this point the concentration, temperature, and pressure are completely defined, addition or withdrawal of heat can only cause a change in the relative amounts of the phases, but no variation of the concentrations of the respective phases. As a matter of fact, continued additi

he univariant system, consisting of two liquid phases and vapour.[204] Such a system will exhibit relationships similar to those already studied in the previous chapter. As the temperature rise

ight of the curve abcdc′e there can be only one liqui

ll be dissolved until the concentration reaches the value on the curve bc, corresponding to the given temperature. On adding the nitrile to water at temperatures between c and d, it will dissolve until a concentration lying on the curve cd is attained; at this point two liquid phases will be formed, and further addition of nitrile will cause the one liquid phase (that containing excess of nitrile)

sired amount without at any time two liquid phases making their appearance; the system can then be cooled down to a temperature represented by any point between the curves dc′e. In this way it is possible to pass

temperature of the invariant point is reached at which, therefore, the formation of two liquid layers is possible, these two liquid layers, as a matter of fact, make their appearance. Suspended transformation can, however, take place from the side of th

g.

have already seen, the less stable form has the greater solubility, it follows that the supercooled liquid, being the less stable form, must have the greater solubility. This was first proved experimentally by Alexejeff[205] in the case of benzoic acid and water, the solubility curves for which are given in Fig. 31. As can be seen from the figure, the prolongation

on of the components in a solution with the temperature, we may conclude the discussion of

pending on the concentration. In order that there may be for each temperature a definite corresponding pressure of the vapour, a third phase must be present. This condition is satisfied by the s

of a salt in water must lie below that for pure water. Further, in the case of a pure liquid, the vaporization curve is a function only of the temperature (p. 63), whereas, in the case of a solution, the pressure varies both with the temperature and the concentration. These two factors, however, act in opposite directions; for although the vapour press

Since at first the effect of increase of temperature more than counteracts the depressing action of increase of concentration, the vapour pressure will increase on raising the temperature above the cryohydric point. If the elevation of temperature is continued, however, to the melting point of the salt, the effect of increasing concentration makes itself more and more felt, so that the vapour-pressure curve of the solution falls more and more below that of the pure liquid, and the pressure will ultimately bec

g.

lution-vapour already considered, three others are possible, vi

added. The vapour pressure of the water, also, is lowered by the solution in it of other substances, so that the vapour pressure of the system ice-solution-vapour must decrea

ution will become more dilute or more concentrated. Since, at the completion of this process, the ice and solution are now in equilibrium when they are not in contact, they must also be in equilibrium when they are in contact (p. 32). But if distillation has taken place the concentration of the solution must have altered, so that the ice will now be in equilibrium with a solution of a different concentration from before. But according to the Phase Rule ice cannot at one and the same temperature be in equilibrium with two solutions of different concentration, for the system ice-

vapour. This curve will also be coincident with the sublimati

rature will be to cause a large change of pressure, as in the case of the fusion point of a pure substance. The direction of this curve will depend on whether

n have constant and definite values. Addition or withdrawal of heat, therefore, can cause no alteration of the condition of the system except a variation of the relative amounts of the phases. Addition of heat at constant volume will ultimately lead to the system salt-solution-vapour or the system ic

us bivariant systems are possible, the conditions for the existence of whi

. Sy

Salt-

on-vapour; s

olution; ic

Ice-

a value lying on this curve at temperatures above the cryohydric point, solution will be formed; for the curve AMF represents the equilibria between salt-solution-vapour. From this, therefore, it is cl

ossible to state in a general manner whether or not salt will be de

the temperature will rise, and the vapour pressure of the solution will increase. The system will, therefore, pass along a line represented diagrammatically by xx′. At the point x′ the vapour pressure of the system becomes equal to 1 atm.; and as the vessel is open to the air, the pressure cannot further rise; the solution boils. If the heating is continued, water passes off, the conce

em salt-solution-vapour never reaches the pressure of 1 atm. Further, since the curve bb lies in the area of the bivariant system solutio

In the case of aqueous solutions of sodium and potassium hydroxide, however, the vapour pressure of the saturated solution never reaches the value of 1 atm., and on evaporating these solutions, therefore, in an open vessel, there is no separ

ny pairs of organic substances; and in all cases the equilibria will be represented by a diagram of the general appearance of Fig. 29 or Fig. 30. That is to say: Starting from the fusion point of component I., the system will pass, by progressive addition of component II., to regions of lower temperature, until at last the cryohydric or eutectic point is reached. On further addition of component II., the system will pass to regions of higher temperature, the solid phase now being component II. If the fused c