The Phase Rule and Its Applications

ous systems consisting of one component. In the present chapter it is proposed to give a short summary of the relatio

will inform them as to the exact behaviour of a substance, it may here be emphasized that the Phase Rule is a general rule; it info

he curves representing the conditions of equilibrium of the three univariant systems formed by the combination of the three phases in pairs. The most common triple point of a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V), but other triple p

eighbourhood of the triple point is taken by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.[100] That is to say, if a line of constant temperature is drawn immediately above or below the triple point so as to cut the th

e triple point,[101] only two of these have been experimentally obtained in the case of the triple poi

g.

g.

n that of the liquid (the substance contracts on fusion); the difference of specific volume will, therefore, be greatest between liquid and vapour. The curve, therefore, for liquid and vapour (or its prolongation) must lie between the other two curves; this

r case, to the left, indicating a lowering of the melting point with the pressure. These conditions are found exemplified in the case of sulphur and ice (pp. 29 and 35). We see further from the two figures, that O in Fig. 13 gives

pressure are altered. For all such changes there exist two theorems, based on the laws of thermodynamics, by means of which the alterations in a system can be qualitatively predicted.[103] The first of these, usually known as van't Hoff's law of movable equilibr

e on a system in equilibrium is increased, that reaction takes place which is accompanied by a diminution of

ion. For this reason they are generally regarded as special cases of the more general law, known as the theorem of Le Chatelier, which may be stated in the words of Ostwald, as follows:[106] If

physical or chemical; to vaporization and fusion; to solution and chemical action. In all cases, whenever changes in the external condition

no change in the temperature or pressure of the system can occur, but only changes in the relative amounts of the phases; that is to say, the effect on the system of change in the external conditions is opposed by the reactions or changes which take place within the system (according to the theorems of

emperature of the system therefore does not rise. Since, however, the melting of the solid is accompanied by an increase of volume, whereby an increase of pressure would result, a certain portion of the vapour must condense to liquid, in order that the pressure may remain constant. The total effect of addition of heat, therefore, is to cause both solid and vapour to pass into liquid, i.e. there oc

ur in order that the pressure may be maintained constant. On addition of heat, therefore, there occurs the reaction S L + V; withdrawal of heat causes the reverse change L + V S. Above the temperature of the triple point the solid cannot

mately cause the formation of the bivariant system vapour alone; continued withdrawal of heat will ultimately cause the formation of solid alone. This will be readily understood from Fig. 15. The dot

g.

e must be constant so long as the three phases are present, increase of volume must be compensated by the evaporation of liquid. This, however, would cause the temperature to fall (since communication of heat from the outside is supposed to be cut off), and a portion of the liquid must therefore freeze. In this way the latent heat of evaporation is counterbalanced by the latent

he triple point, the liquid phase cannot exist. Decrease of volume (increase of pressure), on the other hand, will lead either to the system S-L or L-V, because these systems can exist at pressures higher than that of the triple point. If the vapour ph

g.

g.

phases has disappeared. Continued increase of volume (decrease of pressure) will then cause the disappearance of a second phase, the system passing along the dotted line OE′ (Figs. 16, 17), so that ultimately th

, applies, mutatis mutandis, to all other triple points, so that if the specific volumes of the phases are known, and the sign of the heat effects which accompany the transformation of on

n the case, say, of the transformation from solid to liquid, or liquid to solid, at the melting point with change of temperature, only these two phases appear

ves around the triple point are found. It is, however, unnecessary to give a general treatment of these here, since

d phases is given below. The triple point S-S-V is not precisely the same as the transition point, but is very nearly so. The transition point is the temperature at which the relative stability of the two solid phases undergoes change, when the vap

most important polymorphous substances, and

ce. Tra

erat

ium n

ic α-rh

c rhombo

dral reg

ic iod

um nitr

iodid

nitra

hur

ommetha

ium n

rhombohe

ral regul

um pic

n

temperature rises, the increase of pressure per degree being greater the higher the temperature. The sublimation and vaporization curves,

d. The assumption, however, is entirely justified, not only on theoretical grounds, but also because the existence of a vapour pressure has been observed in t

ttempts have also been made to obtain a general expression for the quantitative changes in the vapour pressure with change of temperature, but with

a univariant system of one component, provided the composition of the vapour phase as a whole is the same as that of the solid or liquid phase (p. 13). For all such substances, therefore, the conditions of equilibrium will be represented by a curve of the same general form as the vapour pressure curve of a non-dissociating substance.

em S-V moving along the curve AO until at the triple point the liquid phase is formed, and the system L-V moving along the curve OB; so long as two phases are present, the condition of the system must be represented by these two curves. Conversely

the temperature of the system will then remain constant until the liquid phase has disappeared (p. 57); the system will then follow the curve OA until the solid phase disappears, and we are ultimately left with vapour. On the other hand, diminution

perature, will cause the system to pass along lines parallel to the temperature and the pressure axis respectiv

e, e.g. a different crystalline modification, is formed. If the sublimation pressure of a substance is greater than the atmospheric pressure at any temperature below the point of fusion, then the substance will sublime without melting when heated in an open vessel; and fusion will be po

ical point where the liquid ceases to exist;[114] the lower limit is de

orresponding to equal vapour pressures is constant, i.e. T1/T′1 = T2/T′2. When the two substances are not closely related, it was found that the relationship could be expressed by the equation T1/T′1 = T2/T′2 + c(t′ - t) where c is a constant having a small positive or negative value, and t′ and t are the temperature

tions of equilibrium between the solid and liquid phase; it shows th

r the matter in the light of the theorem of Le Chatelier (p. 58). Water, on passing into ice, expands; therefore, if the pressure on the system ice-water be increased, a reaction will take place which is accompanied by a diminution in volume, i.e. the ice will melt. Consequently, a lower temperature will be required in ord

lume accompanying the change of state are known, it is poss

stances is also affected by pressure; and in more recent years, ample experimental proof of the change of the melting point with the pressure has been obtained. The change of the melting point is, however, small; as a rule, increase of pressure by 1 atm. changes the melting

s straight, but bends towards the pressure axis, so that, on sufficiently increasing the pressure, a maximum temperature might at length be reached. This maximum has, so far, however, not been attained, although the melting point curves of various substances have been studied up t

id and vapour, so also in the case of solid and liquid, there exists a critical point at which the solid and

r away from or towards the pressure axis. The direction of the transition curve can also be predicted if the change of volume accompanying the passage of one form into the other is known. In the case of sulphur, we saw that the

ture. P

5° 1

8° 1

3° 2

9° 2

out, it appears that in most cases the tran

essure the transition curve passes through a point of maximum temperature, and exhi

o the triple point, solidification did not necessarily take place, although the conditions were such as to allow of its formation. Similarly, we saw that rhombic sulphur can be heated above the transi

sarily be formed immediately the system passes into such a condition that the existence of that phase is possible; but rather, instead of the system undergoing transformation so as to pass into the most stable condition under the existing pressure and tem

rmation of the metastable phase occurs with very varying velocity; in some cases so quickly as to appear almost instantaneous; while in other cases, the change takes place so slowly as to require hundreds of years for its achievement. It is this slow rate of transformation that renders the existence of meta

[126] As the result of these investigations, it was found that, in the case of superfused salol, the very small amount of 1 × 10-7 gm. of the solid phase was sufficient to induce crystallization. Crystallization of a supercooled

ccur. In the case of tin, for example, it was found that the white modification, although apparently possessing permanence, is in reality in a metastable state, un

ty of the change is less in some cases than in others, and appears to decrease with increase of the valency of the elemen

t as we have seen that at any given temperature the less stable form has the higher vapour pressure, but that at the transition point the vapour pressure of both forms becomes identical, so also it can be proved theoretically

posited. A gradual change of the less stable form, therefore, takes place through the medium of the solvent. In this way the more rapid conversion of white tin into grey in presence of a solution of tin ammonium chloride (p. 42) is to be ex

slower the more viscous the solvent;[130] indeed, Kastle and Reed state that yellow crystals of mercuric iodide, which, ordi

on increasing indefinitely the higher the temperature is raised. Below the transition point, however, the two factors act in opposite directions, and the more the temperature is lowered, the more is the effect of removal from the equilibrium point counteracted. A point will therefore be reached at which the velocity is a maximum. Reduction of the tempera

catalyzers-has a great influence on the velocity of transformation. Thus, e.g., the c

ez[132] on the velocity of crystallization of phosphorus and sulphur. Since that time, the velocity of crystallization of other supercooled liquids has been investigated; such as

ummarized as follows. For any given degree of supercooling of a substance, the velocity of crystallization is constant. As the degree of supercooling increases, the velocity of crystallization also increases, until a certain point is reached at which the velocity is a maximum, which has a definite characteristic value for

kes place with very great slowness. If, however, glass is heated, a temperature is reached, much below the melting point of

ubstances. It would hence appear possible to utilize this behaviour as a method for determining molecular weights.[139] The rule is, however, by no means a universal one. Thus it has been found by F. Dreyer,[140] in studying the velocity of crystallization of formanilide, that the diminution

white phosphorus is first formed, and not the more stable form-red phosphorus. It has also been observed that even at the ordinary temperature (therefore much below the transition point) sulphur may crystallize out from solution in benzene, alcohol, carbon dis

of solution, it is first deposited as a liquid, which passes later into the more stable crystalline form. In analysis, also,

ms of monotropic substances, which would otherwise not be obtainable. Although it is not always possible to observe the formation of the least stable form, it should be remembered that that may quite conceivably be due to the great velocity of transformation of the less stable into the more stable form. From what we have learned about the velocity of transformation of metastable phases, we can understand that rapid cooli

w have been found, it may nevertheless be accepted as a very usef