The Phase Rule and Its Applications

es, whether solid, liquid, or vapour, had the same chemical composition (p. 13). In some cases, as, for example, in the case of ph

he different phases have no longer all the same chemical composition, and cann

egarded as of the first order, or a one-component system; if the composition of the different phases varies, the system must contain more than one component. If, in order to express the composition of all the phases present when the system is in equilibrium, t

ponents will best be learned by a study of

Two Components.-App

F =

se); but, as is evident from the formula, there is a higher degree of freedom possible in the case of two-component systems. Two components existing in only one phase constitute a tervariant system, or a system with three degrees of freedom. In addition to the pressure and temperature, therefore, a third variable factor must be chosen, and as such there

g.

temperature axes would then represent the change of pressure with the temperature, the concentration remaining unaltered (pt-diagram); one in the plane containing the pressure and concentration axes (e.g. AF or DF), the change of pressure with the concentration, the temperature remaining constant (pc-diagram), while in the plane containing the concentration and the temperature axes, the simultaneous change of these two factors at consta

n the case of one component. In the case of no two substances, however, have all the possible relationships been studied; so that for the purpose of gaining an insight into

correlation of the comparatively large number of different systems, will probably be rendered easiest by grouping these different phenomena into classes, each of these classes being studi

a of Dis

lready been made to such systems in the case of ammonium chloride. On being heated, ammonium chloride dissociates into ammonia and hydrogen chloride. Since, however, in that case the vapour phase has the same total composition as the

oducts of dissociation be added, the

stances by which the composition of the two phases can be expressed is two; that is, the number of components is two. What, then, are the components? The choice lies between N

omponents be chosen, we should have to introduce negative quantities of one of the components, in order to represent the composition of the vapour phase. Although it must be allowed that the introduction of negative quantities of a

Rule, a two-component system existing in two phases. Such a system will possess two degrees of freedom. At any given temperature, not only the pressure, but also the composition, of the vapour-phase, i.e. the concentration of

light on the relation between these two variables. This relationship, however, can be calculated theoretically by means of the Law of Mass Action.[147] From this we learn t

e of ammonium hydrosulphide, ammonium cyanide,

h systems, there are seven possible, viz. S-S-S, S-S-L, S-S-V, L-L-L, S-L-L, L-L-V, S-L-V; S denoting solid, L liquid, and V vapour. In the

efore univariant. To each temperature, therefore, there will correspond a certain, definite maximum pressure of carbon dioxide (dissociation pressure), and this will follow the same law as the vapour pressure of a pure liquid (p. 21). More particularly, it will be independent of the relative or absolute amounts of the two solid phases, and of the volume of the vapour phase. If the temperatur

y,[149] but more exact measurements have been made by Le Chatelier,[150]

Pressure in

7°

0°

5°

° 2

° 2

° 6

° 7

° 1

below this temperature by the mere heating of the carbonate. If, however, the carbon dioxide is removed as quickly as it is formed, say by a current of air, then the entire decomposition can be made to take place at a much lower temperature. For the dissociation

e with formation of the substances AgCl,3NH3 and 2AgCl,3NH3, according to the conditions of the experiment. These were the first known substances belonging to this class, and were employed by Faraday in his experiments on the liquefaction of ammonia. Similar compounds have also been obtained by th

e substances, ammonia was evolved, and the pressure of this gas was found in the case of both compounds to be constant at a given temperature, but was greater in the case of the former than in the case of the latter s

we are here dealing with two components, AgCl and NH3. On bei

3) 2AgCl,3

H3 2AgCl

imilarly, if, at constant temperature, the volume is increased (or if the ammonia which is evolved is pumped off), the pressure will remain constant so long as two solid phases, AgCl,3NH3 and 2AgCl,3NH3, are present, i.e. until the compound richer in ammonia is completely decomposed, when there will be a sudden fall i

med, and the pressure will now remain constant until all the silver chloride has disappeared. The pressure will again rise, until it has reached the value at which the compound AgCl,3NH3 can be formed, when it will again remain constant unt

of silver chloride and ammonia, as determined by

H3. 2Ag

essure. Tempera

cm. 20.0

5 ,, 31.0

5 ,, 47.0

7 ,, 58.5

.5 ,, 69.

.3 ,, 71.

.4 ,, 77.

.2 ,, 83.

.1 ,, 86.

° 20

l to atmospheric pressure at a temperature of about 20°; above this temperature, therefore, it cannot be formed by the action of ammonia at atmospheric pressure on silver chloride. The triammonia dichloride can, however, be formed, for its dissociation pressure at this tem

te; and for the exact definition of this pressure it is necessary to know, not merely what is the substance undergoing dissociation, but also what is the solid product of dissociation formed. For the

into a lower hydrate (or anhydrous salt) and water vapour. Since we are dealing with two components-salt and water[154]-in three phases, viz. hydrate a, hydrate b (or anhydrous salt), and vapour, the system is univariant, and to each temperature t

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d been given. In the case of salts capable of forming more than one hydrate, we should obtain a series of dissociation curves (pt-curves), as in the case of the different

O4,5H2O CuSO4

SO4,3H2O CuS

CuSO4,H2O

nd as there are now three phases present, viz. CuSO4, CuSO4,H2O, and vapour, the system becomes univariant; and since the temperature is constant, the pressure must also be constant. Continued addition of vapour will result merely in an increase in the amount of the hydrate, and a decrease in the amount of the anhydrous salt. When the latter has entirely disappeared, i.e. has passed into hydrated salt, the system again becomes bivariant, and passes along the line

the hydrate 5H2O had disappeared; further removal of water would then cause the pressure to fall abruptly to the pressure of the system CuSO4,3H2O-CuSO4,H2O-vapour, at which value it would again remain constant until

pressure falls below the dissociation pressure of the pentahydrate, this salt will undergo dehydration. From this, then, it is evident that a crystalline salt hydrate will effloresce when exposed to the air, if the partial pressure of the water vapour in the air is lower than the dissociation pressure of the hydrate. At the ordina

g.

ted salt. A salt hydrate in contact with vapour constitutes only a bivariant system, and can exist therefore at different values of temperature and pressure of vapour, as is seen from the diagram, Fig. 19. Anhydrous copper sulphate can exist in contact with water vapour at all values of tempera

he vapour pressure of a hydrate has a definite meaning only when the second solid phase produced by the dissociation is given. The everyday custom of speaking of the vapour pressure of a hydrated salt acquires a meaning only through the assumption, tacitly made, that the second solid phase, or the solid produced by the dehydration of the hydrate, is the next lo

a fact. Thus CaCl2,6H2O can dissociate into water vapour and either of two lower hydrates, each containing four molecules of water of crystallization, and designated respectively as CaCl2,4H2

e. Pressur

6H2O;

ur. CaCl2,6

β; v

27 cm. 0

2 ,, 0

92 ,, 0

78 ,,

08 ,,

- 0.5

0.680

iation product for the definition of the dissociation pressure of a sa

well known in the case of Glauber's salt, first observed by Faraday. Undamaged crystals of Na2SO4,10H2O could be kept unchanged in the open air, although the vapour pressure of the system Na2SO4,10H2O-Na2SO4-vapour is greater than the ordinary pressure of aqueous vapour in the air. That is to say, the possibility of the for

ossibility, but not a certainty. Although there is no example of this known in the case of hydrated salts, the suspension of the transformation has been observed in the case of the compounds of ammonia with the metal chlorides (p. 82). Horstmann,[158] for example, found that the pressure of ammonia i

possible that at some temperature the vapour pressure curve of a lower hydrate may cut that of a higher hydrate. At temperatures above the point of intersection, the lower hydrate would have a higher vapour pressure than the higher hydrate, and would theref

ing the vapour phase, the pressure remained constant so long as any of the dissociating compound was present, independently of the degree of the decomposition (p. 86). This behaviour, now, has been employed for the purpose of determining whether or not definite chemical compounds are formed. Should compounds be formed between the vapour phase and the solid, then, on continued addition o

adium hydride,[161] and the results obtained appear to show that no compoun

he small pressures exerted by the vapour of salt hydrates, use is very general

as we have learned, suspended transformation may occur, it is advisable to first partially dehydrate the salt, in order to ensure the presence of the second solid product of dissociation; the value of the dissociation pressure being independent of the degree of dissociation of the hydrate (p. 86). The small bulbs d and e having been filled, the apparatus is placed on its side, so as to allow the liquid to run from the bend of the tube into the bulbs a and b; it is then exhausted through f by means of a mercury

g.