The Phase Rule and Its Applications

ed Salt a

ch combination between the components can occur with the formation of definite compounds; such as are found in the case of crystalline salt hydrates. Since a not inconsiderable amount of study has been devoted to the systems formed by hydrated salts and water, syst

s the compounds formed possess a definite melting point, i.e. form a liquid pha

med do not have a De

an where no such combination of the components occurs. For, as has already been pointed out, each substance has its own solubility curve; and there will therefore be as many solubility curves as there are solid phases possible, the curve for e

g.

etermining the solubility of this salt in water, it is found that the solubility increases as the temperature rises, the values of the solubility, represented graphically by

y of Na2S

ure. Sol

5

°

13

16

19

28

40

50

55

lid phase was now different from that in contact with the solution at temperatures below 33°; for whereas in the latter case the solid phase was sodium sulphate decahydrate, at temperatures above

Anhydrous So

ure. Sol

53

52

51

50

49

49

49

5° 4

0° 4

anhydrous sodium sulphate is present as the solid phase, cuts the curve rep

ected against access of particles of Glauber's salt, crystals of a second hydrate of sodium sulphate, having the composition Na2SO4,7H2O, separate out. On determining the compo

ty of Na

ure. Sol

1

30

37

41

44

52

54

be saturated with respect to these two solid substances. But a system of two components existing in four phases, anhydrous salt-hydrated salt-solution-vapour, is invariant; and this invariability will remain even if only three phases are present, provided that one of the factors, pressure, temperature, or concentration of components retains a constant value. This is the case when solubilities are determined in open

ty of the decahydrate at temperatures above the quadruple point is greater than that of the anhydrous salt, the solution which is saturated with respect to the former will be supersaturated with respect to the latter. On bringing a small quantity of the anhydrous salt in contact with the solution, therefore, anhy

ated solution of the anhydrous salt will therefore be supersaturated for the decahydrate, and will deposit this salt if a "nucleus" is added to the solution. From this we see that at temperatures above 32.5° the anhydrous s

perature of 24.2°) must be the transition point for heptahydrate and anhydrous salt. Since at all temperatures the solubility of the heptahydrate is greater than that of the decahydrate, the former hydrate must be metastab

lt has been followed backwards to a temperature of about 18°, it is readily seen, from Fig. 33, that at a temperature of, say, 20° three different saturated solutions of sodium sulphate are possible, ac

only when, the solid phase undergoes change. So long as the decahydrate, for example, remained unaltered in contact with the solution, the solubility

why the latter salt cannot be employed for dehydration purposes at temperatures above the transition point. The dehydrating action of the anhydrous salt depends on the formation of the decahyd

e not only the vapour pressure of the saturated solutions, but also that of the crystalline hydrates. The vapour pressures of salt hydrates have al

res lower than that of the system anhydrous salt (or lower hydrate)-solution-vapour. This, however, is not a necessity; and cases are known where the vapour pres

pour becomes equal to the vapour pressure of the saturated solution of the anhydrous salt, as is apparent from

° 30.83° 31.79° 3

ressure: 23.8 1

the vapour pressure

0H2O-Na2

solutio

nsformation being supposed excluded), and the hydrate will appear to undergo partial fusion; and during the process of "melting" the vapour pressure and temperature will remain constant.[213] This is, however, not a true but a so-called incongruent melting po

y definite, and on this account the proposal has been made to adopt this as a fixed point in thermometry.[214] The temperature is, of course, practically the same as that at which the two solubility curves intersect (p. 112). If, however, the

g.

which, as we have seen, cuts the curve ABCD at the transition temperature, 32.6°. Since at this point the solution is saturated with respect to both the anhydrous salt and the decahydrate, the vapour-pressure curve of the saturated solution of the latter must also pass through the point C.[217] As at te

vapour pressure of the more stable system was always lower than that of the less stable; in the present case, however, we find that this is no longer so. We have already learned that at temperatures below 32.5° the system decahydrate-solution-vapour is more stable than the system anhydrous salt-so

orm is the more soluble, and that the diminution of the v

pour can coexist, the vapour-pressure curves of the systems hydrate-anhydrous salt-vapour (curve EB) and hydrate-solution-vapour (curve FB) must cut the pressure curve of the saturated

ion. The system heptahydrate-anhydrous salt-vapour must be metastable with respect to the system decahydrate-anhydrous salt-vapour, and will pass into the latter.[218] Whethe

been found,[219] and in some cases there is more than one metastable hydrate. This is found, for example, in the case of nickel iodate,[220] the solubility curves for which are given in Fig. 35. As can be seen from the figure, suspended transformation occurs, the solubility curves having in some cases bee

g.

urve of one hydrate cuts the solubility curve, not of the anhydrous salt, but of a lower hydrate; in this case there will be more than one stable hydrate, each having a stable solubility curve; and these curves wi

g.

olubility curve of the latter hydrate cuts that of the former. This is, therefore, the transition temperature for the trihydrate and monohydrate. The solubility curve of the monohydrate succeeds that of the trihydrate, and exhibits a conspicuous point of minimum solubility at about 30°. Below 24.7° the monohydrate is the less stable hydrate, but its

of view. In Fig. 36 there is also shown a faintly drawn curve which is continuous throughout its whole course. This curve represents the solubility of barium acetate as determined by Krasnicki.[223] Since, however, three different

t is of equal importance to determine the composition of the solid phase in contact with it. In view of the fact, also, that the solution equilibrium is in many cases established with comparative slowness, it is necessary to confirm the point of equilibrium, either by approaching it

ormed have a Defin

lphate, Na2S2O3,5H2O, sodium acetate, NaC2H3O2,3H2O) melt completely in their water of crystallization, and yield a liquid of the same composition as the crystalline salt. In the case of sodium thiosulphate pentahydrate the temperature of liquefaction is 56°; in the case of sodium acetate trihydrate,

, each of which possesses its own solubility, it is nevertheless the solubility curve of the hexahydrat

g.

temperature, as is shown by the figures in the following table, and by the (diagrammatic) curve AB in Fig. 37. In the table, the numbers under the heading "solubility" denote the

Calcium Chlori

Solubility.

42.

50.

55.

9.5

65.0

74.5

82.0

90.5

95.5

102.

109.

112.

the water of crystallization of the salt is sufficient for its complete solution. This temperature is 30.2°; and since the composition of the solution is the same as that of the solid salt, viz. 1 mol. of CaCl2 to 6 mols. of water, this tem

he figure, therefore, calcium chloride hexahydrate exhibits the peculiar and, as it was at first thought, impossible behaviour that it can be in equilibrium at one and the same temperature with two different solutions, one

int, the temperature at which the solid hydrate will be in equilibrium with the liquid phase (solution) will be lowered; or if, on the other hand, anhydrous calcium chloride is added to the hydrate at its melting point (or what is the same thing, if water is removed from the solution), the temperature at which

will be continuous. Formerly, however, it was considered by some that the curve was not continuous, but that the melting point is the point of intersection of two curves, a solubility curve and a fusion curv

all attention to the form of the solubility curve in the case of salt hydrates possessing a definite melting point, never

g.

orms, each of which contains four molecules of water of crystallization; these are distinguished as α-tetrahydrate, and β-tetrahydrate. Two

ate, solution, and vapour can coexist. It is also the transition point for these two hydrates. Since, at temperatures above 29.8°, the α-tetrahydrate is the stable form, it is evident from the data given before (p. 146), as also from Fig. 38, that the portion of the solubility curve of the hexahydrate ly

and the solution, which now contains 112.8 parts of CaCl2 to 100 parts of water, is saturated with respect to the two hydrates. Throughout its whole extent the solubility curve EDF of the

urve of the latter hydrate extends to 175.5° (L), and is then succeeded by the curve for the monohydrate. The solubility curve of the anhydrous salt does not begin until a te

great value, and will therefore be omitted here; in general, the same relationships would be found as in the case of sodium sulphate (p. 138), except that the rounded portion of the solubility curve of the hexahydrate would be represented by a similar rounded portion in the pressure curve.[227] As in the c

olidification, without the temperature of the system undergoing change. This behaviour, therefore, is similar to, but is not quite the same as the fusion of a simple substance such as ice; and the difference is due to the fact that in

should expect that the system could exist at different temperatures; which, indeed, is the case. It has, however, already been noted that when the composition of the liquid phase becomes the same as that of the solid, the system then behaves as a u

garded as being composed of one component when the vapour had the same total composition as the solid (p. 13). One component in two phases, however, constitutes a univariant system, and we can therefore see that calcium chloride hexa

al, is known as an indifferent point,[229] and it has been shown[230] that at a given pressure the temperature in the indifferent point is the maximum or minimum temperature pos

of the existence of retroflex solubility curves, is afforded by the hydrates of ferric chloride, which not only possess defini

solubility curves of these different hydrates will exhibit a series of temperature maxima; the points of maximum temperature representing systems in which the composition of the solid and liquid phases is the same. A graphical representation of the solubility relations is given

g.

ted Solutions of Ferric C

he head of each table

c

ure. Com

5°

° 2

.5°

.5°

° 1

°

l6,1

ure. Com

° ±

° 2

° 2

4

°

°

°

°

5°

°

°

10

11

4°

12

13

1

l6,7

ure. Com

11

4°

13

5°

15

15

l6,5

ure. Com

12

13

14

15

15

17

19

20

20

Cl6

ure. Com

19

20

20

21

5°

5°

5°

27

29

(ANHY

ure. Com

29

29

28

29

° 2

ice will melt and the system will pass 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 quantity of ferric chlor

h a point of maximum temperature, the whole series of curves forming an undulating "festoon." To the r

ion 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 the system remaining constant until complete solidification has taken place. If, on the other han

ll, 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 chlo

xtent 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

ted by the point x1, is evaporated at a temperature of about 17° - 18°. As water passes 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 Fe2Cl6,12H2O separates out. As water continues to be remov

g.

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 pass into solution in order that the compositio

ance 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 re

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,

are present, for such a system is invariant. In addition to this, however, the quantity of the solution will also remain unchanged, the water which evaporates being supplied by the higher hydrate. The same phenomenon is also observed in t

g.

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 potassium iodide lowered the freezing point, but the maximum depression obtained was very small, and was reached when the concentration of the potassium 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 repr

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 potassium iodide. On the other hand, solutions co

riment; their interpretation in the lig

tectic point, at which solid sulphur dioxide and the compound KI,14SO2 can exist together in equilibrium with solution and vapour. The curve DE is the solubility curve of the red crystalline solid, and the 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,4SO2.[238] D is, therefore, the eutectic point at which the compounds KI,14SO2 and KI,4SO2 can coexist i

iant (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

rm the compounds KI,14SO2 and KI,4SO2; and that when solutions having a concentration between those represented by the points G and K ar

erature. Co

solu

cent

of SO2)

tic poin

KI,14SO2) -

KI,4SO2)

quid phases) (

solution poi

quid phases) (