The Phase Rule and Its Applications

or were definite chemical individuals.[164] But this invariability of the composition is by no means imposed by the Phase Rule; on the contrary, we shall find in the examples which we now proceed

e, the composition of which can undergo continuous variation wi

ates. We may therefore have solutions of gases in liquids, and of gases in solids; of liquids in liquids or in solids; of solids in liquids, or of solids in solids. Solutions of gases in gases are, of

ses it should be remembered that we are dealing with equilibria between two components (we confine our attention in the first instance to such), the solution being constituted of these components in variable and varying amounts. The change from the case where the one component is in great excess (ordinarily called the solvent) to that in which the other component predominates, may be quite gradual, so that it is difficult

of Gases i

liquid and a gas. These equilibria really constitute a part of the equilibria to be studied more fully in Chapter VIII.; but since the two-phase systems

system is bivariant (two components in two phases); and two of the variable factors, pressure, temperature, and concentration of the components, must therefore be chosen in order that the condition of the system may be defined. If the concentration and the temperature are fixed, then the pressure is a

as is in all cases accompanied by a diminution of the total volume, this process must take place with increase of pressure. This, indeed, is stated in a quantitative manner in the law of Henry, according to which the amount of a gas absorbed is

; and since the absorption of gases is in all cases accompanied by the evolution of heat, the solub

tween the total pressure and the partial pressure of the dissolved gas, in cases where the solvent is volatile. In these cas

of Liquids

alcohol be added in increasing amount to water, at no point, at no degree of concentration, is a system obtained containing more than one liquid phase. At the ordinary temperature, water and alcohol can form only two phases, liquid and vapour. If, however, water be added to ether, or if ether be added to water, solution will not occur to an indefinite extent; but a point will be reached when the water or the ether will no longer dissolve more of the other component, and a further addition of water on the one hand, or ether on the other, will cause the formation of two liquid layers, one containing excess of water, the other excess of ether. We shall, therefor

mposition of the solution and the pressure of the vapour can undergo change; or, if the composition of the solution remains unchanged, the pressure and the temperature can alter. If the second (liquid) component is added in increasing amount, the liquid will at first remain homogeneous, and its composition and pressure will undergo a continuous change; when, however, the concentration has reached a definite value, solution no longer takes pl

ses; and addition of excess of one will merely alter the relative amounts of the two solutions. As the temperature changes, the composition of the two solutions will change, and there will therefore be obtained two solubility curves, one showing the solubility of component I. in component II., the other sh

cially by Alexejeff[168] and by Rothmund.[169] A considerable variety of curves have been obtained, and

ary language it may be called a solution of water in phenol. If now the temperature is raised, this second liquid phase will disappear, and a further amount of phenol must be added in order to produce a separation of the liquid into two layers. In this way, by increasing the amount of phenol and noting the temperature at which the two layers disappear, the so-called solubility curve of phenol in water can be o

logous to those already described. Since, now, in the second case the concentration of the phenol in the solution gradually decreases, while in the former case it gradually increases, a point must at length be reached at which the composition of the two solutions becomes the same. On mixing the two solutions, therefore, one homogeneous liquid w

g.

tions containing water and phenol in different concentration can exist together, one containing excess of water, the other excess

l and

e amount of phenol

,, seco

ature.

8.5

8.7

9.7

12.0

14.2

17.5

22.7

36.1

on 36.1 per cent. of phenol. At all temperatures above 68.4°, only homogeneous solutions

the same, and this disposes of one of the degrees of freedom. The system is therefore univariant; and at a given temperature the pressure will have a definite value. Conversely, if the pressure is fixed (as is the case when the system is under the pressure of its own vapour), then the temperatur

radually change, as shown by the dotted line xy. When, however, the concentration has reached the value represented by the point y, two liquid layers will be formed, the one solution having the composition represented by y, the other that represented by y′. The system is now univariant, and on further addition of phenol, the composition of

s higher than 68.4°, without the formation of two layers. It will therefore be possible to pass from a system represented by x to one represented by x′, without at any time two liquid phases appearing. Starting with x, the temper

g.

rature. There are, however, cases where a maximum or minimum of solubility is found, e.g. methylethylketone and water. The curve which repre

ylketone

C1 per cent

34.

26.

21.9

17.5

16.2

16.1

17.

21.

26.

° 44.

y of the ketone in water, and also a minimum (at about 10°) in the solubility of wa

g.

amine and water mix together in all proportions; but, on raising the temperature, the homogeneous solution becomes turbid and separates into two layers. In this case, therefore, the critical solution temperatu

amine an

C1 per cent

1.

2.

5.

7.3

15

5° ±

come identical, and since all gases are miscible in all proportions, it follows that there must be some temperature at which the liquids become perfectly miscible. In the case of triethylamine and water, which has just been considered, there must therefore be an upper critical solution temperature, so that the complete solubility relations would b

were some discontinuity in one of the phases. No such discontinuity exists. The curve is, therefore, not to be considered as two solubility curves cutting at a point; it is a curve of equilibrium between two components,

components, a distinction must be drawn between the total pressure of the system and the partial pressures o

, and this variation can therefore be represented by a curve. If, however, two liquid phases are formed, the system becomes univariant: and if one of the variables, say the temperature, is arbitrarily fixed, the system no longer possesses

variant system (at constant temperature) lies higher than the vapour pressure of either of the pure components; a phenomenon which is very generally found in the case of partially

g.

e components. An example of this is found in sulphur dioxide and water.[176] On adding sulphur dioxide to water there is an

stem with two liquid phases is less than th

ly proportional to the amount added. If two liquid phases are present, the partial pressure of the components, as well as the total pressure, is constant, and is the same for both phases. That is to say, in the case of t

with the temperature; and liquids which at one temperature can dissolve in one another only to a limited extent, are found at some other temperature to possess the property of complete miscibility. Conversely, we may expect that liquids which at one temperature, say at the ordinary temperature, are miscible in all proportions, will be found at some other tempera

le affords only a slight guidance in the study of such equilibria; and we shall therefore not enter in detail into the behaviour of these homogeneous mixtures. All that the Phase Rule can tell us in connection with these solutions, is that at constant temperature the vapour pressure of the solution varies with the composition of the liquid phase; and if th