The Phase Rule and Its Applications Part 7

Regarded from the point of view of the Phase Rule, we see that we are here dealing with two components, AgCl and NH_{3}. On being heated, the compounds decompose according to the equations:--

2(AgCl,3NH_{3}) <--> 2AgCl,3NH_{3} + 3NH_{3}.

2AgCl,3NH_{3} <--> 2AgCl + 3NH_{3}.

There are, therefore, three phases, viz. AgCl,3NH_{3}; 2AgCl,3NH_{3}, and NH_{3}, in the one case; and 2AgCl,3NH_{3}; AgCl, and NH_{3} in the other.

These two systems are therefore univariant, and to each temperature there must correspond a definite pressure of dissociation, quite irrespective of the amounts of the phases present. Similarly, 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,3NH_{3} and 2AgCl,3NH_{3}, are present, _i.e._ until the compound richer in ammonia is completely decomposed, when there will be a sudden fall in the pressure to the value corresponding to the system 2AgCl,3NH_{3}--AgCl--NH_{3}. The pressure will again remain constant at constant temperature, until all the ammonia has been pumped off, when there will again be a sudden fall in the pressure to that of the system formed by solid silver chloride in contact with its vapour.

The reverse changes take place when the pressure of the ammonia is gradually increased. If the volume is continuously diminished, the pressure will first increase until it has reached a certain value; the compound 2AgCl,3NH_{3} can then be formed, 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,3NH_{3} can be formed, when it will again remain constant until the complete disappearance of the lower compound. _There is no gradual change of pressure_ on pa.s.sing from one system to another; but the changes are abrupt, as is demanded by the Phase Rule, and as experiment has conclusively proved.[152]

The dissociation pressures of the two compounds of silver {84} chloride and ammonia, as determined by Isambert,[153] are given in the following table:--

-------------------------+------------------------- AgCl,3NH_{3}. 2AgCl,3NH_{3}.

-------------+-----------+--------------+---------- Temperature. Pressure. Temperature. Pressure.

-------------+-----------+--------------+---------- 0 29.3 cm. 20.0 9.3 cm.

10.6 50.5 " 31.0 12.5 "

17.5 65.5 " 47.0 26.8 "

24.0 93.7 " 58.5 52.8 "

28.0 135.5 " 69.0 78.6 "

34.2 171.3 " 71.5 94.6 "

48.5 241.4 " 77.5 119.8 "

51.5 413.2 " 83.5 159.3 "

54.0 464.1 " 86.1 181.3 "

88.5 201.3 "

The conditions for the formation of these two compounds, by pa.s.sing ammonia over silver chloride, to which reference has already been made, will be readily understood from the above tables. In the case of the triammonia mono-chloride, the dissociation pressure becomes equal 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 temperature amounts to only 9 cm., and becomes equal to the atmospheric pressure only at a temperature of about 68; and this temperature, therefore, const.i.tutes the limit above which no combination can take place between silver chloride and ammonia under atmospheric pressure.

Attention may be here drawn to the fact, to which reference will also be made later, that _two_ solid phases are necessary in order that the dissociation pressure at a given temperature shall be definite; _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 definition of the equilibrium, the latter is as important as the former. We shall presently find proof of this in the case {85} of an a.n.a.logous cla.s.s of phenomena, viz. the dissociation of salt hydrates.

Salts with Water of Crystallization.--In the case of the dehydration of crystalline salts containing water of crystallization, we meet with phenomena which are in all respects similar to those just studied. A salt hydrate on being heated dissociates 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 there will correspond a certain, definite vapour pressure (the dissociation pressure), which will be independent of the relative or absolute amounts of the phases, _i.e._ of the amount of hydrate which has already undergone dissociation or dehydration.

[Ill.u.s.tration: FIG. 19.]

The constancy of the dissociation pressure had been proved experimentally by several investigators[155] a number of years before the theoretical basis for its necessity had 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 hydrates of copper sulphate. In Fig. 19 there are represented diagrammatically the vapour-pressure curves of the following univariant systems of copper sulphate and water:--

Curve OA: CuSO_{4},5H_{2}O <--> CuSO_{4},3H_{2}O + 2H_{2}O.

Curve OB: CuSO_{4},3H_{2}O <--> CuSO_{4},H_{2}O + 2H_{2}O.

Curve OC: CuSO_{4},H_{2}O <--> CuSO_{4} + H_{2}O.

Let us now follow the changes which take place on {86} increasing the pressure of the aqueous vapour in contact with anhydrous copper sulphate, the temperature being meanwhile maintained constant. If, starting from the point D, we slowly add water vapour to the system, the pressure will gradually rise, without formation of hydrate taking place; for at pressures below the curve OC only the anhydrous salt can exist. At E, however, the hydrate CuSO_{4},H_{2}O will be formed, and as there are now three phases present, viz. CuSO_{4}, CuSO_{4},H_{2}O, 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 pa.s.sed into hydrated salt, the system again becomes _bivariant_, and pa.s.ses along the line EF; the pressure gradually increases, therefore, until at F the hydrate 3H_{2}O is formed, and the system again becomes univariant; the three phases present are CuSO_{4},H_{2}O, CuSO_{4},3H_{2}O, vapour. The pressure will remain constant, therefore, until the hydrate 1H_{2}O has disappeared, when it will again increase till G is reached; here the hydrate 5H_{2}O is formed, and the pressure once more remains constant until the complete disappearance of the hydrate 3H_{2}O has taken place.

Conversely, on dehydrating CuSO_{4},5H_{2}O at constant temperature, we should find that the pressure would maintain the value corresponding to the dissociation pressure of the system CuSO_{4},5H_{2}O--CuSO_{4},3H_{2}O--vapour, until all the hydrate 5H_{2}O had disappeared; further removal of water would then cause the pressure to fall _abruptly_ to the pressure of the system CuSO_{4},3H_{2}O--CuSO_{4},H_{2}O--vapour, at which value it would again remain constant until the tri-hydrate had pa.s.sed into the monohydrate, when a further sudden diminution of the pressure would occur. This behaviour is represented diagrammatically in Fig. 20, the values of the pressure being those at 50.

Efflorescence.--From Fig. 19 we are enabled to predict the conditions under which a given hydrated salt will effloresce when exposed to the air. We have just learned that copper {87} sulphate pentahydrate, for example, will not be formed unless the pressure of the aqueous vapour reaches a certain value; and that conversely, if the vapour 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 ordinary temperature the dissociation pressure of copper sulphate is less than the pressure of water vapour in the air, and therefore copper sulphate does not effloresce. In the case of sodium sulphate decahydrate, however, the dissociation pressure is greater than the normal vapour pressure in a room, and this salt therefore effloresces.

[Ill.u.s.tration: FIG. 20.]

Indefiniteness of the Vapour Pressure of a Hydrate.--Reference has already been made (p. 84), in the case of the ammonia compounds of the metal chlorides, to the importance of the solid product of dissociation for the definition of the dissociation pressure. Similarly also in the case of a hydrated salt. A salt hydrate in contact with vapour const.i.tutes 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 temperature and pressure lying in the field below the curve OC; and the hydrate CuSO_{4},H_{2}O can exist in contact with vapour at all values of temperature and pressure in the field BOC. Similarly, each of the other hydrates can exist in contact with vapour at different values of temperature and pressure.

From the Phase Rule, however, we learn that, in order that at a given temperature the pressure of a two-component system {88} may be constant, there must be three phases present. Strictly, therefore, we can speak only of the vapour pressure of a _system_; and since, in the cases under discussion, the hydrates dissociate into a solid and a vapour, any statement as to the 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 a.s.sumption, tacitly made, that the second solid phase, or the solid produced by the dehydration of the hydrate, is the _next lower_ hydrate, where more hydrates than one exist.

That a hydrate always dissociates in such a way that the next lower hydrate is formed is, however, by no means certain; indeed, cases have been met with where apparently the anhydrous salt, and not the lower hydrate (the existence of which was possible), was produced by the dissociation of the higher hydrate.[156]

That a salt hydrate can exhibit different vapour pressures according to the solid product of dissociation, can not only be proved theoretically, but it has also been shown experimentally to be a fact. Thus CaCl_{2},6H_{2}O can dissociate into water vapour and either of two lower hydrates, each containing four molecules of water of crystallization, and designated respectively as CaCl_{2},4H_{2}O[alpha], and CaCl_{2},4H_{2}O[beta].

Roozeboom[157] has shown that the vapour pressure which is obtained differs according to which of these two hydrates is formed, as can be seen from the following figures:--

-------------+---------------------------------------------------------- Pressure of System.

Temperature. +-----------------------------+---------------------------- CaCl_{2},6H_{2}O; CaCl_{2}, CaCl_{2},6H_{2}O; CaCl_{2}, 4H_{2}O[alpha]; vapour. 4H_{2}O[beta]; vapour.

-------------+-----------------------------+---------------------------- -15 0.027 cm. 0.022 cm.

0 0.092 " 0.076 "

+10 0.192 " 0.162 "

20 0.378 " 0.315 "

25 0.508 " 0.432 "

29.2 -- 0.567 "

29.8 0.680 " -- -------------+-----------------------------+---------------------------

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By reason of the non-recognition of the importance of the solid dissociation product for the definition of the dissociation pressure of a salt hydrate, many of the older determinations lose much of their value.

Suspended Transformation.--Just as in systems of one component we found that a new phase was not necessarily formed when the conditions for its existence were established, so also we find that even when the vapour pressure is lowered below the dissociation pressure of a system, dissociation does not necessarily occur. This is well known in the case of Glauber's salt, first observed by Faraday. Undamaged crystals of Na_{2}SO_{4},10H_{2}O could be kept unchanged in the open air, although the vapour pressure of the system Na_{2}SO_{4},10H_{2}O--Na_{2}SO_{4}--vapour is greater than the ordinary pressure of aqueous vapour in the air. That is to say, the possibility of the formation of the new phase Na_{2}SO_{4} was given; nevertheless this new phase did not appear, and the system therefore became metastable, or unstable with respect to the anhydrous salt. When, however, a trace of the new phase--the anhydrous salt--was brought in contact with the hydrate, transformation occurred; the hydrate effloresced.

The possibility of suspended transformation or the non-formation of the new phases must also be granted in the case where the vapour pressure is raised above that corresponding to the system hydrate--anhydrous salt (or lower hydrate)--vapour; in this case the formation of the higher hydrate becomes a possibility, 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 in contact with 2AgCl,3NH_{3} could be raised to a value higher than the dissociation pressure of AgCl,3NH_{3} without this compound being formed. We see, therefore, that even when the existence of the higher compound in contact with the lower became possible, the higher compound was not immediately formed.

Range of Existence of Hydrates.--In Fig. 19 the vapour {90} pressure curves of the different hydrates of copper sulphate are represented as maintaining their relative positions throughout the whole range of temperatures. But this is not necessarily the case. It is 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 therefore be metastable with respect to the latter. The range of stable existence of the lower hydrate would therefore end at the point of intersection. This appears to be the case with the two hydrates of sodium sulphate, to which reference will be made later.[159]

Constancy of Vapour Pressure and the Formation of Compounds.--We have seen in the case of the salt hydrates that the continued addition of the vapour phase to the system caused an increase in the pressure until at a definite value of the pressure a hydrate is formed; the pressure then becomes constant, and remains so, until one of the solid phases has disappeared.

Conversely, on withdrawing 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 or withdrawal of the vapour phase, it will be found that the vapour pressure remains constant for a certain time, and will then suddenly a.s.sume a new value, at which it will again remain constant. By this method, Ramsay[160] found that no definite hydrates were formed in the case of ferric and aluminium oxides, but that two are formed in the case of lead oxide, viz. 2PbO,H_{2}O and 3PbO,H_{2}O.

The method has also been applied to the investigation of the so-called palladium hydride,[161] and the results obtained appear to show that no compound is formed. Reference will, however, be made to this case later (Chap. X.).

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Measurement of the Vapour Pressure of Hydrates.--For the purpose of measuring the small pressures exerted by the vapour of salt hydrates, use is very generally made of a differential manometer called the _Bremer-Frowein tensimeter_.[162]

This apparatus has the form shown in Fig. 21. It consists of a U-tube, the limbs of which are bent close together, and placed in front of a millimetre scale. The bend of the tube is filled with oil or other suitable liquid, _e.g._ bromonaphthalene. If it is desired to measure the dissociation pressure of, say, a salt hydrate, concentrated sulphuric acid is placed in the flask _e_, and a quant.i.ty of the hydrate, well dried and powdered,[163]

in the bulb d. The necks of the bulbs _d_ and _e_ are then sealed off.

Since, 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 pump, and sealed off. The apparatus is now placed in a perpendicular position in a thermostat, and kept at constant temperature until equilibrium is established. Since the vapour pressure on the side containing the sulphuric acid may be regarded as zero, the difference in level of the two surfaces of liquid in the U-tube gives directly the dissociation pressure of the hydrate in terms of the particular liquid employed; if the density of the latter is known, the pressure can then be calculated to cm. of mercury.

[Ill.u.s.tration: FIG. 21.]

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CHAPTER VI