The Phase Rule and Its Applications Part 6

Velocity of Transformation.--Attention has already been drawn to the sluggishness with which reciprocal transformation of the polymorphic forms of a substance may occur. 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, under the ordinary conditions of temperature and pressure. This great degree of stability is due to the tardiness with which transformation into the grey form occurs.

What was found in the case of tin, is met with also in the case of all transformations in the solid state, but the velocity of the change is less in some cases than in others, and appears to decrease with increase of the valency of the element.[127] To this fact van't Hoff attributes the great permanence of many really unstable (or metastable) carbon compounds.

Reference has been made to the fact that the velocity of transformation can be accelerated by various means. One of the most important of these is the employment of a liquid which has a solvent action on the solid phases. Just 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, and be shown experimentally, that {71} at a given temperature the solubility of the less stable form is greater than that of the more stable, but that at the transition point the solubility of the two forms becomes identical.[128]

If, then, the two solid phases are brought into contact with a solvent, the less stable phase will dissolve more abundantly than the more stable; the solution will therefore become supersaturated with respect to the latter, which will be deposited. 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 explained. Although, as a rule, solvents accelerate the transformation of one solid phase into the other, they may also have a r.e.t.a.r.ding influence on the velocity of transformation, as was found by Reinders in the case of mercuric iodide.[129]

The velocity of inversion, also, is variously affected by different solvents, and in some cases, at least, it appears to be slower the more viscous the solvent;[130] indeed, Kastle and Reed state that yellow crystals of mercuric iodide, which, ordinarily, change with considerable velocity into the red modification, have been preserved for more than a year under vaseline.

Temperature, also, has a very considerable influence on the velocity of transformation. The higher the temperature, and the farther it is removed from the equilibrium point (transition point), the greater is the velocity of change. Above the transition point, these two factors act in the same direction, and the velocity of transformation will therefore go 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 temperature {72} below this point causes a rapid falling off in the velocity of change. The point of maximum velocity, however, is not definite, but may be altered by various causes. Thus, Cohen found that in the case of tin, the point of maximum velocity was altered if the metal had already undergone transformation; and also by the presence of different liquids.[131]

Lastly, the presence of small quant.i.ties of different substances--catalytic agents or catalyzers--has a great influence on the velocity of transformation. Thus, _e.g._, the conversion of white to red phosphorus is accelerated by the presence of iodine (p. 47).

Greater attention, however, has been paid to the study of the velocity of crystallization of a supercooled liquid, the first experiments in this direction having been made by Gernez[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 acetic acid and phenol by Moore;[133] supercooled water by Tumlirz;[134]

and a number of organic substances by Tammann,[135] Friedlander and Tammann,[136] and by Bogojawlenski.[137]

In measuring the velocity of crystallization, the supercooled liquids were contained in narrow gla.s.s tubes, and the time required for the crystallization to advance along a certain length of the tube was determined, the velocity being expressed in millimetres per minute. The results which have so far been obtained may be summarized 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 each substance. This maximum velocity remains constant over a certain range of {73} temperature; thereafter, the velocity diminishes fairly rapidly, and, with sufficient supercooling, may become zero. The liquid then pa.s.ses into a gla.s.sy ma.s.s, which will remain (practically) permanent even in contact with the crystalline solid.

In ordinary gla.s.s we have a familiar example of a liquid which has been cooled to a temperature at which crystallization takes place with very great slowness. If, however, gla.s.s is heated, a temperature is reached, much below the melting point of the gla.s.s, at which crystallization occurs with appreciable velocity, and we observe the phenomenon of devitrification.[138]

When the velocity of crystallization is studied at temperatures above the maximum point, it is found that the velocity is diminished by the addition of foreign substances; and in many cases, indeed, it has been found that the diminution is the same for equimolecular quant.i.ties of different substances. 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 in the velocity produced by equivalent amounts of different substances is not the same, but that the foreign substances exercise a specific influence. Further, von Pickardt's rule does not hold when the foreign substance forms mixed crystals (Chap. X.) with the crystallizing substance.[141]

Law of Successive Reactions.--When sulphur vapour is cooled at the ordinary temperature, it first of all condenses to drops of liquid, which solidify in an amorphous form, and only after some time undergo crystallization; or, when phosphorus vapour is condensed, 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 disulphide, and other {74} solvents, in the prismatic form, the less stable prismatic crystals then undergoing transformation into the rhombic form;[142] a similar behaviour has also been observed in the transformation of the monotropic crystalline forms of sulphur.[143]

Many other examples might be given. In organic chemistry, for instance, it is often found that when a substance is thrown out of solution, it is first deposited as a liquid, which pa.s.ses later into the more stable crystalline form. In a.n.a.lysis, also, rapid precipitation from concentrated solution often causes the separation of a less stable and more soluble amorphous form.

On account of the great frequency with which the prior formation of the less stable form occurs, Ostwald[144] has put forward the _law of successive reactions_, which states that when a system pa.s.ses from a less stable condition it does not pa.s.s directly into the most stable of the possible states; but into the next more stable, and so step by step into the most stable. This law explains the formation of the metastable forms 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 cooling to a low temperature will tend to preserve the less stable form; and, on account of the influence of temperature in increasing the velocity of change, it can be seen that the formation of the less stable form will be more difficult to observe in superheated than in supercooled systems. The factors, however, which affect the readiness with which {75} the less stable modification is produced, appear to be rather various.[145]

Although a number of at least apparent exceptions to Ostwald's law have been found, it may nevertheless be accepted as a very useful generalization which sums up very frequently observed phenomena.

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CHAPTER V

SYSTEMS OF TWO COMPONENTS--PHENOMENA OF DISSOCIATION

In the preceding pages we have studied the behaviour of systems consisting of only one component, or systems in which all the phases, whether solid, liquid, or vapour, had the same chemical composition (p. 13). In some cases, as, for example, in the case of phosphorus and sulphur, the component was an elementary substance; in other cases, however, _e.g._ water, the component was a compound. The systems which we now proceed to study are characterized by the fact that the different phases have no longer all the same chemical composition, and cannot, therefore, according to definition, be considered as one-component systems.

In most cases, little or no difficulty will be experienced in deciding as to the _number_ of the components, if the rules given on pp. 12 and 13 are borne in mind. If the composition of all the phases, each regarded as a whole, is the same, the system is to be regarded 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, two of the const.i.tuents partic.i.p.ating in the equilibrium are necessary and sufficient, the system is one of two components. Which two of the possible substances are to be regarded as components will, however, be to a certain extent a matter of arbitrary choice.

The principles affecting the choice of components will best be learned by a study of the examples to be discussed in the sequel. {77}

Different Systems of Two Components.--Applying the Phase Rule

P + F = C + 2

to systems of two components, we see that in order that the system may be invariant, there must be four phases in equilibrium together; two components in three phases const.i.tute a univariant, two components in two phases a bivariant system. In the case of systems of one component, the highest degree of variability found was two (one component in one phase); 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 const.i.tute 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 is taken the _concentration of the components_. In systems of two components, therefore, not only may there be change of pressure and temperature, as in the case of one-component systems, but the concentration of the components in the different phases may also alter; a variation which did not require to be considered in the case of one-component systems.

[Ill.u.s.tration: FIG. 18.]

Since a two-component system may undergo three possible {78} independent variations, we should require for the graphic representation of all the possible conditions of equilibrium a system of three co-ordinates in s.p.a.ce, three axes being chosen, say, at right angles to one another, and representing the three variables--pressure, temperature, and concentration of components (Fig. 18). A curve (_e.g._ AB) in the plane containing the pressure and 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 constant pressure would be represented (_tc_-diagram). If the points on these three curves are joined together, a surface, ABDE, will be formed, and any line on that surface (_e.g._ FG, or GH, or GI) would represent the simultaneous variation of the three factors--pressure, temperature, concentration. Although we shall at a later point make some use of these solid figures, we shall for the present employ the more readily intelligible plane diagram.

The number of different systems which can be formed from two components, as well as the number of the different phenomena which can there be observed, is much greater than in the case of one component. In the case of no two substances, however, have all the possible relations.h.i.+ps been studied; so that for the purpose of gaining an insight into the very varied behaviour of two-component systems, a number of different examples will be discussed, each of which will serve to give a picture of some of the relations.h.i.+ps.

Although the strict cla.s.sification of the different systems according to the Phase Rule would be based on the variability of the systems, the study of the many different phenomena, and the correlation of the comparatively large number of different systems, will probably be rendered easiest by grouping these different phenomena into cla.s.ses, each of these cla.s.ses being studied with the help of one or more typical examples. The order of treatment adopted here is, of course, quite arbitrary; {79} but has been selected from considerations of simplicity and clearness.

PHENOMENA OF DISSOCIATION.

Bivariant Systems.--As the first examples of the equilibria between a substance and its products of dissociation, we shall consider very briefly those cases in which there is one solid phase in equilibrium with vapour.

Reference has already 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 solid phase, viz. NH_{3} + HCl = NH_{4}Cl, the system consists of only one component existing in two phases; it is therefore univariant, and to each temperature there will correspond a definite vapour pressure (dissociation pressure).[146]

If, however, excess of one of the products of dissociation be added, the system becomes one of two components.

In the first place, a.n.a.lysis of each of the two phases yields as the composition of each, solid: NH_{4}Cl (= NH_{3} + HCl); vapour: _m_NH_{3} + _n_HCl. Obviously the smallest number of substances 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 NH_{3} + HCl, NH_{4}Cl + NH_{3}, and NH_{4}Cl + HCl; for the three substances, ammonium chloride, ammonia, hydrogen chloride, are the only ones taking part in the equilibrium of the system.

Of these three pairs of components, we should obviously choose as the most simple NH_{3} and HCl, for we can then represent the composition of the two phases as the _sum_ of the two components. If one of the other two possible pairs of components be chosen, we should have to introduce negative quant.i.ties 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 quant.i.ties of a component in such cases is quite permissible, still it will be {80} better to adopt the simpler and more direct choice, whereby the composition of each of the phases is represented as a sum of two components in varying proportions (p. 12).

If, therefore, we have a solid substance, such as ammonium chloride, which dissociates on volatilization, and if the products of dissociation are added in varying amounts to the system, we shall have, in the sense of the Phase 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 the components, can vary. Only after one of these independent variables, pressure or composition, has been arbitrarily fixed does the system become univariant, and exhibit a definite, constant pressure at a given temperature.

Now, although the Phase Rule informs us that at a given temperature change of composition of the vapour phase will be accompanied by change of pressure, it does not cast any light on the relation between these two variables. This relations.h.i.+p, however, can be calculated theoretically by means of the Law of Ma.s.s Action.[147] From this we learn that in the case of a substance which dissociates into equivalent quant.i.ties of two gases, the product of the partial pressures of the gases is constant at a given temperature.

This has been proved experimentally in the case of ammonium hydrosulphide, ammonium cyanide, phosphonium bromide, and other substances.[148]

Univariant Systems.--In order that a system of two components shall possess only one degree of freedom, three phases must be present. Of such 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 present chapter we shall consider only the systems S-S-V, _i.e._ those systems in which there are two solid phases and a vapour phase present.

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As an example of this, we may first consider the well-known case of the dissociation of calcium carbonate. This substance on being heated dissociates into calcium oxide, or quick-lime, and carbon dioxide, as shown by the equation CaCO_{3} <--> CaO + CO_{2}. In accordance with our definition (p. 9), we have here two solid phases, the carbonate and the quick-lime, and one vapour phase; the system is therefore 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 temperature is maintained constant, increase of volume will cause the dissociation of a further amount of the carbonate until the pressure again reaches its maximum value corresponding to the given temperature.

Diminution of volume, on the other hand, will bring about the combination of a certain quant.i.ty of the carbon dioxide with the calcium oxide until the pressure again reaches its original value.

The dissociation pressure of calcium carbonate was first studied by Debray,[149] but more exact measurements have been made by Le Chatelier,[150] who found the following corresponding values of temperature and pressure:--

-------------+------------------------- Temperature. Pressure in cm. mercury.

-------------+------------------------- 547 2.7 610 4.6 625 5.6 740 25.5 745 28.9 810 67.8 812 76.3 865 133.3 -------------+-------------------------

From this table we see that it is only at a temperature of about 812 that the pressure of the carbon dioxide becomes equal to atmospheric pressure.

In a vessel open to {82} the air, therefore, the complete decomposition of the calcium carbonate would not take place 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 equilibrium of the carbonate depends only on the partial pressure of the carbon dioxide, and if this is kept small, then the decomposition can proceed, even at a temperature below that at which the pressure of the carbon dioxide is less than atmospheric pressure.

Ammonia Compounds of Metal Chlorides.--Ammonia possesses the property of combining with various substances, chiefly the halides of metals, to form compounds which again yield up the ammonia on being heated. Thus, for example, on pa.s.sing ammonia over silver chloride, absorption of the gas takes place with formation of the substances AgCl,3NH_{3} and 2AgCl,3NH_{3}, according to the conditions of the experiment. These were the first known substances belonging to this cla.s.s, and were employed by Faraday in his experiments on the liquefaction of ammonia. Similar compounds have also been obtained by the action of ammonia on silver bromide, iodide, cyanide, and nitrate; and with the halogen compounds of calcium, zinc, and magnesium, as well as with other salts. The behaviour of the ammonia compounds of silver chloride is typical for the compounds of this cla.s.s, and may be briefly considered here.

It was found by Isambert[151] that at temperatures below 15, silver chloride combined with ammonia to form the compound AgCl,3NH_{3}, while at temperatures above 20 the compound 2AgCl,3NH_{3} was produced. On heating these 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 substance; the pressure, further, was independent of the amount decomposed.

The behaviour of these two substances is, therefore, exactly a.n.a.logous to that shown by calcium carbonate, and the explanation is also similar.

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