Part 6 (1/2)
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.
{76}
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.