The Phase Rule and Its Applications. Alexander Findlay

ordinary glass 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, glass is heated, a temperature is reached, much below the melting point of the glass, 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 quantities 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 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 passes later into the more stable crystalline form. In analysis, 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 passes from a less stable condition it does not pass 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 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.

CHAPTER V

       Table of Contents

      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 constituents participating 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.

      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 constitute 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 constitute 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.