STUDIES I?; T H E SOLUBILITIES OF T H E SOLUBLE ELECTROLTTES
I. RELATIOXSHIPS B E T W E E S T H E T E l I P E R h T U R E COEFFICIEXTS* BY ARTHCR F. SCOTT
Various attempts have been made to formulate a theory of solubility of the soluble electrolytes and, although none is complete, they are all pretty much agreed on three determinant factors which we may describe as ( I ) cohesion of solute; (2) cohesion of solvent; and (3) adhesion of solvent and solute. In a number of recent papers, however, these cohesive and adhesive forces are treated, with very suggestive results, from the standpoint of modern at'omic theory. It is the object of the present study to describe certain relationships which exist between the temperature coefficients of solubility and of which an interpretation in terms of these newer concepts appears possible. K e shall therefore review briefly at the outset the more significant postulates respecting the above three factors. We shall consider the ions of an electrolyte in the solid state to be arranged in a crystal lattice, their positions being controlled by electrostatic forces of attraction and repulsion. .Is a measure of the cohesion of the ions in this state we may take the lattice (free) energy, a characteristic constant which varies but little with temperature. In solution, x e shall assume further, both cation and anion of a salt are able to attract by means of their electrostatic forces the dipolar water molecules. The magnitude of these forces of adhesion between solute and solrent is indicated approximntely by the heats of hydration of the individual ions. S o w , if the solubility of plect'rolytes is determined by the differencr of these two energy factors, we should expect it to vary, qualitatively at least, with the heat of solution because this constant is equal to the heats of hydration of the ions minus the lattice energy of the salt. The possibility of such a relationship has been discussed by Butler.' At this point a word may be said regarding one of the distinctions between soluble and insoluble electrolytcs. Aka general rule the soluble salts have relatively small heats of solution, which fact, according to Fiock and Rode. bush,* means "that t,he electrical forces of an ion are neutralized to about the same ext,ent in solution as in the crystal lattice." On the other hand the insoluble salts hare somewhat larger, negative heats of solution, a condition which Fajane3 has attributed to the abnormally large lattice energies which * Contribution from the Department of Chemistry oi T h e Rice Institute Butler: Z. physik. Chem., 113. 279 (192qj. Fiock a n d Rodebush: J. Am. Chem. *Sac., 48, 25-22 (19261. 3Fajans: Z.Kristall., 61, 1 6 (1g2ji;66,321 (1926).
SOLUBILITIES O F THE SOLUBLE ELECTROLYTES
IO01
result from the deformation in the solid state of the electronic shell of one ion under the influence of the electric field of t'he oppositely charged ion. I n support of this argument, Herzfeld and Fischer' have shown for analogous insoluble salts that a salt, is less soluble the more negative its heat of solution. Since \ye shall deal in the present paper only with the very soluble salt's, it is safe to assume that we shall not meet with any pronounced effects of deformation. Yevertheless it must be remembered that deformation depends upon the particular properties of the constituent ions and that consequently the possibility of its existence cannot be disregarded.? K i t h respect to the hydration of ions we shall accept an additional postulate which was first proposed by Fajans3and which can be stated in the follow ing form: Khen the number of molecules of water to be distributed between the ions of a salt is sufficiently limited, as in the saturated solutions of very soluble salts, the ensuing competition between the ions results in the stronger ion gaining control over these water molecules to the exclusion oE the weaker ion. K e shall hereafter refer to these ions, under the above conditions, as the dominant ion and the subordinate ion, respectively. To estimate the relative .strengths of the ions of a salt we can employ either the free energies4 of hydration of the gaseous ions or the heats; of hydration of the gaseous ions. The former is to be preferred. On the grounds of these over-simplified postulates we may attempt to construct a picture of the saturated state, an equilibrium condition which is reached when the forces tending to unite the ions into a crystal lattice are balanced by the opposing forces tending to keep them in solution. The cornbining action, from our viewpoint, results from the forces of inter-ionic attraction xhich are probably independent of temperature. This variable factor will be indicated by @DS where D and X represent the two ionsinvolved. The action tending to keep the ions separated may be regarded as being composed of two different factors: ( I ) the thermal motion of the particles; and ( 2 ) the attraction betxeen the dominant ion and the water dipoles. Both of these factors, it is obvious, must be dependent on temperature. By this sort of analysis we come, therefore, to t'he usual and plausible conclusion that it would be possible to represent the solubility of a salt by some general, complex function of @DS and T. But in this paper evidence will be adduced which can be taken to indicate that this function may be written in following less general form: Here the solubility S D x is expressed as the number of moles of water per mole of salt. The right hand member of the equation consists of two terms represcnting the oppowig forces at the equilibrium state. @,x IS a constant para-
3
Herzfeld and Fischer: Z.Elektrochemie, 26,460 (1922). See Fajans: "The Theory of Strong Electrolytes," The Faraday Society, page 408. Fajans: Saturn-issenschaften, 9, z (1921). Kebb: J. Am. Chem. Soc., 48, 2600 (1926,. Fajans: I'erh. deutsch. physik. Ges., 21, 549, 709 (1919).
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ARTHUR F. SCOTT
meter, characteristic of the forces of inter-ionic attraction and fD(T) is an indefinite function which represents the variation of the two factors influenced by temperature. Now, although the precise nature of parameter and function is unknown, we can make the important assumption that the latter, a t a given temperature, has the same value for all solutions with a common dominant ion D. For the two factors whose variation with temperature are described by fD(T) are, according to the dominant ion concept, identical under the above condition. I n support of the foregoing deduction we shall consider two relationships which can be deduced from equation ( I ) . For a group of salts, DX, DY, etc., we have equations analogous to ( I ) which on differentiation with respect to temperature become :
Dividing (za) by (zb) we obtain, since f‘n(T) is identical because of the common dominant ion,
I n other words the ratio of the temperature coefficients of solubility a t any given temperature of any two salts which fulfill the above conditions is independent of temperature. I n the second place, if the differentiation be carried out a t a different temperature, say Tz, we obtain equations analogous to (2a) and (zb). They are
Kow, dividing equation (za) by (4a), and equation (2b) by (4b) we get
This relationship means, of course, that the ratio of the temperature coefficient of solubility at one temperature to that at another temperature is identical for all salts with the same dominant ion.
SOLUBILITIES OF THE SOLUBLE ELECTROLYTES
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In what follows we shall consider examples which appear to be in accord with these deductions. It will be recognized, to be sure, that the theory just outlined has been developed to make the empirical relationships intelligible. Nevertheless, it may be mentioned that certain conclusions, which this provisional theory suggests, have been tested and confirmed, and will be reported in some papers in the course of preparation. The selection of typical examples, however, is a matter of considerable difficulty because of the requirements which they must satisfy. Thus, in
FIG. I
S values of salts with common dominant ion plotted against X values of potassium
chloride at corresponding temperatures.
any particular group of salts, each salt must have the same dominant ion and, besides, the solubilities of these salts must be sufficiently great (N small) to allow the dominant ion t o come into exclusive control of the water dipoles. Moreover, there must be no change in the solid state, such as the formation of hydrates, which would affect the parameter ~ 9Although ~ ~ there . are many groups of salts R:hich meet the above conditions, our actual choice is seriously restricted by the fragmentary nature of the available solubility data. Probably the simplest group of salts which we shall consider consists of the chloride, bromide, and iodide of potassium, where the potassium ion is undoubtedly dominant. It appears, further, that two other salts, the chlorides
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ARTHUR F. SCOTT
of rubidum and cesium, also belong in this group, despite the fact that, nccording to the free energies of hydration, the cation in both cases is slightly stronger than the chloride ion. They were included originally, however, because the chloride ion has a greater heat of hydration than the cations and would therefore be dominant. Moreover, it should be noted that both potassium and chloride ion have the same electronic structure and almost the same heats of hydration. In order to show to what extent these five salts satisfy the rule expressed by equation (3) we have plotted in Fig. I the N values of each salt against the h' values of potassium chloride at the corresponding temperatures. The necessary data for the construction of this graph are contained in Table I.
TABLE I Values* of S a t Different Temperatures
T
KC1
O0
14.79 13.37 12.18 I1 I8 10.3j 9.72 9.10 8,57 8.19 7 .66 7.31
10 20
30
40 50
60 io
80 90 IO0
IiBr
RbCl
I
