HEAT OF FORMATION AND MOLECULAR CONCENTRATION OF IONIC COMPOUNDS AND THEIR SOLID SOLUTIONS

P. A. SAVINTSEV, M. S. IVANKINA

(Presented by Professor Doctor A. A. Vorob’ev)

The heat of formation of a solid compound is one of the most important quantities characterizing the properties of a crystal. It is measured by the amount of heat released in the formation of the given compound from the elements under standard conditions. If, during the formation of a compound, heat is absorbed, the heat of formation is customarily regarded as negative; when heat is evolved—as positive. The heat of formation characterizes the degree of stability of a compound. The higher the positive value of the heat of formation (heat is evolved), the more stable the compound is under mechanical, thermal, electrical, and other effects [1].

The heat of formation also largely determines the properties of solid solutions. By the heat of formation of a solid solution is meant the difference between the heats of dissolution in water of a mechanical mixture and of a solid solution of the same weight and composition. The heat of dissolution of a mechanical mixture of alkali-halide salts exceeds the heat of dissolution of the corresponding solid solution of the same salts. The greater the difference between these heats of dissolution, the greater the potential energy of the solid solution and the weaker the bonding of ions in the lattice. Consequently, the magnitude of the heat of formation is a measure of the stability of solid solutions.

The heat of formation of solid solutions has been calculated theoretically and determined experimentally by many scientists [3—15].

The values of the heats of formation of solutions obtained in various investigations are given in Tables 1—3, which contain experimental and theoretical data, sometimes differing considerably from one another. The discrepancy among theoretical values is explained by the different degree to which the interaction between particles is taken into account in calculating the heat of formation. Thus, Grimm and Herzfeld [3] calculate the interaction by Born’s formula without allowing for van der Waals forces.

Ulich [4] adopts the Born–Mayer model and takes van der Waals forces into account.

Durkheim and Hocking [5] take into account the mixing of solvent ions in the formation of a substitutional solid solution.

Vazastern [6] takes into consideration the effect of displacement of ions in the crystal lattice and introduces into the discussion the degree of local order in the arrangement of particles. The degree of order is the higher, the more unlike ions surround a given ion.

Table 1

Heat of formation, in cal/mole, of sodium chloride crystals containing impurities of sodium bromide (molecular concentration 31 cm\(^{-3}\) mole) and potassium chloride (molecular concentration 26 cm\(^{-3}\) mole)

Table 2

Heat of formation, in cal/mole, of potassium bromide crystals containing impurities of sodium bromide (molecular concentration 31 cm\(^{-3}\) mole) and sodium chloride (molecular concentration 26 cm\(^{-3}\) mole)

Such assumptions are made by Hovi [7]. In calculating the heat of formation of the sodium chloride—sodium bromide system, he obtained a smooth curve relating the degree of order to the composition of the alloy. On this cur-

Table 3

Heat of formation, in cal/mol, of sodium bromide crystals containing impurities of sodium chloride
(molecular concentration 7 cm\(^{-3}\) mol) and potassium bromide
(molecular concentration 22 cm\(^{-3}\) mol)

its maximum degree of order corresponds to an equimolar solution.

The difference in the experimental values is explained by the nonidentical methods used in carrying out the experiments by different investigators. S. Zhemchuzhnyi and F. Rambach [8], in order to determine the heat of formation, used a single-vessel calorimetric method. As far as we know, the two-vessel calorimetric method was first used by Fonselius [9].

Barrett and Wallis [10] drew attention to the fact that the results of experiments on determining the heat of formation depend on the conditions under which the specimens are stored. In their experiments, in order to protect the specimens from the influence of moisture, they were placed at high temperature in an ampoule with gel. The influence of moisture on other properties of alkali-halide crystals was found in the works [11].

The heat of formation of solid compounds is a quantity that characterizes the interaction of the particles of the lattice; consequently, it is connected with the energy of the latter. One of us [2] has shown the dependence of the energy of the crystal lattice on the molecular concentration. The molecular concentration is readily determined experimentally and is a characteristic of a real crystal. This gives us the right to seek a relation between the heat of formation and the molecular concentration.

From Figs. 1–4 it is seen that the heat of formation increases with increasing molecular concentration. An especially simple relation between the heat of formation and the molecular concentration occurs in the case of alkali-halide crystals. Evidently, in this case one may speak of the presence of a linear dependence of the heat of formation on the molecular concentration. It must be emphasized that the coefficients relating the heat of formation to the molecular concentration change in passing from compounds of one metal to compounds of another metal.

Fig. 1. Relation of the heat of formation of alkali-halide crystals to molecular concentration

Fig. 2. Relation of the heat of formation of halide compounds of ammonium and silver to molecular concentration

Fig. 3. Relation of the heat of formation of calcium and barium compounds to molecular concentration

Fig. 4. Relation of the heat of formation of oxides of elements of Group II of D. I. Mendeleev’s table to molecular concentration

Let us proceed to a comparison of the results entered in Tables 1–3. Each of these tables shows the value of the heat of formation of the solvent crystal upon the introduction into it of various impurities. It may be assumed that, with the solvent unchanged, the value of the heat of formation will be determined by the molecular concentration of the substance that is the impurity. We shall test this assumption by using the values of the molecular concentrations of different impurities in analyzing the results entered in Tables 1–3.

In Fig. 5, obtained on the basis of the data of Table 1, we compare the values of the heat of formation of sodium chloride crystals containing impurities of sodium bromide and potassium chloride.

Fig. 5. Heat of formation of solid solutions of sodium bromide in sodium chloride and potassium chloride in sodium chloride

For comparison, we have taken the results obtained by Fajans and Ullis [12] for the sodium chloride—sodium bromide system, and by Zemczuzny and Rambach [8] for the sodium chloride—potassium chloride system.

In Fig. 5 it is seen that the curve characterizing the influence of the potassium chloride impurity in sodium chloride, with a molecular concentration equal to 26, lies above the curve characterizing the influence of the sodium bromide impurity in sodium chloride, with a value of the molecular concentration equal to 31.

In Fig. 6, obtained on the basis of the data entered in Table 2, the influence of impurities of potassium chloride (molecular concentration equal to 26) and sodium bromide (molecular concentration equal to 31), introduced into a potassium bromide crystal, is compared. The comparison is made on the basis of data obtained by one method, i.e., from the works of Zemczuzny and Rambach. From Fig. 6 it is seen that the impurity with the smaller value of molecular concentration has the greater influence on the change in the heat of formation.

A comparison of the influence of impurities of sodium chloride and potassium bromide on the heat of formation of sodium bromide crystals is shown in Fig. 7, which was obtained on the basis of a comparison of the data (Table 3) of Fajans and Ullis [12] for the sodium bromide—sodium chloride system (molecular concentration equal to 37) with the data of S. Zemczuz—

and F. Rambach [8] for the system sodium bromide—potassium chloride (molecular concentration equal to 22).

From Fig. 7 it is evident that the impurity with the smaller value of the molecular concentration has the greater influence on the change in the heat of formation.

Fig. 6. Heat of formation of solid solutions of sodium bromide in potassium bromide and potassium chloride in sodium bromide

Fig. 7. Heat of formation of solid solutions of sodium chloride in sodium bromide and potassium bromide in sodium bromide

Conclusion

Despite the considerable divergence in the numerical results for the heats of formation of solid solutions obtained by various authors, it has been possible to establish the dependence of the heat of formation on the molecular concentration of the substance that is the impurity. It is shown that the heat of formation of solid solutions will be greater when those impurities are introduced for which the value of the molecular concentration is smaller. On the basis of this dependence, one may draw a conclusion about the influence of molecular concentration on the stability of a solid solution. The higher the molecular concentration, the more stable the given solid solution, and conversely. This is in agreement with the facts [2] that, with increasing molecular concentration, the electrical and mechanical strength of crystals increases.

References

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