ON THE REGULARITY OF CERTAIN PHYSICAL PROPERTIES OF CHEMICAL COMPOUNDS

P. A. SAVINTSEV, M. S. IVANKINA

(Presented by the Scientific Seminar on Dielectrics)

The physical properties of crystals depend on the structure and the interaction between the particles of the crystal lattice. To estimate this interaction one may use the values of a number of physical quantities: heats of melting, heats of sublimation, heats of formation, the coefficient of linear expansion, etc. At present a sufficiently large body of experimental material has been accumulated on the heats of formation of crystals. A regularity has been established in the change of the heat of formation in passing from one compound to another. One of the first to solve this problem was Berkengeim [1], who proceeded from the following regularity, established by D. I. Mendeleev for all elements of the periodic system: the atomic weight of any element is the arithmetic mean of the atomic weights of the neighboring elements in the system. A similar regularity was found [1] for the heats of formation of chemical compounds formed by elements of one period or of one vertical series of D. I. Mendeleev’s table.

The heats of formation \(Q\) of compounds of elements of period 3 and group 2 of D. I. Mendeleev’s system are given in Tables 1 and 2, from which it is seen that the value of the heat of formation, calculated per gram-equivalent,

\[ \frac{Q}{W} \]

(\(W\) is the valence), is equal to the arithmetic mean of the values

\[ \frac{Q}{W} \]

of the neighboring compounds to the right and to the left.

Berkengeim’s results suggest that the properties of chemical compounds are determined by the position of the elements in D. I. Mendeleev’s system. From Tables 1 and 2 it is also seen that the molecular weight of similar chemical compounds changes regularly in passing from one compound to another. Therefore one may seek a relation between

\[ \frac{Q}{W} \]

and the molecular weight.

From Figs. 1 and 2 it is seen that

\[ \frac{Q}{W} \]

changes regularly with increasing molecular weight. For compounds of one period the heat of formation, calculated per gram-equivalent, decreases with increas-

…of molecular weight. For similar compounds of one group of elements, \(\frac{Q}{W}\) increases with increasing molecular weight.

A. F. Kapustinskii [2] established a linear dependence between the heat of formation, referred to one gram-equivalent, \(\frac{Q}{W}\), and the logarithm of the atomic number of the reacting atom \(Z\) (Figs. 3, 4). The relation between \(Z\) and the molecular weight of the compound \(\mu\) is presented by us in Fig. 5, on the basis of which it may be asserted that \(\frac{Q}{W}\) will be proportional not only to \(\lg Z\), but also to \(\lg \mu\).

Fig. 1. Relation of the heat of formation, calculated per one gram-equivalent of compounds of elements of the 3rd period of D. I. Mendeleev’s table, to molecular weight

Fig. 2. Relation of the heat of formation, calculated per one gram-equivalent of compounds of elements of group 2 of D. I. Mendeleev’s table, to molecular weight

The heat of formation is connected with other physical constants. G. A. Kontorova [3] refers to the work of Austin, who, using data [4], showed that the product of the heat of formation of a crystal by the coefficient of thermal expansion is a constant quantity. A relation has been established [5] between the heat of formation and the electric strength of dielectrics. This gives grounds for comparing with molecular weight not only \(\frac{Q}{W}\), but also other physical quantities characterizing…

… properties of chemical compounds of elements of one period or group of the system of D. I. Mendeleev.

Fig. 3. Relation of the heat of formation, calculated per one gram-equivalent, to the logarithm of the atomic number of the reacting atom

Fig. 4. Relation of the heat of formation, calculated per one gram-equivalent, to the logarithm of the atomic number of the reacting atom

Fig. 5. Relation between the charge of the reacting atoms and the molecular weight of the compounds

Table 1

Heat of formation of chlorides formed by elements of the 3rd period of the system of D. I. Mendeleev

Table 2

Heat of formation of compounds formed by elements of Group 2
of the D. I. Mendeleev system

Table 3

Comparison of the physical properties of lithium and sodium compounds
with molecular weight

Table 4

Comparison of the properties of potassium and rubidium compounds with molecular weight

Continuation of Table 4

Table 5

Comparison of the activation energy of the electrical-conductivity process of calcium compounds with molecular weight

Table 6

Comparison of the activation energy of the electrical-conductivity process of magnesium compounds with molecular weight

In Tables 3–4 and in Figs. 6, 7, 8, constructed using the data of [6–10], a comparison is made of the physical constants of alkali-halide crystals with their molecular weight. From these tables and figures it is evident that, on passing to compounds with greater molecular weight, there is observed a regular decrease in the energy of the crystal lattice, the electric strength of the crystals, the activation energy of the electrical-conductivity process, the heat of fusion, the heat of sublimation, hardness, modulus of elasticity, and yield pressure. Under these same conditions there is an increase in the refractive index of light, the electronic component of the dielectric constant, the coefficient of linear expansion of the crystals, and the tangent of the dielectric-loss angle.

A comparison of the properties of the oxides of elements of group 2 of the D. I. Mendeleev system with molecular weight is made in Figs. 9–11, from

from which it is evident that, with increasing molecular weight, the heat capacity and entropy increase. Under the same conditions, the heat of sublimation decreases.

Bush, Juno, Katz, and Winkler [11] measured the electrical conductivity of the intermetallic compounds Ca₂Si, Ca₂Sn, and CaPb. All these substances

Fig. 6. Comparison of the electric strength of alkali-halide crystals with their molecular weight

Fig. 7. Comparison of the coefficient of linear expansion of alkali-halide crystals with their molecular weight

possess semiconductor properties. From the curves of the dependence of electrical conductivity on temperature, the authors found the values of the activation energy, which are given in Table 5. It follows from the latter that the activation energy of the compounds considered decreases with in-

Fig. 8. Comparison of the refractive index of light of alkali-halide crystals with their molecular weight

Fig. 9. Relationship of the entropy of compounds of Group II elements of D. I. Mendeleev’s table with their molecular weight

as the molecular weight increases. We arrived at similar conclusions when comparing the activation energy for electrical conductivity of alkali-halide crystals with their molecular weight.

Winkler [12] found the value of the activation energy for electrical conductivity of the semiconducting compounds Mg₂Si, Mg₂Ge, Mg₂Sn. A comparison

Fig. 10. Relationship of the heat capacity of compounds of elements of Group 2 of D. I. Mendeleev’s table to molecular weight

Fig. 11. Relationship of the heat of sublimation of compounds of elements of Group 2 of D. I. Mendeleev’s table to molecular weight

of the activation energy with the molecular weight of the magnesium compounds is given in Table 6, from which an increase in the activation energy with decreasing molecular weight follows.

Thus, changes in the thermal and other physical properties of compounds formed by elements of one period or group of D. I. Mendeleev’s table may be judged from the change in molecular weight.

REFERENCES

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3. Kontorova T. A. On the thermal expansion and thermal conductivity of certain crystals. ZhTF 26, 69, 2021, 1956.

4. Henglein F. A. Thermal expansion of certain alkali-halide metals at low temperatures. Z. f. Phys. Chem. 115, 1—6, 91, 1925.

5. Vorob’ev A. A., Zavadovskaya E. K., and Trubitsyn A. M. On the correspondence between the stability of chemical compounds and electric strength. DAN SSSR 100, No. 6, 1065, 1955.

6. Vorob’ev A. A. On the properties of ionic dielectrics. Izv. Tomskogo politekhn. in-ta 91, 173, 1956.

7. Vorob’ev A. A. and Zavadovskaya E. K. Physical and electrical properties of ionic crystals. Izv. Tomskogo politekhn. in-ta 83, 3, 1956.

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10. Collection of Physical Constants, ed. by Ya. G. Dorfman and S. E. Frish, ONTI, 1937.

11. Busch G., Junod P., Katz U., Winkler U. Electrical conductivity of the intermetallic compounds Ca₂Si, Ca₂Sn, Ca₂Pb, and SnSb. Helv. Phys. acta. 27, 3, 193, 1954.

12. Winkler U. Electrical properties of the intermetallic compounds Mg₂Si, Mg₂Ge, Mg₂Sn, and Mg₂Pb. Helv. Phys. acta, 28, 7, 633, 1955.