On a Differential Calorimetric Method for Measuring the Heats of Formation of Solid Solutions

M. S. Ivankina

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

The formation of a solid solution is accompanied by a change in the free and internal energy of the system and in its entropy. The change in the internal energy of the system is equal to the heat of formation of the solid solution.

Academician N. S. Kurnakov, S. F. Zhemchuzhnyi, and F. Rambach \[1, 2\] understand by the heat of formation a quantity numerically equal to 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 binding of ions in the lattice. Consequently, the magnitude of the heat of formation is a measure of the stability of solid solutions.

Comparisons of the electrical strength of a number of solid solutions with their heats of formation—\(Q\), carried out in \[3, 4\], showed that:

1) an increase in the value of \(Q\) corresponds to a decrease in electrical strength;

2) the maximum value of \(Q\) coincides with the minimum of electrical strength;

3) with a decrease in the value of \(Q\), the electrical strength increases.

Such an unambiguous correspondence between the values of electrical strength and \(Q\) increases interest in the investigation of the latter.

The heat of formation of a solid solution can be determined experimentally by several methods \[5\]. For water-soluble solid solutions of alkali-halide salts, the calorimetric method is usually used.

S. F. Zhemchuzhnyi and F. Rambach \[2\], and somewhat later S. Wrzhesnevsky \[6\], using a single-vessel calorimetric method, determined the heats of formation of a number of solid solutions. But the data \[2, 6\] are overestimated and do not agree with the values of the heats of formation presented by the later theory of Grimm and Herzfeld \[7\]. A procedure analogous to \[2, 6\] was used in their work by Tammann and Krings \[8\], and considerably later by M. M. Popov and his collaborators \[9, 10\].

More convenient in many respects than measurement methods using only one vessel is the two-vessel method, based on the differential principle, the use of which makes it possi-

possibility of reducing the effect of heat losses on the final result to a minimum. In 1938 Fontell [11] used the differential calorimetric method to determine the heats of formation of solid solutions of the KCl—KBr system. Subsequently this method was applied by Fajneman and Wallis [12], Hovi [13, 14], and others.

In our measurements a differential calorimeter was also used, the design of which is considerably simplified. A brief description of it is given below.

The arrangement of the calorimeter is shown in Fig. 1. The calorimetric vessel was a Dewar vessel (1), of capacity 350 cm³, with a textolite lid

Fig. 1. Diagram of the calorimeter
1 — Dewar vessel, 2 — thermistor, 3 — device for introducing the weighed portion of salt, 4 — stirrer, 5 — calorimeter lid, 6 — flange, 7, 8 — stand for the calorimeter.

of textolite (5). The lid was pressed tightly by means of 6 bolts to the textolite flange (6) with a rubber gasket. In the calorimeter lid there are 3 openings, into which glass tubes were inserted for introducing the glass stirrer (4), the leads from the thermistor (2), and the device for the weighed portion of salt (3). The latter is a glass-

... a spoon 18 mm in diameter and 15 mm high, closed with a ground glass lid; the ground joint was lubricated with vacuum grease. A loop with a silk thread tied to it was made on the lid; by pulling this thread the lid of the holder could be removed, bringing the substance into contact with the water of the calorimeter.

Two such calorimeters were placed in a thermostat, which was a wooden reservoir with a capacity of 90 liters. The general appearance of the thermostat with the calorimeters is shown in Fig. 2. By means of a zigzag-shaped mercury-toluene thermoregulator (3), connected to an electromagnetic relay, and a thermal resistance in the thermostat (17), the temperature was maintained constant to within ±0.005°C. The thermostatic liquid was stirred by means of a stirrer (14) driven by an electric motor (1). The glass stirrers (8) of both calorimeters were rotated synchronously by the same electric motor, as a result of which the temperature difference caused by friction of the stirrers against the water remained constant during the experiment. The temperature in the thermostat was recorded with a Beckmann thermometer (2). All experiments were carried out at the standard temperature of 25.0°C. The apparatus was located in a thermostated room.

Fig. 2. General view of the thermostat with calorimeters.
1 — electric motor, 2 — Beckmann thermometer, 3 — thermoregulator, 4 — pulley, 5, 6 — thermostat covers, 7 — device for suspending the salt, 8 — stirrer, 9 — thermistor, 10 — calorimeter cover, 11 — flange, 12 — Dewar vessel, 13, 15, 16 — stand for installing the calorimeter, 17 — thermostat.

Measurements of the heats of formation of solid solutions were carried out as follows. Into the Dewar vessels were poured 200 cm³ each of distilled water, previously heated to 25°C. Into the holder of the first vessel were placed 500–600 mg of a solid solution of definite molecular composition; into the holder of the second vessel, a mechanical mixture of the salts constituting the solid solution, of the same weight and composition. The calorimeters were then tightly closed with lids and placed in the ther-

thermostat. MMT-4 thermistors were connected in a bridge circuit, the indicator of which was an M21-1 mirror galvanometer, with a sensitivity of \(10^{-10}\) A/mm.

To achieve a state of thermal equilibrium in the calorimeters, thermostating for 4–5 hours is necessary. When thermal equilibrium had been reached, as indicated by the constancy of the galvanometer readings, the covers were removed from the devices for weighing out the salts, and the substance dissolved in the water.

As already mentioned above, upon dissolution of a mechanical mixture and a solid solution of the same weight and composition, different amounts of heat are absorbed; therefore, after dissolution of the salts, a temperature difference naturally arises between the two calorimetric vessels, as indicated by the deflection of the galvanometer. Having calibrated the galvanometer scale in calories,

Table 1

Values of the heats of formation of KCl—KBr solid solutions as a function of composition

Table 2

Values of the heats of formation of NaCl—KCl solid solutions as a function of composition

from the galvanometer deflection using the heats of solution of KCl at \(+25^\circ\mathrm{C}\) for infinitely dilute solutions [11], we calculated, from the difference between the heats of solution of the mechanical mixture and of the solid solution, the heat of formation of the latter. The experiment was carried out twice. In the second measurement, the mechanical mixture was placed in the holder of the first vessel, and the solid solution in the holder of the second vessel. The mean of the two measurements was taken as the value of the heat of formation of the solid solution under study. The thermal sensitivity of the apparatus was \(0.01\ \mathrm{cal/mm}\), or \(1.4\cdot 10^{-4}\ \mathrm{deg/mm}\).

To check the perfection of the differential calorimeter described, we measured the heats of formation of solid solutions of the fairly well-studied systems KCl—KBr and NaCl—KCl as a function of composition. The results of our measurements are given in Tables 1–2 and in Figs. 3–4.

Fig. 3. Dependence of the heat of formation of solid solutions of the KCl—KBr system on composition.
\(\Delta\)—Fontell’s data,
\(\square\)—Hovi’s data,
\(\times\)—Popov’s data,
\(\circ\)—author’s data

Fig. 4. Dependence of the heat of formation of solid solutions of the NaCl—KCl system on composition.
\(\times\)—data of Zhemchuzhnyi and Rambach,
\(\Delta\)—data of Barrett and Wallace,
\(\circ\)—author’s data

As is evident from Figs. 3–4, our data are in fairly good agreement with the data of Fontell [15], Hovi [13], and Barret and Wallace [16].

Thus, the differential calorimeter described is simpler in design in comparison with those used previously [11, 17]. In it, the thermopile, complicated in construction and consisting of 750 thermocouples, has been replaced by semiconductor thermoresistances. Owing to the small thermal inertia of the thermistors, heaters in the Dewar vessels are eliminated. Despite the simplifications introduced, the calorimeter provides sufficiently high accuracy in measuring the heats of formation of solid solutions.

REFERENCES

1. Kurnakov N. S. and Zhemchuzhnyi S. F. Isomorphism of potassium and sodium compounds. Collection of Selected Works of N. S. Kurnakov, 1, 186, ONTI, 1938.

2. Zhemchuzhnyi S. F. and Rambakh F. Alloys of chlorides of the alkali metals. Izvestiya SPB. P. I. 12, 349, 1909.

3. 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, 6, 1065, 1955.

4. Gorodetskii A. F. On the electric strength of solid solutions. Izv. Tomsk Polytechnic Institute, 71, 21, 1952.

5. Weibke F. Thermochemistry of Alloys, 1943.

6. Wrzesniewski J. B. Heat of formation of solid solutions KCl—KBr. Z. anorg. Chem. 74, 111, 1912.

7. Grimm H. G. und Herzfeld K. F. On the energy and lattice constant of mixed crystals. Z. f. Physik 16, 77, 1923.

8. Tammann G. und Krings W. On the differences of mixed crystals obtained from the melt and from solution. Z. anorg. allg. chem. 130, 229, 1923.

9. Popoff M. M., Choller. Heats of formation of mixed crystals KCl—KBr. Z. Phys. Chem. A, 147, 302, 1930.

10. Popoff M. M., Jaworowskaja S. F. Heats of formation of mixed crystals KCl—KBr. Zs f. Phys. Chem. A. 167, 180, 1933.

11. Fontell N. On a differential method for measuring heats of formation. Soc. Scient. Fenn. Comment. Phys—Math. X, 5, 1938.

12. Fineman M. A., Wallace W. E. Heat of formation and certain thermodynamic properties of solid solutions NaCl—NaBr. J. Amer. Chem. Soc. 70, 12, 1948.

13. Hovi V. Heat of formation of the solid solution KCl—KBr. Ann. Acad. Scient. Fenn. A 1, 55, 1948.

14. Fontell N., Hovi V., Mikkola A. Heat of formation of mixed crystals KCl—KBr precipitated from aqueous solution. Ann. Acad. Scient. Fenn. A. 1, 54, 1948.

15. Fontell N. On the heats of formation of mixed crystals KCl—KBr and KCl—RbCl. Soc. Scient. Fenn Comment. Phys—Mathem. X. 6, 1940.

16. Barret B. T., Wallace W. E. Study of the solid solution NaCl—KCl. J. Amer. Chem. Soc. 76, 2, 336, 1954.

17. Kapustinskii A. F., Drakin S. I. A microcalorimeter for studying heats of dissolution with an accuracy of 0.001 cal. Zh. F. Kh., XXVI, 4, 1952.