IDENTIFICATION OF ASSOCIATES IN SOLUTIONS WITH POSITIVE DEVIATIONS FROM RAOULT’S LAW

To identify associates in a binary metal solution with positive deviations from Raoult's law, a version of ideal associated solution model was used that only took into account self-association of one solution component. Besides, absolute (rather than relative) characteristics of mass were used to identify chemical equilibrium of components according to the law of mass action. As a result, this allowed finding the chemical equilibrium constants between solution associates and monomers, which have a clear physical meaning, rather than empirical constants of associates' complex formation. This technique, however, required introduction of an additional calculated characteristic - the sum of all chemical compounds in the solution. It was found that this value was numerically equal to the reverse activity coefficient of the solution's non-associated component. The possibility of independent determination of such characteristic allowed notable simplifying the initial system of computational equations, i.e. excluding the equation of solution's molar composition normalization, only keeping two equations of material balance of solution components. The resulting algorithm allowed using the numerical method to solve both the "inverse' problem (finding the degree and thermodynamic properties of the self-associate based on testing data) and the "direct' problem (finding solution component activities according to their thermodynamic properties). At the present time, there is almost no reference information about thermodynamic properties of self-associates; therefore, the solution of the direct problem currently will only be useful for the verification of the inverse problem solution results. Associates were identified for 11 binary alloys containing chromium or copper, i.e. chemical elements mostly amenable to self-association. It was found that each of the mentioned elements could form associates of different degrees, from 3 to 16. For alloys that form associates with low degrees (less than 10), the calculated energy of associate formation necessary for one chemical bond was found to be about 15 kJ/mole. The full calculated energy of associate formation for alloys with high degree of associates (more than 10) was found to be about 360 kJ/mole. It was noted that concentration dependence of the association degree was not quite stable and tended to increase at low concentrations of the associated component. Under the employed calculating model, however, the absolute error of activity isotherm approximation of tire analyzed alloys remained low and ranged 0.004 - 0.025.

1. Prigogine I., Defay R. Chemical thermodynamics. London: Prentice Hall Press, 1954. (Russ.ed.: Prigogine I., Defay R. Khimicheskaya termodinamika. Novosibirsk: SONauka, 1966, 512 p.).

2. Morachevskii A.G. Termodinamika rasplavlennykh metallicheskikh i solevykh system [Thermodynamics of melted metallic and salt systems], Moscow: Metallurgiya, 1987, 240 p. (In Russ.).

3. Morachevskii A.G., Sladkov I.B. Termodinamicheskie raschety v metallurgii [Thermodynamic calculations in metallurgy], Moscow: Metallurgiya, 1993, 304 p. (In Russ.).

4. Morachevskii A.G., Mokrievich A.G., Maiorova E.A. Applying the model of ideal associated solution to liquid metal systems with positive and sign-variable deviations from Raul's law. Zhurnal prikladnoi khimii. 1993, vol. 66, Issue 9, pp. 2006-2011. (In Russ.).

5. Shunyaev K.Yu., Vatolin N.A. Thermodynamic characteristics of mixture and fusion in the associated solutions model. In: Fiziches- kaya khimiya i tekhnologiya v metallurgii. Sb. nauch. trudov [Physical chemistry and technology in metallurgy. Coll. of sci. works], Ekaterinburg: Uro RAN, 1996, pp. 91-99. (In Russ.).

6. Gul'tyai 1.1., Lenrenev M.M. Types of deviations from ideality in binary metallic melts and their description using ideal chemical theory. Russian Metallurgy (Metally). 2005, vol. 2005, no. 1, pp. 12-19.

7. Moiseev G.K., Vatolin N.A., Marshuk L.A., Il'inykh N.I. Temperaturnye zavisimosti privedennoi energii Gibbsa nekotoiykh neorganicheskikh veshchestv (al'ternativnyi bank dannykh ASTRA. OWN)\Ths temperature dependence of the reduced Gibbs energy of some inorganic substances (alternative database ASTRA OWN)]. Ekaterinburg: UrO RAN, 1997, 231 p. (In Russ.).

8. Electronic resource: Database HSC Chemistry 6 Antti Roine - Pori (Finland): Research Oy Information Sen’ice, 2006.

9. Trusov B.G. Baza dannykh "Terra 2.1" [Data base “Terra 2.1”]. Moscow: MGTU inr. N.Ye. Baumana, 2007. (In Russ.).

10. Moiseev G.K., Vatolin N. A., Il'inykh N.I. Thermodynamical investigations of the system of "liquid lithium-Аг' with regard to the existence ofLi„-Li5 clusters. Rasplavy. 2002, no. 3, pp. 3-13. (In Russ.).

11. Moiseev G.K. Estimation of the thermochemical properties and thermodynamic functions for some volatile and condensed clusters of the alkaline metals. Rasplavy 2003, no. 4, pp. 68-84. (In Russ.).

12. Moiseev G.K. Activities of components and mixing characteristics in the melts of binary systems of alkali metals with consideration of the ' small' clusters and associates. Review of results of the computer experiments. Rasplavy. 2004, no. 5, pp. 62-77. (In Russ.).

13. Berdnikov V.I., Gudim Yu.A., Karteleva M.I. Appling the model of ideal associated solutions to the systems with positive deviations from Raul's law. Izvestiya VUZov. Chernaya metallurgiya = lzvestiya. Ferrous Metallurgy. 2003, no. 5, pp. 11-17. (In Russ.).

14. Berdnikov V.I., Gudim Yu.A. Thermodynamic model of associated solutions with positive deviations from the Raoult law. Izvestiya VUZov Chernaya metallurgiya = Izvestiya. Ferrous Metallurgy. 2013. vol. 57, no. 9, pp. 29-32. (In Russ.).

15. Terekhov S.V. Modelirovanie teplovykh i kineticheskikh svoistv real’nykh system [Simulation of the thermal and kinetic properties of real systems], Donetsk: Izd-vo Veber, Donetskoe otdelenie, 2007, 306 p. (In Russ.).

16. Belousov A.A., Bakhvalov S.G., Aleshina S.N. etc. Fiziko-khimicheskie svoistva zhidkoi medi i ее splavov. Spravochnik [Physicochemical properties of liquid copper and its alloys. Reference book], Ekaterinburg: UrO RAN, 1997, 124 p. (In Russ.).

17. Batalin G.I. Termodinamika zhidkikh splavov na osnove zheleza [Thermodynamics of iron-based liquid alloys], Kiev: Vishcha shko- la. 1980. 132 p. (In Russ.).

18. Morachevskii A.G., Kolosova E.Yu., Tsynrbulov L.B., Tsemekhnran L.Sh. Thennodynanric properties of liquid Cu-Ni-Co-Fe alloys. Russian Journal of Physical ChemistiyA. 2006, vol. 80, no. 11, pp. 1786-1789.

19. SvidunovichN.A., Glybin V.P., Svirko L.K. Vzaimodeistvie komponentov v splavakh [Interaction of components in alloys], Moscow: Metallurgiya, 1989, 158 p. (In Russ.).

20. Desai P.D. Thermodynamic properties of binary aluminum alloys. J. Phys. Chem. Ref. Data. 1987, vol. 16, no. 1, pp. 110-124.