A universal algorithm for the calculation of vapor-liquid equilibrium diagrams in quasi-simple multicomponent systems

Nikolay A. Charykov; Alexey V. Rumyantsev; Viktor A. Keskinov; Konstantin N. Semenov; Valerya A. German; Natalya A. Kulenova; Marina V. Charykova; Mariia V. Keskinova; Mikhail Yu. Arshinov

doi:10.17308/kcmf.2025.27/12491

Nikolay A. Charykov St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation; D. Serikbayev East Kazakhstan Technical University, Center of Excellence “VERITAS”, 69. A. K. Protosanova ul., Ust-Kamenogorsk 070004, Republic of Kazakhstan; St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova ul., Saint Petersburg 197022, Russian Federation https://orcid.org/0000-0002-4744-7083
Alexey V. Rumyantsev St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation https://orcid.org/0000-0003-3985-2086
Viktor A. Keskinov D. Serikbayev East Kazakhstan Technical University, Center of Excellence “VERITAS”, 69. A. K. Protosanova ul., Ust-Kamenogorsk 070004, Republic of Kazakhstan https://orcid.org/0000-0003-3227-122X
Konstantin N. Semenov St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation; St. Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russian Federation; Pavlov First Saint Petersburg State Medical University, 6 - 8 L’va Tolstogo st., Saint Petersburg 197022, Russian Federation https://orcid.org/0000-0003-2239-2044
Valerya A. German St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation
Natalya A. Kulenova D. Serikbayev East Kazakhstan Technical University, Center of Excellence “VERITAS”, 69. A. K. Protosanova ul., Ust-Kamenogorsk 070004, Republic of Kazakhstan https://orcid.org/0000-0002-7063-4899
Marina V. Charykova St. Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russian Federation https://orcid.org/0000-0001-8311-0325
Mariia V. Keskinova St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation https://orcid.org/0000-0002-8359-9594
Mikhail Yu. Arshinov St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation

DOI: https://doi.org/10.17308/kcmf.2025.27/12491

Keywords: Zdanovskii’s rule, Quasi-simple systems, Vapor-liquid equilibrium diagrams, Partial molar Gibbs energy, Analogues, Gibbs–Konovalov’s laws, Gibbs–Roozeboom rules

Abstract

The purpose of the study was to consider isothermal vapor-liquid diagrams of quasi-simple systems and to develop a universal algorithm for the calculation of isothermal vapor-liquid diagrams of these systems independent of the type of valence of the electrolyte, the number of components in the system, and the types of solid solutions. The suggested analogues of the three Gibbs–Konovalov and Gibbs–Roozeboom laws are true when moving along the univariant equilibrium lines on the solubility diagrams of systems with a random number of components.

The study did not involve any experiments. The suggested algorithm was applied for the description of solubility (solidliquid) diagrams and vapor-liquid equilibrium diagrams of three- and four-component systems with one, two, or three volatile components. In all the cases, the results of thermodynamic first-principles calculations agreed well with the experimental data presented in the literature.

Both the experimental data presented in the literature and the results of the thermodynamic first-principles calculation performed by the authors are also in good agreement with the suggested analogues of the Gibbs–Konovalov and Gibbs–Roozeboom laws

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Author Biographies

Nikolay A. Charykov, St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation; D. Serikbayev East Kazakhstan Technical University, Center of Excellence “VERITAS”, 69. A. K. Protosanova ul., Ust-Kamenogorsk 070004, Republic of Kazakhstan; St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova ul., Saint Petersburg 197022, Russian Federation

Dr. Sci. (Chem.), Professor at the Department of Physical Chemistry, Saint-Petersburg State Technological Institute (Technical University) (Saint-Petersburg, Russian Federation)

Alexey V. Rumyantsev, St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation

Dr. Sci. (Chem.), Head of the Department of Engineering Radioecology and Radiochemical Technology, Saint-Petersburg State Technological Institute (Technical University) (Saint-Petersburg, Russian Federation)

Viktor A. Keskinov, D. Serikbayev East Kazakhstan Technical University, Center of Excellence “VERITAS”, 69. A. K. Protosanova ul., Ust-Kamenogorsk 070004, Republic of Kazakhstan

Cand. Sci. (Chem), Leading Researcher «Veritas» Center, Kazakhstan State Technical University (Ust-Kamenogorsk, Republic of Kazakhstan)

Konstantin N. Semenov, St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation; St. Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russian Federation; Pavlov First Saint Petersburg State Medical University, 6 - 8 L’va Tolstogo st., Saint Petersburg 197022, Russian Federation

Dr. Sci. (Chem.), Professor, Head of the Department of General and Bioorganic Chemistry, Pavlov First Saint Petersburg State Medical University (Saint-Petersburg, Russian Federation)

Valerya A. German, St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation

graduate student at the Department of Physical chemistry, Saint-Petersburg State Technological
Institute (Technical University) (Saint-Petersburg, Russian Federation)

Natalya A. Kulenova, D. Serikbayev East Kazakhstan Technical University, Center of Excellence “VERITAS”, 69. A. K. Protosanova ul., Ust-Kamenogorsk 070004, Republic of Kazakhstan

Cand. Sci. (Chem), Head of «Veritas» Center, Kazakhstan State Technical University (Ust-Kamenogorsk, Republic of Kazakhstan)

Marina V. Charykova, St. Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russian Federation

Dr. Sci. (Geol.), Professor, Head of the Department of Geochemistry of the Faculty of Geology, Saint-Petersburg State University (Saint-Petersburg, Russian Federation)

Mariia V. Keskinova, St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation

Assistant of the Department of Theoretical Foundations of Materials Science, Saint-Petersburg State Technological Institute (Technical University) (Saint-Petersburg, Russian Federation)

Mikhail Yu. Arshinov, St. Petersburg State Institute of Technology, 26 Moskovsky pr., Saint Petersburg 190013, Russian Federation

graduate student at the Department of Physical chemistry, Saint-Petersburg State Technological
Institute (Technical University) (Saint-Petersburg, Russian Federation)

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