Abstract
The question of nonuniqueness of the solution of the reverse problem of chemical kinetics has been investigated. The subject of investigation is the situation in which some of the substances participating in the reaction are not accessible for measurement (intermediate substances). The investigation was performed on models of first-order reactions, using Laplace transforms. Direct mathematical formulas have been derived, through which an answer can be obtained to the question of how many independent functional combinations of constants, and which combinations, and will specifically admit an unambiguous evaluation on the basis of kinetic information on the initial reactants and the reaction products. The reaction of ethylene chlorination is examined as an illustrative example.
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Literature cited
S. I. Spivak and V. G. Gorskii, “Completeness of available kinetic measurements in determining rate constants of a complex chemical reaction,” Khim. Fiz., No. 2, 237–242 (1982).
V. G. Gorskii and S. I. Spivak, “Nonlinear models with incomplete rank and nonlinear parametric functions in reverse problems of chemical kinetics,” Zavod. Lab.,47, No. 10, 39–47 (1981).
V. G. Gorskii and S. I. Spivak, “Degree of completeness of experimental information in reconstructing kinetic or equilibrium constants of complex chemical reactions,” in: Mathematical Methods of Chemical Thermodynamics [in Russian], Nauka, Novosibirsk (1982), pp. 139–158.
V. N. Lukashenok, “Determination of kinetic constants of a complex physical reaction with incomplete information,” in: Chemical Kinetics and Catalysis [in Russian], Nauka, Moscow (1979), pp. 9–13.
G. M. Fichtenholtz (Fikhtengol'ts), Course in Differential and Integral Calculus [Russian translation], Vol. 1, Nauka, Moscow (1951).
L. V. Bystrov and V. G. Gorskii, “Technique for revealing nonlinear models of incomplete rank in solving reverse problems in chemical equilibrium,” in: Mathematical Problems in Chemical Thermodynamics [in Russian], Nauka, Novosibirsk (1985), pp. 9–42.
G. Doetsch, Guide to the Application of Laplace and Three-Transforms, 2nd edn., Van Nostrand-Reinhold (1971).
N. M. Rodigin and E. N. Rodigina, Consecutive Chemical Reactions (Mathematical Analysis and Calculation) [in Russian], Izd. Akad. Nauk SSSR, Moscow (1960).
V. G. Gorskii, Design of Kinetic Experiments [in Russian], Nauka, Moscow (1984).
A. P. Sage, Optimal Systems Control, Prentice-Hall, Englewood Cliffs, N. J. (1968).
R. Ya. Shostak, Operational Calculus [in Russian], Vysshaya Shkola, Moscow (1972).
V. P. Gerdt, O. V. Tarasov, and D. V. Shirkov, “Analytical calculations in a computer in application to physics and mathematics,” Usp. Fiz. Nauk,130, No. 1, 113–147 (1980).
R. J. Duffin, E. Peterson, and K. Zener, Geometric Programming, Wiley, New York (1967).
E. S. Lyapin, Course in Higher Algebra [in Russian], Uchpedgiz, Moscow (1955).
S. I. Spivak and Z. Sh. Akhmadishin, “Nonuniqueness of solutions of reverse problem of chemical kinetics,” React. Kinet. Catal. Lett.,10, No. 3, 271–274 (1979).
G. A. Korn and T. M. Korn, Manual of Mathematics, McGraw-Hill, New York (1970).
H. F. Trotter, “Transposition generator (Algorithm 115),” in: Library of Algorithms 101b–150b [inRussian], Sov. Radio, Moscow (1978), pp. 20–22.
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Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 6, pp. 701–708, November–December, 1985.
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Bystrov, L.V., Gorskii, V.G. & Spivak, S.I. Nonuniqueness of solution of reverse problem of chemical kinetics for first-order reactions. Theor Exp Chem 21, 667–673 (1985). https://doi.org/10.1007/BF00945144
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DOI: https://doi.org/10.1007/BF00945144