Calculation of Standard Thermodynamic Potentials for Na-Zeolites with the Use of Linear Programming Problems

Author(s)
Oleg Viacheslavovich Yeriomin

ABSTRACT

Linear programming problems for Na-Al-Si-O-H system have been formulated and solved for calculations of standard enthalpies and Gibbs potentials of zeolites with unknown thermodynamic properties. The calculations are based on dual solutions of linear programming problems. Comparison of numerical results with published data gives relative mistakes of estimations less than one percent. On the basis of calculated potentials the standard entropies have been estimated. The standard thermodynamic potentials for eight natural zeolites with unknown properties have been calculated. The presented method does not demand any information about crystal structure of zeolites and can be applied to any of their stoichiometric presentation.

Linear programming problems for Na-Al-Si-O-H system have been formulated and solved for calculations of standard enthalpies and Gibbs potentials of zeolites with unknown thermodynamic properties. The calculations are based on dual solutions of linear programming problems. Comparison of numerical results with published data gives relative mistakes of estimations less than one percent. On the basis of calculated potentials the standard entropies have been estimated. The standard thermodynamic potentials for eight natural zeolites with unknown properties have been calculated. The presented method does not demand any information about crystal structure of zeolites and can be applied to any of their stoichiometric presentation.

Cite this paper

nullO. Yeriomin, "Calculation of Standard Thermodynamic Potentials for Na-Zeolites with the Use of Linear Programming Problems,"*International Journal of Geosciences*, Vol. 2 No. 3, 2011, pp. 227-230. doi: 10.4236/ijg.2011.23024.

nullO. Yeriomin, "Calculation of Standard Thermodynamic Potentials for Na-Zeolites with the Use of Linear Programming Problems,"

References

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[10] E. C. Moloy, Q. Liu and A. Navrotsky, “Formation and Hydration Enthalpies of the Hydrosodalite Family of Materials,” Microporous and Mesoporous Materials, Vol. 88, No. 1-3, 2008, pp. 283-292. doi:10.1016/j.micromeso.2005.09.020

[11] V. V. Bakakin and Yu. V. Seryotkin, “Unified Formula and Volume Characteristics in Comparative Crystal Chemistry of Natural Zeolites,” Journal of Structural Chemistry, Vol. 50, No. 1, 2009, pp. 116-123. doi:10.1007/s10947-009-0199-4

[12] L. Mercury, Ph. Vieillard and Y. Tardy, “Thermodynamics of Ice Polymorphs and “ice-like” water in hydrates and hydroxides,” Applied Geochemistry, Vol. 16, No. 2, 2001, pp. 161-181. doi:10.1016/S0883-2927(00)00025-1

[1] J. Shi, G. Lu and G. Cao, “A New Method of Estimating Standard Enthalpies of Formation of Zeolites,” Journal of Porous Materals, Vol. 15, No. 5, 2008, pp. 513-517. doi:10.1007/s10934-007-9105-7

[2] R. Mathieu and Ph. Vieillard, “A Predictive Model for the Enthalpies of Formation of Zeolites,” Microporous and Mesoporous Materials, Vol. 132, No. 3, 2010, pp. 335-351.doi:10.1016/j.micromeso.2010.03.011

[3] K. V. Chudnenko, “Thermodynamic Modelling in Geochemistry: The Theory, Algorithms, Software, Examples,” in Russian, Publishing house GEO, Novosibirsk, 2010, p. 287.

[4] O. V. Yeriomin, S. V. Vinnichenko and G. A. Yurgenson, “Evaluation of Standard Gibbs Potentials for Copper Hydroxosulfate Hydrates from Solutions of Dual Linear Programming Problems,” in Russian, Doklady Akademii Nauk, Vol. 409, No. 3, 2006, pp. 386-388.

[5] N. F. Stepanov, M. Y. Yerlukina and G. G. Fillipov, “The Methods of Linear Algebra in Physical Chemistry,” in Russian, Publishing Moscow State University, Moscow, 1976, p. 360 .

[6] V. I. Shmuriov, “Introduction in Mathematical Programming,” in Russian, Institute of Computer Researches, Moscow, 2002, p. 192.

[7] T. L. Wood and R. M. Garrels, “Thermodynamic Values at Low Temperature for Natural Inorganic Materials,” Oxford University Press, Oxford, 1987, p. 265.

[8] A. A. Ravdel and A. M. Ponomariova, “The Brief Handbook of Physico-chemical Data,” in Russian, Khimiya, Leningrad, 1983, p. 232.

[9] L. P. Ogorodova, L. V. Melchakova and I. A. Kiseleva, “A Study of Dachiardite, a Natural Zeolite of the Mordenite Group,” in Russian, Zhurnal Fizicheskoy Khimii, Vol. 81, No. 11, 2007, pp. 1953-1955.

[10] E. C. Moloy, Q. Liu and A. Navrotsky, “Formation and Hydration Enthalpies of the Hydrosodalite Family of Materials,” Microporous and Mesoporous Materials, Vol. 88, No. 1-3, 2008, pp. 283-292. doi:10.1016/j.micromeso.2005.09.020

[11] V. V. Bakakin and Yu. V. Seryotkin, “Unified Formula and Volume Characteristics in Comparative Crystal Chemistry of Natural Zeolites,” Journal of Structural Chemistry, Vol. 50, No. 1, 2009, pp. 116-123. doi:10.1007/s10947-009-0199-4

[12] L. Mercury, Ph. Vieillard and Y. Tardy, “Thermodynamics of Ice Polymorphs and “ice-like” water in hydrates and hydroxides,” Applied Geochemistry, Vol. 16, No. 2, 2001, pp. 161-181. doi:10.1016/S0883-2927(00)00025-1