Determinación de las concentraciones al equilibrio en una reacción química
Keywords:Chemical equilibrium, Polynomial equations, Numerical methods, Didactics and teaching of Physical Chemistry
In this work, the problem of the computation of equilibrium concentrations of a chemical reaction is discussed, when higher than second order polynomial equations are involved. This situation depends on the number of reactants and products of the chemical reaction, as well as its stoichiometric coefficients. Despite this being a frequent case, the problem is not addressed in introductory chemical and physical chemistry textbooks, since the equations must be solved numerically. In this manuscript, three programs are provided for the bisection, Newton-Raphson and secant numerical methods. These codes can be easily utilized for reactions involving up to seven reactants and seven products. The iterative methods are explained in detail with the explicit intention of preventing their use as black boxes. In this way, this constitutes an interesting application from physical chemistry for students of Mathematics, while it is a didactical exposition to the numerical solution of non-linear equations for students of Physics, Chemistry and Engineering. The example provided can also be used in numerical methods courses. Finally, the performance of the three methods is discussed using as an example the Haber-Bosch process. No installations on devices are required in order to execute the codes.
T. L. Brown, H. E. Lemay Jr., B. E. Bursten, C. J. Murphy, P. M. Woodward, Química. La ciencia central. 12a edición, Pearson Education, México, 2014.
R. Chang, Química. 7a edición, McGraw Hill, México, 2002.
E. E. Stone. Complex Chemical Equilibria. Application of Newton-Raphson method to solve non-linear equation, J. Chem. Educ., 43 (1966) 241, https://doi.org/10.1021/ed043p241
R. N. Mioshi, C. L. do Lago, An equilibrium simulator for multiphase equilibria based on the extent of reaction and NewtonRaphson method with globally convergent strategy (SEQEx2), Anal. Chim. Acta, 334 (1996) 271, https://doi.org/10.1016/S0003-2670(96)00342-X
J. J. Baeza-Baeza, M. C. García-Alvarez-Coque, Systematic Approach To Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems, J. Chem. Educ., 88 (2011) 169, https://doi.org/10.1021/ed100784v
A. Raviolo, Using a Spreadsheet Scroll Bar to Solve Equilibrium Concentrations, J. Chem. Educ., 89 (2012) 1411, https://doi.org/10.1021/ed3002144
E. Weltin, A Numerical Method To Calculate Equilibrium Concentrations for Single-Equation Systems, J. Chem. Educ., 68 (1991) 486, https://doi.org/10.1021/ed068p486
G. Colonna, A. D’Angola, A hierarchical approach for fast and accurate equilibrium calculation, Comp. Phys. Comm., 163 (2004) 177, https://doi.org/10.1016/j.cpc. 2004.08.004
A. L. Magalhaes, Introducing Iterative Methods to Undergraduate Chemistry Students − A Spreadsheet-Based Approach, J. Chem. Educ., 97 (2020) 1908, https://doi.org/10.1021/acs.jchemed.0c00252
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