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The present study shows how the direct Gibbs free energy minimization technique is sometimes superior to the reaction coordinates—equilibrium constants method when the thermodynamic analysis of complex systems is performed. In this respect, the above two methods are applied for two different processes to determine their equilibrium compositions: (1) the Haber process: a simple problem consisting of a single gas-phase reaction where both methods are expected to give the same result and (2) steam-coal gasification process which is more complex since it involves numerous reactions and solid-phase chemical species (i.e., coal or carbon). Thus, in the second case the reaction coordinates—equilibrium constants method fails to provide correct predictions of the equilibrium composition. In addition, the authors give the optimum conditions for the two processes: high pressure for Haber process and high temperature for steam-coal gasification in agreement with LeChatelier principle. In order to deal with deviation from the ideal-case assumption, the Peng–Robinson Equation of State (PR EOS) is implemented for both techniques and both case studies. All computations and figures are generated using a single computer algebra, Mathematica©.
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