Haber process and steam-coal gasification: Two standard thermodynamic problems elucidated using two distinct approaches

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.