When calculating the combustion equilibrium based on the Gibbs free energy minimization principle, no reaction mechanism is required, and whether the calculated results are close to the actual experimental results or the results of complex reaction mechanism calculations. There is probably a big difference between them.
Gibbs free energy is a function of both the enthalpy, which is the energy possessed by a mixture of chemicals in a system, and the entropy, or disorder, of the system.The conditions for thermodynamic equilibrium are derived from the second law of thermodynamics. These conditions may be concisely stated in terms of the Gibbs free energy, G = H - TS. For a closed system at a constant temperature and pressure, the Gibbs free energy is a minimum at thermodynamic equilibrium. Thus, for any change away from an equilibrium state at constant T and p, dG > O. The Gibbs free energy is a function of the temperature, pressure, and composition [i.e., G = G( T, p, n\, n2' ..)].For any other temperature one may write following very plausible relationship in practice.
Del G= Del H - T Del He/Te
Where it has been assumed that the entropy of combustion doesn't change very much with temperature. As far as the Kinetics of reaction parameter K is concerned one would have.
K = exp - DelG/RT = exp [DelHe /R Te]exp (- DelH /RT)
Where is the temperature independent first factor above is known as the 'stering factor' in Reaction Kinetics.
ΔG=ΔH−TΔS(18.8.2)(18.8.2)ΔG=ΔH−TΔS
where all thermodynamic quantities are those of the system. Recall that at constant pressure, ΔH=qΔH=q, whether a process is reversible or irreversible, and TΔS = qrev. Using these expressions, we can reduce Equation to ΔG=q−qrevΔG=q−qrev. Thus ΔG is the difference between the heat released during a process (via a reversible or an irreversible path) and the heat released for the same process occurring in a reversible manner. Under the special condition in which a process occurs reversibly, q = qrev and ΔG = 0. As we shall soon see, if ΔGΔG is zero, the system is at equilibrium, and there will be no net change. We can predict whether a reaction will occur spontaneously by combining the entropy, enthalpy, and temperature of a system in a new state function called Gibbs free energy (G). The change in free energy (ΔG) is the difference between the heat released during a process and the heat released for the same process occurring in a reversible manner.
https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_A_Molecular_Approach_(Tro)/18%3A_Gibbs_Energy_and_Thermodynamics/18.08%3A_Gibbs_Energy_Changes_in_Chemical_Reactions
https://www.sciencedirect.com/topics/earth-and-planetary-sciences/gibbs-free-energy
https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/gibbs-free-energy/a/gibbs-free-energy-and-spontaneity
You might ask if anyone has ever compared the results of GFE minimization to actual data. I have on 4 different problems. Setting up the experiment and collecting the data were extremely expensive so these are fairly rare occurrences. The first test was on the dissolution of transite (asbestos cement fiber board in warm water). This research was conducted by myself and others (funded by the USTVA) and in parallel with two people at the University (Prof. Schweitzer and post-doc Murray, funded by the USDOE). The ideal calculations did not match the data but the nonideal ones did (more on this distinction below). The second test was at a CCPP where ammonia injection was used to control NOx (the funding agent [a large power producer] and data are confidential). The third test was on the use of crushed limestone to bind sulfur and reduce SOx (this funding agent [a different large power producer] and data are also confidential). The fourth test was on the inadvertent production of cyanide gas by introducing ammonia into the exhaust of a combustion turbine burning landfill gas (also confidential, sorry). The USEPA is focusing on formaldehyde emissions now (see figure showing "perfect storm" for operators). While the ideal calculation is often adequate for gases, sometimes the nonideal calculations are necessary, particularly when aqueous solutions are involved. I first solved the nonideal GFE minimization problem in 1986, published the results in 1991, and revealed the secret in 2019. You can use the software for free http://dudleybenton.altervista.org/projects/reactions/index.html
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