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In this work, we discussed the solution of a chemical equilibrium problem aiming to obtain it’s fixed point. To do this, the preliminary and basic ideas introducing the fixed point theory were X-rayed and the Newton-Raphson’s iterative method for solving the system of non-linear equations discussed; then, the problem of the chemical equilibrium involving principal reactions in the production of synthesis gas by partial oxidation of methane with oxygen was stated. Using a computer program, the O reactant ratio that produces an adiabatic equilibrium temperature was obtained by developing a system of seven simultaneous non-linear equations that have the form which we now solve using the Newton-Raphson’s method described in section 2.2 and hence the desired fixed point of the chemical equilibrium problem.
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