In the kinetics of CO2 methanation or hydrogenation of CO2, how do we determine the term equilibrium constant, Keq. In many kinetic models, rate equations we have the term Keq in the equation, how this constant is found ?
Open a handbook, find the standard formation Gibbs energies and enthalpies of CH4, CO2 and H2O, use Hess's law to find the standard Gibbs energy and the enthalpy of the reaction, and use van 't Hoff's equation to find Keq at the temperature of interest. If you need it more accurate, correct for the heat capacity of the reaciton via Kirchhoff. Consult any book on chemical thermodynamics for examples; look for equilibria in the gas phase.
I have some minor disagreement with Radomir, but completely agree with his main answer. "Open a handbook" and learn basics of chemical thermodynamics.
Methanation CO + 3H2CH4 + H2O is the reverse reaction of steam methane reforming probably the most studied equilbrium reaction in history. The water gas shift reaction CO +H2O CO2 + H2 is also usually at or near equilibrium and often need to be considered. A third reaction 2 CO C + CO2 (carbon dusting) also occurs if you operate in a range where it is favored by equilibrium. Let me know if you need more information.
Temperature dependence of Ka is available in the scientific literature. Just search.
Samim Ghafoori When people answer questions that you ask it is customary to acknowledge the response and thank them or to ask for additional information about the response.