The equilibrium constant for the reactions given is equal to the ratio of product concentrations to the ratio of reactant concentrations. In this case, it can be written as:

K_eq = [CO₆]/[propane]

The concentration of carbon oxide is dependent on the partial pressures of oxygen and carbon monoxide in the reaction mixture. Since the reaction involves combustion, the partial pressure of oxygen remains constant.

Assuming ideal gas behavior, the equilibrium constant is given by:

K_eq = (p_CO6) / (p_propane)

Where p is the partial pressure of the respective species in the reaction mixture.

Hence, the equilibrium constant for the given reactions is dependent on the partial pressure of carbon monoxide in the reaction mixture.

However, it must be noted that the concentration of carbon monoxide in the reaction mixture will not be equal to the stoichiometric ratio of 2:6 as stated in the prompt. This is due to the fact that propane is not an intermediate in the production of carbon oxide from carbon dioxide, and thus its concentration is not directly related to the reaction process.