You can't apply the terminology (1st or 2nd order) developed for the homogeneous reactions to the heterogeneous one. The first order means d[A]/dt = -k[A]. What are the concentrations in you case? The reaction rate is dA/dt, where A is the amount of the reagent A in moles at time t.

you have to apply 0, first and second-order kinetic equations and check which one fit your reaction

I would focus on the reaction being first order in carbon dioxide, and zero order in the solid. It is likely that the reaction may be mass transfer-limited, therefore the first-order model would apply under this scenario.

Dear Colleague,

A reaction order is defined only for elementary reactions in homogeneous systems. Formal reaction orders are to describe the dependence of the reaction rate from input components concentration in more complicated homogeneous reaction systems. Sometimes they are helpful to make conclusions about the rate controlling step of the reaction.

In your case the reaction occurs in a two phase system. Therefore, please do not use the terminus "reaction order" in connection with your reaction. It does not make any sense.

Dear Hermann Ehwald , I agree with you except this "A reaction order is defined only for elementary reactions in homogeneous systems." The elementary reactions in homogeneous systems are classified as uni- or bimolecular reactions. A formal reaction order is commonly called just a reaction rate order with respect to concentration of one of the reagent.

Please take the concentrations of the reactants with respect to time and consider it for zero, first and second orders. For zero-order it's simply [reactant] and for first order, natural logarithmic [conc] and second-order 1/[conc] and plot a graph between the take values [reatant conc], ln[Conc.], and 1/[conc.] and time on X-axis individually. Find the R2 value, the one which is closer to 1 will be your best fit, and follow that order. I hope it will serve your purpose.

Too little information to settle anything definitively. What means that at the temperature of 120 oC CO2 "has been adsorbed". Where? On the outer surface of solid particles? What is the particle size? What shape are they? This is a typical gas-solid reaction. But how is the progress of the reaction (conversion) tracked? etc. etc. There are many equations since the days of Sohn and Evans. However, in order to use them effectively, one needs to know the dependence of the reaction progress on time.