Propane steam reforming over an alumina supported Ni metal catalyst:
C3H8 (g) + H2O (g) → CO2 (g) + H2 (g)
is proposed to follow these mechanisms:
C3H8 + 2S1 ↔ C2H5-S1 + CH3-S1 (M1)
H2O + 2S2 ↔ OH-S2 + H-S2 (M2)
CH3-S1 + OH-S2 → CH3O-S1 + H-S2 (M3)
CH3O-S1 + S1 ↔ CHO-S1 + H2-S2 (M4)
CHO-S1 + S2 ↔ CO-S1 + H-S2 (M5)
CO-S1 + OH-S2 ↔ COO-S1 + H-S2 (M6)
CO-S1 ↔ CO + S1 (M7)
COO-S1 ↔ CO2 + S1 (M8)
H-S2 + H-S2 ↔ H2 + 2S2 (M9)
where S1 and S2 represent two different active sites. Assuming that (M3) is the rate-determining step and CH3 and H are the most abundant reactive species, develop a rate law which is consistent with the proposed mechanism.
To develop a rate law consistent with the proposed mechanism, we need to determine the slowest step, which in this case is step (M3) since it is assumed to be the rate-determining step.
The rate-determining step is the slowest step in a reaction and determines the overall rate of the reaction. In this case, step (M3) involves the reaction between CH3-S1 and OH-S2 to form CH3O-S1 and H-S2.
Based on the given information, we can assume that the concentration of CH3-S1 and OH-S2 are both involved in the rate-determining step. Therefore, we can write the rate law for this step as:
Rate = k * [CH3-S1]α * [OH-S2]β
Where k is the rate constant, α and β are the respective order of the reactants CH3-S1 and OH-S2 determined from the rate-determining step.
Next, we need to determine the overall order of the reaction. Since CH3 and H are the most abundant reactive species, it is safe to assume that they are involved in prior steps and their concentrations remain relatively constant throughout the reaction. As a result, their concentrations can be approximated as being constant and integrated into the rate constant, k.
Therefore, the rate law for the overall reaction can be written as:
Rate = k' * [CH3-S1]α * [OH-S2]β
Where k' is the modified rate constant that includes the concentrations of CH3 and H.
It is important to note that the exponents, α and β, cannot be determined directly from the given mechanism and will require further experimental data or kinetic analysis to evaluate.