Question

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.