“…Adsorption rate constants were determined using collision theory as k normala = 1000 A N normalA 4 [ g a s ] ( 8 R T π M ) 1 / 2 where R is the gas constant, T is the temperature, M is the molar mass, A is the area of the active site (1.27 × 10 –18 m 2 ), and [gas] is the concentration of the adsorbing methane or methanol molecules. The rate of photoactive MO x species activation is calculated by k normala normalc normalt = normalΦ w I 2 h c ( λ f 2 − λ i 2 ) ( w t % ) where Φ is the quantum yield, I is the photon intensity, w is the weighting factor for the percentage of the incident photons irradiating the photocatalyst that are in a specific wavelength range, h is Planck’s constant, c is the speed of light, (λ f 2 – λ i 2 ) gives the range of photon wavelengths that will activate the photocatalyst, and the wt % factor is the experimental weight percent of metal loading for each of the transition metals doped into the MCM-41 amorphous SiO 2 (1.91% for Cr, 3.5% for Nb, 20.0% for W). ,, The Cr, Nb, and W MO 4 /MCM-41 materials activate under UV light giving w = 0.05 to account for the 5% of total solar irradiation in the UV range λ f = 400 nm and λ i = 100 nm. I is measured as 1370 W m –2 for solar irradiance, , while Φ is set as a stochastic array of activation percentages to observe the changes to the POM mechanism on the MO 4 /MCM-41 materials during the MKM simulations.…”