Methanol can be synthesized from CO2 and H2 (A reaction that is very promising for carbon dioxide utilization). The reaction is catalyzed by copper. 3H2 + CO2 CH3OH + H2O The mechanism can be described as follows: three hydrogen molecules adsorb dissociatively on the copper surface and one CO2 molecule adsorbs molecularly (associatively). Adsorbed CO2* is sequentially hydrogenated to HCO2* and H2CO2*. The last species undergoes the following reaction that is the rate-determining step for the reaction: H2CO2* + H* H3C0* + 0* The rds is followed by hydrogenation of H3C0* to adsorbed CH3OH* that then desorbs. Adsorbed O* is hydrogenated by H* sequentially to OH* and H20* that desorbs as H20. (a) Write the complete reaction mechanism, including free sites. (b) (61) Derive the rate expression assuming that for the reaction conditions the surface is nearly free of adsorbates (O+ = 1), and the forward rate can be considered only (rds is irreversible). (62) Determine the reaction orders with respect to H2 and CO2. (c) Determine the mol fraction of hydrogen in a H2/CO2 feed that maximizes the rate. (d) Under conditions of nearly empty surface the following data were obtained for the turnover frequency of CO2 at 2 bar total pressure for a 1:1 CO2:H2 mixture on Cu (100) surface. T(K) Turnover Frequency (site s)-1 485 4.5 x 10-5 525 1.7 x 104 570 6.0 x 10-4 (d1) Determine the activation energy E for the reaction. (d2) Why is Ea constant in this temperature range