Answer Happy

Carbon dioxide (CO2) from waste sources is a sustainable feedstock for chemicals production if new technologies can be developed to carry out the reduction of CO2, the most oxidized form of carbon, to a more reactive molecule. Recently, solar-energy-driven reactor concepts have emerged that harness the sun's energy to sustainably drive the thermocatalytic reduction of CO2 to reactive CO over a Ceria catalyst at high temperatures. A highly simplified version of this concept is provided in the figure below, which is operated at 750 °C and 0.95 atm. The reactor is rectangular with a depth D into the page) of 5 cm. The thickness of the porous catalyst lining the base of the reactor is 0.25 cm, and the gas space above the porous catalyst layer can be considered well mixed. Pure CO2 is fed into the reactor and diffuses into the porous catalyst layer, which drives the reaction CO2(g) → CO(g) + 1/2O2(g), which is approximated as first order with a rate constant of 3.1 s 1 at 750 °C. The effective diffusion coefficient, Dae, of CO2 in the gas mixture within the porous catalyst is 0.22 cm²/s at 0.95 atm and 750 °C. It is desired to achieve 4.0 mole% CO in the exiting outlet gas for a total molar flow rate at the exit, n2, of 2.0 gmole/min. What must the length of the reactor, L, be to achieve that conversion? Sunlight 一 n2 = 2.0 gmole/min 100% CO2 total molar flow rate na Yco = 0.040 Yo2 = 0.020 Depth (into page) = D = 5 cm Transparent cap Well-mixed gas 750 °C, 0.95 atm Catalyst layer I 0.25 cm L CO2(g) → CO(g)+1/202(g) k = 3.1 s-1 Dae = 0.22 cm2/s