Determine the catalyst weight necessary to achieve 50% conversion when ethylene oxide is to be made by the vapor-phase catalytic oxidation of ethylene with air: C2H4 +0.502 → CH₂OCH2 A +0.5B → C Ethylene and oxygen (in air) are fed in stoichiometric proportions to a packed-bed reactor isothermally at 260°C. Ethylene is fed at a rate of 0.30 lbmol/s at a pressure of 10 atm. It is proposed to use 10 banks of 1.5 in-diameter schedule 40 tubes packed with catalyst with 100 tubes per bank. Consequently, the molar flow rate to each tube is to be 3×104 lbmol/s. The properties of the reacting fluid are to be considered identical to those of air at this temperature and pressure. The density of the catalyst particles is 120 lb/ft³ and the bed void fraction is 0.40. The rate law is - r'a = k(PA)¹/³ (PB) 2/3 lbmol/(lb cat-hr), 0.0141 lbmol/(atm·lb cat·hr) at 260°C. The pressure drop along the reactor can be with k = neglected. Note: Show the differential equation that needs to be solved. If you use MATLAB to solve the differential equation, submit your MATLAB code along with your solution.