To design a chemical reactor for the production of ethylene oxide, we first need to determine the reaction rate and the required reactor volume. The reaction between ethylene C2H4 and oxygen O2 to produce ethylene oxide C2H4O can be represented as:C2H4 + 1/2 O2 C2H4OGiven the conversion of ethylene X is 90% and the selectivity of ethylene oxide S is 97%, we can calculate the molar flow rates of the reactants and products.1. Molar flow rates:Molecular weights: C2H4 = 28 g/mol, O2 = 32 g/mol, C2H4O = 44 g/mol500 kg/h of C2H4O = 500,000 g/h / 44 g/mol = 11,364 mol/hSince the selectivity is 97%, the molar flow rate of ethylene F_C2H4 can be calculated as:F_C2H4 = 11,364 mol/h / 0.97 = 11,720 mol/hThe molar flow rate of oxygen F_O2 can be calculated using the stoichiometry of the reaction:F_O2 = 1/2 * F_C2H4 = 1/2 * 11,720 mol/h = 5,860 mol/h2. Reaction rate:Assuming the reaction is first-order with respect to both ethylene and oxygen, the reaction rate r can be expressed as:r = k * [C2H4] * [O2]The rate constant k can be determined using the Arrhenius equation:k = A * exp -Ea / R * T Where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant 8.314 J/molK , and T is the temperature in Kelvin 250C = 523 K . The values of A and Ea can be obtained from the literature or experimental data.3. Reactor volume:For a plug-flow reactor PFR , the reactor volume V can be calculated using the following equation:V = F_C2H4 * 1 - X / -r For a continuous stirred-tank reactor CSTR , the reactor volume can be calculated using the following equation:V = F_C2H4 * X / -r Choose the reactor type PFR or CSTR based on the desired residence time, mixing requirements, and other factors.4. Reactor dimensions and cost:Once the reactor volume is determined, the reactor dimensions diameter and height can be calculated based on the desired aspect ratio. The cost of the reactor can be estimated using the cost of stainless steel per unit volume and the required thickness of the reactor wall.In summary, to design a chemical reactor for the production of ethylene oxide, you need to determine the reaction rate, reactor volume, and reactor dimensions based on the given operating conditions and the desired reactor type PFR or CSTR . The cost of the reactor can be estimated based on the stainless steel construction and the required reactor wall thickness.