To design a chemical reactor for the production of ethylene oxide, we need to follow these steps:1. Calculate the molar flow rates of the reactants.2. Determine the reaction rate expression.3. Choose the appropriate reactor type.4. Calculate the reactor volume.5. Determine the operating conditions.Step 1: Calculate the molar flow rates of the reactantsFirst, we need to determine the molar flow rates of ethylene C2H4 and oxygen O2 in the feed stream. The molecular weights of C2H4 and O2 are 28 g/mol and 32 g/mol, respectively.The production rate of ethylene oxide EO is 500 kg/day, which corresponds to:500,000 g/day / 44 g/mol = 11,364 mol/day EO Since the conversion of ethylene is 85%, the molar flow rate of ethylene F_C2H4 can be calculated as:F_C2H4 = 11,364 mol/day / 0.85 * 0.95 = 14,084 mol/dayThe molar flow rate of oxygen F_O2 can be calculated using the stoichiometry of the reaction 1:1 ratio :F_O2 = 14,084 mol/dayThe total molar flow rate F_total is:F_total = F_C2H4 + F_O2 = 14,084 + 14,084 = 28,168 mol/dayNow, we can calculate the molar flow rates of each component in the feed stream:F_C2H4_feed = 0.15 * F_total = 0.15 * 28,168 = 4,225 mol/dayF_O2_feed = 0.05 * F_total = 0.05 * 28,168 = 1,408 mol/dayF_N2_feed = 0.80 * F_total = 0.80 * 28,168 = 22,534 mol/dayStep 2: Determine the reaction rate expressionThe reaction rate expression for the oxidation of ethylene can be written as:r = k * [C2H4] * [O2]where k is the rate constant, and [C2H4] and [O2] are the concentrations of ethylene and oxygen, respectively. The rate constant k can be determined from 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, and T is the temperature.Step 3: Choose the appropriate reactor typeA packed-bed reactor PBR is suitable for this reaction, as it allows for the use of a solid catalyst silver and provides good contact between the gas-phase reactants and the catalyst.Step 4: Calculate the reactor volumeTo calculate the reactor volume, we need to integrate the reaction rate expression along the length of the reactor. For a PBR, this can be done using the following equation:V = F_C2H4_feed / -r dXwhere V is the reactor volume, and X is the conversion of ethylene. We can solve this equation numerically to obtain the reactor volume.Step 5: Determine the operating conditionsThe reactor should operate at 3 atm and a temperature range of 200-250C. The optimal temperature can be determined by evaluating the reaction rate and selectivity at different temperatures within this range. The temperature that provides the highest selectivity and reaction rate should be chosen as the operating temperature.In summary, to design a chemical reactor for the production of ethylene oxide, we need to calculate the molar flow rates of the reactants, determine the reaction rate expression, choose the appropriate reactor type packed-bed reactor , calculate the reactor volume, and determine the optimal operating conditions pressure and temperature .