Design a continuous stirred-tank reactor (CSTR) for the exothermic reaction of A + B → C with a rate constant of 0.05 L/mol/min. The reactor should produce a minimum of 500 g of C per minute, while maintaining a conversion of at least 90%. The feedstream of A and B is available with a flow rate of 2 L/min and an initial concentration of 1 M for both reactants. The reactor should be operated at a temperature of 50°C and a pressure of 1 atm. What should be the volume of the CSTR and the flow rate of the cooling medium used to maintain the desired temperature?

Question

Design a continuous stirred-tank reactor (CSTR) for the exothermic reaction of A + B → C with a rate constant of 0.05 L/mol/min. The reactor should produce a minimum of 500 g of C per minute, while maintaining a conversion of at least 90%. The feedstream of A and B is available with a flow rate of 2 L/min and an initial concentration of 1

Answer 1

To design the CSTR, we first need to determine the reaction rate at the desired conversion. The reaction rate is given by:rate = k * [A] * [B]where k is the rate constant  0.05 L/mol/min , and [A] and [B] are the concentrations of A and B, respectively.At 90% conversion, the concentrations of A and B will be reduced to 10% of their initial values:[A] = [B] = 0.1 * 1 M = 0.1 MNow we can calculate the reaction rate:rate = 0.05 L/mol/min * 0.1 M * 0.1 M = 0.0005 mol/L/minTo produce 500 g of C per minute, we need to determine the molar flow rate of C:500 g/min *  1 mol/ Molar_mass_C g  = F_CAssuming the molar mass of C is 100 g/mol:F_C = 500 g/min *  1 mol/100 g  = 5 mol/minNow we can use the CSTR design equation to determine the volume of the reactor:V = F_C / rate = 5 mol/min / 0.0005 mol/L/min = 10,000 LSo, the volume of the CSTR should be 10,000 L.To maintain the desired temperature, we need to determine the heat generated by the reaction and the cooling medium flow rate. We'll need the heat of reaction  H_rxn  and the heat capacity of the cooling medium  Cp_cooling . Assuming the heat of reaction is -50 kJ/mol and the heat capacity of the cooling medium is 4 kJ/kgK:Heat generated = F_C * H_rxn = 5 mol/min *  -50 kJ/mol  = -250 kJ/minThe cooling medium needs to remove this heat to maintain the temperature. Assuming the cooling medium enters at 20C and leaves at 50C:T_cooling = 50C - 20C = 30 KHeat removed by cooling medium = m_cooling * Cp_cooling * T_coolingwhere m_cooling is the mass flow rate of the cooling medium.Now we can set the heat generated equal to the heat removed and solve for the cooling medium flow rate:-250 kJ/min = m_cooling * 4 kJ/kgK * 30 Km_cooling = -250 kJ/min /  4 kJ/kgK * 30 K  = 2.08 kg/minSo, the flow rate of the cooling medium should be 2.08 kg/min to maintain the desired temperature.