To design a chemical reactor to produce 10 kg/hr of product X with a yield of at least 90%, given a feed of 100 kg/hr of reactants A and B, and assuming a first-order reaction, follow these steps:1. Determine the desired product formation rate:Since the desired yield is 90%, the product formation rate should be 0.9 * 100 kg/hr = 90 kg/hr of product X.2. Calculate the reaction rate constant k :To determine the reaction rate constant, you need to know the reaction rate equation and the reaction conditions temperature, pressure, etc. . For a first-order reaction, the rate equation is:Rate = k * [A] * [B]Assuming equal concentrations of A and B, the rate equation becomes:Rate = k * [A]^23. Choose the type of reactor:There are several types of reactors, such as batch reactors, continuous stirred-tank reactors CSTR , and plug flow reactors PFR . For this problem, we will assume a continuous process, so we will choose between CSTR and PFR. PFRs are generally more efficient for first-order reactions, so we will select a PFR for this design.4. Design the PFR:To design the PFR, we need to determine the reactor volume V based on the desired product formation rate and the reaction rate constant. The general equation for a PFR is:V = F_in - F_out / -r_A Where F_in is the molar flow rate of reactant A entering the reactor, F_out is the molar flow rate of reactant A leaving the reactor, and -r_A is the rate of consumption of reactant A.5. Calculate the reactor volume:First, determine the molar flow rates of reactant A entering and leaving the reactor. Assuming a stoichiometric ratio of 1:1 for reactants A and B, the molar flow rate of reactant A entering the reactor F_in is 50 kg/hr half of the total feed . Since the desired yield is 90%, the molar flow rate of reactant A leaving the reactor F_out is 10% of the entering flow rate, or 5 kg/hr.Next, calculate the rate of consumption of reactant A -r_A using the rate equation:-r_A = k * [A]^2Assuming a known value for k, calculate -r_A.Finally, calculate the reactor volume V using the PFR equation:V = F_in - F_out / -r_A 6. Additional design considerations:In addition to the reactor volume, consider other design factors such as heat transfer, pressure drop, and mixing. These factors will influence the choice of materials, reactor geometry, and any additional equipment needed e.g., heat exchangers, pumps, etc. .By following these steps, you can design a chemical reactor to produce 10 kg/hr of product X with a yield of at least 90%, given a feed of 100 kg/hr of reactants A and B, and assuming a first-order reaction.