To design a chemical reactor system for the production of methanol, we need to consider the stoichiometry of the reaction, the desired conversion rate, and the operating conditions. The reaction for methanol production is:CO + 2H2 CH3OH1. Calculate the molar flow rates of CO and H2:First, we need to determine the molar flow rates of CO and H2 required to produce 500 kg/hr of methanol. The molecular weights of methanol, CO, and H2 are 32 g/mol, 28 g/mol, and 2 g/mol, respectively.Methanol production rate = 500 kg/hr * 1000 g/kg / 32 g/mol = 15,625 mol/hrFrom the stoichiometry of the reaction, we can determine the molar flow rates of CO and H2:CO molar flow rate = 15,625 mol/hrH2 molar flow rate = 2 * 15,625 mol/hr = 31,250 mol/hr2. Determine the type of reactor:Since the reaction involves gases and operates at high pressure, a packed bed reactor PBR is a suitable choice for this process. Packed bed reactors are commonly used for gas-phase reactions and can handle high-pressure operations.3. Calculate the required reactor volume:To determine the reactor volume, we need to use the reaction rate expression. For the methanol synthesis reaction, the rate expression is given by:r = k * P_CO * P_H2^2 / 1 + K_p * P_CO * P_H2 where r is the reaction rate, k is the rate constant, P_CO and P_H2 are the partial pressures of CO and H2, and K_p is the equilibrium constant.At 300C and 100 atm, the rate constant k and equilibrium constant K_p can be found in the literature or calculated using thermodynamic data. For simplicity, we will assume k = 0.01 mol/ Latm^3hr and K_p = 10 atm^-1.The conversion rate is given as 80%, so the exit molar flow rate of CO will be 20% of the inlet flow rate:CO exit molar flow rate = 0.2 * 15,625 mol/hr = 3,125 mol/hrUsing the stoichiometry of the reaction, we can calculate the exit molar flow rate of H2:H2 exit molar flow rate = 31,250 mol/hr - 2 * 15,625 - 3,125 mol/hr = 6,250 mol/hrNow we can calculate the partial pressures of CO and H2 at the exit of the reactor:P_CO = 3,125 mol/hr / 15,625 + 6,250 + 31,250 mol/hr * 100 atm = 6.25 atmP_H2 = 6,250 mol/hr / 15,625 + 6,250 + 31,250 mol/hr * 100 atm = 12.5 atmUsing the rate expression, we can calculate the reaction rate at the exit:r_exit = 0.01 * 6.25 * 12.5^2 / 1 + 10 * 6.25 * 12.5 = 0.00156 mol/ Lhr The reactor volume can be calculated using the exit reaction rate and the production rate of methanol:V = 15,625 mol/hr / 0.00156 mol/ Lhr = 10,000 L4. Determine the reactor dimensions:Assuming a cylindrical packed bed reactor, we can determine the dimensions using the reactor volume and an aspect ratio height/diameter of 3, which is typical for packed bed reactors:V = * D/2 ^2 * H10,000 L = * D/2 ^2 * 3D Solving for D, we get D 1.3 m. The height of the reactor is H = 3D 3.9 m.5. Summary:To produce 500 kg/hr of methanol with a minimum conversion rate of 80%, a packed bed reactor with a volume of 10,000 L and dimensions of 1.3 m in diameter and 3.9 m in height is required. The required flow rates of CO and H2 gas are 15,625 mol/hr and 31,250 mol/hr, respectively. The reactor should operate at a pressure of 100 atm and a temperature of 300C.