To design a chemical reactor system for the production of ammonia using the Haber-Bosch process, we need to consider the stoichiometry of the reaction, the reaction rate, and the conversion rate. The balanced equation for the production of ammonia is:N2 + 3H2 2NH31. Molar flow rates of reactants:First, we need to determine the molar flow rates of nitrogen and hydrogen gases. The molar mass of ammonia NH3 is 17 g/mol, nitrogen N2 is 28 g/mol, and hydrogen H2 is 2 g/mol.100 kg/hr of ammonia is equivalent to 100,000 g/hr / 17 g/mol = 5882.35 mol/hr.From the stoichiometry of the reaction, we need 1 mol of N2 and 3 mol of H2 to produce 2 mol of NH3. Therefore, the molar flow rates of N2 and H2 are:N2: 5882.35 mol/hr * 1 mol N2 / 2 mol NH3 = 2941.18 mol/hrH2: 5882.35 mol/hr * 3 mol H2 / 2 mol NH3 = 8823.53 mol/hr2. Conversion rate:The reactor should have a 90% conversion rate. This means that 90% of the reactants are converted into ammonia. The conversion rate for N2 is:2941.18 mol/hr * 0.9 = 2647.06 mol/hr3. Reaction rate:The reaction rate is given by the Arrhenius equation:k = A * exp -Ea / R * T where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. For the Haber-Bosch process, the typical values are A = 4.0 x 10^4 L/mol/min, Ea = 120 kJ/mol, and R = 8.314 J/mol/K.The reactor temperature is 450C, which is equivalent to 723.15 K. Therefore, the rate constant k is:k = 4.0 x 10^4 * exp -120,000 / 8.314 * 723.15 = 0.026 L/mol/min4. Reactor volume:The reactor volume can be determined using the rate constant and the conversion rate. The rate equation for the Haber-Bosch process is:rate = k * [N2] * [H2]^3Assuming a plug flow reactor PFR , the reactor volume can be calculated as:V = F_N2 * X_N2 / k * [N2] * [H2]^3 where V is the reactor volume, F_N2 is the molar flow rate of N2, X_N2 is the conversion rate of N2, and [N2] and [H2] are the molar concentrations of N2 and H2, respectively. The reactor pressure is 200 atm, and the ideal gas law can be used to calculate the molar concentrations:[N2] = 2941.18 mol/hr / 200 atm * 723.15 K / 8.314 J/mol/K * 60 min/hr * 1000 L/m^3 = 0.006 mol/L[H2] = 8823.53 mol/hr / 200 atm * 723.15 K / 8.314 J/mol/K * 60 min/hr * 1000 L/m^3 = 0.018 mol/LSubstituting the values into the reactor volume equation:V = 2941.18 mol/hr * 0.9 / 0.026 L/mol/min * 0.006 mol/L * 0.018 mol/L ^3 = 102,215 L5. Catalyst amount:The amount of catalyst needed for the process depends on the specific activity of the catalyst and the reaction rate. Assuming a typical catalyst activity of 10 mol NH3 / g_cat * hr , the required catalyst amount can be calculated as:catalyst_amount = 100 kg/hr / 10 mol NH3 / g_cat * hr * 1 mol NH3 / 17 g NH3 = 5882.35 g_cat/hr6. Reactor dimensions:Assuming a cylindrical reactor, the dimensions can be determined using the reactor volume. Let's assume a height-to-diameter ratio of 2:1 for the reactor. Then, the reactor height H and diameter D can be calculated as:V = * D/2 ^2 * H102,215 L = * D/2 ^2 * 2D D = 6.07 mH = 12.14 mIn summary, the designed chemical reactor system for the production of 100 kg/hr of ammonia using the Haber-Bosch process has a volume of 102,215 L, dimensions of 6.07 m in diameter and 12.14 m in height, and requires 5882.35 g/hr of catalyst.