Design a chemical reactor to produce 500kg of ammonia per hour from hydrogen and nitrogen gases. You are given the rate equation for the reaction as follow: N2(g) + 3H2(g) → 2NH3(g) The reaction is exothermic and a temperature range of 400-500°C is recommended for optimal production rate. The pressure of the system should be between 150-200 atm. You are required to determine the required size of the reactor and the flow rates of hydrogen and nitrogen gas.

Question

Design a chemical reactor to produce 500kg of ammonia per hour from hydrogen and nitrogen gases. You are given the rate equation for the reaction as follow: N2(g) + 3H2(g) → 2NH3(g) The reaction is exothermic and a temperature range of 400-500°C is recommended for optimal production rate. The pressure of the system should be between 150-200 atm. You are required to determine th

Answer 1

To design a chemical reactor for the production of ammonia, we need to determine the flow rates of hydrogen and nitrogen gas, as well as the size of the reactor. We will use the stoichiometry of the reaction and the desired production rate to calculate the flow rates. Then, we will use the reaction conditions to estimate the size of the reactor.1. Calculate the flow rates of hydrogen and nitrogen gas:We want to produce 500 kg of ammonia  NH3  per hour. The molar mass of NH3 is 14  N  + 3  H  = 17 g/mol. Therefore, we need to produce: 500 kg/h  *  1000 g/kg  /  17 g/mol  = 29,412 mol/h of NH3From the stoichiometry of the reaction, 1 mol of N2 reacts with 3 mol of H2 to produce 2 mol of NH3. Therefore, we need:29,412 mol/h *  1 mol N2 / 2 mol NH3  = 14,706 mol/h of N229,412 mol/h *  3 mol H2 / 2 mol NH3  = 44,118 mol/h of H22. Estimate the size of the reactor:We will use a plug flow reactor  PFR  for this process, as it is suitable for gas-phase reactions with high pressure and temperature. The size of the reactor can be estimated using the space velocity  SV  and the volumetric flow rate  Q  of the reactants:SV = Q / VWhere SV is the space velocity  h^-1 , Q is the volumetric flow rate  m^3/h , and V is the reactor volume  m^3 .We will assume a space velocity of 2 h^-1, which is a typical value for ammonia synthesis reactors. We also need to calculate the volumetric flow rate of the reactants. We will assume an average temperature of 450C  723 K  and a pressure of 175 atm  17,750 kPa  for the reaction.Using the ideal gas law, PV = nRT, we can calculate the volumetric flow rate for each reactant:Q_N2 = n_N2 * R * T / P =  14,706 mol/h  *  8.314 J/molK  *  723 K  /  17,750 kPa  = 48.7 m^3/hQ_H2 = n_H2 * R * T / P =  44,118 mol/h  *  8.314 J/molK  *  723 K  /  17,750 kPa  = 146.1 m^3/hThe total volumetric flow rate is Q_total = Q_N2 + Q_H2 = 48.7 + 146.1 = 194.8 m^3/h. Now we can calculate the reactor volume:V = Q_total / SV = 194.8 m^3/h / 2 h^-1 = 97.4 m^3So, the required size of the reactor is approximately 97.4 m^3.In summary, to produce 500 kg of ammonia per hour, we need a plug flow reactor with a volume of 97.4 m^3, and flow rates of 14,706 mol/h of nitrogen gas and 44,118 mol/h of hydrogen gas. The reaction should be carried out at a temperature of 450C and a pressure of 175 atm.