Question

Design a chemical reactor for the reaction A + B --> C at a rate of 2 moles/min, with a reaction temperature of 300°C and a pressure of 3 atm. The reaction is exothermic and has a heat of reaction of -200 kJ/mol. The reactants A and B are fed into the reactor at a flow rate of 1 mole/min each. Choose the appropriate reactor design and calculate the volume needed to achieve a conversion of 95%.

Answer 1

To design a chemical reactor for the given reaction, we need to consider the reaction kinetics, heat management, and the desired conversion. Since the reaction is exothermic, a Continuous Stirred Tank Reactor  CSTR  or a Plug Flow Reactor  PFR  can be used. We will choose a Plug Flow Reactor  PFR  for this design, as it is more suitable for exothermic reactions and can handle higher conversions.Let's assume the reaction follows first-order kinetics for both reactants A and B:rate = k * [A] * [B]Given the rate of reaction is 2 moles/min, we can write:2 = k * [A] * [B]Since the flow rate of A and B is 1 mole/min each, and the stoichiometry is 1:1, we can assume that the concentration of A and B are equal:[A] = [B]Thus, the rate equation becomes:2 = k * [A]^2Now, we need to find the value of k. We can use the Arrhenius equation to find the rate constant at the given temperature  300C or 573.15 K :k = A * exp -Ea /  R * T  where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant  8.314 J/mol*K , and T is the temperature in Kelvin. However, we don't have enough information to determine the values of A and Ea. Therefore, we will assume that k is constant at the given temperature and pressure.Let's denote the conversion of reactants A and B as X. Since the flow rate of A and B is 1 mole/min each, the rate of disappearance of A and B is:-1 * dX/dt = k *  1 - X ^2Integrating this equation with respect to time and conversion, we get: dX /  1 - X ^2  = -k * dtUpon integrating, we get: 1 /  1 - X   = -k * t + CTo find the constant C, we can use the initial condition that at t = 0, X = 0:C = 1Now, the equation becomes: 1 /  1 - X   = -k * t + 1We want to achieve a conversion of 95%  X = 0.95 . Rearranging the equation to solve for t:t =  1 -  1 /  1 - 0.95    / kt =  1 - 0.05  / kt = 0.95 / kNow, we can find the volume of the PFR using the equation:V = F * twhere F is the molar flow rate of the reactants  1 mole/min for A and B . Substituting the values:V = 1 *  0.95 / k V = 0.95 / kSince we don't have enough information to determine the value of k, the volume of the PFR cannot be calculated explicitly. However, the equation V = 0.95 / k can be used to find the volume once the rate constant k is known.