Example 8-1 Maximizing the Selectivity for the Famous Trambouze Reactions Reactant A decomposes by three simultaneous reactions to form three products, one that is desired, B, and two that are undesired, X and Y. These gas-phase reactions, along with the appropriate rate laws, are called the Trambouze reactions [AIChE J., 5, 384]. 1) A -A=x=k₁ = 0.0001- mol dm-s (zero order) 2) A B -AB-C (0.0015 C (first order) dm³ mol (second order) 3) AY -==₂-(0.008 dms) The specific reaction rates are given at 300 K and the activation energies for reactions (1), (2), and (3) are E1 = 10,000 kcal/mole, E2 = 15,000 kcal/mole, and E3 = 20,000 kcal/mole. (a) How and under what conditions (e.g., reactor type(s), temperature, concentrations) should the reaction be carried out to maximize the selectivity of species B for an entering concentration of species A of 0.4 M and a volumetric flow rate of 2.0 dm3/s? (b) How could the conversion of B be increased and still keep selectivity relatively high? Solution Part (a) The instantaneous selectivity of species B with respect to species X and Y is (E8-1.1) (E8-1.1) Sexy= B KCA => rx+ry k₁+kC Plotting SB/XY vs. CA, we see that there is a maximum, as shown in Figure E8-1.1. Figure E8-1.1 Selectivity as a function of the concentration of A. Saxy 10 7.68 6.72 5.00 504 420 Saxy 252 Selectivity: Trambouze Reactions 1.08 084 000 000 00 00 01 020 025 03 ex ox Ca As we can see, the selectivity reaches a maximum at a concentration C, we differentiate C. That is, (E8-1.2) dSp/xy, dCA [k₁+kC-₂C[2kCA] [k₁+k]² Solving for (E8-1.3) 0.0001( mol/dm-s), 0.112 mol/dm³ 0.008 (dm³/mol-s) (a) Example 8-1. (1) What are CA, Cx, and Cy at CA? (2) What would have been the selectivity SB/XY and conversion, X, if the reaction had been carried out in a single PFR with the same volume as the CSTR? (3) How would your answers change if the pressure were increased by a factor of 100? (b) Example 8-2. Make a table/list for each reactor shown in Figure 8-2, identifying all the types of reactions that would be best carried out in this reactor. For example, Figure 8-2(d) Semibatch: used for (1) highly exothermic reactions and (2) increase selectivity. (c) Example 8-3. How would topt change if k1 = k2 = 0.25/h at 300 K? (d) Example 8-4. (1) What are SB/C and YB? What CSTR operating temperature (with T = 0.5s) would you recommend to maximize B for CAO = 5 mol/dm3, k1 = 0.4 s-1 and k2 = 0.01 s-1 with E1 = 10 kcal/mol and E2 = 20 kcal/mol ? [Hint: Plot CB versus T.] A+2BC with the equilibrium constant KC = 0.002 (dm3/mol)2.