Question

QUESTION 1: 20 marks 20 points It is planned to carry out the following second-order, elementary, non- catalytic gas-phase reaction in an adiabatic CSTR: A+B_C+3D. Only A and B (no inerts) are fed to the reactor at equimolar flow rates of 150 mol/min each. The rate constant is related to the temperature by Arrhenius law as follows: k = 37.68x10^10 exp(-80000/RT) L/mol.min. The heats of formation of A, B, C and D (at 298 K) in kJ/mol are -235.3, -393.5, -241.8 and O respectively: Specific heats (in J/(mol.K)) of A, B, C and D are 61.3, 36.1, 33.5 and 29 respectively. Inlet pressure is 1 atm and assume that the pressure drop across the reactor is negligible. Assume that the gas mixture behaves like an ideal gas. a) Calculate the Standard Heat of Reaction at 298K and ACP. Is this an endothermic or exothermic reaction? Why? (5marks) b) If the target temperature in the reactor is 3000C and conversion is 95%, what must the inlet temperature be? (5marks) c) Determine the expansion factor, ε. Set up a stoichiometric table and express concentrations of reactants in terms of conversion. (4marks) d) Calculate the rate of reaction and determine the reactor volume for 95% conversion if the reactor is operated at 300C. (6marks)

Answer 1

Date At с + 3D k CA Co - do dt dG dt -SA = k (Call-Xo) ] [ coo (1-xn)] k CAO (1-XA) ( Ben Bo Xo) k Con (1-XA) (CB. - COXA) Amount of A & B reacted time are equal te CAO XA = Golb any k CAO (1-X) CA (BO CAO XA k Coo (1-XA) CAO (1-XA) For equal molar flow rates Go CAO k cana (I-XA) ² where, ke 37.68 X1010 expl -80000 RT L mol. min a

Heat of formation | A = -235.3 X I mol mot B= -393.5 I mul -241.8 mol KJ mol 3 mil = 0 mel Heat of reaction Ahr (2981) A Hf (product) 294 Alf reactut 25th (-241.8) (-393.5-23513) 387 KJ AHY The reaction us. endothermie ( heat is absorbed by the System) ДСр Hangot En Cp prod. En o react = (x 33.5 + 3x29)-( 1x 61.3 + 1 x 36-1) 23.1 23.1 alp K

300 c Tfinal Xo = Tin بلارو 0.95 ? for Adiabatir reactor we know that COOT - Ar 23.1( 300- 387 15.91 300 - Tin 284.08 2 c) Expansion factor & is given as CA E s you TAL where S = (Sum of coeff of prad. ) - (Sum of coeff of reactant (1+3) -(1+1) 2. mole fraction of A in feed equinolar feed of A&B) Stoichiometric Coff of A VA

Date EA 2x or method y At B C + 3D EA = VXA=1 where Val vol of react system at complete conversion no At Vx=0 At VxAal A В 150 С. 450 D 600 Total 300 EA 600 3.00 300

Date: Page : CA = CAO CI-XA) It AXA It EB XB T= 300°c 573K ka 37.68x10 10 expf - 89000) 10 37.68x10 1 expl 8.314 X 573 k 19189 mol, men Inlet pressure P I atm = 101325 Pa ideal gas PV = nRT * P = (2) RT 3 P = CRT 21 Р RT inlet partial pressure of A رة لحج دو PAO О. Р poo

Date : Page : 10.63 mol Pro RT 0.5x 101325 8.314X 573 10.63 x 10 3 A = m3 | | 7 = 10*) CAO mol L for CSTR, XA FAO mol/min 150 For XA = 0.95 rate of react + n = k Can (1-x)² 1 9189 X (10.63 x 10°)x (1-0,95.)? 0,00542 mol L. min 095 0.00542 10 V L 26287.9 26. 28 2 m²