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Problem 1 A dimerization reaction 2AD for obtaining dimer D from reactant A is carried out in the gas phase in a plug-flow reactor (PFR). The reaction follows the mechanism:

→

→ where the first reaction is the rate-determining step, with rate constant k1 = 0.05 s-1, and the second reaction is very fast. The reactor temperature and pressure are constant, T = 400K and P = 10 atm, respectively. Heat transfer is improved by adding an inert component, I, to the reactor feed, such that the feed contains equal molar amounts of A and I. The volumetric feed rate of the combined A/I mixture is Qf = 1.2 m3/min. (R = 0.082 liter-atm/mole-K) Compute:

1. The reactor volume VR, required to obtain a 90% conversion of the reactant A. 2. The molar flow rate of the product D at the reactor outlet.

Problem 2 The reactions indicated below take place in the liquid phase in a CSTR with the indicated rate expressions.

A → B 20ksec

A → C 2m /kmole∙ksec The feed stream consists of A dissolved in a solvent S such that the initial concentration of A is 2 kmoles/m3. The volumetric flow rate into and out of the reactor can be considered the same and constant. If 50% of A in the feed undergoes reaction, determine the concentrations of A, B and C in the effluent. What is the residence time of the CSTR?

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Problem 3 A plug flow reactor for SO2 oxidation to SO3

SO12O ↔ SO

is operated adiabatically with countercurrent heat exchange between the feed and product streams. The inlet gas composition is 10% SO2, 10% O2, and 80% N2. The feed gas is preheated to 725K by the heat exchanger and this is the temperature it enters the plug flow reactor. Equilibrium is attained by the time the fluid reaches the reactor outlet. The conversion of SO2 to SO3 is 70%. Pressure is constant and 1 atm. Data: ln Ka = -11.2755 + 11794/T , (T in degrees Kelvin) Cp = 6.66 + 0.00105 T , cal/gmol-K ∆Hr = -23250 – 1.45T + 0.0021 T2 , cal/gmol SO3 produced Answer the following questions.

a. Find the temperature of the reactor outlet. b. Will the conversion of SO2 increase or decrease if the temperature of the feed at the

reactor inlet is increased from 725K to 735K? c. If you use two stages of a plug flow reactors to increase conversion, should you heat or

cool the gas between the reactors? Problem 4 The following heterogeneously catalyzed reaction

A → B 8.2 10 exp

is to be conducted in an isothermal fixed-bed reactor operating at a constant pressure of 1.5 atm. The reactant and product are gases. When the feed to the reactor is pure A with NAf = 4.3 mol/s and the temperature is 650 K, the reactor volume is 108,200 cm3 for 80% conversion of A. What will the reactor volume be for 80% conversion of A if the feed composition, feed molar flowrate and diffusivity stay the same but the temperature is reduced to 600K? For this catalyst, the bed porosity is 0.35, the spherical pellet radius is R = 0.8 cm, and the diffusivity of A is DA = 0.0065 cm2/s. You may neglect external gradients. (R = 82 cm3 atm/K mol)

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Problem 5 A batch reactor has a 500 lb charge of solution of acetic anhydride at a concentration of 0.0135 lbmol/ft3 and a temperature of T = 520 R. The solution has a density of 65.5 lb/ft3 and its specific heat is 0.9 Btu/(lb-F). The heat of reaction is ∆HR = 90, 000 Btu/lbmol. The hydrolysis of dilute acetic anhydride

(CH3CO)2O + H2O 2CH3COOH follows first-order kinetics,

exp 17.852 min-1

Assuming constant physical and thermodynamic properties

(a) Find the time to achieve 70% conversion under isothermal conditions.

(b) Find the time to achieve 70% conversion under adiabatic conditions.