CSTR 1 CSTR 2 X A =?

Transcription

1 hemical Engineering HE 33 F Applied Reaction Kinetics Fall 014 Problem Set 3 Due at the dropbox located in the hallway outside of WB 5 by Monday, Nov 3 rd, 014 at 5 pm Problem 1. onsider the following liquid-phase, reversible isomerization reaction: k1 A B k 1 k 1 = 1 s -1 k -1 = 0.1 s -1 where the forward and reverse reaction rates are first-order in species A and B, respectively. This reaction occurs at steady-state in the following reactor scheme: F A0 STR 1 STR X A =? F B,SS A stream containing pure A (10 mol s -1 ) is fed to the first STR (50 dm 3 ) at a volumetric flow rate of 0 dm 3 s -1. The effluent from the first STR enters a separation unit that selectively removes a side-stream of B from a mixture of the two isomers, at a molar flow rate given by F B,SS. The rest of the mixture is fed into the second STR (10 dm 3 ). Determine the overall conversion of A if: (a) The separation unit removes 0% of B from the effluent of the first STR. (b) The separation unit removes 60% of B from the effluent of the first STR. Explain briefly why removing B in the middle of the process has this effect on the overall conversion of A.

2 Problem. Ammonia is produced from reactions between N and H at pressures of 100 bar and o 0.5N 1.5H NH 3 Thermochemical data for ammonia synthesis Species G f (kj / mol ) H f (kj / mol ) Ammonia The rates of forward and reverse reactions, and, are r f r r r k P P r H 1 f f N k P r r NH H 3 P a) Show that the rate equations for the forward and reverse reactions are consistent with thermodynamics. b) Express the equilibrium constant for the chemical equation above in terms of concentrations of reactants and products. c) How does the equilibrium constant d) Plot P and P relate to? Assuming ideal gas behavior. as a function of inverse temperature, assuming that the Gibbs free energy and the enthalpy of formation do not vary with temperature. omment on the changes in equilibrium conversion with temperature. e) Determine the equilibrium conversion for an equi-molar feed mixture at 773 K and at 1, 10, and 100 bar. How does the change in pressure affect the equilibrium conversion? Should we operate the reactor at high or low pressure? f) Express the net reaction rates in terms of fractional conversion, forward reaction rate constant, and equilibrium constant. Show that the net reaction rates approach zero when the composition of gas mixtures approaches equilibrium values. g) Plot the inverse of the net reaction rates as a function of conversion for P=1 and 100 bar, forward reaction rate constant of 1 atm -3 s -1 [note: this is given as the turnover rate, the unit of the rate is s -1 ]. omment on the relative magnitude of the rates and the maximum conversion reached for both pressures.

3 Problem 3. A Mickey Mouse Balloon (see cartoon below) is filled with reactants A(g) and B(g) that undergo a reversible reaction to form (g): Initial conditions (time=0 s): A = 1 mol/l B = mol/l Volume (t=0) = 5 L This is a constant pressure and constant temperature balloon and the concentrations of all species (A, B, and ) are uniform throughout. The rate equation for the forward reaction is and k f is 1.5 L (s-mol) -1 at 400 K. The equilibrium constant (based on concentration), K, is Temperature (K) a) ircle the correct answer. The reaction is an EXOTHERMI or ENDOTHERMI reaction. Determine the heat of reaction, assuming that the heat of reaction and entropy of reaction do not vary with temperature. b) Determine the equilibrium constant (based on partial pressure), K p, at 300 K. c) Write the expression(s) used to determine the final volume of the Mickey Mouse Balloon at 400 K. Note: Final volume is defined at the volume after the reaction is completed. The number of expression is equal to the number of unknown. You need to label your final expressions as EQN 1,, etc. and state the unknowns to receive the full credit. d) Provide the expression of the reverse rate (r r ) in terms of fractional conversion X A. e) (For this part only) There is a new material used as the wall of the Mickey Mouse Balloon. This new material can selectively remove all the species that are formed during the reaction instantaneously. omparing this balloon (with permeable wall for removal of ) with the non-permeable Balloon (no species is being removed), is the time required for A to reach 0.5 mol/l longer or shorter? Write the design equations for the two cases in terms of all the given terms. Based on the design equations, provide your explanation by discussion the differences and the relative magnitudes of each term in the equation. Hint: you need to consider the changes in volume as is being removed.

4 Problem 4. Assuming that all the following six reactions are reversible, use your reasoning to determine whether or not these reactions are elementary reactions. State your reasoning and conclusion for each case to achieve full mark. H OH H H O a. 6 5 H HO H H H OH H b. 3 c. H O OH H OH H H OH d. 3 3 e. O3 O O f. 3I S O I SO Problem 5 The reversible gas phase decomposition of A proceeds at constant pressure inside a spherical bubble: The rate constants of the thermodynamically consistent reaction are: kf = forward rate constant kr = reverse rate constant Equilibrium constant values: = 0.01 mol L -1 at 0 and = mol L -1 at 100. A kf kr B + The reverse reaction is zero order and kr has a pre-exponential factor: Ar = mol L -1 s -1, and activation energy: Ea,r = 60 kj mol -1. At time equals zero, the bubble s volume is 1 ml and contains pure A at 50 and 1 atm total pressure. Given: The universal gas constant R= atm L mol -1 K -1 a) Determine the heat of reaction and the activation energy for the forward step.

5 b) On the graph provided, draw a potential energy diagram of the reaction and label the reactants, products, transition state, forward and reverse activation energies (with numerical values), and the heat of reaction (with numerical values). Potential Energy (kj/mol) Reaction oordinate c) Provide the rate equation (in terms of pressures) for species A at 50. Substitute the numerical values for the forward and reverse rate constants to receive full credit. d) The bubble s volume increases at constant pressure during reaction at 50. If the bubble volume reaches a critical value of ml, it will burst. Determine if the bubble volume reaches this value. If it did, calculate the time required for the bubble to burst. If it did not, calculate the final volume of the bubble.