# k 2f, k 2r C 2 H 5 + H C 2 H 6

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1 hemical Engineering HE 33 F pplied Reaction Kinetics Fall 04 Problem Set 4 Solution Problem. The following elementary steps are proposed for a gas phase reaction: Elementary Steps Rate constants H H f, r H 4 + M H 4 * + M f, r H 4 *+ H H 5 + H H 5 H 6 3f, 3r 4f : quasi-equilibrated step : reversible step : irreversible step i,j : rate constant for step i, subscript j = forward reaction (f) or reverse (r) reaction M: atom with high energy. M transfers its energy to H 4 to promote excitation of H 4 to form H 4 * H 4 *: a H 4 molecule at excited state) : radical The pre-exponential factors and activation energies for each step in the forward the reverse directions are given in Table. Table. Step Forward Step Forward Step Reverse Step Reverse Step Pre-exponential Factor ctivation Energy (J/mol) Pre-exponential Factor ctivation Energy (J/mol) 0 6 s L (mol s) L (mol s) L (mol s) L (mol s) s L (mol s) a. Provide the chemical equation for the overall reaction. b. Derive the rate equation for H 6 formation. c. ssume that the rate for the reverse reaction 3 (reverse of step 3) is small. Determine the effective preexponential factor. (0 Points) d. ssume that the rate for the reverse reaction 3 (reverse step 3) is small. This gas phase reaction is carried out in a plug flow reactor at 500 K. The feed mixture contains H and H 6 at a : molar ratio. The total molar flow rate is 00 mol s - and the pressure is atm. Setup the design equation for the PFR reactor based on the molar species balance for hydrogen to obtain the fractional conversion as a function of reactor volume (dx /dv). Substitute all numerical values and describe the method of solving the equation.

2 a. Provide the chemical equation for the overall reaction. () H + H 4 H 6 b. Derive the rate equation for H 6 formation. (8) r [ H ] [ H ] H f [ H * ] K [ H ] 4 4 [ H ] K [ H ] [ H * ] [ H ] [ H ] [ H ] [ H ] 0 3 f 4 3 r 5 4 f 5 [ H * ] [ H ] K [ H ] K [ H ] 3 f 4 3 f 4 [ H ] 5 [ H ] [ H * ] K [ H ] 3 r 4 f 4 3 r 4 f K [ H ] K [ H ] 3 f 4 r H 6 4 f K [ H ] K [ H ] 3 r 4 f c. ssume that the rate for the reverse reaction 3 (reverse of step 3) is small. Determine the effective preexponential factor. (0) r K [ H ] K [ H ] H f d. ssume that the rate for the reverse reaction 3 (reverse step 3) is small. This gas phase reaction is carried out in a plug flow reactor at 500 K. The feed mixture contains H and H 6 at a : molar ratio. The total molar flow rate is 00 mol s - and the pressure is atm. Setup the design equation for the PFR reactor. Start from the molar species balance for hydrogen, derive the fractional conversion as a function of reactor volume (dx /dv). Substitute all numerical values and describe how the method of solving the equation. DO NOT SOLVE. (5) K [ H ] K [ H ] 3 f 4 r r H H 6 4 f K [ H ] K [ H ] 3 r 4 f r r K [ H ] K [ H ] H H f d F ( X ) F ( X ) H, 0 H, 0 P F ( X ) H 4, 0 P r K [ H ] K [ H ] K K d V F ( X ) R T F ( X ) R T H 3 f 4 3 f T, 0 T, E f e x p ( ) 0 e x p ( ) f E 3 f R T L R T K e x p ( ) e x p ( ) 3 f 3 f R T E r. ( ) s L e x p ( ) 0 e x p ( ) r R T R T L K f 05. s K FH, 0 F H 4, 0 ( X ) ( X ) d F ( X ) H, 0 F F T, 0 P T, 0 P r K [ H ] K [ H ] K K d V F R T F R T H 3 f 4 3 f FT, 0 H, 0 FT, 0 H, 0 X X F F F F T, 0 T, 0 T, 0 T, 0 05.

3 d F ( X ) H, ( X ) P 0. 5( X ) P r K K H 3 f d V 0. 5 X R T 0. 5 X R T d X K 3 f 0. 5( X ) P d V F 0. 5 X R T H, 0 5. K L d X 0 5 s. ( X ) a tm d V 0. 5 X a tm L K h r K Problem. onsider the following elementary reactions at solid surfaces with active sites (S denotes an active site): Step : Step : Step 3: Step 4: O + S HHO + O-S + S HOO-S + S O-S HOO-S + H-S O -S + H-S H-S H + S f, r f 3f 4f, 4r Step 5: O -S O + S 5f, 5r Quasi-equilibrated step Reversible step Irreversible step a) Write a balanced hemical Equation for the overall reaction b) Draw the arrow diagram for Steps and c) Provide the rate equation for O formation ( r ) O d) For this part only. The reaction occurs in a gas phase STR reactor filled with solid catalyst pellets, maintained at 500 K and 0 atm. The reaction occurs on catalyst pellets and the density of active sites, which is the number of sites per reactor volume {[S T *]/V R }, is 000 sites (L - ). The catalyst surface is covered by O-S as the most abundant surface intermediate (MSI) beca use there is an excess amount of oxygen. The feed contains 0% HHO and 90% O and the total flow rate of the feed is 00 mol/h. The fractional conversion of the limiting reactant is 50 %. Determine the volume of the reactor. Table. Kinetic Parameters at 500 K Step Forward Step Reverse Step f r (min) -.5 mol (L min) - 6 (min) - -

4 mol (L min) mol (L min) - 3 (min) mol (L min) - 5 (min) - a) Write the hemical Equation for the overall reaction. O H H O O H b) Provide the stoichiometric coefficients (σ) for Steps -5. Step : Step : Step 3: Step 4: Step 5: c) Draw the arrow diagram for the reaction sequence. d) Provide the rate equation for O formation. r r r r r r r σ σ σ O H H O 3 f f 4 f 4 r ro r3f 3 4 [S ] r r [ H O O S ] O 3 f 3 f [S * ] T d [ H O O S ] f [ H H O ][O S ][S ] 3 f [ H O O S ][S ] 0 dt [ H H O ][O S ] [ H H O ] f f f [ H O O S ] [O ][S ] f [O S ] [ O ][S ] r O [ O S ] [S ] [S ] 5f K 5 5r 3 f 3 f r O d [ H S ] f [ H H O ][O S ][S ] 3 f [ H O O S ][S ] 4 f [ H S ] 4 r [ H ] [S ] 0 dt d [ H H O ] f f f [ H S ] f [ H H O ] [O ][S ] 3 f [O ][S ] 4 f [ H S ] 4 r [ H ][S ] 0 d t r 3 f r [ H H O ] f f f [ H H O ] [O ] [O ] [ H ] f 3 f 4 r r 3 f r [ H S ] [S ] 4f Total site balance: 0.5

5 [S * ] [S ] [ H S ] [ O S ] [ O S ] [ H O O S ] T [ H H O ] f f f [ H H O ] [ O ] [O ] [ H ] f 3 f 4 r r 3 f r O [ H H O ] f f f [S * ] [S ] [S ] [O ][S ] [S ] [ O ][S ] T K 4 f r 5 3 f r 0.5 [S ] 0.5 [S * ] T [ H H O ] f f f [ H H O ] [O ] [O ] [ H ] f 3 f 4 r r 3f r O [ H H O ] f f f [O ] [O ] K 4 f r 5 3 f r [S ] 0.5 [S * ] T [ H H O ] K [O ] [ H H O ] K [O ] [ H ] f f 4 r O f K [O ] [ H H O ] K [O ] K 4 f 5 3 f [ H H O ] [S ] f f r r [O ][S ] O 3 f 3 f [S * ] 3 f r T [ H H O ] f f [O ] 3 f 3 f r r r [S * ] O 3 f T 0.5 [ H H O ] K [O ] [ H H O ] K [O ] [ H ] f f 4 r O f K [O ] [ H H O ] K [O ] K 4 f 5 3 f e) For this part only. The reaction occurs in a gas phase STR reactor filled with solid catalyst pellets, maintain at 500 K and 0 atm. The reaction occurs on catalyst pellets and the concentration of active sites (S T *) on the solid catalyst pellets is 000 sites (g - of catalyst). The catalyst surface is covered by O-S as the most abundant surface intermediates (MSI) because there is an excess amount of oxygen. The feed contains 0% HHO and 90% O and the total molar feed flow rate is 00 mol/h. The fractional conversion of the limiting reactant is 50 %. Determine the mass of catalyst inside the reactor. Table. Kinetic Parameters at 500 K Step Forward Step Reverse Step f r (min site) -.5 mol (L min site) (min site) mol (L min - site) mol (L min site) (min site) mol (L min site) - 5 (min site) -

6 [ H H O ] K [O ] [ H H O ] r r [S * ] [S * ] f f O 3 f T T K [O ] K [O ] [ H H O ] K [O ] [ H H O ] r r [S * ] [S * ] f f O 3 f T T K [O ] K [O ] [ H H O ] [ H H O ] [ H H O ] f r [S * ] L [S * ] [S * ] O T T T K [O ] site m in site m in L [O ] m in site [O ].5 L.5 L site m in Exit stream composition: F 5 / h 0 ( X ) H H O h F 9 0 / h.5 / h 0 (9 X ) / h O h FO FH 5 / h 5 / h 0 ( X ) 5 FH H O h h [ H H O ] v ( ε X ) v ( ε X ) L L 4 0 ( ( 0.5 )(0.5 )) h F 0 (9 X ) O h h [O ] v ( ε X ) v ( ε X ) L L 4 0 ( ( 0.5 )(0.5 )) h L a tm K n R T h K L v 4 0 P 0 a tm h F F r V 0 O,0 O O R F r V O O R [ H H O ] site F r V 6 [S * ] M g site m in L g c a ta lyst [O ].5 O O R T c a ta lyst L s ite [S * ] M g T h s ite m in L g c a ta lyst L M.5 8 g c a ta lyst c a ta lyst

7 Problem 3 (Final Exam 0). Oxidation of 3 H 6 proceeds via the following elementary steps in the presence of a gas P that poisons the catalyst surfaces by dissociative adsorption of P on catalytic sites (S). Step Step Step 3 Quasi-equilibrated Irreversible step Reversible step Step 4 Quasi-equilibrated a) Write the hemical Equation for the overall reaction. b) Provide the stoichiometric coefficients (σ) for Steps -3. Step : Step : Step 3: c) Draw the arrow diagram. Remember to include all steps above. d) Derive the rate equation of O consumption from the sequence of elementary steps, if is the Most bundant Surface Intermediates (MSI). e) Provide a condition in which the rate equation derived in (d) becomes identical to the one derived based on QE assumption on step 3 and is the Most bundant Surface Intermediates (MSI). f) If is the Most bundant Surface Intermediates (MSI) and step 3 is irreversible, how does rate depend on O and 3 H 6 pressures? Provide a reason to the dependence. What is the effective rate constant? g) Setch the reactant and product energy levels for Step 4 in the following diagram (Enthalpy vs. Reaction oordinate): Enthalpy Reaction coordinate

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12 Problem 4 Reaction ) O H O H O Reaction ) O H HHO T e m p e ra tu re (K ) K P (R e a c tio n ) K P (R e a c tio n ) (b a r - /3 ) (b a r - ) Reaction and Reaction above were carried out in an isothermal, isobaric PBR reactor operated at essentially equilibrium conversion with pressure held at bar. The feed consisted of 50 mol/h of O and 50 mol/h of H. In the case of parallel reactions, extent of reactions (, ) are used instead of fractional conversion, and the extent of reaction and carry the units of the number of mol of O reacted for Reaction and Reaction, respectively. ssume ideal gas behavior. a) Formulate a stoichiometric table in terms of extent of reactions (, ) that are based on amount of O reacted in reactions and. b) Using the stoichiometric table, determine the mol fraction of HHO in the product stream, when the reactor is operated isothermally at temperatures of 700K as well as 000K. p Rx c) Temperature dependence of K P is given by Van t Hoff s equation d ln K Based on this correlation, identify if Reaction ) and Reaction) above are endothermic or exothermic? The selectivity towards HHO is defined as S = number of mol of O reacted to form HHO / the total number of mol of O reacted What is the selectivity for the reaction systems in (b) at 700K and 000K? dt H RT ( T )

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14 Problem 5. onsider the following elementary vapor phase reactions that occurring in a constant volume, isothermal BSTR: + B + a) Find the expression that describes the change in the concentration of with respect to the change in the concentration of B in terms of the rate constants. dn dt dn dt dn dn B B N V N V

15 B d d b) What is the instantaneous selectivity of with respect to, s(/), when X is 0.3, 0.5, and 0.7? omment on the trend. r r,, r r, r r c r r ) / s( s(/) is always a constant and independent of X. c) Which types of ideal reactor would you use to optimize the overall yield of B with respect to, Y(B/)? Explain in less than three sentences. Since s(/) is independent of average concentration, it does not matter.

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