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Q1: Given the discussion on the different reactor types and the assumptions that are used in developing mole balances for each reactor type, answer the following: 1) (5 points) State an assumption that is the same between a batch reactor and a CSTR. 2) (5 points) State an assumption that is different between a batch reactor and a CSTR. 3) (5 points) State an assumption that is the same between a CSTR and a PFR. 4) (5 points) State an assumption that is different between a CSTR and a PFR.See Answer
Q2: Find the conversion after one-hour in a batch reactor for (15 points) A R -r_{A}=3 C_{A}^{0.5} \quad \text { aqol/lit/hr } \quad \text { CAQ=1.5 mol/lit }See Answer
Q3: The process shown in Figure P3.91 is the dehydrogenation of propane (C,Hg) topropylene (C,H) according to the reaction \mathrm{C}_{3} \mathrm{H}_{8} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6}+\mathrm{H}_{2} The conversion of reactor at F, is 40%. The product flow rate F, is 50 kg, mol/hr.propane to propylene based on the total propane feed into the (a) Calculate all the six flow rates F, to F, in kg mol/hr. (b) Whal 18of propane in the reactor based on the freshpropane fed to the process (F,). See Answer
Q4: A reaction of great social significance is the fermentation of sugar with yeast. Thisis a zero-order (in sugar) reaction, where the yeast is a catalyst (it does not enterthe reaction itself). If a 0.5-L bottle contains 4 g of sugar, and it takes 30 min toconvert 50% of the sugar, what is the rate constant?See Answer
Q5: A batch reactor is designed to remove gobbledygook by adsorption. The data are asfollows: What order of reaction does this appear to be? Graphically estimate the rateconstant.See Answer
Q6: ammonia is synthesized from dinitrogen and dihydrogen in the presenceof a metal catalyst. Fishel et al. used a constant volume reactor systemthat circulated the reactants over a heated ruthenium metal catalyst andthen immediately condensed the product ammonia in a cryogenic trap [c.T. Fishel, R. J. Davis, and J. M. Garces, J. Catal. 163(1996) 148]. A schematic diagram of the system is: From the data presented in the following tables, determine the rates ofammonia synthesis (moles NH3 produced per min per gcat) at 350°Cover a supported ruthenium catalyst (0.20 g) and the orders of reactionwith respect to dinitrogen and dihydrogen. Pressures are referenced to298 K and the total volume of the system is 0.315 L. Assume that noammonia is present in the gas phase. See Answer
Q7:The gas phase reaction A + B → C occurs in a flow reactor. The rate law is given below. KCACB -TA 1 + KCA The initial concentration of A is 1 M and the initial concentration of B is 1.5 M in the feed. k = 0.1 min¹ M-¹ and K = 2.5 M¹¹. The inlet volumetric flow rate is 2 L/min. Assume that the reactors are isothermal and isobaric./na. If the reaction takes place in a CSTR, what is the volume of the CSTR that is needed to achieve 70% conversion? b. If the reaction takes place in a PFR, what is the volume of the PFR that is needed to achieve 70% conversion? For the remainder of this problem assume that there is an inert gas in the feed with concentration c₁ = 4 M. c. If the reaction takes place in a CSTR, what is the volume of the CSTR that is needed to achieve 70% conversion? d. If the reaction takes place in a PFR, what is the volume of the PFR that is needed to achieve 70% conversion? e. If the reaction takes place in a PFR, what is the volume of the PFR that is needed to achieve 70% conversion if K = 0.25 M¹¹?See Answer
Q8:The gas phase reaction A + B → C follows an elementary rate law and occurs in a 1 m³ CSTR. The inlet volumetric flow rate is 0.5 m³ min¹¹ and the entering concentration of A is 1 M. The reaction occurs isothermally at 300K. For an equimolar feed of A and B, a 20% conversion is achieved. When the reaction is carried out adiabatically, the exit temperature is 350K and the conversion is 40%. The heat capacities of A, B, and C are 25, 35, and 60 kJ/(mol*K), respectively and are independent of temperature. It is proposed to add a 2nd CSTR of the same size in series with the first CSTR. There is a heat exchanger attached to the 2nd CSTR with UA = 4.0 kJ/(min*K), and the coolant fluid enters and exits the heat exchanger at the same temperature of 350K. Assume all reactors operate isobarically. A. What is the rate of heat removal needed for isothermal operation in the first CSTR? B. What is the final conversion at the exit of the second reactor if the first reactor is operated isothermally? C. What would the final conversion be if the second CSTR were replaced with a 1 m³ PFT with Ua = 10(kJ/(m³*min*K)) and T₁ = 300K. D. A chemist suggests that the reverse reaction cannot be neglected. From thermodynamics, we know that Kc = 2 L/mol at 310K. What conversion can be achieved if the entering temperature to the PFR in part C is 300K and Ta = 300K? You may assume that the first CSTR achieves a conversion of 0.2 for the problem.See Answer
Q9:Question 3 1 a. Molecular hydrogen, H₂, undergoes dissociative chemical adsorption (chemisorption) on Ni- metal surfaces via an activated process. Experimentally, it is found that the enthalpy change for the chemical adsorption (AHca) is -148 kJ mol-¹ and the activation energy barrier, Ead is 12 kJ mol-¹ i. Explain what are meant by the following terms (one sentence for each): dissociative chemical adsorption activated adsorption process. (3 marks) ii. Describe how you can tell from a Lennard-Jones plot whether a process is activated or not. (2 marks) iii. Figure 3.1 shows a partially complete schematic potential energy profile (Lennard-Jones plot) to represent the chemical adsorption of H₂(g) onto the Ni metal. Given that Ead = 12 kJ mol-¹, complete the potential energy profile by adding a second curve, with appropriate labels, to represent the physical adsorption of H₂(g) onto Ni. Include arrows and labels on your sketch to indicate the values Ead, AHca, and Edes. (Note a copy of Figure 3.1 is provided in the Assessment area as a png file. You should paste a scanned image of your completed plot into your answer). (5 marks)/npotential energy (not to scale) O HH 1+1 "Ni Ni 2*Ni + H(g) + H(g) distance from surface Figure 3.1 A partially complete schematic potential-energy profile (Lennard-Jones plot) which shows the chemical adsorption of H₂(g) onto the Ni metal. iv. Briefly explain how your plot accounts for the fact that adsorbed hydrogen atoms are formed on the Ni surface without prior dissociation of molecular hydrogen in the gas phase. (No more than 100 words). (4 marks) v. Write an expression for the activation energy for desorption (Edes) of hydrogen molecules from the Ni surface and calculate the value of Edes. (3 marks)/nb. The selective oxidation of butan-2-one, B, produces diacetyl, D, over a vanadium phosphorus oxide catalyst by way of the following reaction: CH3COC₂H5 (g) + O₂(g) = CH₂ COCOCH3(g) + H₂O(g) B D Under certain experimental conditions the reaction appears to involve a Langmuir-Hinshelwood mechanism, with non-dissociatively adsorbed reactants: B(g) = B(ad) O2(g) → 0₂ (ad) B(ad) + O₂ (ad) → 'free 'products where 'free' products represents CH3COCOCH3(g) + H₂O(g) which both desorb as quickly as they are formed. dрB dt dpo2 dt i. Identify which of the reactions (3.1 -3.3) in the mechanism is the rate-limiting step if the reaction were to obey a Langmuir-Hinshelwood mechanism. (1 mark) ii. Write down the rate equation for this reaction and hence show that the theoretical rate equation is given by: = ke bврвbо₂Ро₂ (1+bBPB +bo₂po₂) ² (3.1) where ke is the theoretical rate constant. You should explain why it is not necessary to include terms for the products in your equation. (7 marks) (3.2) (3.3) (3.4)/niii. At high partial pressure of butan-2-one, the experimental rate equation is given by: dpo2 dt PO₂ PB where KR is the experimental rate constant. Show how this is consistent with the theoretical rate equation (Equation 3.4). [Hint: Remember to relate KR to ke in your answer.] (4 marks) iv. What other experimental condition would enable reduction of the theoretical rate equation to be consistent with this experimental rate equation (Equation 3.5) (one sentence)? (1 mark) dрB dt = KR (3.5)See Answer
Q10:1. A mixture of benzene (A), toluene (B) and xylene (C) is separated by a set-up of 3 distillation columns and a mixer as shown in Figure 1 below. At steady state, the data in Table 1 are taken. Calculate the values for all the unknowns Table 1 and fill in the values in the table. Give all your answers to an accuracy of 2 decimal places. Show your working clearly in your answer sheet. Material Streams kg/h M1 (Feed) Components A B C M1 100.0 45.0 30.0 25.0 Column 1 M2 11.83 M2 M3 M3 Figure 1 Column 2 Table 1 M4 M5 2.73 0 M4 M6 Composition in wt% 2.5 M5 25.0 Column 3 M6 10.15 M7 M8 M7 32.0 6.25 M8 4.17 (50 marks) 192 ZSee Answer
Q11:2. Methanol is produced by reacting a mixture of carbon dioxide and carbon monoxide with hydrogen over a catalyst. The reactions are: CO(g) + 2H₂(g) → CH₂OH(g) CO₂(g) + 3H₂(g) → CH3OH(g) + H₂O(g) The composition of the fresh feed is 14 mol % CO2, 14 mol % CO, 70 mol % H2 and 2 mol % CH4. The fresh feed is mixed with a recycle stream before entering the reactor. The single pass conversion of CO and CO2 are 20% each. The product gases are cooled to condense out all the water and methanol. All the unreacted gases are then recycled. Part of the recycle stream is purged to keep the content of the inert CH4 in the reactor feed to 5 mol %. It is desired to produce 100 mol/s of methanol. a) Sketch the Process Flow Diagram (PFD and indicate all the components of each stream. (18 marks) b) Determine the following: i) molar flow rate of fresh feed, ii) molar flow rate of the stream at the reactor inlet, iii) molar flow rate and composition of the purge stream. End of paper (32 marks)See Answer
Q12:3.3 Calculate the size of a PFR and MFR for the following reaction: a) A R We assume that the reaction is elementary and takes place in the liquid phase, XA=0.98 and, (30) b) A 2R We assume that the reaction is elementary and takes place in the gas phase, XA=0.90 (30) For a) and b) we assume that: AG298-20000 J mol-¹ AH298 -90000 J mol-¹ T = 335K Cp are considered constant over the temperature range 298-335 K Cao = 1 mol m 3 FAO = 50 mol s¹ For the forward reaction: E₁ = 60000 J mol-¹ ko = 10¹⁰ S-1See Answer
Q13:< 11:45 CSTR Report (Group 5) FINAL (1) 3 of 13 Then substitute Equation 8 in Equation 7: = X₁ CAR KCACE The volumetric flow rate of sodium hydroxide and ethyl acetate will be adjusted to be equal, and since we have the same molar flow rate. Cao Cao and X₁ -XB From Equation 5: C, CAO (1-X) and C- Cao (1-X) - Co (1-XA) KC) (1-XA)² TRCA (1-X₁² - Linearizing the Arrhenius equation: Arrhenius equation: K(T) = Ae-E/RT Linearized equation: Ln (ka) =+Ln (A) Where, A-pre-exponential factor or frequency factor, E- activation energy, J/mol or cal/mol, R = gas constant = 8.314 J/mol K=1.987 cal/mol K, T-absolute temperature, K - Calculate sodium hydroxide conductivity: ()=0.195[1 +0.0184(T-294)]CA - Calculate initial concentration of NaOH and ethyl acetate after mixing using dilution equation (₁) before = (C₂0) after *(-)- Ac()= 0.07[1+0.0284(7-294)] define terms Sm Where, T: temperature (K), CA: Sodium hydroxide concentration in mixed feed (before reaction) (mol/L) - Calculate acetate conductivity: %error Theoretical-Experimental x 100 Theoretical Eq. (15) [9] Where, T: temperature (K), Ce: Sodium acetate concentration in product if the limiting reactant undergoes full conversion (mol/L) - Calculate sodium hydroxide concentration at steady state: Calculate standard deviation . Theoretically Eq (9) must be CA,SS at steady state CASCAD Eq. (16) [9] wrong, not time dependent Where, Ag Conductivity at inlet before reaction started (s/cm), A conductivity at any time (s/cm) and A: Conductivity if the limiting reactant undergoes full conversion (s/cm) -Percentage error: Eq (10) combine table 1 and 2 together Eq. (11) [7] Eq. (12) 303 XXX-M³ 8-1 Eq. (18) [11] Where: S is Standard deviation, Σ is Summation, X is Individual score, is the data points (conductivity points), M is mean of all scores, n is sample size (number of scores). Objective 1: Study the effect of total volumetric flow rate on the reaction conversion 311.7 Eq. (13) [8] Q Eq. (14) [9] Using dilution equation (eq (13)) to calculate the concentration of A and B after mixing ( CA and Co) (C₁8₁)before (C₂₁) after 0₂ = 0₁ +08 Adjust the volumetric flow rate to be 0 = 08 → 0₁=20₁ (0.1 x 0) (CAO X 20A) mol Cao = Cho 005 2 → Determining the reaction rate constant theoretically: From literature the reaction rate constant is provided to be as follows: [12] 2.66 x 10-1 Eq. (17) [10] Table (1): Rate Constant of the Saponification Reaction at Different Temperatures. Temperatures (K) Rate Constant (L. mol¹x¹) 1.62 x 10-1See Answer
Q14:Experiment 2: Plug Flow Reactor 1. Introduction In a tubular reactor, the feed enters at one end of a cylindrical tube and the product stream leaves at the other end. The long tube and the lack of provision for stirring prevents complete mixing of the fluid in the tube. Hence the properties of the flowing stream will vary from one point to another in axial directions. In the ideal tubular reactor, which is called the "plug flow" reactor, specific assumptions are made about the extent of mixing and velocity profile. The absence of longitudinal mixing is the special characteristics of this type of reactor. It is an assumption at the opposite extreme from the complete mixing assumption of the ideal stirred tank reactorSee Answer
Q15:Problem 3. Residence time distribution (Total: 20 Marks) Dr Doolittle carries out the liquid-phase first-order reaction A → B with reaction rate constant, k = 1h-¹, and inlet reactant concentration, CA,0 = 1 mol/m³ in a reactor cascade consisting of two CSTRs in series of equal volume, each one 1 m³ (overall cascade volume V = 2 m³). The overall reactor cascade space time is 0.67 h. Overnight her competitor, Dr Darkforce, tampers with the reactor system to lower its productivity. The morning after, Dr Doolittle observes that the reactant conversion has dropped. She gets suspicious, so she stops the reaction and performs a pulse tracer experiment, finding the following residence time distribution. E, h-¹ -1 0.64 0.5 0.4 0.3 0.2 0.1 Ө -0.1 1 2 RTD 3 t, h 4 2 6 7 8 The measured RTD is composed by a sharp peak (E₁ (t)) at t = 0 h, where the area under this peak is 0.33 (blue arrow) followed by an orange broad peak E₂. The values of E₂ (t) are reported in the table below. a) Evaluate the conversion of the reactor cascade as designed by Dr Doolittle, before Dr Darkforce's tampering. [4] b) What do you think Dr Darkforce did to the reactor cascade? Suggest a compartment model that fits quantitatively the RTD that Dr Doolittle measured and calculate the parameters of this compartment model.See Answer
Q16:Problem 1. Non-isothermal reactor (Total: 35 Marks) The elementary, irreversible gas-phase reaction A B+C is carried out in an adiabatic catalytic packed bed reactor, which behaves as a pseudo-homogeneous PFR without any internal or external mass transfer resistances. Pure A enters the reactor at a volumetric flow rate of 20 L/s, at a pressure of 10 atm, and a temperature of 450 K. The reaction rate constant is given by -0.133-exp(450K7 L kg a) Assuming that there is no pressure drop along the reactor, plot the conversion and temperature along the reactor packed with 50 kg catalyst and calculate the catalyst weight required for a 75% conversion. [11] Next, consider that pressure drop exists along the PFR. The Ergun equation, -G1-150(1-0)µ D₂ for varying gas density gives dP dz pgp P TOFT p=POPOT Fr dP dW = q₂T_ Po (1+x) 2 Cooling fluid: Heat capacity Inlet temperature, where a, is a parameter dependent on the system operating conditions and characteristics of the catalyst used &=2.P.RO (17) (2) (1) 150(1-0)+1.750 D₂ +1.750) (1) -5 (3) A(1-0) Ifa, = 0.0075 kg: ¹for the catalyst particles, the reactor and the conditions used b) Plot the temperature, conversion and pressure along the length of the reactor packed with 50 kg catalyst. How does reactor behaviour change as compared to a)? J s-kgk [12] A heat exchanger is added to the PFR to keep the outlet temperature at 700K, as above this temperature undesired reactions occur. For the heat exchanger Ua P₂ Cong3 J/gK Tooting 400 K. 1 Po (4) where, pe is the bulk density of the catalyst (kg/m'eactor), a is the heat-exchange area per unit volume of reactor (m²reactor/acter) and U is the overall heat-transfer coefficient (J/s-m²actar K). c) Calculate the outlet temperature of the coolant and its flowrate for co-current heat exchange, ignoring pressure drop. Plot the conversion, the temperature of the cooling fluid and the temperature of the reaction mixture as a function of catalyst weight. [12] Additional Information Activation energy: E = 31.4 kJ/mol Heat capacities: C = 40 J/mol K, Cas= 25 J/mol K, Cpc = 15 J/mol K Heats of formation at 273K: H=-70 kJ/mol, H₂= -50 kJ/mol, H = -40 kJ/molSee Answer
Q17:Problem 2. Internal and external mass transfer (Total: 15 Marks) The first order, gas-phase catalytic reaction A-B with reaction rate constant, k = 0.017-10 cm/s, catalyst surface area, S, 150, and catalyst density, p. = 3.95 g/cm³) takes place in a spherical catalyst pellet of radius, R=2.5 cm. The effective diffusivity of A in the pellet is, D, = 0.015 cm²/s. The reactant A is carried in a stream at a bulk concentration, CA = 10 mol/cm³. The concentration of A at the surface of the pellet is, C3-10-5 mol/cm². a) Determine the value of the external mass transfer coefficient. [5] b) Calculate the conversion achieved in a packed bed reactor, where the catalyst pellets operate with the same internal and external resistances as above. Assume the reactor operates as a pseudo-homogeneous PFR with a space time of 30 s, an inlet reactant concentration, CA= 10 mol/cm³, bed void fraction = 0.4 and negligible pressure drop. [10]See Answer
Q18:Problem 4. Lab experiment - Adiabatic Batch Reactor (Total: 30 Marks) In the lab experiment, you performed the reaction of sodium thiosulphate with hydrogen peroxide in a batch reactor. 2 Na2S2O3 + 4H2O2 → Na2S306+ Na2SO4 + 4H₂O You mixed different volumes of solutions of 1 M Na2S2O3 and 1 M H2O2 keeping the total volme of reaction mixture at 120 ml, and you obtained the temperature profile of the reaction mixture with time as the reaction progressed. Using values of heat of reaction, preexponential factor and activation energy from [1], assuming the reaction rate law is first order with respect to sodium thiosulphate and first order with hydrogen peroxide and making any other suitable assumptions simulate the temperature profiles that you obtained in 3 different experiments (mixing ratio 1, 2 and 3). More specifically: a) Show the relevant mass and energy balances that describe this system. [9] b) Plot the simulated and the experimental profiles of temperature vs time (for mixing ratio 1, 2 and 3). [9] c) Perform a sensitivity analysis, i.e., (manually) adjust the values of heat or reaction, preexponential factor and activation energy. Your goal here is to maximise the agreement between the simulations and one of experiments above (i.e., mixing ratio 1, or 2 or 3). Show the plot of the simulated and the experimental profiles of temperature vs time with the best agreement (i.e., for the optimised values of the above parameters) for your chosen experiment. Discuss your results. d) State clearly and justify the main assumptions you have made. [9] [3]See Answer
Q19:1. The reaction B → C is carried out in a flow reactor under isothermal conditions. The inlet volumetric flow rate is 10 L/h and the inlet molar flow rate of B is 4 mol/h. The volumetric flow rate changes little (~o). Calculate the CSTR and PER reactor volumes needed to consume 90% of B, assuming the reaction rate, r is: (a) r=k, with k= 0.05 mol/h-L (b) r=kCB, with k = 1x104 /s (c) r= KCB², with k = 3 L/mol-h What if you instead used a 2000 L batch reactor loaded with the same feed material? How long would it take to consume 90% of B, assuming (d) r = k, with k= 0.05 mol/h-L (e) r=kCB², with k = 3 L/mol-hSee Answer
Q20:2. There are initially 500 rabbits (x) and 200 foxes (y) on Old McDonald's Farm. Use Polymath to plot the number of foxes and rabbits as a function of time for a period of up to 500 days. In addition, plot the number of foxes versus the number of rabbits. The predator/prey relationships are given by the following set of coupled ordinary differential equations: =k₁x-k₂x-y dx dt dy=k₂x-y-kay dt Where: Constant for growth of rabbits k₁ = 0.02 day-¹ Constant for death of rabbits k₂ = 0.00004 / (day x number of foxes) Constant for growth of foxes after eating rabbits k₂ = 0.0004 / (day x number of rabbits) Constant for death of foxes k4 = 0.04 day¹ Be sure to "Explain why..." and "Discuss which..." I want you to think a little about what your results mean. Not just what happens (ie. rabbits increase then decrease) but why (ie. do the rabbits starve to death or are they eaten by the foxes?) For help with Polymath, see the tutorials posted on Blackboard (available in the Documents section) What do your results look like for the case of k₂ = 0.00004/(day × number of rabbits) and trivel = 800 days? Again plot x and y versus time and y versus x.See Answer

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