EXAM I Fall 2019 - Solution 2

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Chemistry

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CHEG332 Fall 2019 Exam 1 Name______________________ 1 Midterm Exam 1 CHEG 332 Fall 2019 October 3 rd , 2019 In-class Instructions : Read the examination questions carefully before you begin to work on the problems. Organize your thoughts and your written solution. State all assumptions and complete the problems given the data in each part. Partial credit will be given and key steps in the problem solution should be clearly stated along with any final answer . Use quantitative reasons in your response to the exam questions whenever possible. Make sure to draw a diagram describing the physical system being analyzed and indicating all reaction streams and the name of all the important variables for the problem. Good Luck. Time: 75 Minutes I certify that I have read these instructions and have adhered to them and the honor code of the University of Delaware (http://www1.udel.edu/stuguide/17-18/code.html#honesty). Signature: ______________________________________________________________________ Grade: Problem 1 /45 Problem 2 /55 Total /100

CHEG332 Fall 2019 Exam 1 Name______________________ 2 Useful unit conversions and other information Pa = N/m 2 J= N-m 100 cm = 1 m 1 W = 1 J/s 1 L = 0.001 m 3 R=8.314 J/K-mol 1 L = 0.264 gallons Common integrals (from Integral-Table.com) Common derivatives (where u=f(x))

CHEG332 Fall 2019 Exam 1 Name______________________ 3 Problem 1. To earn some money for a winter vacation, you have decided to pursue a side hustle this semester. You and a few friends decide to build a couple of 10 L batch reactors in your dorm rooms to try out different ways to convert sugar ( “ A ” ) to ethanol ( “ B ” ). Each 1 molecule of A generates 2 molecules of B . Assume this is a liquid phase isothermal reaction represented by a first-order rate expression with a constant of 8.1 x 10 -5 h -1 . You look up the solubility limit of A and find that 100 mM is as high as you can go at room temperature. Assume the reactors are well-mixed. a) (21 points) Your friend takes a relaxed approach and lets their batch reactor go with no intervention after starting it with 100 mM A . What concentration of B do they have at the end of the semester, 10 weeks from the start ? Draw a diagram. Show all your steps including the analytical solution to the definite integral by hand, then plug in provided values.

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CHEG332 Fall 2019 Exam 1 Name______________________ 4 b) (12 points) You notice evaporation in the reactor in your room and decide to take a more ambitious approach to keep the volume constant . You obtain pumps, tubing, and a container for an inlet stream to your reactor . You initially fill the 10 L batch reactor to 8 L of 100 mM A. You then continuously pump 0.2 L/week of 100 mM A into the reactor, succeeding in maintaining constant volume. Draw a diagram. Write out the mole balance for this system and simplify your differential equation to the following form : 𝑑? 𝑑? + ?(?) ∙ ? = ?(?) . You do not have to solve the ODE.

CHEG332 Fall 2019 Exam 1 Name______________________ 5 c) (12 points) The demand for product B at 10 mM is high enough that you consider building a CSTR . Assume you would have 0.2 L/week going in and out of the reactor , 100 mM A in the feed , and the same rate expression and rate constant as above. Draw a diagram. How large would the reactor volume have to be to produce 10 mM B?

CHEG332 Fall 2019 Exam 1 Name______________________ 6 Problem 2. Waste water containing a contaminant A is flowed at volumetric flow rate v o =100L/h with concentration of C Ao = 10 mol/L into a CSTR with a volume V=1000 L operated at room temperature ( 298 K ). This CSTR serves as a holding tank where A decomposes to product B , a benign molecule that is safe for disposal. The decomposition of A to B (A → B) follows first order reaction kinetics (-r A =kC A ) with a rate constant k (298 K) =0.05 h -1 and activation energy E a =40 kJ/mol . New regulations require that the concentration of A in the effluent from the system be reduced to a lower value than can be achieved with the current CSTR. Given the small space in which the system currently operates, there is little room for significant changes to the process, you and your team investigate options for meeting this new requirement, tackling the calculations for each approach below. a) (15 points) You first examine if changing the temperature at which the current CSTR is operated could be an effective solution, which would not require any additional capital investments in new equipment. Draw a diagram. What is the concentration of A in the effluent from the CSTR if operated at 340K ?

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CHEG332 Fall 2019 Exam 1 Name______________________ 9 d) (10 points) A technician in your group suggests adding a small PFR after the single CSTR from part a) to achieve the low concentration of A that is required for meeting the new regulatory guideline. Assume that C A in the effluent from the CSTR is 0.2 mol/L (note, this is NOT the answer to part a)). Draw a diagram of this system of CSTR followed by PFR, operated at T=340 K. Write the design equation that would allow you to solve for the volume of PFR required to achieve a system effluent concentration of C Aeffluent = 0.05 mol/L , including the explicit assignment of the boundary conditions with numerical values . Do not solve.

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CHEG332 Fall 2019 Exam 1 Name______________________ 6 Problem 2. Waste water containing a contaminant A is flowed at volumetric flow rate v o =100L/h with concentration of C Ao = 10 mol/L into a CSTR with a volume V=1000 L operated at room temperature ( 298 K ). This CSTR serves as a holding tank where A decomposes to product B , a benign molecule that is safe for disposal. The irreversible decomposition of A to B (A à B) follows first order reaction kinetics (-r A =kC A ) with a rate constant k (298 K) =0.05 h -1 and activation energy E a =40 kJ/mol . New regulations require that the concentration of A in the effluent from the system be reduced to a lower value than can be achieved with the current CSTR. Given the small space in which the system currently operates, there is little room for significant changes to the process, you and your team investigate options for meeting this new requirement, tackling the calculations for each approach below. a) (15 points) You first examine if changing the temperature at which the current CSTR is operated could be an effective solution, which would not require any additional capital investments in new equipment. Draw a diagram. What is the concentration of A in the effluent from the CSTR if operated at 340K ? liquid phase in c 3401K A B GA ra k CA w k Ltd _ku7 exp th f osh7expfCfITIImoe.I a d FEE I Fiori v CAow CAI vk.GE G w Cau k CA Ca Virtu Crow CA CAI V k t U comin

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alum Ea I i k kha Xa XA kik Xs o 367 h y Fok 3.67 20 785 100 L l t 367 It T o 367 h l Cf Cao Exa 10mL 1 70.785 2.14110

CHEG332 Fall 2019 Exam 1 Name______________________ 7 b) (20 points) An intern in your group suggests splitting the one tank effectively into two tanks by inserting a baffle down center of the original tank and connecting the resulting two half- sized ‘tanks’ with a pipe. The modification will make the system two CSTRs in series that are each half the volume of the original single CSTR . Draw a diagram of this effective system of two CSTRs in series. Operating the system at room temperature , what is the concentration of A in the effluent from the system with this approach? Justify your answer both quantitatively and graphically on graph below. D E CSR insures 72 l Aw Xan ra Xan J I Eastman Constante CAL CAz Wo u also can solve D E s for single Tks sequentially CA CA U 10M 1004in 4kt U so L o 05h I t 0o CA Y mid CA CA U L 8M 1004in 2 Ktv 5002 on 05h I t 00 6 ymo Xa CAO CA lo 87mL o z Cao Lo Mof Xa a Ch o CA2_ 1a 6.4M 0.36 Cao

CHEG332 Fall 2019 Exam 1 Name______________________ 8 c) (5 points) Can the same graph from part b) of -1/r A vs. conversion be used for the system described in part a)? Briefly (~1-2 sentences) justify your answer. 0 5 10 15 20 25 30 35 40 45 0 0.2 0.4 0.6 0.8 1 1/-r A Conversion of A U Fo I Pmo areal area 2 z f Ao Fao waka U 2 L2 O S v e 2107 too SOO L V z O 36 0 2 l 3 Go 700 480L 2500L No Since ra k CA g ra function oft since part a F 340K and part b F 298k VA will be different for each system and same graph of Ira vs Xa cannot be used

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alternatVM I o o s d v dE Edi fYdu T o n ra k CA O 05 DE for system V2 Voz f dia o 2 CA with Cp as variable

CHEG332 Fall 2019 Exam 1 Name______________________ 10 e) (5 points) Someone on the team suggests adding a second CSTR after the single CSTR from part a) to achieve the lower concentration of A in the effluent. For achieving the same final concentration of A in the effluent from the system of reactors, would you expect this additional CSTR to be larger, smaller, or the same size as adding a PFR? Briefly justify your answer with quantitative arguments. Cbo en ralCAD cm racers 2cg FR Y U 2 PPR CSR operates at effluent concentration fixing it at a low reaction rate relative to PFR PFR rate varies down its length staring at highest rate of inlet and decreasing to lowest rate at outlet The rate outlet of FFR is the rate which Csm operates nooo Volume required to achieve same conversion will always be higher for CSTR than PFR Xa out of XA pectment ppp FAS Vegas Foto XA RA XA XA Yan Texas

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