Mole Balances in Chemical Reaction Engineering

This chapter is from the book

Elements of Chemical Reaction Engineering, 6th Edition

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This chapter is from the book

This chapter is from the book 

Elements of Chemical Reaction Engineering, 6th Edition

Learn More Buy

Questions, Simulations, and Problems

I wish I had an answer for that, because I’m getting tired of answering that question.

—Yogi Berra, New York Yankees
Sports Illustrated, June 11, 1984

The subscript to each of the problem numbers indicates the level of difficulty, that is, A, least difficult; B, moderate difficulty; C, fairly difficult; D, (double black diamond), most difficult. A = • B = ▪ C = ♦ D = ♦♦ For example, P1-5_B means “1” is the Chapter number, “5” is the problem number, “_B” is the problem difficulty, in this case B means moderate difficulty.

Before solving the problems, state or sketch qualitatively the expected results or trends.

Questions

Q1-1_A QBR Questions Before Reading. Research has shown (J. Exp. Psychol. Learn. Mem. Cogn., 40, 106–114 (2014)) that if you ask a question of the material before reading the material you will have greater retention. Consequently, the first question of every chapter will have such a question on that chapter’s material. For Chapter 1, the question is “Is the generation term, G, the only term in the mole balance that varies for each type of reactor?”

Q1-2_A Go to Chapter 1 Evaluation on the Web site. Click on i>Clicker Questions (http://www.umich.edu/~elements/6e/01chap/iclicker_ch1_q1.html) and view at least five i>clicker questions. Choose one that could be used as is, or a variation thereof, to be included on the next exam. You also could consider the opposite case: explaining why the question should not be on the next exam. In either case, explain your reasoning.

Q1-3_A What if... the PFR in Example 1-2 were replaced by a CSTR, what would be its volume?

Q1-4_A What if... you were asked to rework Example 1-2 to calculate the time to reduce the number of moles of A to 1% if its initial value for a constant volume BR, what would you say? Would you do it? If your answer is “yes,” go ahead and calculate it; if your answer is “NO, I won’t do it!” then suggest two ways to work this problem incorrectly.

Q1-5_A Read through the Introduction. Write a paragraph describing both the content goals and the intellectual goals of the course and text. Also describe what’s on the Web site and how the Web site can be used with the text and course.

Q1-6_A Go to Chapter 1 Useful Links (http://www.umich.edu/~elements/6e/01chap/obj.html#/) and click on Professional Reference Shelf to view the photos and schematics of real reactors. Write a paragraph describing two or more of the reactors. What similarities and differences do you observe between the reactors on the Web site (e.g., www.loebequipment.com), and in the text? How do the used reactor prices compare with those in Table 1-1?

Q1-7_A What assumptions were made in the derivation of the design equation for: (a) The batch reactor (BR)? (b) The CSTR? (c) The plug-flow reactor (PFR)? (d) The packed-bed reactor (PBR)? (e) State in words the meanings of –r_A and .

Q1-8_A Fill out the following table for each of the reactors discussed in this chapter, BR, CSTR, PBR, and Fluidized Bed:

Q1-9_A Define Chemical Process Safety and list four reasons we need to study it and why it is particularly relevant to CRE (http://umich.edu/~safeche/index.html).

Q1-10_A Go to Chapter 1 Extra Help on the Web site and click on LearnChemE ScreenCasts (http://www.umich.edu/~elements/6e/01chap/learn-cheme-videos.html). Choose one of the LearnChemE videos and critique it for such things as (a) value, (b) clarity, (c) visuals, and (d) how well it held your interest. (Score 1–7; 7 = outstanding, 1 = poor)

Q1-11_A Go to Chapter 1 Extra Help on the Web site and click on LearnChemE ScreenCasts (http://www.umich.edu/~elements/6e/01chap/learn-cheme-videos.html) the How to Study screencast and list three ways that screencasts can help you learn the material.

Q1-12_A Go to Extra Help then click on Videos of Tips on Studying and Learning. Go to Chapter 1 (http://www.umich.edu/~elements/6e/01chap/obj.html#/video-tips/).

1. View one of the 5- to 6-minute video tutorials and list two of the most important points in the video. List what two things you think this screencast did well?

2. After viewing the three screencasts on How to Study (http://www.learncheme.com/student-resources/how-to-study-resources), describe the most efficient way to study. In video 3 How to Study, the author of this book has a very different view of one of the points suggested. What do you think it is?

3. View the video 13 Study Tips**** (4 Stars) (https://www.youtube.com/watch?v=eVlvxHJdql8&feature=youtu.be). List four of the tips that you think might help your study habits.

4. Rate each of the sites on video tips, (1) Not Helpful, (5) Very Helpful.

Computer Simulations and Experiments

Before running your experiments, stop a moment and try to predict how your curves will change shape as you change a variable (cf. Q1-1_A).

P1-1_A

1. Revisit Example 1-3.

   Wolfram and Python

   1. Describe how C_A and C_B change when you experiment with varying the volumetric flow rate, υ₀, and the specific reaction rate, k, and then write a conclusion about your experiments.

   2. Click on the description of reversible reaction A ⇄ B to understand how the rate law becomes . Set K_e at its minimum value and vary k and υ₀. Next, set K_e at its maximum value and vary k and υ₀. Write a couple sentences describing how varying k, υ₀, and K_e affect the concentration profiles. We will learn more about K_e in Section 3.2.

   3. After reviewing Generating Ideas and Solutions on the Web site (http://www.umich.edu/~elements/6e/toc/SCPS,3rdEdBook(Ch07).pdf), choose one of the brainstorming techniques (e.g., lateral thinking) to suggest two questions that should be included in this problem.

      Polymath

   4. Modify the Polymath program to consider the case where the reaction is reversible as discussed in part (ii) above with K_e = 3. How do your results (i.e., C_A) compare with the irreversible reaction case?

Problems

P1-2_B Schematic diagrams of the Los Angeles basin are shown in Figure P1-2_B. The basin floor covers approximately 700 square miles (2 × 10¹⁰ ft²) and is almost completely surrounded by mountain ranges. If one assumes an inversion height in the basin of 2,000 ft, the corresponding volume of air in the basin is 4 × 10¹³ ft³. We shall use this system volume to model the accumulation and depletion of air pollutants. As a very rough first approximation, we shall treat the Los Angeles basin as a well-mixed container (analogous to a CSTR) in which there are no spatial variations in pollutant concentrations.

Figure P1-2_B Schematic diagrams of the Los Angeles basin.
(http://www.umich.edu/~elements/6e/web_mod/la_basin/index.htm)

We shall perform an unsteady-state mole balance (Equation (1-4)) on CO as it is depleted from the basin area by a Santa Ana wind. Santa Ana winds are high-velocity winds that originate in the Mojave Desert just to the northeast of Los Angeles. Load the Smog in Los Angeles Basin Web Module. Use the data in the module to work parts 1–12 (a) through (h) given in the module. Load the Living Example Polymath code and explore the problem. For part (i), vary the parameters υ₀, a, and b, and write a paragraph describing what you find.

There is heavier traffic in the L.A. basin in the mornings and in the evenings as workers go to and from work in downtown L.A. Consequently, the flow of CO into the L.A. basin might be better represented by the sine function over a 24-hour period.

P1-3_B This problem focuses on using Polymath, an ordinary differential equation (ODE) solver, and also a nonlinear equation (NLE) solver. These equation solvers will be used extensively in later chapters. Information on how to obtain and load the Polymath Software is given in Appendix D and on the CRE Web site.

1. Professor Sven Köttlov has a son-in-law, Štěpán Dolež, who has a farm near Riça, Jofostan where there are initially 500 rabbits (x) and 200 foxes (y). Use Polymath or MATLAB to plot the concentration of foxes and rabbits as a function of time for a period of up to 500 days. The predator–prey relationships are given by the following set of coupled ordinary differential equations:

   
   
   

   Constant for growth of rabbits k₁ = 0.02 day^–1

   Constant for death of rabbits k₂ = 0.00004/(day × no. of foxes)

   Constant for growth of foxes after eating rabbits k₃ = 0.0004/(day × no. of rabbits)

   Constant for death of foxes k₄ = 0.04 day^–1

   What do your results look like for the case of k₃ = 0.00004/(day × no. of rabbits) and t_final = 800 days? Also, plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do. Polymath Tutorial (https://www.youtube.com/watch?v=nyJmt6cTiL4)

2. Using Wolfram and/or Python in the Chapter 1 LEP on the Web site, what parameters would you change to convert the foxes versus rabbits plot from an oval to a circle? Suggest reasons that could cause this shape change to occur.

3. We will now consider the situation in which the rabbits contracted a deadly virus also called rabbit measles (measlii). The death rate is r_Death = k_Dx with k_D = 0.005 day^–1. Now plot the fox and rabbit concentrations as a function of time and also plot the foxes versus rabbits. Describe, if possible, the minimum growth rate at which the death rate does not contribute to the net decrease in the total rabbit population.

4. Use Polymath or MATLAB to solve the following set of nonlinear algebraic equations

   x³y – 4y² + 3x = 1

   6y² – 9xy = 5

   with inital guesses of x = 2, y = 2. Try to become familiar with the edit keys in Polymath and MATLAB. See the CRE Web site for instructions. You will need to know how to use this solver in later chapters involving CSTRs.

   Screen shots on how to run Polymath are shown at the end of Summary Notes for Chapter 1 or on the CRE Web site, www.umich.edu/~elements/6e/software/polymath-tutorial.html.

Interactive Computer Games

P1-4_A Find the Interactive Computer Games (ICG) on the CRE Web site (http://www.umich.edu/~elements/6e/icg/index.html). Read the description of the Kinetic Challenge module (http://www.umich.edu/~elements/6e/icm/kinchal1.html) and then go to the installation instructions (http://www.umich.edu/~elements/6e/icm/install.html) to install the module on your computer. Play this game and then record your performance number, which indicates your mastery of the material.

Jeopardy Game Held at Annual AIChE Student Chapter Meeting

ICG Kinetics Challenge 1 Performance # ___________________________

Problems

P1-5_A OEQ (Old Exam Question) The reaction

A + B → 2C

takes place in an unsteady CSTR. The feed is only A and B in equimolar proportions. Which of the following sets of equations gives the correct set of mole balances on A, B, and C? Species A and B are disappearing and species C is being formed. Circle the correct answer where all the mole balances are correct. (a) (b)

1. 
2. 
3. 
4. 

5. None of the above.

   This problem was written in honor of Ann Arbor, Michigan’s own Grammy winning artist, Bob Seger (https://www.youtube.com/channel/UComKJVf5rNLl_RfC_rbt7qg/videos).

P1-6_B The reaction

A → B

is to be carried out isothermally in a continuous-flow reactor. The entering volumetric flow rate υ₀ is 10 dm³/h. Note: F_A = C_Aυ. For a constant volumetric flow rate υ = υ₀, then F_A = C_Aυ₀. Also, C_A0 = F_A0/υ₀ = ([15 mol/h]/[10 dm³/h])0.5 mol/dm³.

Calculate both the CSTR and PFR volumes necessary to consume 99% of A (i.e., C_A = 0.01C_A0) when the entering molar flow rate is 5 mol/h, assuming the reaction rate –r_A is

1. −r_A = k with [Ans.: V_CSTR = 99 dm³]

2. −r_A = k_CA with 0.0001 s⁻¹

3. −r_A = with [Ans.: V_CSTR = 660 dm³]

4. Repeat (a), (b), and/or (c) to calculate the time necessary to consume 99.9% of species A in a 1000 dm³ constant-volume batch reactor with C_A0 = 0.5 mol/dm³.

P1-7_A Enrico Fermi (1901–1954) Problems (EFP). Enrico Fermi was an Italian physicist who received the Nobel Prize for his work on nuclear processes. Fermi was famous for his “Back of the Envelope Order of Magnitude Calculation” to obtain an estimate of the answer through logic and then to make reasonable assumptions. He used a process to set bounds on the answer by saying it is probably larger than one number and smaller than another, and arrived at an answer that was within a factor of 10.

See http://mathforum.org/workshops/sum96/interdisc/sheila2.html.

Enrico Fermi Problem

1. EFP #1. How many piano tuners are there in the city of Chicago? Show the steps in your reasoning.

   1. Population of Chicago __________

   2. Number of people per household __________

   3. And so on, __________

   An answer is given on the CRE Web site under Summary Notes for Chapter 1.

2. EFP #2. How many square meters of pizza were eaten by an undergraduate student body population of 20,000 during the Fall term 2016?

3. EFP #3. How many bathtubs of water will the average person drink in a lifetime?

P1-8_A What is wrong with this solution? The irreversible liquid-phase second-order reaction

is carried out in a CSTR. The entering concentration of A, C_A0, is 2 molar, and the exit concentration of A, C_A is 0.1 molar. The volumetric flow rate, υ₀, is constant at 3 dm³/s. What is the corresponding reactor volume?

Solution

1. Mole Balance

   

2. Rate Law (second order)

   

3. Combine

   
4. 
5. 
6. 

If you like the Puzzle Problems in “What is wrong with the solutions”^† you can find more for later chapters on the Web site under Additional Material for that chapter.

For more puzzles on what’s “wrong with this solution,” see additional material for each chapter on the CRE Web site home page, under “Expanded Material.”

NOTE TO INSTRUCTORS: Additional problems (cf. those from the preceding editions) can be found in the solutions manual and on the CRE Web site. These problems could be photocopied and used to help reinforce the fundamental principles discussed in this chapter.