Issuu

Solutions Manual for Elements of Chemical Reaction Engineering 7th

Edition

by

Fogler, Goldsmith, Nikolla, Singh

ISBN: 9780135337554

Solutions Manual for Elements of Chemical Reaction Engineering

Seventh Edition

H.Scott Fogler

Ame and Catherine Vennema Professor of Chemical Engineering and the Arthur F. Thurnau Professor

Bryan R. Goldsmith

Associate Professor of Chemical Engineering

Eranda Nikolla Professor of Chemical Engineering

Nirala Singh

Associate Professor of Chemical Engineering

University of Michigan, Ann Arbor

May 2025

Hoboken, New Jersey

The author and publisher have taken care in the preparation of this work but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein.

Visit us on the Web: informit.com

This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

ISBN-13: 978-0-13-534732-4

ISBN-10: 0-13-534732-7

Version 1, May 2025

Acknowledgment

The following students participated in the solutions to the end of chapter problems of the Elements of Chemical Reaction Engineering, editions 1 through 6:

Max Nori

Brian Vicente

Sombudda Ghosh

Nihat Gürman

Yongzhong Lui

Duc Ahn Nguyen

Vishal Chaudhary

Ravi Kapoor

Manosij Basu

Arpit Gupta

Sneh Shriyansh

Utkarsh Prasad

Darshan Shah

Anamika Singh

Sravya Jangareddy

Fan Zhang

Keyvan Edrisi

Richa Motwani

Prafful Bhansali

Maithri Venkat

Yimeng Lyu

Sheng Mark Zheng

Mayur Tikmani

Ayush Agarwal

Vaibhav Jain

Devosmita Sen

Manjeet Singh

Jnana Sai Jagana

While many, many students contributed to the Elements of Chemical Reaction Engineering Solutions Manual, special mention is necessary to Mayur Tikmani who after graduating from IIT Guwahati spent 6 months in Ann Arbor working with Prof. Fogler, before he joined Reliance Industries Limited, to prepare all the Wolfram and Python LEPs.

Screen Shot of Web Home Page ..........................................................................................

Screen Shot of Interactive Computer Games (ICGs) .......................................................... ii

Screen Shot of Polymath Living Example Problems (LEPs) ............................................. iv

Algorithm to Decode ICGs..................................................................................................

Sample Course Syllabus .....................................................................................................

Solutions to Chapter 1 – Mole Balances

Questions Q1-1 through Q1-12

Problems P1-1 through P1-8

Solutions to Chapter 2 – Conversion and Reactor Sizing

Questions Q2-1 through Q2-6

Problems P2-1 through P2-11

Solutions to Chapter 3 – Rate Laws

Questions Q3-1 through Q3-7

Problems P3-1 through P3-16

Solutions to Chapter 4 – Stoichiometry

Questions Q4-1 through Q4-9

Problems P4-1 through P4-13

Solutions to Chapter 5 – Isothermal Reactor Design: Conversion

Questions Q5-1 through Q5-13

Problems P5-1 through P5-26

Solutions to Chapter 6 – Isothermal Reactor Design: Moles and Molar Flow Rates

Questions Q6-1 through Q6-7

Problems P6-1 through P6-13

Solutions to Chapter 7 – Collection and Analysis of Rate Data

Questions Q7-1 through Q7-7

Problems P7-1 through P7-12

Solutions to Chapter 8 – Multiple Reactions

Questions Q8-1 through Q8-5

Problems P8-1 through P8-18

Solutions to Chapter 9 – Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Questions Q9-1 through Q9-4

Problems P9-1 through P9-23

Solutions to Chapter 10 – Catalysis and Catalytic Reactors

Questions Q10-1 through Q10-9

Problems P10-1 through P10-23

Solutions to Chapter 11 – Nonisothermal Reactor Design: The Steady-State Energy Balance and Adiabatic PFR Applications

Questions Q11-1 through Q11-14

Problems P11-1 through P11-10

Solutions to Chapter 12 – Steady-State Nonisothermal Reactor Design: Flow Reactors with Heat Exchange

Questions Q12-1 through Q12-6

Problems P12-1 through P12-27

Solutions to Chapter 13 – Unsteady State Nonisothermal Reactor Design

Questions Q13-1 through Q13-5

Problems P13-1 through P13-11

Solutions to Chapter 14 – Mass Transfer Limitations in Reacting Systems

Questions Q14-1 through Q14-8

Problems P14-1 through P14-17

Solutions to Chapter 15 – Diffusion and Reaction

Questions Q15-1 through Q15-8

Problems P15-1 through P15-17

Solutions to Chapter 16 – Residence Time Distributions of Chemical Reactors

Questions Q16-1 through Q16-5

Problems P16-1 through P16-13

Solutions to Chapter 17 – Predicting Conversion Directly from the Residence Time Distribution

Questions Q17-1 through Q17-4

Problems P17-1 through P17-18

Solutions to Chapter 18 – Models for Nonideal Reactors

Questions Q18-1 through Q18-6

Problems P18-1 through P18-20

Solutions to Chapter 19 – Electrochemical Reactor Design

Questions Q19-1 through Q19-8

Problems P19-1 through P19-11

WEB HOME PAGE

Interactive Computer Games (ICGs)

The Interactive Computer Games (ICGs) listed below arecontained on thewebsite below Game players can click on the Run from the website link to begin play each ICG title Note that there will be a pa.Jsewhlle the game is loaded tromour servers Alternately, one can use the Install to PC link to install each g.:rne on the PC This installation will typically instaJl an icon on the desktop Please take the default location 1orthe Installation files. Detailed instructions for installing and using the ICGs are available

As these interactive games are played, the player will t>e asked a number of questions related to thecorresponding material in the textbook, The computer will keep track of all the correct answers and at the end of the game will displaYa roded performance number that reflects how well the player mastered the materiaJin the text Instructors will havea manual to decode the perforrre,ce number.

Note: The Interactive Computer Games may NOT work onoximately 10% of Windows machines. We can't find a specific reason, so if it doesn't work, pleasetry th911on a different Windows computer.

Kinetics Challenge I ( lnstaJI to PC, lnstaJlatlon Instructions)

Oul2 Show Introduction to Kinetics

DescriP-tion of the Module

Ol>lectlves for Chapter One

Staging ( Install to PC1 Installation Instructions)

Reactor Sequencing Optimization

Descrigtlonof the Module

Oofectlves tor Chapter Two

Kinetics Challenge II ( Install to PG Installation Instructions)

Oul2Show

Stoichiometry and Rate Laws

DescriP-t on of the Module

Obfectlves for Chapter Four

r-h..Jrder Mystery(Install to PC, Installation Instructions)

CSTR Volume Algorithm

Descriptionof the Module

Oofectlves for.G.b_gpter Five

Tic Tac Toe( Install to PC, Installation Instructions)

Isothermal Reactor Design: Ergun, Arrhenius, and Van t Hoff Equations

DescrlP-tlonof the Module

Oofectlves for Chapter Six

Ecology A Wetlands Protllem ( Install to PC Installation Instructions)

Collection and Analysis of Rate Date: Ecological Engineering

DescriP-tion of the Module

Oofectlves for Chapter Seven

Great Race ( Install to PC, Installation Instructions)

Multiple Reactions

DescriP-tionof the Module

Oofectlves for ChaP!.§!::_fj_Q.O!

Enzyme Man ( Install to PC Installation Instructions I

Enzyme Kinetics

DescrlP-tlonof the Module

Ol>lectlves for Chapter Nine

INTERACTIVE COMPUTER GAMES (ICGs)

Heterogeneous Catalysis [ lnstaJIto PC, lnstaJlatlon Instructions)

Catalytic Rate

Equatlons,Status:Alpha Release

Warning: This module is not tullytested You may encounter abnormal behavior

Descriptionof the Module

Ol>lectlves for Chaoter Ten

Heat Effects 1 ( Install to PC lnstallatlon Instructions)

Basketbal Challenge

Mole and Energy Balances In a CSTR

DescrlP-tlonof the Module

Oofectlves for Chapter Thirteen

Heat Effects 2 ( Install to PC, Installation Instructions)

Effect of Parameter Variation on a PFR

Mole end Energy Balances In e PFR,Stetus: Alpha Release

Warning: This module is not tullytested You may encounter abnormal behavior

Descrigtlonof the Module

Oofectlves tor chapter ThIrteen

LIVING EXAMPLE PROBLEMS (LEPs)

Wolfram and Python can be downloaded and installed on your computer free of charge

ALGORITHM TO DECODE ICGs

UNIVERSITY OF MICHIGAN

INTERACTIVE COMPUTER MODULES FOR CHEMICAL ENGINEERING CHEMICAL REACTION ENGINEERING MODULES

H. Scott Fogler, Project Director

M. Nihat Gürmen, Project Manager (2002-2004) Susan Montgomery, Project Manager (1991-1993)

Department of Chemical Engineering University of Michigan Ann Arbor, MI 48109-2136

INTERPRETATION OF PERFORMANCE NUMBERS

Students should record their Performance Number for each program, along with the name of the program, and turn it in to the instructor. The Performance Number for each program is decoded as described in the following pages.

Please report problems to icm.support@umich.edu.

ICMs with Windows® interface

Module Format Interpretation

KINETIC CHALLENGE I

CzBzzAzz

KINETIC CHALLENGE II

CzBzzAzz

MURDER MYSTERY

zzAzz

TIC TAC TOE

zDzCzBzA

Score = 1.5 * AB.C z = random numbers

Note: 75% constitutes mastery.

Score = 2.0 * AB.C z = random numbers

Note: 75% constitutes mastery.

A even: Killer and victim correctly identified

A odd: Killer and victim not identified z = random numbers

Perf. No. = 75241692

Score = 1.5*(62.7) = 94 %

Perf. No. = 03776467

Score = 2.0*(47.0) = 94 %

Perf. No. = 50732

Score: No credit

Note: An even number for the middle digit constitutes mastery.

Score = 4.0 * AB.C

Perf. No. = 77803581 z = random numbers

Configurations

Score = 4*(15.0) = 60 configuration 7 completed

Note: Student receives 20 points for every square answered correctly. A score of 60 is needed for mastery of this module.

GREAT RACE

zzzCzABz

Score = 6.0 * AB.C

Perf. No. = 77738078 z = random numbers

Score = 6*(07.3) = 44

Note: A score of 40 is needed for mastery of this module.

ECOLOGY

AzBCzaaD z = random numbers a = random characters

A gives info on r^2 value of the student’s linearized plot

A=Y if r^2 >= 0.9

A=A if 0.9 > r^2 >= 0.8

A=X if 0.8 > r^2 >= 0.7

A=F if 0.7 > r^2

A=Q if Wetland Analysis/Simulator portion has not been completed

B gives info on alpha

B=1 to 4 => student's alpha < (simulator's alpha  0.5)

B=5 to 9 => student's alpha > (simulator's alpha  0.5)

B=X if Wetland Analysis/Simulator portion has not been completed

C indicates number of data points deactivated during analysis

C=number of deactivated data points if at least 1 point has been deactivated

C=a randomly generated letter from A to Y if 0 points deactivated

C=Z if Wetland Analysis/Simulator portion has not been completed

D gives info on solution method used by student

D=1 if polynomial regression was used

D=2 if differential formulas were used

D=3 if graphical differentiation was used

D=4 to 9 if Wetland Analysis/Simulator portion has not been completed

Perf No. = A7213DF2

1) A => 0.9 > r^2 >= 0.8

2) 2 => student’s alpha < (simulator’s alpha  0.5)

3) 1 => one data point was deactivated

4) 2 => differential formulas were used

STAGING

Final conversion = 2*AB.C

Final flow rate = 2*DE.F flow rate = 2*31.2 = 62.4

Please make a pass/fail criterion based on these values.

ICMs

with Dos® interface

Module Format

HETCAT

Interpretation

zzABzCD

A=2,3,5,7: interaction done

B=2,3,5,7: intro done

C=2,3,5,7: review done

D denotes how much they

Example

Perf. No. = 8027435

A: Worked on interaction

B: Looked at intro

C: Looked at review did in the interaction:

D<2

2 < D:5 4

4 < D:5 6

6<D

z = random numbers

HEATFX1

zzAzz

HEATFX2

zzzAzz

D: found parameter values, didn’t find mechanism

Not done

Dependences

Parameter values

Mechanism

Note: Performance number given only if student goes through the interaction portion of the module

A even: score > 85 %

z = random numbers

Perf. No. = 53607

Score > 85 %

Note: Student told they have achieved mastery if their score is greater than 85%

A even: completed interaction

z = random numbers

Perf. No. = 407582

Interaction not completed

Note: Performance number given only if student goes through the interaction portion of the module.

SAMPLE COURSE SYLLABUS

ChE 344: CHEMICAL REACTION ENGINEERING

Fundamentals of chemical reaction engineering. Rate laws, kinetics, and mechanisms of homogeneous and heterogeneous reactions. Analysis of rate data, multiple reactions, heat effects, bioreactors. Design of industrial reactors.

Prerequisite: ChE 330, ChE 342

Fall

Lectures: M,W 8:40 (Sharp) to 10:30 (not so sharp) – Room: 1013 Dow

Instructor:

Professor Bryan R. Goldsmith 3168 Dow, bgoldsm@umich.edu

Office Hours: M,W 10:30a to 11:30a

Course assistants include: Instructional aids, tutor, proctors, and graders

Text Required

Elements of Chemical Reaction Engineering, 7th edition, H. Scott Fogler

Web sites: Chemical Reaction Engineering, http://www.umich.edu/~elements/7e/index.html

Process Safety Across the Chemical Engineering Curriculum, http://umich.edu/~safeche/

Synopsis for Chapter 1 – Mole Balances

Mole balances are the first building block of the chemical reaction engineering algorithm. General: The goal of these problems are to reinforce the definitions and provide an understanding of the mole balances of the different types of reactors. It lays the foundation for step 1 of the algorithm in Chapter 5.

Key to Nomenclature

AA = Always assign one from the group of alternates

O = Often assigned

I = Infrequently assigned

S = Seldom assigned

G = Graduate level

N = Never assigned

E.g., means problem P1-3B will be assigned every time I teach the course, problem AA P1-8 means that this problem or one of the other problems with the prefix AA is always assigned for this chapter, Problem l P1-2 will be infrequently assigned, Problem O P1-6B will often be assigned, and Problem S P3-16B is seldom assigned.

Alternates: In problems that have a dot in conjunction with AA means that one of the problems, either the problem with a dot or any one of the alternates are always assigned.

Time: Approximate time in minutes it would take a B student to solve the problem.



Q1-1A (9 seconds) Questions Before Reading (QBR).

(a) John Falconer at the University of Colorado gives workshops on Teaching in which he points out that students have a better comprehension if they ask themselves a question before reading the text. The first question of each chapter, Q1, is just such a question.

(b) The students are asked, at a minimum read through the Questions to help put the chapter and their studies in perspective.



Q1-2A (8-10 min) i>Clicker

Q1-5A (5-75 min) through Q1-12A. To get a “feel” of the resources available, the students should spend a total of about 50-75 minutes on these questions.

Computer Simulations and Experiments (5-15 minutes per simulation)

These problems are interactive and are a minor paradigm shift in the way we use homework problems. Here the students are asked to explore the reaction and the reactor in which they occur to get an intuitive feel and understanding of the reactor system. This procedure is called Inquiry Based Learning (IBL).

 P1-1A (10-15 min) Good introduction to the use of Wolfram and Python.

Problems

I P1-2B (60 min) Problem reinforces wide range of applications of CRE and problem is given in the web module which can be accessed from the Web Home Page (www.umich.edu/~elements). Many students like this straight forward problem because they see how CRE principles can be applied to



an everyday example. It is often assigned as an in-class problem where parts (a) through (f) are printed out from the web and given to the students in class. Part (g) is usually omitted.

P1-3B (45 min) I always assign this problem so that the students will learn how to use Polymath/MATLAB, Wolfram and Python before needing it for chemical reaction engineering problems. Most problems will use either Polymath or MATLAB to solve the end of chapter problems.



P1-4A (30 min) The Interactive Computer Games (ICGs) have been found to be a great motivation for this material. This ICG will help student AIChE chapters prepare for the Jeopardy Competition at the Annual AIChE Meeting.



P1-5A (10 min) Old Exam Question (OEQ) to reinforce the convention and stoichiometry in mole balances.

P1-6B (30 min) A hint of things to come on sizing reactors. Fairly straight forward problem to make a calculation. Uses Example 1-1 to calculate a CSTR volume. It is straight forward and gives the student an idea of things to come in terms of sizing reactors in chapter 4.

I P1-7A (30 min) Helps develop critical thinking and analysis.

AA P1-8A (20 min) Puzzle problem to identify errors in the solution. Many students especially those who enjoy working Sudoku or crossword puzzl es enjoy working these types of problems.

Useful Links:

Solutions for Chapter 1 – Mole Balances

1. Click on the link given below to download Wolfram/python codes for Ch-1 http://umich.edu/~elements/5e/01chap/obj.html#/

2. Click on the link given below to view Wolfram tutorial (for running Wolfram Codes) http://umich.edu/~elements/5e/software/Wolfram_LEP_tutorial.pdf

3. Click on the link given below to view Polymath tutorial (for running Polymath Codes) http://umich.edu/~elements/5e/tutorials/Polymath_LEP_tutorial.pdf

Q1-1 Individualized solution.

Q1-2 Individualized solution.

Q1-3 For CSTR:

Q1-4 Individualized solution.

Q1-5 Individualized solution

Q1-6 Individualized solution

Q1-7 (a)

The assumptions made in deriving the design equation of a batch reactor are: - Closed system: no streams carrying mass enter or leave the system - Well mixed, no spatial variation in system properties - Constant Volume or constant pressure

Q1-7 (b)

The assumptions made in deriving the design equation of CSTR, are: - Steady state

- No spatial variation in concentration, temperature, or reaction rate throughout the vessel

Q1-7 (c)

The assumptions made in deriving the design equation of PFR are: - Steady state

- No radial variation in properties of the system

Q1-7 (d)

The assumptions made in deriving the design equation of PBR are: - Steady state

- No radial variation in properties of the system

Q1-7 (e)

For a reaction

A➔ B

 -rA is the number of moles of A reacting (disappearing) per unit time per unit volume [=] moles/ (dm3.s).

 -rA’ is the rate of disappearance of species A per unit mass (or area) of catalyst [=] moles/ (time. mass of catalyst).

 rA’ is the rate of formation (generation) of species A per unit mass (or area) of catalyst [=] moles/ (time. mass catalyst).

 -rA is an intensive property, that is, it is a function of concentration, temperature, pressure, and the type of catalyst (if any), and is defined at any point (location) within the system. It is independent of amount. On the other hand, an extensive property is obtained by summing up the properties of individual subsystems within the total system; in this sense, -rA is independent of the ‘extent’ of the system.

Q1-8 Individualized solution.

Q1-9 Individualized solution.

Q1-10 Individualized solution.

Q1-11 Individualized solution.

Q1-12 Individualized solution.

P1-1 (a) Example 1-3

The above graph represents intial Ca and Cb profiles for k=0.23 and v0 = 10.

(i) With an increase in k (lets take k =0.35) for same volume and v0 , Ca decreases and Cb increases

Now lets make k=0.23(initial value) and make an increase in v0 (change from 10 to 15) for same volume. We notice that now Ca increases and Cb decreases. All of these graphs of concentration profiles are ta ken from Wolfram player by shifting the sliders.

We can observe that varying rate constant has more effect on concentration profiles as compared to varying volumetric flow rate.

(ii) CA decreases and CB increases with an increase in k and Ke, and a decrease in v0 for the same volume.

(iii) Individualized solution

(iv) See the following polymath code:

Polymath Code:

d(Ca)/d(V) = ra / v0

d(Cb)/d(V) = rb / v0

k = 0 23

Ke=3

ra = -k * (Ca-Cb/Ke)

rb = -ra

v0 = 10

V(0)=0

V(f)=100

Ca(0)=10

Cb(0)=0

Output:

POLYMATH Report

Ordinary Differential Equations

Calculated values of DEQ variables

Differential equations

d(Ca)/d(V) = ra / v0

d(Cb)/d(V) = rb / v0

Explicit equations

1 k = 0.23

Ke = 3

ra = -k * (Ca-Cb/Ke)

rb = -ra

v0 = 10

P1-2 Given A  2*1010 ft2 TSTP  491.69R

*1013 ft3

R atm ft

FS = CO in Santa Ana winds FA = CO emission from autos vA  3000 ft3 hr per car at STP

P1-2 (a)

Total number of lb moles gas in the system:

N  P0V RT

N = 1atm(4 1013 ft3)  atm. ft3

= 1.025 x 1011 lb mol

P1-2 (b)

Molar flowrate of CO into L.A. Basin by cars. • no. of cars

FA  yAFT  yA vA CT STP F 3000 ft3 1lbmol

T  hrcar  359 ft3 400000 cars (See appendix B)

FA = 6.685 x 104 lb mol/hr

P1-2 (c)

Wind speed through corridor is U = 15mph W = 20 miles

The volumetric flowrate in the corridor is vO = U.W.H = (15x5280)(20x5280)(2000) ft3/hr = 1.673 x 1013 ft3/hr

P1-2 (d)

Molar flowrate of CO into basin from Santa Ana wind.

FS : v0 CS = 1.673 x 1013 ft3/hr 2.04 10 10 lbmol/ft3 = 3.412 x 103lbmol/hr

Rate of emission of CO by cars + Rate of CO in Wind - Rate of removal of CO = dNCO dt

P1-2 (f)

P1-2 (g)

Time for concentration to reach

Now solving this equation using POLYMATH we get plot between Cco vs. t

See the following polymath code:

Polymath Code:

v0 = 1 67*10^12

A= 35000

B = 30000

F = 341 23

V = 4*10^13

d(C)/d(t) = (A+B*sin(3.14*t/6)+F-v0*C)/V

C(0)=2 0e-10

t(0)=0

t(f)=72

Output:

Report

Calculated values of DEQ variables

3 C

4 F

5 t 0 0

Differential equations

1 d(C)/d(t) = (A+B*sin(3.14*t/6)+F-v0*C)/V

Explicit equations

v0 = 1.67*10^12

A = 35000

B = 30000

F = 341.23

V = 4*10^13

Polymath Code:

v0 = 1 67*10^12

A= 35000

B = 30000

F = 341 23

V = 4*10^13

d(C)/d(t) = (A+B*sin(3 14*t/6)+F-v0*C)/V

C(0)=2 0e-10

t(0)=0

t(f)=48

Output:

POLYMATH Report

Ordinary Differential Equations

Calculated values of DEQ variables

4 F

5 t 0 0

6 V

Differential equations

1 d(C)/d(t) = (A+B*sin(3.14*t/6)+F-v0*C)/V

Explicit equations

1 v0 = 1.67*10^12

A = 35000

B = 30000 F = 341.23

V = 4*10^13 2 3 4 5

P1-2 (i)

Changing a -+ Increasing ‘a’ reduces the amplitude of ripples in graph. It reduces the effect of the sine function by adding to the baseline.

Changing b -+ The amplitude of ripples is directly proportional to ‘b’. As b decreases amplitude decreases and graph becomes smooth.

Changing v0 -+ As the value of v0 is increased the graph changes to a “shifted sin-curve”. And as v 0 is decreased graph changes to a smooth increasing curve.

P1-3 (a)

Initial number of rabbits, x(0) = 500

Initial number of foxes, y(0) = 200

Number of days = 500

dt  k1x k2xy................................ (1)

dy  k xy k y ............................... (2)

3 4

Given,

k1  0.02day 1

k2  0.00004 / (day  foxes)

k3  0.0004 / (day  rabbits)

k4  0.04day 1

See the following polymath code:

Polymath Code:

d(x)/d(t) = (k1*x)-(k2*x*y)

d(y)/d(t) = (k3*x*y)-(k4*y)

k1 = 0 02

k2 = 0 00004

k3 = 0 0004

k4 = 0 04

t(0)=0

t(f)=500

x(0)=500

y(0)=200

Output:

POLYMATH Report

Ordinary Differential Equations

Calculated values of DEQ variables

Differential equations

1 2

d(x)/d(t) = (k1*x)-(k2*x*y)

d(y)/d(t) = (k3*x*y)-(k4*y)

Explicit equations

1 k1 = 0.02

2 k2 = 0.00004

3 k3 = 0.0004

4 k4 = 0.04

When, tfinal = 800 and k3  0.00004 /(day  rabbits)

POLYMATH Report

Ordinary Differential Equations

Calculated values of DEQ variables

5 t 0 0 800. 800.

7 y

Differential equations

1 d(x)/d(t) = (k1*x)-(k2*x*y) d(y)/d(t) = (k3*x*y)-(k4*y) 2

Explicit equations

1 k1 = 0.02

2 k2 = 0.00004

3 k3 = 0.00004

4 k4 = 0.04

Plotting rabbits vs. foxes

P1-3 (b)

By increasing k4 and decreasing k2, foxes verses rabbits plot tends to become circular

P1-3 (c)

Below are the graphs when death rate is taken in to account

P1-3 (d)

To solve the system of equation, we can use Polymath Nonlinear Equation Solver

Polymath Code:

f(x) = (x^3)*y-4*y^2+3*x-1

x(0) = 2

f(y) = 6*y^2-9*x*y-5

y(0) = 2

Polymath Output:

Calculated values of NLE variables

Variable Value f(x) Initial Guess

1 x 2.385039 2.53E-11 2. y 3.797028 1.72E-12 2.

Nonlinear equations

f(x) = (x^3)*y-4*y^2+3*x-1 = 0 f(y) = 6*y^2-9*x*y-5 = 0

P1-4 Individualized solution

P1-5

P1-6 (a)

– rA = k with k = 0.05 mol/h dm3

CSTR: The general equation is V  FA0 FA rA

Here CA = 0.01CA0 , v0 = 10 dm3/min, FA = 5.0 mol/hr Also, we know that FA = CAv0 and FA0 = CA0v0, CA0 = FA0/ v0 = 0.5 mol/dm3

Substituting the values in the above equation we get, V  CA0v0 CAv0  (0.5)10 0.01(0.5)10 k 0.05

➔ V = 99 dm3 1 2

PFR: The general equation is

Integrating the above equation, we get

v0 CA V  dCA   dV => V  v0 (C C ) k k

CA0 0

Hence V = 99 dm3

Volume of PFR is same as the volume for a CSTR since the rate is constant and independent of concentration.

P1-6 (b)

–rA = kCA with k = 0.0001 s-1

CSTR:

We have already derived that V  CA0v0 CAv0 rA  v0CA0(1 0.01) kCA

k = 0.0001s-1 = 0.0001 x 3600 hr-1= 0.36 hr-1

PFR: ➔ V  (10dm3 / hr)(0.5mol / dm3)(0.99) (0.36hr 1)(0.01*0.5mol / dm3) => V = 2750 dm3

From above we already know that for a PFR dCAv0  r  kC dV A A

Integrating v CA dC V 0  A   dV k C CA0 0 v0 ln CA0  V k CA

Again k = 0.0001s-1 = 0.0001 x 3600 hr-1= 0.36 hr-1

Substituting the values in above equation we get V = 127.9 dm3

P1-6 (c)

–rA = kC 2 with k = 300 dm3/mol.hr

CSTR: V  CA0v0 CAv0 rA  v0CA0(1 0.01) kC2

A0 A A A A dFA  r  k , Now FA = CAv0 and FA0 = CA0v0 => dCAv0  k dV A dV

Substituting all the values we get

Integrating

(d)

Second order:

P1-7 Enrico Fermi Problem

P1-7 (a)Population of Chicago = 4,000,000

Size of Households = 4

Number of Households = 1,000,000

Fraction of Households that own a piano = 1/5

Number of Pianos = 200,000

Number of Tunes/year per Piano = 1

Number of Tunes Needed Per Year = 200,000 Tunes per day = 2

250 days 2

Tunes per year per tuner = yr  day  500/yr/tuner

200,000 tunes 1 yr  500 tunes / yr / tuner  400 Tuners

P1-7(b) Assume that each student eats 2 slices of pizza per week. Also, assume that it is a 14” pizza, with 8 pieces. Hence, the area of 1 slice of pizza = 19.242 inch2 = 0.012414 m2 Thus, a population of 20000, over a span of 4 months, eats 20000 * 2 slices * 4 months * 4 weeks/month = 640000 slices of pizza, with a total area of 640000 * 0.012414 m2 = 7945 m2 of pizza in the fall semester.

P1-7(c) Assume you drink 1L/day

Assume you live 75 years*365days/year = 27375 days 1L/day*27375 days = 27375 L drank in life

Bathtub dimensions: 1m*0.7m*0.5m = 0.35m3 = 350L/tub

Bathtubs drunk = 27375L*1tub/350L = 78 tubs

P1-7(d) Jean Valjean, Les Misérables.

P1-8 Mole Balance: V = FA0 FA rA Rate Law : rA  kC2 Combine: V = FA0 FA kC2

(6 0.3)

1900dm3

V = s  19000 dm3 (0.03 dm3 )(0.1 mol )2 mol s dm3

The incorrect part is in step 6, where the initial concentration has been used instead of the exit concentration.

Page intentionally blank

Elements Of Chemical Reaction Engineering 7Th Fogler Solutions Manual

Solutions Manual for Elements of Chemical Reaction Engineering 7th

by

Solutions Manual for Elements of Chemical Reaction Engineering

Acknowledgment

Table of Contents

WEB HOME PAGE

Interactive Computer Games (ICGs)

INTERACTIVE COMPUTER GAMES (ICGs)

LIVING EXAMPLE PROBLEMS (LEPs)

ALGORITHM TO DECODE ICGs

INTERPRETATION OF PERFORMANCE NUMBERS

ICMs with Windows® interface

GREAT RACE

ECOLOGY

ICMs

with Dos® interface

Module Format

Interpretation

Example

SAMPLE COURSE SYLLABUS

Synopsis for Chapter 1 – Mole Balances

Solutions for Chapter 1 – Mole Balances

P1-3 (a)