Solution Manual For MWH'S WATER TREATMENT: PRINCIPLES AND DESIGN 3RD EDITION By John C. Crittenden R. Rhodes Trussell David W. Hand {Chapter 6: Principles Of Reactor Analysis And Mixing} ||Complete Guide3r Edition

PRINCIPLES OF REACTOR ANALYSIS AND MIXING




Solution Manual For

MWH'S WATER TREATMENT: PRINCIPLES AND DESIGN 3RD EDITION By
John C. Crittenden R. Rhodes Trussell David W. Hand {Chapter 6: Principles Of
Reactor Analysis And Mixing} ||Complete Guide3r Edition

, PRINCIPLES OF REACTOR ANALYSIS AND MIXING

Problem 6-1

Instructors Note: Some of the solutions shown in Table 6-3 will be derived in this
problem.

Problem Statement - Derive The Solution To Mass Balance Equations For The Second- And
Nth-Order Reactions Occurring In A Cmbr.

Solution
1. Write The Mass Balance Equation For The 2nd And Nth Order Reactions In A Cmbr.
a. General Mass Balance Equation For A Cmbr (Eq. 6-25):
Dc
R
Dt
b. Rate Expression For The Reactions (See Table 6-3): 2nd
Order: R K C2

Nth Order: R K Cn
c. Final Expression Of Mass Balance Equations:
Dc
2nd Order: K C2
Dt
Dc
Nth Order: K Cn
Dt
2. Derive The Solution By Integrating The Above Expressions.
a. For The Second Order Reactions:
Dc
 = 0 Kdt
C t
C 2
0 C
1 1 Kt
C C0
1 1 Kt
C C0
b. For The Nth Order Reactions:
C T
C Ndc Kdt
C0
N 1
1
Homework Solution Manual Page 2 of 151
MWH’s Water Treatment: Principles and Design, 3rd ed. Version 1
Chapter 6 - Principles of Reactor Analysis and Mixing

, PRINCIPLES OF REACTOR ANALYSIS AND MIXING



0



CN1 C N 1
Kt 0




Homework Solution Manual Page 3 of 151
MWH’s Water Treatment: Principles and Design, 3rd ed. Version 1
Chapter 6 - Principles of Reactor Analysis and Mixing

, PRINCIPLES OF REACTOR ANALYSIS AND MIXING


CN1 C N 1
0
Kt N 1
N 1
C
C N1 N 1 Kt 0

N 1

C N 1
C N 1

N 1) Kt 0
N 1
(N 0,N 1)



Problem 6-2

Problem Statement - A Second-Order Irreversible Elementary Reaction 2a → Products Is Carried
Out In A Batch Reactor. For A Certain Set Of Conditions, It Is Found That It Took 20 Min For
A Reaction To Reach 60 Percent Completion. What Would Be The Time Required To Reach
The Same Degree Of Completion If (A) The Initial Concentration Of A Were Doubled And
(B) The Reaction Rate Constant Were Doubled?

Solution
1. Determine The Rate Constant K.
a. Obtain The Solution For A 2nd Order Reaction From Table 6-3.
1 1
Kt
C C0
b. Solve For K When The Reaction Is 60 Percent Complete, Which Occurs At T = 20
Min.
T = 20 Min, C 1 0.6 C0 0.4c0

1 1 1 1 1 1 3
K
T C C0 20 0.4c0 C0 40c0
2. Determine The Time Required To Reach The Same Degree Of Completion Under
Scenario A And B.
a. Determine The Time Required If C0 Was Doubled.

C 0.4 2c0 0.8c0


Homework Solution Manual Page 4 of 151
MWH’s Water Treatment: Principles and Design, 3rd ed. Version 1
Chapter 6 - Principles of Reactor Analysis and Mixing