CVEN 5464 HW 6 CVEN 5464 Environmental Engineering Processes - HW #6 Below are three sets of reaction data (concentration vs time) taken from a CMBR. Nothing is known about the reactions as only the...

Solution manual for Assignment 97230
    Reaction A
    Time, t (min)
    Conc, c (mg/L)
    0
    100
    1
    50
    2
    35
    3
    27
    4
    26
    5
    22
    6
    17
    7
    15
    8
    13
    9
    12
    10
    11
    11
    10
    Reaction B
    Time, t (min)
    Conc, c (mg/L)
    0
    100
    5
    81
    10
    67
    15
    55
    20
    40
    25
    37
    30
    27
    35
    25
    40
    20
    45
    17
    50
    14
    60
    9
    Reaction C
    Time, t (min)
    Conc, c (mg/L)
    0
    100
    5
    90
    10
    82
    20
    68
    30
    57
    40
    49
    60
    38
    90
    28
    120
    21
    180
    13
    240
    9
    300
    6.5
1. Given below are the plots of Time vs Concentration without any further manipulation for all three reactions.
Reaction - A
Reaction - B
Reaction - C
2. Calculating characteristic reaction times from the plots by using definition 1.
Using definition 1: the time where the difference between instantaneous concentration and ultimate concentration, is reduced to of initial concentration. Let us assume the reactions are irreversible and thus the = 0. Therefore, the tchar will be at , where
· For reaction A: = From the graph, the time corresponding to the concentration value 37 is approximately 1.9.
· For reaction B: From the graph, .
· For reaction C: From the graph, .
    Reaction
    tchar(min)
    A
    1.9
    B
    25
    C
    61
3. To determine the order, n and reaction rate constant, k by differential and integral methods.
i. Differential method: Using the rate equation as ;
Taking on both sides, gives: , where .
i) Reaction A
    Time, t
(min)
    Conc, c
(mg/L)
    dt
    dc
    dc/dt
(mg/L-min)
    ln(-dc/dt)
    ln(c)
    0
    100
    1
    
    
    
    4.60517019
    1
    50
    1
    -50
    -50
    3.912023005
    3.91202301
    2
    35
    1
    -15
    -15
    2.708050201
    3.55534806
    3
    27
    1
    -8
    -8
    2.079441542
    3.29583687
    4
    26
    1
    -1
    -1
    0
    3.25809654
    5
    22
    1
    -4
    -4
    1.386294361
    3.09104245
    6
    17
    1
    -5
    -5
    1.609437912
    2.83321334
    7
    15
    1
    -2
    -2
    0.693147181
    2.7080502
    8
    13
    1
    -2
    -2
    0.693147181
    2.56494936
    9
    12
    1
    -1
    -1
    0
    2.48490665
    10
    11
    1
    -1
    -1
    0
    2.39789527
    11
    10
    1
    -1
    -1
    0
    2.30258509
From the graph, the slope of the line gives the order of the reaction A i.e., (approx.).
For calculating choosing data point 6. So, for , .
For ease of writing units, let us take , then
ii) Reaction B
    Time, t
(min)
    Conc, c
(mg/L)
    dt
    dc
    dc/dt
(mg/L-min)
    ln(-dc/dt)
    ln(c)
    0
    100
    
    
    
    
    4.60517019
    5
    81
    5
    -19
    -3.8
    1.335001067
    4.39444915
    10
    67
    5
    -14
    -2.8
    1.029619417
    4.20469262
    15
    55
    5
    -12
    -2.4
    0.875468737
    4.00733319
    20
    40
    5
    -15
    -3
    1.098612289
    3.68887945
    25
    37
    5
    -3
    -0.6
    -0.510825624
    3.61091791
    30
    27
    5
    -10
    -2
    0.693147181
    3.29583687
    35
    25
    5
    -2
    -0.4
    -0.916290732
    3.21887582
    40
    20
    5
    -5
    -1
    0
    2.99573227
    45
    17
    5
    -3
    -0.6
    -0.510825624
    2.83321334
    50
    14
    5
    -3
    -0.6
    -0.510825624
    2.63905733
    60
    9
    10
    -5
    -0.5
    -0.693147181
    2.19722458
From the graph, the slope of the line gives the order of the reaction B i.e., (approx.).
For calculating choosing data point 6. So, for , .
For ease of writing units, let us take , then
iii) Reaction C
    Time, t
(min)
    Conc,...