Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 1.
A 2nd order reaction is conducted in 6 ideal mixed flow reactors in series. Each
individual reactor has a volume of 250 L.
a. Calculate the overall conversion in this reactor system. Using
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Name:
Instructions:
1. Put your name on every sheet of paper you hand in for grading, including these
exam sheets. You must hand in these test sheets and printed/written solutions for all
problems at
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Ideal Reactor Design
The rate equa(on for a reac*ng component i is an
intensive measure, and it tells how rapidly component i
forms or disappears in a given environment a
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
v=VM[S]/(KM+[S])
VM=kcat[E0]
kcat = turnover number, maximum rate of
substrate conversion per enzyme molecule
Note: for single substrate enzyme, kcat=k2
Most enzymes kcat ranges from 1 to 104/sec
(car
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
ABE 370 Quiz 1
Name:
Problem 1 (4 points). For the following rate models, write the integrated rate model C(t), assuming the
initial concentration is Co at t=0.
r = k
r = kC
C(t)= ?
C(t)= ?
r = k
r
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Solutions for Homework 1
2.12 if the reaction is assumed to be elementary reaction. If not, the order of the
reaction cannot be predicted from the stoichiometry equation. Experimental
methods are requ
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Other inhibition models
Uncompe(ve inhibi(on
Noncompe(ve inhibi(on
Binding of inhibitors changes binding of substrate
General Inhibition Model
General Model
KM
k2
E+S ES E+P + I
KM = [E
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Study Guide Test 1
In order to do well on the next test, you should be able to do the following:
1. Define stoichiometry and be able to apply the concept to bala
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Trimolecular Reacons
Similarly, for the reacon
Trialanderror soluon:
Select a value for n and calculate k
The value of n which minimizes the variaon in k is the
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Spacetime and Spacevelocity
The performance measure for a batch reactor is t.
For steady flow reactor (MFR and PFR) the proper
performance measures are:
spacetime = 1/s
spacevelocity s = 1/
Space
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 1 Solution (35 points)
The chemical reaction is a 2nd order reaction, hence the solutions to these rate equations
are:
Enzyme rate equation 1
Chemical equation
c kt
o rate
k
m
1
t(X
)
l
n
c
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 1 (55 points)
Reactant A is converted to product B in a batch reactor (see data below). The chemical reaction rate is 2nd order
with respect to A with k=0.025 L/molhr.
Data: Co = 10 mol/L
rea
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 1 (25 points)
A spherical particle of reactant B is reacted with liquid reactant A to make product C. It takes 4.85 min to
convert 50% of the sphere into product C. It takes 23.5 min to comple
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 1(50 points)
0
1
5
time 10
20
30
35.6
gm
de nsity 3.2
3
cm
R 3cm
solubility 10
Cw 1
gm
3
2.97
2.85
rad 2.687
2.28
1.62
0
data from experiment
30
3
time 20
cm
10
0
react
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 1 Modeling drug delivery (50 points)
Medicine is to be delivered to sick lung tissue by injection into the venous blood stream. The medicine goes to
the heart and is then pumped to the lung vi
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Name:
Instructions:
1. Put your name on every sheet of paper you hand in for grading, including these pages.
2. Circle or clearly indicate all solutions correspondingly to the numbers/letters on this
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Welcome to
ABE 370 Biological and Microbial
Kine5cs and Reac5on Engineering
Fall 2016
Monday, Wednesday, and Friday
12:30 1:20 PM
LYNN G167
Instructor
Meng Deng, Ph.D.
Dept. of Agricultural
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Problem 4.2
Since this is an aqueous system, the volume is assumed to be constant.
A + 2 B > R + S
From the stoichiometry, for every mole of A reacted, 2 moles of B are reacted.
Therefore,
XB = 2*XA*
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
Inhibition
Enzyme inhibitors are substances that reduce rate of reaction.
Enzyme inhibitors are usually defined as substance that specifically
affect the enzymatic mechanism. Substances that alter th
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
What is the reac+on rate model for this reversible elementary reac+on?
2A + B <> C
Rate Equa+on
The determina+on of the rate equa+on
follows a twostep procedure
th
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
ABE 370 Quiz 2
Name:
Problem 1 (2 points). Prove that dX/dt =  (1/No)(dN/dt). X fractional conversion, N moles, t time
X = 1C/Co
C = N/V
dX/dt =  (1/Co)(dC/dt) =  (1/Co)(V/V)(dC/dt) =  (1/No)(V)(
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Fall 2014
If the input signal Cin is measured and the exit
age distribu5on func5ons Ea, Eb, and Ec are
known, then C1 is the convolu5on of Ea with
Cin and so on, thus
Exampl
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Spring 2014
Problem 4.2
Since this is an aqueous system, the volume is assumed to be constant.
A + 2 B > R + S
From the stoichiometry, for every mole of A reacted, 2 moles of B are reacted.
Therefore,
XB = 2*XA*
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Spring 2014
Problem 1.
Derive the equation giving Cout as a function of Co, qm, qp, m, p, and k, assuming an
zero order reaction occurs in the ideal reactors of this steady state system.
qm
MFR
Co, q
m
Cout, q
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Spring 2014
Problem 1.
Derive the equation giving Cout as a function of Co, qm, qp, m, p, and k, assuming an
zero order reaction occurs in the ideal reactors of this steady state system.
qm
MFR
Co, q
m
Cout, q
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Spring 2014
ABE 370 Quiz 2
Name:
Problem 1 (2 points).
For an enzymatic reaction (see below, if needed), what are the dimensions/units of the rate constants Vm
and Km?
r = Vm*C/[Km + C]
Vm [=] mol/volumetime
Km
Biological/Microbial Kinetics And Reaction Engineering
ABE 37000

Spring 2014
5.
6.
Solution:
First order reaction, ln(Co/C) = k*t or k = 1/t*ln(Co/C) or t = (1/k)*ln(Co/C)
At 298 K (T1), k1 = 1/(300*24*60) * ln (2) = 1.6045 x 10 6 min1.