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CE 561 Lecture Notes
Fall 2009
p. 1 of 6
Day 19:
Review for 1
st
Exam
Here, I will attempt to outline what we have covered during the first half of the course.
This
completes the portion of the course devoted to reaction kinetics.
After the exam, we will begin
the reactor and reaction engineering portion of the course.
What did we learn so far?
Introduction and review:
Definitions of:
reaction rate, rate coefficient, reaction order, molecularity, elementary
reaction, law of mass action, reactive intermediates, unimolecular reaction, bimolecular
reaction, termolecular reaction, molecularity of a reaction, principle of microscopic
reversibility, Arrhenius equation, reaction mechanism
.
How to write rate equations and how to analytically integrate simple rate expressions for a
single reaction (0
th
order, 1
st
order, 2
nd
order, etc.).
How to use integrated rate expressions to determine the reaction order and find the rate
constant for a single reaction given concentration vs. time data.
How to make an Arrhenius plot and extract rate parameters from it.
How and when to use classical analytical approximations made in analyzing reaction
mechanisms: the
partial equilibrium
approximation and the
pseudosteadystate
approximation.
Matrix Methods and Notation
Writing reactions in matrix notation
1
0,
1,
N
ij
j
j
A
iM
α
=
=
=
∑
(
α
ij
<0 for reactants, >0 for products), or
0
A
=
Writing rate equations in matrix notation
T
dC
r
dt
=
and
MC
dt
=
Finding a set of linearly independent reactions by finding the rank of the stoichiometric
matrix.
General solution of
linear
1
st
order ODE’s (rate equations) in matrix form:
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View Full DocumentCE 561 Lecture Notes
Fall 2009
p. 2 of 6
( )
exp(
)
o
C t
Mt C
=
, which becomes
1
( )
( exp(
)
)
o
Ct
T
t T
C
=
Λ
using eigenvalues and
eigenvectors of
M
.
This includes understanding the definitions of eigenvalues and
eigenvectors and how they are calculated.
Solution of linear ODE’s using Laplace transform methods.
Stochastic methods for analyzing chemical reaction processes
Definition and use of the
conditional probability
of having a particular state of a system
given after some time given the state of the system at some earlier time
Basic algorithm for kinetic Monte Carlo simulation of a reacting system
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 Fall '09

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