CE 561 Lecture Notes
Fall 2009
p. 1 of 13
Days 1 and 2: Introduction and Overview
Motivation for understanding chemical kinetics and reaction design:
This is what makes us
chemical
engineers – the reactor is the central feature of most
chemical processes.
Even if separation costs dominate, the reactor often determines the
separation costs.
Chemical reactions are ubiquitous in nature and industry.
In this course, we will construct
mathematical descriptions
of chemical reactions and chemical
reactors.
These allow us to
predict
and
understand
the behavior of these reactions and reactors.
Definitions of, and Notation for, Reaction Rates:
Reaction rate: In a perfectly mixed, closed, constant volume system (or in some region of space
over which conditions are uniform) with the generic reaction
a
A +
b
B
↔
c
C +
d
D
The
reaction rate
is defined as
1
111
C
AB
D
dC
dC
dC
dC
r
a dt
b dt
c dt
d dt
=
=
=
In these expressions, 
a
, 
b
,
c
, and
d
are the stoichiometric coefficients of the chemical species A,
B, C, and D, respectively.
C
A
,
C
B
,
C
C
, and
C
D
are the concentrations (number of molecules or
moles per unit volume) of the chemical species.
For a more general system of reactions, written as
1
0,
1,
N
ij
j
j
A
iM
α
=
=
=
∑
(
α
ij
< 0 for reactants, > 0 for products)
where
N
is the number of species,
M
is the number of reactions, and
ij
is the stoichiometric
coefficient of species
j
in reaction
i
, the rate of reaction
i
is defined such that the rate of change
of concentration of species
j
is given by
1
j
M
A
ij i
i
dC
r
dt
=
=
∑
Note that for multiple reactions, this may not uniquely define the rates of reaction.
There is
some minimum set of reactions required to describe the rates of change of species
concentrations.
Any linear combination of those reactions could equally well be used to describe
the overall changes in composition.
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Fall 2009
p. 2 of 13
For a homogeneous reaction (occurring in the gas, liquid, or solid phase) the rate has units of
concentration per time or moles per volume per time.
For a heterogeneous reaction (occurring at a surface or interface) the rate has units of moles per
area per time or surface concentration per time.
As presented here, the rate is an intensive quantity, which means that it is independent of the size
of the system, and is defined for a homogenous system.
Sometimes, it is more appropriate to
describe systems in terms of the extensive rate, which is simply the intensive rate multiplied by
the total system volume.
In general, the reaction rate is a function of temperature, pressure, and composition.
At fixed
temperature and pressure, the reaction rate is usually expressed as a function of the species
concentrations.
That is
12
(
,
,...,
)
N
i
AA
A
r fC C
C
=
The most commonly used functional dependence of the rate on the concentrations is to set the
rate proportional to a product of algebraic powers of the species concentrations:
1
ij
j
N
iA
j
rC
ν
=
∝
∏
or
1
ij
j
N
ii
A
j
rk C
=
=
∏
The constant of proportionality (
k
i
) is often referred to as the
rate constant
.
Perhaps a better term
is
rate coefficient
– since it is only constant with respect to the species concentrations.
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 Fall '09
 Reaction, Chemical reaction, Rate equation, CDO

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