CE 561 Homework 2:
(assigned 9/9/09, due 9/14/09)
(1)
Consider the network of 1
st
order reactions given by
A
1
A
2
A
3
k
k
k
A
4
k
where for simplicity, we have given all four reactions the same rate constant and made all
four reactions irreversible (note that a cyclic system of irreversible reactions with
identical rate constants would be
extremely
unlikely to occur in practice, but it’s a nice
problem).
(a)
Write this set of reactions in matrix form (i.e.
0
=
A
α
)
(b)
Write the rate equations in terms of the reaction rates in matrix form using the
stoichiometric matrix (i.e.
r
dt
C
d
T
α
=
).
(c)
Write the rate equations in terms of a matrix of rate constants and a vector of
concentrations (i.e.
C
M
dt
C
d
=
).
How are the matrices
T
α
and
M
related?
(d)
Find an analytical solution to the rate equations (for
C
A
1
(
t
=0)=
C
o
,
C
A
2
(
t
=0)=
C
A
3
(
t
=0)=
C
A
4
(
t
=0)=0) using the matrix method discussed in class.
(e)
If there are
i
A
1
molecules,
j
A
2
molecules, and
k
A
3
molecules in the system at
time
t
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 Fall '09
 Chemical reaction, Rabbit, Rate equation, Rate Equations

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