Biomedical Engineering Reference
In-Depth Information
K
%
O
þ
M
þ
H
C
þ
H
O
ð
W
Þ
; rapid
(3)
3
2
(a)
Show that the rate law for this mechanism, with M present in great excess, is
r
E
¼
kLc
A
c
HCl
=ð
L
þ
c
w
Þ;
(4)
where
L
¼
c
M
K
¼
c
C
c
W
=
c
H
3
O
þ
(5)
Assume all H
þ
is present in C and in H
3
O
þ
.
(b)
Show that the integrated form of
Eqn (4)
for a constant-volume batch reactor
operating isothermally with a fixed catalyst concentration is
k
¼½ð
L
þ
c
A0
Þ
ln
ð
c
A
0
=
c
A
Þð
c
A
0
c
A
Þ=
c
HCl
Lt
:
This is the form used by Smith (1939) to calculate k and L.
(c)
Smith found that L depends on temperature and obtained the following values
(what are the units of L?):
T,
C
0
20
30
40
50
L:
0.11
0.20
0.25
0.32
0.42
Does L follow an Arrhenius relationship?
6.5.
Consider the following reversible reaction:
CO þ Cl
2
% COCl
2
The rate of formation of
COCl
2
has been observed to follow the rate expression:
k
f
½Cl
2
3
=
2
½CO
k
r
½Cl
2
1
=
2
½COCl
2
r
COCl
2
¼
A proposed mechanism is:
Cl
2
%2Cl
Equilibrium
CO þ Cl
%COCl
Equilibrium
COCl
þ Cl
2
%COCl
2
þ Cl
Rate determining
Use the rate-determining step/equilibrium assumption to determine if the proposed
mechanism is consistent with the observed rate expression.
6.6.
Under the influence of oxidizing agents, hypophosphorous acid is transformed into
oxidizing agent
phosphorous acid: H
3
PO
2
!
H
3
PO
3
. The kinetics of this transformation
present the following features. At a low concentration of oxidizing agent,
r
H
3
PO
3
¼
k
½
oxidizing agent
½
H
PO
2
3
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