Environmental Engineering Reference
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(b) If the overall rate constant is 2 h
−
1
, and the initial concentration of
A is 10 mol/m
3
, what is the initial rate of formation of C?
5.43
2
For the reaction 2A
k
→
B,
(a) Write the differential rate equation for the dissipation of A.
(b) Integrate the above expression with the initial condition that at
t
=
0,
[
A
]=[
A
]
0
, and obtain the equation for A as a function of time.
(c) If the rate constant is 2 h
−
1
, what is the half-life of the reaction?
5.44
3
The decomposition of di-2-methylpropan-2-yl into propanone and ethane
goes through free radical mechanisms given as follows:
k
1
−−→
2
(
CH
3
)
3
CO
•
,
(
CH
3
)
COOC
(
CH
3
)
3
k
2
(
CH
3
)
3
CO
•
−−→
CH
3
COCH
3
+
CH
3
,
CH
3
+
CH
3
k
3
−−→
C
2
H
6
.
Formulate the expression for the rate of production of ethane and show
that the reaction is first order in the reactant di-2-methylpropan-2-yl. Use
the pseudo-steady-state approximation and perform algebra. Remember
that two (CH
3
)
3
CO
•
radicals are formed for every one molecule of the
reactant.
5.45
2
For the reaction A
+
B
k
k
2
−−→
D, obtain the expression for the rate of
k
−
1
C
production of D in terms of the reactant concentrations. What is the order
of the overall reaction?
5.46
3
The reaction of gas-phase ozone with dimethyl sulfide (DMS) in a glass
reactor occurs via the following two-step mechanism:
k
1
−−→
wall decay,
O
3
k
2
−−→
products.
O
3
+
DMS
Experiments were conducted under a large excess of DMS concentration,
[DMS]
0
, to obtain the value of
−
dln
[
O
3
]
/
d
t
(Du et al., 2007):
[DMS]
0
/10
14
mol/cm
3
O
3
]
/
d
t
/
10
5
s
−1
−
dln
[
0
0.609
3.63
6.00
4.84
7.29
6.05
7.83
Derive the rate equation for the conditions stated, and from an appropriate
plot of the data obtain
k
1
and
k
2
.
REFERENCES
Atkinson, R. and Pitts, J.N. 1975. Temperature measurements of the absolute rate constants
for the reaction of oxygen (
3
P) atoms with a series of aromatic hydrocarbons over the
temperature range 299-292 K.
The Journal of Physical Chemistry
79, 295.
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