L. Qi et al. / Catalysis Communications 49 (2014) 6–9
7
3
. Results and discussion
TBHP in the reaction system is thoroughly deperoxidated into TBA
and O ; at a later time t, the concentration of TBHP is [TBHP] and
the subtraction of [TBHP] from [TBHP] is proportional to V with
the same coefficient λ, viz. [TBHP] ; hence the
2
3
.1. Kinetics
0
t
0
− [TBHP] = λV
t
For a real-time kinetic analysis of TBHP decomposition, the change in
first-order integral equation of TBHP decomposition can be arrived
TBHP concentration with time must be accurately traced while the reac-
tion is in progress. Only because of the formation of di-tert-butyl perox-
ide and fragmented products (e.g. acetone and methanol), was the
quantitative measurement of the time-dependent TBHP concentration
therein conducted with iodometric titration [10,14] and in situ UV–vis
spectroscopy [13], respectively. Provided that by an appropriate choice
of catalysts and reaction conditions, TBHP is completely decomposed
at as in Eq. (4) by integrating Eq. (3):
ꢀ
ꢁ
1
′
1
V∞
ln
¼ k t þ ln
:
ð4Þ
V∞−Vt
Consequently, the pseudo-first-order kinetics of TBHP in Eq. (3)
leads to a straight line of ln[1 / (V )] versus t defined by Eq. (4),
∞
− V
t
into TBA and O
2
, the rate of TBHP disappearance will be followed by
(V ) evolved from the reaction system
whose slope is the pseudo-first-order rate constant k′ in Eqs. (3)
and (4).
monitoring the volume of O
2
t
with time (t). The case is true here in our studies due to the observation
that TBA was yielded as a single organic product (Table 1). In addition,
neither induction period nor deactivation occurred for the M-OL-1s
under the selected conditions.
The catalytic decomposition of TBHP with the M-OL-1s is supposed
to have a rate law equation involving TBHP and M-OL-1 as in Eq. (1):
In contrast, if the order α in Eq. (2) is assumed to be 2, the resultant
pseudo-second-order integrated rate expression can be written
into Eq. (5), thus a straight line being predicted with a slope of λk′
when 1 / (V
∞
t
− V ) is plotted against t:
1
′
1 :
¼
λk t þ
ð5Þ
V −V
V
∞
∞
t
d½TBHPꢀ
α
β
−
¼ k ½TBHPꢀ ½M‐OL‐1ꢀ
ð1Þ
a
dt
Fig. 1 represents the results of the TBHP decomposition catalyzed by
Cu-OL-1 at four [Cu-OL-1]s, where ln[1 / (V − V )] was plotted against
∞
t
a
where k is the apparent rate constant, α the order in TBHP, β the order
t. As shown in Fig. 1, the four sets of kinetic data can be linearly fitted by
the least squares, suggesting that the order α in Eqs. (1) and (2) has a
value of 1; although the net reaction does not implicate Cu-OL-1, k′,
which was measured from the slope, increases with [Cu-OL-1] for a
in M-OL-1 (the overall order the sum of α and β), [TBHP] the concentra-
tion of TBHP and [M-OL-1] the formal concentration of M-OL-1 (sieved
to −300/+500 mesh); [M-OL-1] was calculated by dividing the desired
loading of M-OL-1 (mg) by the total volume of TBHP and acetonitrile
given [TBHP]
0
and a given temperature.
(
mL). If no deactivation of M-OL-1 exists and [M-OL-1] is unchanged
β
In consideration of k′ = k
a
[Cu-OL-1] , a new form of k′ expression is
β
throughout the course of the reaction, [M-OL-1] in Eq. (1) is so left
deduced as in Eq. (6):
constant and absorbed into k
a
, giving rise to the underlying rate law
equation:
′
lnk ¼ β ln½Cu‐OL‐1ꢀ þ lnk
ð6Þ
a
d½TBHPꢀ
′
α
−
¼ k ½TBHPꢀ
ð2Þ
so that another type of straight line may arise from a plot of lnk′ versus
ln[Cu-OL-1], its slope being the order β. Indeed, the plot of lnk′ versus ln
[Cu-OL-1] (Fig. 2) gives a straight line with a slope of 1.0690 ± 0.0291.
The order β in Eq. (6) is then fitted to be equal to 1. As a result, the TBHP
decomposition has been determined kinetically to be first order in both
TBHP and Cu-OL-1, i.e. second order overall. As usual, the Arrhenius-
dt
β
a
where k′ = k [M-OL-1] is pseudo rate constant. According to Eq. (2),
the simplest rate law concerns a first-order reaction of TBHP decompo-
sition (α = 1) as in Eq. (3):
type behavior was exhibited between k′ and reaction temperature (T/K)
and so an apparent activation energy E (142 ± 9 kJ mol ) was calcu-
a
d½TBHPꢀ
′
−
¼ k ½TBHPꢀ
ð3Þ
−1
dt
lated from the Arrhenius plot of lnk′ versus 1 / T (Figs. S3,S4). The
success in these linear fittings negates the possibility of coexistence of
other side reactions otherwise the deviation from the specific form of
which is then integrated in the time interval of zero to t. Noting that
at t = 0, the initial concentration of TBHP, [TBHP] is proportional to
, viz. [TBHP] = λV , where V is the volume of O evolved when
0
V
∞
0
∞
∞
2
-
0.90
-1.05
1.20
-1.35
Table 1
Kinetics and activity for the M-OL-1s to catalyze the decomposition of TBHP into TBA and
O .
2
(
d)
-
a
a
a
4b
M-OL-1
α
β
E
(
a
k′ × 10
Conversion
(%)
kJ mol−1)
(s
−1
)
-
-
1.50
1.65
K-OL-1
1
1
1
1
1
1
1
1
1
1
83
6.8792
7.1120
7.2875
8.3583
25.9000
78c
(c)
(b)
d
(
85
76)
c
-1.80
-1.95
Mg-OL-1
Fe-OL-1
Ni-OL-1
Cu-OL-1
98
95
59
d
d
d
(
82
83)
c
-
2.10
-2.25
2.40
-2.55
(
87
80)
c
(a)
(
89)
-
c
142
98
96)d
(
a
0
50
100
150
200
250
300
350
400
a
α, β and E were determined from Figs. 1,2 and S3–S20.
b
time (s)
2
k′ was obtained under the conditions where T 338 K, TBHP (65 wt.% in H O) 1.00 mL,
−
1
[
M-OL-1] 8.33 mg mL and acetonitrile 5.00 mL, respectively.
c
t 1 h, the other conditions were the same as in footnote b; the TBHP conversion was
determined by GC with a 100% selectivity towards TBA for all the M-OL-1s.
Fig. 1. Plots of ln[1 / (V∞ − V )] versus t. Reaction conditions: T 338 K, TBHP (65 wt.% in
t
H O) 1.00 mL, [Cu-OL-1] 1.67 mg mL−1, [Cu-OL-1] 3.33 mg mL−1, [Cu-OL-1]c
2
a
b
d
−1
−1
The parenthesized TBHP conversion was determined by the V
t
/ V
∞
ratio (t 1 h).
5.00 mg mL , [Cu-OL-1]d 8.33 mg mL , acetonitrile 5.00 mL.