Kinetic study of the oxidation of maltose by peroxydisulfate

Kinetic study of the oxidation of …
Mawia Hassan & other's
Kinetic study of the oxidation of maltose by
peroxydisulfate
Mawia Hassana, Elnoor Abakerb, Elhaj. J. Ma, Rasha Jameband
Ibrahim Mukhtarc
a
State Key Laboratory of Chemical Resource Engineering, College of Science, Dalanj
University, Dalanj, P. R. Sudan Tel: 00249912417018; Email:[email protected].
b
State Key Laboratory of Chemical Resource Engineering, College of
Education, Dalanj University, Dalanj, P. R. Sudan. 00249116519174
E-mail: [email protected].
c
State Key Laboratory of Chemical Resource Engineering, College of
Education, Khartoum University, Khartoum, P. R. Sudan .
*
Corresponding authors:
State Key Laboratory of Chemical Resource Engineering, College of
Science, Dalanj University, Dalanj, P. R. Sudan Tel:
00249123282825; E-mail: [email protected]
Abstract
For the first time, the kinetic study of the oxidation of maltose by
peroxydisulfate under catalyzed and un-catalyzed conditions has been
investigated. The kinetic study reveals that the reaction follow first
order of reaction with respect to peroxydisulfate and silver ion as
catalyst while a fractional order of reaction with respect to
maltose.The activation energy EA entropy of the reaction ∆S and free
energy ∆G has been calculated for this reaction. The reaction products
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Kinetic study of the oxidation of …
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are analyzed by using FT-IR which reveals the presence of
formaldehyde and formic acid in the product.
Keywords: Peroxydisulfate, Kinetic study, Maltose.
‫ﻣﺳﺗﺧﻠص‬
(‫ﺗﻘدم ﻫذة اﻟورﻗﺔ اﻟﻌﻠﻣﻳﺔ دراﺳﺔ ﻋن أﻛﺳدة ﺑﻌض اﻟﺳﻛرﻳﺎت اﻟﺑﺳﻳطﺔ )ﻣﺎﻟﺗوز‬
‫ﺑواﺳطﺔ ﺑروﻛﺳﻲ ﺛﻧﺎئ ﻛﺑرﻳﺗﺎت اﻟﺑوﺗﺎﺳﻳﺳوم ﻓﻲ ﺣﺎﻟﺔ ﻋدم وﺟود ﻋﺎﻣﻝ ﻣﺳﺎﻋد وﻛذﻟك ﻓﻲ‬
‫ وﻗد أﺛﺑﺗت اﻟدراﺳﺔ اﻟﺣرﻛﻳﺔ ﻟﻠﺗﻔﺎﻋﻼت اﻋﻼة اﻧﻬﺎ ﻣن‬.‫ﺣﺎﻟﺔ أﻳون اﻟﻔﺿﺔ ﻛﻌﺎﻣﻝ ﻣﺳﺎﻋد‬
‫ ﺑﻳﻧﻣﺎ ﻛﺎﻧت ﻣن‬,‫اﻟرﺗﺑﺔ اﻻوﻟﻲ ﺑﺎﻟﻧﺳﺑﻪ ﻟﺑروﻛﺳﻲ ﺛﻧﺎئ ﻛﺑرﺗﺎت اﻟﺑوﺗﺎﺳﻳوم واﻟﻌﺎﻣﻝ اﻟﻣﺳﺎﻋد‬
‫( ﺑﺎﻟﻧﺳﺑﺔ ﻟﺳﻛر اﻟﻣﺎﻟﺗوز ﻛﻣﺎﺗم ﺣﺳﺎب اﻟﻘﻳم اﻟدﻳﻧﺎﻣﻳﻛﻳﺔ اﻟﺣ اررﻳﺔ وﻫﻲ‬0.2) ‫اﻟرﺗﺑﺔ اﻟﻛﺳرﻳﺔ‬
‫طﺎﻗﺔ اﻟﺗﻧﺷﻳط واﻧﺗروﺑﻳﺎ اﻟﺗﻧﺷﻳط واﻟطﺎﻗﻪ اﻟﺣرﻩ ﺗﻣت ﻋﻣﻠﻳﻪ ﺗﺣﻠﻳﻝ اﻟﻧواﺗﺞ وذﻟك ﺑﺈﺳﺗﺧدام‬
‫اﻻﺷﻌﻪ ﺗﺣت اﻟﺣﻣراء اﻟﺗﻲ أﺛﺑﺗت وﺟود اﻟﻔورﻣﺎﻟدﻫﻳد وﺣﻣض اﻟﻔورﻣﻳك وﻗد ﺗم أﻗﺗراح اﻟﻳﻪ‬
.‫ﻣﻧﺎﺳﺑﻪ ﻟﺗﻔﺳﻳر ﻗﺎﻧون اﻟﻣﻌدﻝ وﻧواﺗﺞ اﻟﺗﻔﺎﻋﻼت‬
Introduction
Reaction kinetics is the study of rate of chemical reaction and the
influence of reaction condition on the rate of chemical reaction
(Litwinienko and Ingold2007). Several chemical reactions are not
kinetically simple; they ensue through number of steps or stagesto
convert from reactants to final products. Complex reactions are
invented by a sequence of elementary reactions and each of which
proceed in a single step. Chemical reactions are classified by their
order of reaction or molecularity i.e. the number of atoms, molecules
or other species taking part in an elementary process or step.
Molecularity must be a whole number like one, two or three (Binder
and Raines 2009). Bimolecular reactions are second order reaction but
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in fact it is not true all time because some second order reactions are
not bimolecular reactions. Molecularity of reaction must always be an
integer and greater than zero but rarely three or more while order of
reaction can be zero, greater than zero or fractional. Both physical and
chemical methods depending on the nature of the reactants and
products have been used for the estimation of rate of chemical
reactions (Seddonet al., 2000). The rate of chemical reaction is
determined by the slowest step of the reaction mechanism and
proposed mechanism must be in agreement with the observe kinetics
of the reaction. Therefore, stationary or steady state concept is used
which has been employed intensively in the interpretation of rate of
the reaction taking place in stages. According to stationary state
concept, the concentration of the species initially rise at the beginning
of the reaction up to a certain concentration and then reaches a
constant or steady value which persists until the end of the reaction
(Guerrero et al., 2008). In the steady state, unstable species is
removed by subsequent reactions as fast as formed in the earlier
stages. Generally, most of reactions take place in solutions and redox
reaction is one of thoroughly investigated type of reactions in
solution.
There are several factors which elucidate the mechanism of a
particular redox reaction in solution; the most important being order
of the reaction, PH, specific ion effect, dielectric constant and effect
of temperature etc. The mechanism of the catalyzed reaction is
completely different from that of the un-catalyzed reaction, although
the final products are the same. Another factor that is important for
the elucidation of the reaction mechanism is the identification of the
mechanism takes place through the detection ofproducts; also the
intermediates can play important role in the identification of
mechanism, and becomes more important when the intermediates
have a litter stability to be identified. The kinetic and mechanism of
the oxidation of inorganic and organic substrates by peroxydisulfate
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Kinetic study of the oxidation of …
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under both catalyzed and un-catalyzed conditions have received
considerable attention (Wilmarth and Haim, 1961; House, 1962). The
first-order un-catalyzed peroxydisulfate oxidation is well studied in
solution. Bartlett and Cottman (Barlett and Cotman, 1994) have
suggestedthat radicals produced in peroxydisulfate decomposition in
aqueous solution cannot induce the peroxydisulfate decomposition
and based on their statement, auto-catalysis is not observed in the
thermal decomposition and that reaction is first order reaction in
peroxydisulfate concentration.
However, to explain the increase in the rate on addition of an
oxidizable substrate, it is necessary to postulate that radicals produce
from the reducing agent can induce peroxydisulfate decomposition.
The radical anion SO4- can be generated by the photolysis or
thermolysis of the peroxydisulfate as well as by the one –
electronreduction of peroxydisulfate (Clifton and Huie, 1989).(Gibert
and Stell, 1999) found that the reaction of SO4- with the y-glucose is
selective towards the C2, C5 and C6 positions.This reflects the
activating effect of β–oxygen substituent where the radical orbital can
eclipse the β-C-O bond, providing a SOMO-δ* interaction which
stabilizes the developing radical center (Gibertet al., 1999).The
oxidization of essential sugars is utmost importance, both a purely
chemical point and view of its bearing on the mechanism of essential
sugars metabolism. It has been observed that there is not enough
information in the literature on the kinetics and mechanism of all
essential sugars by peroxydisulfate, and present work is a part of our
broad program of studying mechanistic aspects of the oxidation of
essential sugars by peroxydisulfate.
Materials and methods
The redox reaction of peroxydisulfate with maltose was studied as
follow:
46 ‫مجلة البحث العلمي للعلوم واآلداب – العدد الخامس عشر‬
Kinetic study of the oxidation of …
i.
ii.
iii.
iv.
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To establish the rate laws for the reaction between
peroxydisulfate and maltose.
To study the effect of temperature and evaluation of the
thermodynamic parameters.
To investigate the effect of catalyst and surface.
To analyze the reaction products.
Kinetic Measurements:
It was found that the reaction between peroxydisulfate and maltose at
ordinary temperature was slow in the absence of catalyst. The
appropriate rate of the oxidation reaction was carried out at 70oC;
therefore the temperature range of (60-80 o C) was selected.
The aim of kinetic measurements was to establish asuitable rate law
for the reaction investigation.This required a set of runs to be
accomplishedin which the concentration of one reactant was changed
while the concentration of the other reactant was kept constant.
General Procedure:
50cm3 of both substrate and peroxydisulfate solution were placed in
the thermostat for approximately 20 minutes, separately. Then these
solutions were transferred to the 250 cm3 round bottom flask. The
residual peroxydisulfate was estimated by an iodometric method
which was modified by Bartlett and Cottman, and used by Vasudiva
and Wasif. 5cm3 of the reaction mixture containing residual
peroxydisulfate was added to 250 cm3 conical flask containing a
mixture of5cm3 of sodium bicarbonate solution, 1cm3 of sulfuric acid
solution and 5cm3 of 20% potassium iodide solution. Then it was
placed in the dark for 20 minutes till all iodine was liberated. After
that starch was added drop wise and then the liberated iodine was
titrated against standard thiosulfate solution.
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Preparation of solutions:
The oxidation of organic compounds by peroxydisulfate required the
use of double distilled water because it is highly susceptible to
impurities in solution and often leads to erratic values. Double
distilled water was obtained by redistilling water over alkaline
potassium permanganate in Pyrex glass. Solutions used in this work
were prepared in the following manner.
1-Potassium peroxydisulfate
6.76g of K2S2O8 (M.W=270.33)was dissolved in 250cm3 of double
distilled water to get 0.10 mol.dm-3solution. The solution was always
prepared fresh and never used after more than 48 hours from the time
of preparation. The solution was kept at room temperature (30-40⁰C)
in the dark.
2-Maltose:
0.10M maltose solution was prepared by dissolving 9.008g of maltose
(M.W=360.22) in 250cm3 of double distilled water, it was prepared
one day before kinetic measurement for optical equilibrium. Fresh
maltose solution was prepared for every kinetic run.
3-Sodium thiosulfate
0.01M sodium thioslfate (M.W =248.19) solution was prepared by
dissolving 2.48g of Na2S2O3.5H2Oin 1000cm3 of double distilled
water, it was then standardized against standard solution of K2S2O8
and kept for 4-5 days as stock solution.
4-Potassium iodide
20g of potassium iodide (M.W=166.0) was dissolved in 100cm3 of
double distilled water to get 20% freshly prepared solution.
5-Sodium bicarbonate
0.10 mol.dm-3 of bicarbonate (M.W=84.01) solution was prepared by
dissolving 4.20g of NaHCO3 (BDH) in 500cm3 of double distilled
water.
6- Sulfuric acid
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0.50Msulfuric acid solution was prepared by dissolving 1cm3 of
H2SO4 conc. (1.84 g\cm3, 98%, BDH) in 35cm3 of double distilled
water.
7-Silver nitrate
0.17g of AgNO3 (M.W=169.87.BDH) was dissolved in 100cm3 of
double distilled water to get 0.01 mol.dm-3 of silver nitrate solution
and used as catalyst.
8-Starch
1g of soluble starch was dissolved in 30cm3double distilled water and
heated .Starch solution was used as an indicator.
9-2, 4- Dinitrophenylhydrazine
10g of 2, 4-Dinitrophenylhdrazine (BDH Laboratory reagent) was
dissolved in 30cm3of double distilled water. 5cm3 and 10cm3 of
methanol and concentrated sulfuric acid were added respectively to
obtain complete solution.
Results and discussion:
Effect of peroxydisulfate concentration on Kinetic order:
Table 1 represent the effect on the kinetic order, measured by varying
the concentration of the peroxydisulfate from 10x10-3 mol.dm-3 to 40
x 10 mol.dm-3, maltose concentration and temperature were constant
at 20x 10-3 mol.dm-3 and 70 respectively. Peroxydisulfate
concentration effect was carried out in two steps. In the first step, the
rate law (R) was calculated in the manner outline from the literature
value while in the second step, the observe rate constant (ko) was
calculated by the integrated rate law at each peroxydisulfate
concentration and mean values were obtained. Figure 1b reveals the
effect of peroxydisulfate concentration on the average rate and
observed that average rate varies linearly with the peroxydisulfate
concentration. The rate equation obtained from Figure 1, can be
written as following from:
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R=k0[S2O82-]
The values of ko were obtained from the slop of Figure 2, in which ko
was clearly independent of peroxydisulfate concentration.
Table 1: Effect of peroxydisulfate concentration on rate law (R)
and rate constant (ko).
-3
2[S2O8 ] x 10
R x 104 (mol.dm-3.sko x 104 (s-1)
1
)
(mol.dm-3)
10
7.46
1.11
15
10.19
1.20
20
13.68
1.37
25
16.61
0.97
30
19.25
1.15
35
22.24
1.20
40
24.59
1.20
-3
-3
Maltose concentration =20 x 10 mol.dm and Temperature
= 70 ⁰C.
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Figure 1: Plots between [S2O8 ] and time at [Maltose] = 20 x 10-3
mol.dm-3 and Temperature = 70 ⁰C.
2-
Figure 2: Plots between R and [S2O82-] at [Maltose] = 20 x 10-3
mol.dm-3 and Temperature = 70 ⁰C.
Effect of maltose concentration on Kinetic order:
The effect on the kinetic order in the maltose-peroxydisulfate reaction
was studied by varying the maltose concentration from 2.5 x 10-3 to
25 x 10-3 mol.dm-3 at constant 20 x 10-3 mol.dm-3peroxydisulfate
concentration and 70⁰C temperatureFigure 3. The rate of reaction and
rate constant were calculated at different concentration of maltose
while temperature was constant and tabulated in table 2. Plots
between average rate and maltose concentration indicated that the
order is fractional (i.e = 0.2) with respect to maltose concentration as
shown in Figure 4.
Table 2: Effect of maltose concentration on rate law (R) and rate
constant (ko).
-3
[Maltose] x 10
R x 104
ko x 104
[Maltose]0.2
(mol.dm-3)
(mol.dm-3.s-1)
(s-1)
(mol.dm-3)
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10
12
15
18
20
25
30
12
13.34
13.26
13.27
13.68
13.49
12.38
Mawia Hassan & other's
1.01
1.46
1.38
1.13
1.37
1.21
1.10
0.35
0.40
0.34
0.45
0.46
0.50
0.53
Peroxydisulfate concentration =20 x 10-3 mol.dm-3 and Temperature = 70 .
Figure 3: Plots between [Maltose] and time at [S2O82-] = 20 x 10-3
mol.dm-3 and Temperature = 70 .
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Figure 4: Plots between R and [Maltose] at [S2O82-] = 20 x 10-3
mol.dm-3 and Temperature = 70
Effect of silver nitrate concentration on Kinetic order:
The kinetics of the oxidation of maltose by peroxydisulfate had also
been investigated under silver nitrate as catalyst and effect on the
kinetic order was measured by varying the concentration of the
AgNO3. While theconcentration of peroxydisulfate and maltose were
kept constant at 20 x 10-3 mol.dm-3 and temperature at 70 as shown
in Table 3 and Figure 5. Figure 6 represents the effect of silver nitrate
concentration as catalyst on the average rate in oxidation of maltose
by peroxydisulfate and average rate observed first order rate constant,
can be expressed as:
R=ko [Ag+]
The rate equation indicated that reaction followed first order with
respect to Ag+ and the ko values increase linearly with increasing the
sliver concentration.
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Table 3: Effect of silver nitrate concentration on rate law (R) and
rate constant (ko).
-4
[AgNO3] x 10
R x 104
ko x 104
(mol.dm-3)
(mol.dm-3.s-1)
(s-1)
1
14.42
1.44
2
15.14
1.64
3
15.76
2.03
4
16.22
2.01
5
17.05
2.36
-3
Peroxydisulfate concentration =20 x 10 mol.dm-3,
Maltose concentration =20 x 10-3 mol.dm-3 and
Temperature = 70 ⁰C.
Figure 5: Plots between [AgNO3] and time at [Maltose] = 20 x 10-3
mol.dm-3, [S2O82-] = 20 x 10-3 mol.dm-3 and Temperature = 70
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Figure 6: Plots between R and [AgNO3] at [Maltose] = 20 x 10-3
mol.dm-3, [S2O82-] = 20 x 10-3 mol.dm-3 and Temperature = 70 .
Effect of reaction temperature on Kinetic order:
Reaction temperature is an important the concentration of
peroxydisulfate and maltose were kept constant at
20x10-3 mol.dm-3 factor in kinetic study of a reaction. In this case, the
reaction was studied at different temperatures (60-80 ) and kept
peroxydisulfate and maltose concentration constant at 20x10-3
mol.dm-3. The rate of reaction (R) and rate constant (ko) were
calculated at different temperature and tabulated in table 4 as well as it
also observed that the reaction followed first order with respect to
temperature. Using the slope and intercept of the line in Figure 7,the
activation energy Ea and frequency factor A were calculated by using
Arrhenius Equation. These values were further used to calculate other
parameters like∆Sand ∆Gfor the reaction; results are tabulated in
table 5.
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Table 4: Effect of reaction temperature on rate law (R) and rate
constant (ko).
Temperature
(⁰C)
60
65
70
75
80
T
(K)
333
338
343
348
353
(1/T) 103
(K-1)
3.00
2.96
2.92
2.87
2.83
R x 104
(mol.dm-3.s-1)
11.42
12.19
13.68
15.22
15.56
ko x 104
(s-1)
0.78
1.09
1.37
1.54
1.69
log ko
5+logko
-4.10
-3.96
-3.85
-3.82
-3.77
0.90
1.04
1.15
1.18
1.23
Peroxydisulfate concentration =20 x 10-3 mol.dm-3, Maltose
concentration =20 x 10-3 mol.dm-3
Table 5: thermodynamic activation parameters for rate constant
(ko) in oxidation of maltose by peroxydisulfate.
A
EA
∆S
∆G
-1
-3 -1
-1
mol.dm .s
KJ.mol
J.K
KJ.mol-1
43.74
7.17x10-2
28,00
56.61
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Figure 7: Plots between Temperature and time at [Maltose] = 20 x
10-3 mol.dm-3 and [S2O82-] = 20 x 10-3 mol.dm-3.
Figure 8: Plots between 5+log ko and (1/T) at [Maltose] = 20 x 10-3
mol.dm-3 and [S2O82-] = 20 x 10-3 mol.dm-3.
Effect of surface on Kinetic order:
The effect of surface on the reaction kinetics was investigated by
using the reaction mixture containing 20 x 10-3 mol.dm-3 of
peroxydisulfate and maltose respectively, at 70⁰C temperature with
different surfaces (i.e glass rod and cotton wool) were added in
reaction mixture. The rate of reaction (R) and rate constant (ko) were
calculated at each surface and results summarized in table 6. There is
no evidence of effect of surface on rate of reaction was found.
Table 6: Effect of surface on rate law (R) and rate constant (ko).
ko x 104
Weight
R x 104
Surface
(mol.dm-3.s-1)
(s-1)
(g)
No surface
……..
13.68
1.37
Glass rod
6.0
13.77
1.27
Cotton wool
1.0
14.31
1.28
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-3
Maltose concentration =20 x 10 mol.dm-3 and
Temperature = 70 ⁰C. Figure 9: Plots between [S2O82-] and time at [Maltose] = 20 x 10-3
mol.dm-3 and Temperature = 70 ⁰C.
Product Analysis:
A certain weight of potassium peroxydisulfate was allowed to react
with equal weight of the substrate at 70 ⁰C. The reaction mixture was
left under reflux condition for five days and took special care to avoid
the loss of any volatile product, by circulating the cold water in the
condenser throughout the experiment. Then reaction mixture was
collected and subjected to fractional separation of the products. The
volatile fraction collected by distillation over the temperature 97105⁰C and was stored in a tube closed with rubber in an ice bath. The
product was analyzed by FT-IR spectroscopy and confirmed the
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presence of formaldehyde and formic acid as shown in Figure 10. The
presence of formaldehyde and formic acid was confirmed as follow:
Formaldehyde: 2, 4-dinitrophenylhydrazone derivative was prepared
by adding 2, 4-dinitrophenylhydrazine to the distillate fraction when
recrystallized from ethanol gave a melting point 166-167 o C
Formic
acid:2,
4-dinitrophenylhydrazone
derivative
was
recrystallized from water and dried, gave a melting point 194-195 o C
which was the same with the pure derivative.
Figure 10: FT-IR spectroscopy of reaction product.
Conclusion:
The present work deals with a systematic study of oxidation reaction
of maltose by peroxydisulfate under un-catalyzed condition over
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temperature range (60-80 ⁰C) and in the presence of AgNO3 as
catalyst at 70oC.It is well known that peroxydisulfate decomposes
thermally in the absence of reducing substance. Therefore, there are
two main paths for the reaction:
Path (1): represents the thermal decomposition of peroxydisulfate.
Path (2): represents the bimolecular reaction of peroxydisulfate with
reducing substrate
In the present work an attempt is made to estimate path (1) and path
(2) and involves the study of two main aspects:
(a) Kinetic study of oxidation of maltose by peroxydisulfate.
(b) An investigation of the product of the reaction.
The kinetic study of oxidation of maltose by peroxydisulfate shows
that this reaction follows fractional (0.2) order with respect to maltose
and first order with respect to peroxydisulfate and the catalyst AgNO3.
The experimental rate law of the reaction can be expressed as follows:
-d [S2O82-]/dt= k1 [S2O82-]+k2 [S2O82-] [Substrate] 0.2=ko[S2O82-]
Where kois rate constant which consist of k1 and k2. K1 refers to the
rate constant of the thermal decomposition of peroxydisulfate and
k2refers to the rate constant of the bimolecular reaction between
peroxydisulfate and substrate. Thus, ko = k1 + k2. Substrate refers to
maltose in this kinetic study of reaction because literature reviews of
peroxydisulfate shows that reactions with peroxydisulfate pursue in
the presence of organic substrate.
60 ‫مجلة البحث العلمي للعلوم واآلداب – العدد الخامس عشر‬
Kinetic study of the oxidation of …
Mawia Hassan & other's
Temperature effect investigates over the range 60-80 ⁰C and observes
that the oxidation of maltose by peroxydisulfate follows first order
kinetics at different temperature meanwhile activation energy EA,
frequency factor A, entropy ∆ S and free energy of activation ∆ G
calculates for the reaction. It also observes that there is non-significant
effect of surface on the rate of reaction. The impurities present in the
system have great effect on the rate of the reaction. Reproducible
results can only be obtained by taking extra-ordinary care during
experimentation, by using distilled water and pure chemical in the
reaction.
Acknowledgement
This work was supported by Beijing University of Chemical
Technology and University of Khartoum.
Nomenclature
A
EA
∆G
ko
R
∆S
Frequency factor
Activation energy
Free energy
Rate constant
Rate of reaction
Entropy of the
reaction
mol.dm-3.s-1
KJ.mol-1
KJ.mol-1
s-1
mol.dm-3.s-1
J.K-1
References
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Chem. Soc., 71, 1419(1994).
61 ‫مجلة البحث العلمي للعلوم واآلداب – العدد الخامس عشر‬
Kinetic study of the oxidation of …
Mawia Hassan & other's
Binder, J. B. and Raines, R. T., Simple chemical transformation of
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Guerrero, M., Ruiz, M. P., Millera, A., Alzueta, M. U. and Bilbao, R.,
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peroxydisulfate, Chem. Rev., 62, 185 (1962).
of
oxidation
by
Litwinienko, C. and Ingold, K. U., Solvent effects on the rates of
mechanisms of reaction of phenols with free redicals. Acc. Chem.
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Seddon, K. R., Stark, A. and Torres, M. J., Influence of chloride,
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62 ‫مجلة البحث العلمي للعلوم واآلداب – العدد الخامس عشر‬
Kinetic study of the oxidation of …
Mawia Hassan & other's
Wilmarth, W.K, and Haim, A., Mechanism of oxidation by
peroxydisulfate ion, ed. J. O. Edwards. London: Interscience, 175
(1961)
63 ‫مجلة البحث العلمي للعلوم واآلداب – العدد الخامس عشر‬
Kinetic study of the oxidation of …
64 Mawia Hassan & other's
‫مجلة البحث العلمي للعلوم واآلداب – العدد الخامس عشر‬

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