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The use of permanganate solutions for in-situ chemical oxidation (ISCO) is a well-established groundwater remediation technology, particularly for targeting chlorinated ethenes. The kinetics of oxidation reactions is an important ISCO remediation design aspect that affects the efficiency and oxidant persistence. The overall rate of the ISCO reaction between oxidant and contaminant is typically described using a second-order kinetic model while the second-order rate constant is determined experimentally by means of a pseudo first order approach. However, earlier studies of chlorinated hydrocarbons have yielded a wide range of values for the second-order rate constants. Also, there is limited insight in the kinetics of permanganate reactions with fuel-derived groundwater contaminants such as toluene and ethanol. In this study, batch experiments were carried out to investigate and compare the oxidation kinetics of aqueous trichloroethylene (TCE), ethanol, and toluene in an aqueous potassium permanganate solution. The overall second-order rate constants were determined directly by fitting a second-order model to the data, instead of typically using the pseudo-first-order approach. The second-order reaction rate constants (M(-1)s(-1)) for TCE, toluene, and ethanol were 8.0×10(-1), 2.5×10(-4), and 6.5×10(-4), respectively. Results showed that the inappropriate use of the pseudo-first-order approach in several previous studies produced biased estimates of the second-order rate constants. In our study, this error was expressed as a function of the extent (P/N) in which the reactant concentrations deviated from the stoichiometric ratio of each oxidation reaction. The error associated with the inappropriate use of the pseudo-first-order approach is negatively correlated with the P/N ratio and reached up to 25% of the estimated second-order rate constant in some previous studies of TCE oxidation. Based on our results, a similar relation is valid for the other volatile organic compounds studied.
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Evaluation of the kinetic oxidation of aqueous volatile organic
compounds by permanganate
Mojtaba G. Mahmoodlu
a,
, S. Majid Hassanizadeh
a,b
, Niels Hartog
a,c
a
Utrecht University, Department of Earth Sciences, The Netherlands
b
Soil and Groundwater Systems, Deltares, Utrecht, The Netherlands
c
KWR Watercycle Research Institute, Nieuwegein, The Netherlands
HIGHLIGHTS
Oxidation of chlorinated and non-chlorinated VOCs in aqueous phase by permanganate was investigated.
A second-order kinetic model simulated the oxidation process of TCE, toluene, and ethanol.
Errors in k due to the inappropriate use of the pseudo rst-order model were discussed.
abstractarticle info
Article history:
Received 15 July 2013
Received in revised form 12 November 2013
Accepted 12 November 2013
Available online 2 December 2013
Keywords:
Volatile organic compounds
Permanganate
Kinetic parameters
Chemical oxidation
The use of permanganatesolutions for in-situ chemicaloxidation (ISCO)is a well-established groundwater reme-
diation technology, particularly fortargeting chlorinated ethenes. Thekinetics of oxidation reactions is an impor-
tant ISCO remediation design aspect that affects the efciency and oxidant persistence. The overall rate of the
ISCO reaction between oxidant and contaminant is typically described using a second-order kinetic model
while the second-order rate constant is determined experimentally by means of a pseudo rst order approach.
However, earlier studies of chlorinated hydrocarbons have yielded a wide range of values for the second-order
rate constants. Also, there is limited insight in the kinetics of permanganate reactions with fuel-derived ground-
water contaminants such as toluene and ethanol. In this study, batchexperiments were carried out to investigate
and compare the oxidation kinetics of aqueous trichloroethylene (TCE), ethanol, and toluene in an aqueous po-
tassium permanganate solution. The overall second-order rate constants were determined directly by tting a
second-order model to the data,instead of typically using the pseudo-rst-order approach. The second-order re-
action rate constants (M
1
s
1
) for TCE, toluene, and ethanol were 8.0 × 10
1
,2. 10
4
,and6.5 ×10
4
,re-
spectively. Results showed that the inappropriate use of the pseudo-rst-order approach in several previous
studies produced biased estimates of the second-order rate constants. In our study, this error was expressed as
a function of the extent (P/N) in which the reactant concentrations deviated from the stoichiometric ratio of
each oxidation reaction. The error associated with the inappropriate use of the pseudo-rst-order approach is
negatively correlated with the P/N ratio and reached up to 25% of the estimated second-order rate constant in
some previous studies of TCE oxidation. Based on our results, a similar relation is valid for the other volatile or-
ganic compounds studied.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Groundwater contamination with volatile organic compounds
(VOCs) is a major environmental problem at sites (formerly) occupied
by large-scale chemical industries or small scale users such as dry-
cleaners or fuel stations (Rivett et al., 2011; Schubert et al., 2011).
These compounds are also present in some household products and au-
tomobile liquids (Berscheid et al., 2010). VOCs are groundwater con-
taminants of widespread concern because of (1) very large volumes
that are sometimes released into the environment, (2) their toxicity,
and (3) the fact that some VOCs, once they have reached groundwater,
tend to persist and migrate to drinking water wells or upward by diffu-
sion through the unsaturated zone to indoor spaces. Exposure to some
VOCs may cause damage to the centralnervous system and internal or-
gans and may lead to symptoms such as headache, respiratory tract ir-
ritation, dizziness and nausea, known as the Sick Building Syndrome
(Yu and Lee, 2007).
Of the different VOCs present, we selected for our study TCE, toluene,
and ethanol as the model VOCs (target compounds) for chlorinated sol-
vents, mineral oil, and biofuel, respectively. TCE has been widely used as
a dry cleaning solvent, degreasing product and chemical extraction
Science of the Total Environment 485486 (2014) 755763
Corresponding author. Tel.: +31 302535024; fax: +31 30 2534900.
E-mail address: m.gharehmahmoodlu@uu.nl (M.G. Mahmoodlu).
0048-9697/$ see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.scitotenv.2013.11.066
Contents lists available at ScienceDirect
Science of the Total Environment
journal homepage: www.elsevier.com/locate/scitotenv
agent. Inappropriate TCE disposal has produced widespread groundwa-
ter contamination. Since TCE is carcinogenic, its movement from con-
taminated groundwater and soil into the indoor air of overlying
buildings is a serious concern (EPA, 2011). Similarly, toluene, an addi-
tive to improve the octane number of gasoline, is one of the main organ-
ic compounds found frequently in indoor environments. Toluene is
listed as one of thesix major classes of indoor VOCs (aromatic, aldehyde,
alkane, ketone, alcohol, and chlorocarbon) (Yu and Lee,2007). Exposure
to toluene may cause irritation of the eye, nasal and mucous mem-
branes, and the respiratory tract (Yu and Lee, 2007).
More recently, ethanol is being used increasingly in (renewable)fuel
alternatives and as a replacement for methyl tertiary-butyl ether
(MTBE), which, despite helping to accomplish Clean Air Act goals, has
caused widespread water contamination (Capiro et al., 2007; Johnson
et al., 2000). Also, the presence of ethanol in groundwater can reduce
the biodegradation rates of benzene, toluene, ethylbenzene, and xylene
isomers (BTEX) in groundwater and soil (Freitas et al., 2010; Mackay
et al., 2007). Extended exposure to ethanol can damage liver, kidneys,
and the central nervous system (Yu and Lee, 2007). A need hence exists
to improve our understanding of the oxidation and fate of ethanol in
contaminated groundwater.
In-situ chemical oxidation (ISCO) is one of the technologies available
for in-situ remediation of VOC-contaminated groundwater. Chemical
oxidation technology is a potent soil remedial option that can effectively
eliminate an extensive range of VOCs (Yen et al., 2011). The oxidizing
agents most commonly used for the treatment of hazardous contami-
nants are permanganate, ozone, hydrogen peroxide, and Fenton's re-
agent. Of these oxidants, potassium permanganate has received much
attention for the treatment of liquid, slurry soils, and sludges polluted
with VOCs. Potassium permanganate is often used as an ISCO agent for
the following ve reasons: (1) its oxidation potential (E
0
=0.5
1.7 V), (2) its ability to oxidize a variety of organic chemicals (Powers
et al., 2001; Siegrist et al., 2001; Struse et al., 2002; Mumford et al.,
2004; Hønning et al., 2005; Mumford et al., 2005; Urynowicz, 2008),
(3) its effectiveness over a wide range of pH values, (4) its relatively
low cost, and (5) its signicantly higher stability in the subsurface as
compared to other chemical oxidants (Bryant et al., 2001; Huang et al.,
1999).
Depending upon the soil matrix and groundwater composition, per-
manganate in an aquifer may be stable for as long as several weeks
(Cave et al., 2007; Siegrist et al., 2001). The injection of dissolved potas-
sium permanganateinto plumes to remediate contaminatedgroundwa-
ter has been used for the in-situ treatment of chlorinated hydrocarbons
(Damma et al., 2002). Moreover, since oxidation reactions with per-
manganate proceed by electron transfer rather than more rapid free
radical processes, as with Fenton's reagent, potassium permanganate
appears amenable to application in low permeability soils (Kao et al.,
2008). Permanganate reacts with organic compounds to produce man-
ganese dioxide (MnO
2
) as well as carbon dioxide (CO
2
) or intermediate
organic compounds (Yin and Herbert, 1999) of the form:
RaqðÞ
þMnO
4aqðÞ
MnO2sðÞþCO2gðÞ or Rox þothers ð1Þ
where R denotes an organic contaminant and R
ox
is an oxidized inter-
mediate organic compound.
A number of processes such as cleaving, hydroxylation, and hydroly-
sis lead to theproduction of intermediates and eventually to carbon di-
oxide and water. The permanganate ion is especially useful in oxidizing
organics that have carboncarbon single and double bonds (for exam-
ple, chlorinated ethylenes, aldehyde groups, or hydroxyl groups) (Lee
et al., 2003).
The full oxidation of TCE, toluene, and ethanol by permanganate fol-
lows Eqs. (2) to (4), respectively. Permanganate breaks down TCE to
CO
2
and Cl
, while ethanol and toluene are transformed into CO
2
and
H
2
O. In all reactions, MnO
4
reduces to manganese dioxide which is a
solid precipitate at circumneutral pH values. Moreover, in the absence
of reductants, permanganate can react with water and produce manga-
nese dioxide particles (Kao et al., 2008) as given by Eq. (5). However,
this reaction typically takes place at very low rates.
C2HCl3aqðÞ
þ2KMnO4aqðÞ
2Kþþ2MnO2sðÞþ3Clþ2CO2gðÞþHþð2Þ
C6H5CH3aqðÞ
þ12KMnO4aqðÞ
þ12Hþ12Kþþ12MnO2sðÞþ10H2OaqðÞ
þ7CO2gðÞ
ð3Þ
C2H5OH aqðÞ
þ4KMnO4aqðÞ
þ4Hþ4Kþþ4MnO2sðÞþ2CO2gðÞ
þ5H2OaqðÞ
ð4Þ
4MnO
4aqðÞ
þ2H2OaqðÞ
3O2gðÞ
þ4MnO2sðÞþ4OH
:ð5Þ
For the design and monitoring of an ISCO remediation approach, the
kinetics of oxidation reactions is an important aspect that may affect the
efciency and oxidant persistence. ISCO using potassium permanganate
solution is a well-established remediation technology, particularly for
targeting chlorinated ethenes (Huang et al., 2001; Urynowicz, 2008;
Waldemer and Tratnyek, 2006). However, the earlier studies of chlori-
nated ethenes have yielded a wide range for the estimated second-
order rate constants. In large part these estimates were derived using
the pseudo-rst order experimental approach that requires one of the
reactants to be present in signicant excess (Huang et al., 2001;
Siegrist et al., 2001; Urynowicz, 2008; Waldemer and Tratnyek, 2006).
Also, there is still limited insight in the kinetics of permanganate reac-
tions with fuel-derived VOC groundwater contaminants such as toluene
(Rudakov and Lobachev, 2000; Waldemer and Tratnyek, 2006) and eth-
anol (Barter and Littler, 1967). In this study we therefore determined ki-
netic parameters for the oxidation of threedissolved VOCs (TCE, toluene
and ethanol) by permanganate. For this purpose we performed a series
of batch experiments with three objectives: (1) to determine the oxida-
tion kinetic parameters of TCE, toluene, and ethanol by aqueous per-
manganate, (2) to establish a suitable kinetic reaction rate model, and
(3) to estimate errors caused by the inappropriate use of the pseudo
rst-order model.
2. Materials and methods
2.1. Materials
Chemicals used in this study included TCE, ethanol, and toluene (99%
purity, Sigma-Aldrich, Merck and ACROS, respectively), potassium per-
manganate (99% purity, Sigma-Aldrich), sodium bicarbonate (99.7% pu-
rity, Merck), ammonium chloride(99.8% purity, Merck) and oxalic acid
(99% purity, Merck).Stock solutions of aqueous-phase TCE, ethanol, and
toluene were individually prepared in 2-liter glass vessels by dissolving
the chemicals in deionized (DI) water. The vessels were vigorously
shaken and allowed to equilibrate overnight. Then, they were preserved
at 8 °C for further use. Potassium permanganate solutions of desired
concentrations were prepared by dissolving solid potassium permanga-
nate in DI water. To prevent the photodecomposition of permanganate,
the stock solutions were covered by aluminum foil.
Two separate buffer solutions of pH 9.0 and 6.0 were prepared. This
was performed by adding the required amounts of either sodium bicar-
bonate (for the pH of 9.0) or ammonium chloride (for the pH of 6.0) to
DI water. A solution of oxalic acid was prepared bydissolvingan appro-
priate amount of oxalic acid in DI water.
2.2. Sampling and analyses
During the batch experiments, aqueous samples of 1.5 ml were pe-
riodically taken from the kinetic (including both reactant) and control
batches using a 2.5 ml gas tight syringe (SGE Analytical Science,
Australia). The aqueous sample was injected to a 10-ml transparent
756 M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
glass vial. 100 μl of oxalic acid (0.5 M) was immediately added to each
sample to prevent any further oxidation of the VOC compounds. Then,
the samplewas capped with a magnetic cap and hard septum (Magnetic
Bitemall; Red lacquered, 8 mm center hole; Pharma-Fix-Septa, Silicone
blue/PTFE gray; Grace Alltech). Batches were sampled until no detect-
able VOC concentration was found in the kinetic batches.
Concentrations of the target compounds were measured with a gas
chromatograph (GC). The GC (Agilent 6850) was equipped with ame
ionization detector (FID) and separation was done on an Agilent HP-1
capillary column (stationery phase: 100% dimethylpolysiloxane, length:
30 m, ID: 0.32 mm, lm thickness: 0.25 μm). A temperature pro-
grammed run was used to analyze the samples. The concentration of
VOC compounds was determined using a headspace method as used
in previous studies (e.g. Almeida and Boas, 2004; Przyjazny and
Kokosa, 2002; Sieg et al., 2008; Snow, 2002). The limits of quantication
(LOQ) were calculated by using a signal-to-noise ratio of 10:1 (Kubinec
et al., 2005).
To measure the concentration of permanganate, the samples were di-
luted immediately after collection and centrifuged (Heraeus/Kendro
Biofuge) for 4 min at 13,000 rpm to settle suspended manganese diox-
ide particles. The aqueous concentration of permanganate was measured
subsequently using a UVSpectrophotometer (UV-1800, Shimadzu) at a
wavelength of 525 nm. TCE oxidation was also monitored by measuring
the production of chloride. Chloride concentrations were determined by
ion chromatography (e.g. He and Zhao, 2005; Huang et al., 1999; Morales
et al., 2000; Tyrrell et al., 2009). The ion chromatograph (Dionex DX-
120) was equipped with a 4-mm Dionex IonPacAS22 capillary col-
umn. During the experiments, acidity was measured using a pH meter
(HANNA, HI 8314).
2.3. Experimental and simulation procedure
The oxidation of target compounds with potassium permanganate
was investigated in 120-ml glass vial reactors at room temperature
(21 ± 1 °C). All experiments were carried out using a basic orbital lab-
oratory shaker (IKA KS 260 B). The experiments were conducted using
different combinations of the initial concentrations of the target com-
pounds and potassium permanganate (Table 1). For two experiments,
the initial concentration of the potassium permanganate was identical,
while the initial concentration of the target compounds was different.
For two other experiments, the initial concentration of permanganate
was different, but with identical initial concentration of the target
compounds.
We also prepared a series of control batches containing stock solu-
tions of either the VOC or potassium permanganate. Control experi-
ments were performed for each compound under identical conditions
to ensure that the loss of target compound or permanganate due to
reaction with water, photodecomposition or adsorption to the rubber
stopper was negligible over the course of the experiments.
Additional experiments for each compound were performed with
the pH buffer to determine the effect of pH on the kinetics of oxidation
of target compounds by permanganate. All the experiments were per-
formed in duplicate.
The second-order rate constants were derived by tting a second-
order rate model to the batch data. The obtained kinetic parameters
for TCE, toluene and ethanol were compared with literature values de-
rived mostly using pseudo-rst-order approaches (Table 2). The
second-order rate constants were also estimated using the pseudo-
rst order experimental approach. Then, the error due to the inappro-
priate use of pseudo-rst-order reaction rate was estimated by compar-
ing k of the pseudo-rst-order reaction rate model with the value of
second-order reaction rate model. Estimated errors were plotted versus
the P/N value for data from the present study and TCE data from the lit-
erature (Huang et al., 1999; Huang et al., 2001; Kao et al., 2008;
Urynowicz, 2008). Alldata points in gures are shown with 5% error bar.
2.4. Kinetics of VOC oxidation
The stoichiometric reaction for a target compound can be written in
the following form:
AþNBProducts ð6Þ
where A and B denote the target compound and potassium permanga-
nate, respectively, and N is the number of moles of potassium perman-
ganate in the stoichiometric reaction.
As shown by the stoichiometric reaction, full oxidation of one mole
of a target compound requires N moles of potassium permanganate.
Thus, the consumption of permanganate and target compounds is relat-
ed by:
ΔCB¼NΔCAð7Þ
where C
A
denotes the concentration of the compound (M), C
B
is the
concentration of potassium permanganate (M), and ΔC denotes the
consumed concentration of reactants (M).
Typically, second-order reaction rate constants for the oxidation of
VOC compounds by permanganate have been obtained using a pseudo-
rst-order approach by assuming that either the contaminant or per-
manganate concentration is constant (Urynowicz, 2008; Waldemer
and Tratnyek, 2006). However, the general form of a second-order reac-
tion rate equation, as a function of the target compound and potassium
permanganate concentrations in the aqueous phase, can be written as
follows:
dCA
dt ¼kCACBð8Þ
where k denotes the reaction rate constant and t represents the time (s).
We now reformulate Eq. (8) in terms of consumed fraction of reac-
tants, X
A
(=(C
A0
C
A
)/C
A0
)andX
B
(=(C
B0
C
B
)/C
B0
). Here, C
A0
is
the initial concentration of target compound (M). From Eq. (7) and
the denition of P (=C
B0
/C
A0
), we have: X
B
=NX
A
/ P. Substitution
of these denitions into Eq. (8) and rearranging yields the following
equation:
dXA
dt ¼kCA0 1XA
ðÞPNXA
ðÞ:ð9Þ
Integration of Eq. (9) gives the following generalformula for the var-
iation of X
A
with time:
1
CA0 PN
ðÞ
ln PNXA
ðÞ
P1XA
ðÞ

¼kt where PN:ð10Þ
Table 1
Experimental conditions for the three target compounds.
Compound Experiment [VOC]° (mM) [KMnO
4
]° (mM) ~P/N
TCE 1 42.0 × 10
3
17.0 × 10
2
2.0
242.0×10
3
3.4 × 10
1
4.0
385.0×10
3
17.0 × 10
1
10.0
442.0×10
3
17.0 × 10
1
20.0
521.0×10
3
17.0 × 10
1
40.5
Toluene 1 15.0 × 10
1
100.0 5.5
265.0×10
2
100.0 12.8
332.5×10
2
100.0 25.6
432.5×10
2
200.0 51.3
516.2×10
2
100.0 51.3
Ethanol 1 40.0 200.0 1.25
2 40.0 400.0 2.5
3 30.0 400.0 3.33
4 10.0 400.0 10.0
5 2.5 200.0 20.0
757M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
According to Eq. (10), a plot of 1/C
A0
(P N)ln[(P NX
A
)/P
(1 X
A
)] vs. time should yield a straight line, with its slope being the
second-order reaction rate constant k.
The solution for X
B
follows from Eq. (10) by substituting X
A
=PX
B
/N
to obtain:
P
CB0 PNðÞ
ln N1XB
ðÞ
NPXB
ðÞ

¼kt where NNPXB:ð11Þ
The assumption for the commonly used pseudo-rst-order ap-
proach of constant concentration of one of the reactants is only valid if
the amount of the target compound or permanganate is sufciently
high to neglect any change in the concentration during the course of
an experiment (Huang et al., 2001; Siegrist et al., 2001; Urynowicz,
2008; Waldemer and Tratnyek, 2006). If permanganate is in excess,
this means that P/N is much larger than unity. Therefore, Eq. (10) for
such conditions may be simplied to yield:
1
CB0
ln CA
C0
¼kt where PNNN:ð12Þ
To estimate k using the pseudo-rst-order approach, Eq. (12) can be
used with a constant concentration of permanganate, equal to its initial
value.
3. Results and discussion
3.1. Oxidation of VOC compounds
The oxidation of VOC compounds by permanganate was monitored
until VOC concentrations were below detection. Fig. 1 depicts the nor-
malized concentration (C/C
0
) of the VOC compounds as a function of
time. The experiments lasted from less than an hour for TCE to up to a
week for toluene, with experimental durations for ethanol oxidation
being intermediate. Concentration of the target compounds in the con-
trols did not decrease during the experiments. Since no additional peaks
were observed in the chromatogram of the samples, we concluded that
the VOCs were fully mineralized according to Eqs. (2) to (4).
The experiments were conducted with excess potassiumpermanga-
nate using varying initial reactant concentration ratios that deviated
from the stoichiometry of the reactions (Table 1). The extent of the de-
viations was expressed as the ratio of the initial molar concentration of
potassium permanganate over the required stoichiometric concentra-
tion (i.e., P/N). As illustr ated in Fig. 1, oxidation rates increased for larger
values of P/N.
Both the VOC and permanganate concentrations were found to de-
crease as expected based on the stoichiometry of full oxidation accord-
ing to reactions 24. Also, for TCE, approximately 97.5% of the chloride
ions for the TCE experiments with an initial concentration of 0.042
(mM) were recovered during the TCE oxidation stage (Fig. a, Supple-
mentary material). This also indicated that TCE was completely oxidized
to produce CO
2
,H
+
,andCl
. The measured Cl
concentration in all TCE
experiments closely followed the calculated value based on the stoi-
chiometric reaction (Eq. (2)).
Results revealed that the measured consumed fractions of perman-
ganate agreed with values calculated based on stoichiometric reactions
(Fig. b, Supplementary material). This means that the consumption of
permanganate was only due to the oxidation of target compounds,
and that decomposition reactions with water were negligible during
the experiments.
3.2. Kinetics analysis of data
We used Eq. (10) and all data from experiments 15(Table 1), to es-
timate k for each compound. Fig. 2 shows that the plots of1/C
A0
(P N)
ln[(P NX
A
) / (P(1 X
A
)] vs. time for all compounds. The square of
Table 2
Second-order rate constants and the corresponding experimental conditions for the oxidation of target compounds with potassium permanganate.
VOC [VOC] (mM) [KMnO
4
](mM) pH T(°C) ~P/N Method K(M
1
s
1
) Reference
TCE 8.0 × 10
2
3.2 × 10
1
6.08.0 RT 1.0 NA 7.9 × 10
1
(DI water), 8.5 × 10
1
(in tap water) Vella and Veronda (1993)
8.0 × 10
3
7.0 × 10
1
8.0 RT 21.85 NA 4.2 × 10
1
Tratnyek et al. (1998)
3.1 × 10
2
8.3 × 10
2
3.7 × 10
1
1.2 4.08.0 21.0 3.03.6 First-order model 6.7 × 10
1
±3.0×10
2
Yan and Schwartz (1999)
1.0 × 10
1
6.3 4.08.0 21.0 15.75 First-order model 6.5 × 10
1
6.8 × 10
1
Yan and Schwartz (2000)
1.4 × 10
1
±7.0×10
2
1.9 ± 7.0 × 10
2
7.0 20.0 3.4 First-order model 8.0 × 10
1
±1.2×10
1
Huang et al. (2001)
NA NA 6.9 20.0 NA First-order model 8.9 × 10
1
Siegrist et al. (2001)
1.04.0 1.0 × 10
1
7.0 25.0 6.25 × 10
3
2.5 × 10
2a
First-order model 7.6 × 10
1
±3.0×10
2
Waldemer and Tratnyek (2006)
3.8 × 10
2
1.5 × 10
1
7.6 × 10
2
7.6 × 10
1
6.3 25.0 0.512.5 Second-order model 8.0 × 10
1
Kao et al. (2008)
.9 × 10
1
6.3 NA 20.0 10.85 First-order model 9.5 × 10
1
Urynowicz (2008)
2.1 × 10
2
8.5 × 10
2
3.4 × 10
1
1.7 4.37.0 20.0 2.040 First-order model 6.7 × 10
1
(r
2
= 0.99) This study
Second-order model 8.0 × 10
1
(r
2
= 0.99)
Toluene 4.0 1.0 × 10
1
7.0 25.0 1.67 × 10
4a
First-order model 83.2 × 10
5
Waldemer and Tratnyek (2006)
NA NA 5.07.0 20.0 NA First-order model 23.0 × 10
5
Rudakov and Lobachev (2000)
NA NA 5.07.0 30.0 NA First-order model 61.0 × 10
5
Rudakov and Lobachev (2000)
16.2 × 10
2
1.5 100200 7.08.5 20.0 25.751.2 First order model 18.8 × 10
5
(r
2
= 0.96) This study
Second-order model 25.0 × 10
5
(r
2
= 0.99)
Ethanol 171.5 9.2 4.6 20.0 3.35 × 10
3a
First-order model 16.7 × 10
4
Barter and Littler (1967)
171.5 9.2 4.6 30.0 3.35 × 10
3a
First-order model 40.3 × 10
4
Barter and Littler (1967)
2.580.0 200400 7.07.8 20.0 1.2520 First-order model 53.3 × 10
5
(r
2
= 0.96) This study
Second-order model 65.0 × 10
5
(r
2
= 0.99)
NA: not available, RT: room temperature, r
2
: the square of linear correlation coefcient.
a
Concentration of the target compound was kept constant.
758 M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
linear correlation coefcients (r
2
) values of the regressions obtained for
TCE, toluene, and ethanol were 0.990, 0.987 and, 0.971, respectively. The
corresponding reaction rate constants are given in Table 2. The results
showed thatthe reaction rate constant for TCE washigher than for eth-
anol and toluene, consistent with previous studies on the oxidation of
these compounds by permanganate in both aqueous (Waldemer and
Tratnyek, 2006) and vapour phase (Mahmoodlu et al., 2013).
We also used Eq. (11) to estimate k again; this time based on the
consumed fraction of permanganate (X
B
). Fig. c (Supplementary mate-
rial) depicts plots of P/C
B0
(P N)ln[N(1 X
B
)/(NPX
B
)] vs. time
for all target compounds. The results show that Eq. (11) can simulate
very effectively the consumption of permanganate during oxidation of
the target compounds. Reaction rate constants (M
1
s
1
) based on
Eq. (11) were found to be 7.83 × 10
1
,2.610
4
, and 6.67 × 10
4
Fig. 1. Oxidation of TCE, toluene, and ethanol vs. time forthree different P/N ratios.
759M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
for TCE, toluene, and ethanol, respectively. For the calculations we used
all available data for the degradation of potassium permanganate.
We applied Eq. (12) to all data from experiments 15 for each com-
pound. Fig. 3 shows plots of 1/C
B0
lnC
A
/C
0
versus time for all compounds.
Values of k were calculated from the slope of the line for each
compound. The r
2
values for the pseudo-rst order approach were
smaller than those for the second-order model, having values of 0.977,
0.969, and 0.956 for TCE, toluene, and ethanol, respectively.
Comparison of simulation results obtained with the two models re-
vealed that the oxidation reaction of the target compounds was better
Fig. 2. Plots of 1/C
A0
(P N)ln[(P NX
A
)/P(1X
A
)] vs. time for the target compounds, corresponding to Eq. (10) (Exp. x y: x denotes number of experiments and y is the exper-
iment repetition).
760 M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
Fig. 3. Plots of 1/C
B0
lnC
A
/C
0
vs. time for the target compounds, corresponding to Eq. (12).
761M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
represented by the second-order model, rather than the pseudo-rst
order model. This indicates that the permanganate abundances (P/N
up to 50) were insufcient to ignore changes in the initial permanga-
nate concentrations. Rate constants derived using the second-order
model hence should be considered more appropriate.
With increasing stoichiometric abundance of one of the reactants,
the error associated with assuming a constant initial concentration in
the pseudo-rst-order approach is expected to decrease. To assess the
inuence of reactant abundance on the error in estimating second-
order rate constants with a pseudo-rst order approach, Eqs. (10) and
(12) were used to determine k for each experiment (experiments 1 to
5) individually. We subsequently estimated the error by comparing k
of a pseudo-rst-order reaction rate model with the value of second-
order reaction rate model. The results show that the errors were nega-
tively correlated with the P/N, with the largest error corresponding to
the lowest ratio of P/N ratio (Fig. 4). Moreover, for the largest values
of P/N, the errors became smaller, but neverzero since the consumption
of excess reactant is never really zero. However, with a stoichiometric
excess of P/N N40, the error (using the pseudo-rst-order model to es-
timate the second-order rate constant) fell below 5%.
Literature has shown a range of estimated second-order rate con-
stants, mainly using the pseudo-rst order approach (Table 2). As
these studies used varying degrees of reactant excess, we investigated
to what extent this range was inuenced by errors due to the inappro-
priate use of the pseudo-rst order approach. For this purpose we tted
the second-order and pseudo rst-order models to literature data for
TCE oxidation (Huang et al., 1999; Huang et al., 2001; Kao et al., 2008;
Urynowicz, 2008) and calculated the difference between the k values
of the two models for different P/N values (Fig. 4). The results conrmed
that the magnitude of errors was negatively correlated with P/N ratio,
similar to the analysis of our own data (Fig. 4).
In Table 2, the reported estimates for the second-order reaction rate
constants for the oxidation of target compounds by permanganate and
their corresponding experimental conditions are presented. Evidently, a
wide range of the second-order reaction rate constant values are reported
for TCE oxidation. Those values varied between 4.2 × 10
1
and 11.9 × 10
1
M
1
s
1
for different conditions (Huang et al., 2001; Kao et al., 2008;
Siegrist et al., 2001; Waldemer and Tratnyek, 2006). Our value for the TCE
reaction rate constant, 8.0 × 10
1
M
1
s
1
, was identical to the value
obtained by Kao et al. (2008), who also used the second-order modeling
approach. Hence, despite different experimental conditions, the calculat-
ed value of the TCE reaction rate constant in our study was consistent
with this literature value for the second order rate constant.
Several studies provided data on the oxidation of toluene by per-
manganate (Rudakov and Lobachev, 2000; Waldemer and Tratnyek,
2006). A comparison of all available reaction rate constants for toluene
and their corresponding experimental conditions showed that our
value of 2.5 × 10
4
M
1
s
1
is at the low end of the reported range.
The estimation method used to determine the second-order reaction
rate constant (either the pseudo-rst-order or second order modeling
approach)can be a reason for this difference.
For the second-order reaction rate constant of ethanol oxidation by
permanganate, only two values could be found in the literature
(Table 2). Those values are higher than the value obtained in our study
(6.5 × 10
4
M
1
s
1
at ~ 20 °C). In the study by Barter and Littler
(1967), the ethanol concentration was kept in excess (P/N 1), which
should yield a very low error using the pseudo-rst-order approach,
equivalent to a P/N of 298. However, their study was conducted at
much lower pH values of about 34, while our experiments were per-
formed at groundwater relevant pHs in the range of 7 to 7.8. Higher oxi-
dation rates at lower pHs may be explained by the overall reaction
equation (Eq. (4)), which shows a net 1:1 proton demand for each mol
of permanganate consumed. A similar pH dependency may be expected
for the oxidation of toluene (Eq. (3)). Changes in pH during our toluene
and ethanol oxidation experiments were however limited, and did not af-
fect the reaction rates. The results of our experiments showed, the pH de-
creased from 7 down to 4.3 during TCE oxidation, but increased to 7.8 and
8.6 for ethanol and toluene oxidation, respectively. As shown by
Eqs. (2)(4), the oxidation of TCE produced H
+
, which caused a decrease
in pH, while ethanol and toluene oxidation produced OH
, which caused
an increase in pH.
Since groundwater pH values are commonly around 7, an experi-
ment was performed at this pH value for each compound (Fig. d, Sup-
plementary material). The results produced the same reaction rate
constants, thus showing that the pH does not have a signicant effect
on the reaction rate constant within the range of pH values from 4.3
to 7.0, 7 to 8.5, and 7.0 to 7.8 for TCE, toluene, and ethanol, respectively.
These results are consistent with those by Waldemer and Tratnyek
(2006) and Kao et al. (2008) who found that the pH did not signicantly
affect the TCE reaction rate within this pH range.
4. Conclusions
In this study, the kinetics of the oxidation of dissolved chlorinated
hydrocarbon (TCE) and non-chlorinated hydrocarbons (toluene and
ethanol) by permanganate were investigated at room temperature
(~20 °C). The results showed that the oxidation rate of ethanol and tol-
uene by permanganate were lower compared to TCE. Rather than
employing the common pseudo-rst-order kinetic analysis, we used a
more realistic and accurate second-order formulation for the oxidation
of target compounds by permanganate. The reaction rate constants
based on the second-order model for TCE, toluene, and ethanol were
found to be 8.0 × 10
1
(M
1
s
1
), 2.5 × 10
4
(M
1
s
1
), and
6.5 × 10
4
(M
1
s
1
), respectively.
Our results further revealed that the reaction rate constants of TCE,
toluene, and ethanol are independent of pH within the range of 4.3
7.0, 78.5, and 7.07.8, respectively. For TCE, this dependency had
been reported previously in the literature (Kao et al., 2008; Waldemer
and Tratnyek, 2006). The oxidation of toluene and ethanol is however
expected to increase with increasing acidity.
The degree of reactant excess (P/N value) was found to strongly in-
uence the accuracy of the pseudo-rst-order approach. In general, the
reaction rate constant obtained from the pseudo-rst-order model is
smaller than the second-order rate constant. The difference is larger
for P/N ratios closer to unity. The inappropriate use of the pseudo-
rst-order model resulted in a deviation of 5% to 25% from the actual
second-order reaction rate constant. Neglecting these errors may have
asignicant effect on design, modeling, and performance of an ISCO re-
mediation approach. Therefore, errors in k can also affect the desired in-
jection rate and concentration of potassium permanganate solution at a
contaminated site.
Despite the slower oxidation kinetics of ethanol and toluene in com-
parison to TCE, their reaction rates, correspond to half-lives of one to
several hours, are still fast enough for the eld application of permanga-
nate to remediate these compounds.
Fig. 4. Relativeerrors in k using the pseudo rst-order reaction rate model versus the P/N
value.
762 M.G. Mahmoodlu et al. / Science of the Total Environment 485486 (2014) 755763
Acknowledgments
The authors would like to thank Jan Kubiak (Wageningen Universi-
ty) and G.C. van de Meent-Olieman (Utrecht University), for valuable
technical assistance, Maryam Imanpour (Utrecht University) for her
helpful comments and suggestions to improve the equations of the
manuscript, and Dr. Amir Raoof (Utrecht University),Dr. Emilio Rosales
Villanueva (University of Vigo), and Prof. Rien van Genuchten (Depart-
ment of Mechanical Engineering, COPPE/LTTC Federal University of Rio
de Janeiro) for their thoughtful review and providing critical comments.
Thorough review comments by two anonymous referees helped to im-
prove the manuscript. This work was supported by the Ministry of Sci-
ence, Research and Technology of Iran.
Appendix A. Supplementary data
Supplementary data to this article can be found online at http://dx.
doi.org/10.1016/j.scitotenv.2013.11.066.
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... The kinetics of oxidation reactions between TCE and KMnO 4 would affect the TCE degradation efficiency and amount of oxidant supplement (Dash et al. 2009). The pseudo-first-order and second-order models have been used by researchers to study the oxidation reaction between TCE and KMnO 4 (Kao et al. 2008;Mahmoodlu et al. 2014;Cui et al. 2017;Chen et al. 2018). If the TCE dissolution rate is faster than its degradation rate plus its volatilization rate, the TCE solution concentration can be viewed as a constant. ...
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