Kinetics of formation of peroxyacetic acid

Article abstract of DOI:10.1007/s11176-005-0378-8

The kinetics of the reaction of acetic acid with hydrogen peroxide, leading to peroxyacetic acid, were studied at various molar reactant ratios (AcOH-H₂O₂ from 6 : 1 to 1 : 6) at 20, 40, and 60°C and sulfuric acid (catalyst) concentrations of 0 to 9 wt %. The reaction is reversible, and the equilibrium constant decreases as the temperature rises: K = 2.10 (20°C), 1.46 (40°C), 1.07 (60°C); Δ_r H ⁰ = - 13.7±0.1 kJ mol^-1, Δ_r S = -40.5±0.4 J mol^-1 K^-1. The maximal equilibrium concentration of peroxyacetic acid (2.3 M) is attained at 20°C and a molar AcOH-to-H₂O₂ ratio of 2.5 : 1. The rate constants of both forward and reverse reactions increase with increase in sulfuric acid concentration from 0 to 5 wt %. Further raising the catalyst concentration does not affect the reaction rate. The reaction mechanism is discussed. 2005 Pleiades Publishing, Inc.

Full text of DOI:10.1007/s11176-005-0378-8

Russian Journal of General Chemistry, Vol. 75, No. 7, 2005, pp. 1125 1130. Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 7, 2005,
pp. 1187 1193.
Original Russian Text Copyright
2005 by Dul’neva, Moskvin.
Kinetics of Formation of Peroxyacetic Acid
L. V. Dul’neva* and A. V. Moskvin**
* Pavlov St. Petersburg State Medical University, St. Petersburg, Russia
** St. Petersburg State Chemical and Pharmaceutical Academy, St. Petersburg, Russia
Received June 3, 2004
Abstract The kinetics of the reaction of acetic acid with hydrogen peroxide, leading to peroxyacetic acid,
were studied at various molar reactant ratios (AcOH H2O2 from 6:1 to 1:6) at 20, 40, and 60 C and sulfuric
acid (catalyst) concentrations of 0 to 9 wt%. The reaction is reversible, and the equilibrium constant decreases
1
as the temperature rises: K = 2.10 (20 C), 1.46 (40 C), 1.07 (60 C); rH0
=
13.7 0.1 kJ mol , rS =
40.5 0.4 J mol 1 K . The maximal equilibrium concentration of peroxyacetic acid (2.3 M) is attained at
20 C and a molar AcOH-to-H2O2 ratio of 2.5:1. The rate constants of both forward and reverse reactions
increase with increase in sulfuric acid concentration from 0 to 5 wt%. Further raising the catalyst concentra-
tion does not affect the reaction rate. The reaction mechanism is discussed.
1
Peroxyacetic acid is widely used as component of
disinfectants. It is usually prepared in situ just before
use. An aqueous solution of peroxyacetic acid, which
is used as disinfectant, can be obtained by reaction of
hydrogen peroxide with acetic acid in water. The
process is described by the following scheme.
hydrogen peroxide were studied previously. It was
shown that the process is of first order with respect to
carboxylic acid and hydrogen peroxide [1, 2]. Using
an 18O isotope label it was found that the reaction
does not involve dissociation of the O O bond in
initial hydrogen peroxide [3]. The hydrolysis of
peroxy acids synthesized from HC18OOH or CH3
C18OOH and H2O2 afforded hydrogen peroxide
containing no heavy oxygen (18O). This means that
both in the formation and in the hydrolysis of peroxy
acids the bond between the acyl group and oxygen
atom is cleaved and that the two processes may be
described by the following scheme.
AcOH + H2O2
AcOOH + H2O.
The reaction is reversible, and the concentrations
of all four components at the equilibrium state are
comparable. Both forward and reverse reactions are
fairly slow at room temperature, and a long time is
necessary for equilibrium to establish. Therefore, the
kinetic parameters and equilibrium constant of this
reaction are to be known to predict the equilibration
time and equilibrium composition of the solution.
Ac18OH + H2O2
AcOOH + H218O.
The reaction is catalyzed by mineral acids; the
following mechanism was proposed in [4, 5]:
The kinetics of reactions of carboxylic acids with
OH
OH
H+
H+
H2O2
CH3COOH + H+
H3C C O+ OH
CH3C+(OH)2
H3C C OOH
H2O2
OH
OH
H
A
B
O+H2
H3C C OOH
H+
H+
H2O
OH
CH3COOOH + H+.
H3C C+
H+
OOH H+
H O
2
OH
C
1070-3632/05/7507-1125 2005 Pleiades Publishing, Inc.

1126
DUL’NEVA, MOSKVIN
It is also known that the reaction of acetic acid
AcOOH
AcOH +0.5O2.
with hydrogen peroxide in water is accompanied by
weak evolution of heat. The heat effect rH was
Therefore, we also tried to estimate how decompo-
sition of peroxyacetic acid affects its equilibrium
concentration in solution. First of all, we examined
the kinetics of the reaction of hydrogen peroxide with
acetic acid at various initial molar reactant ratios (1:6
to 1:0.167) at 20 C. The progress of the reaction was
monitored by measuring the concentration of peroxy-
acetic acid, and the latter parameter was plotted
against reaction time. The kinetic parameters were
calculated on the basis of Eq. (1) which takes into
consideration the rates of both forward and reverse
reactions. In keeping with the data of [1, 2], we
assumed that the forward reaction is first-order in
acetic acid and hydrogen peroxide and that the reverse
reaction is first-order in peroxyacetic acid and water.
1
estimated by different authors at 4.5 to 7.2 kJ mol
[6, 7]. Some publications reported on the effect of
catalyst concentration on the kinetic parameters of this
reaction [8, 9]. The rate of formation of peroxyacetic
acid was shown to increase, and the energy of activa-
tion, to decrease, as the catalyst (sulfuric acid) con-
centration rises. As might be expected for a reversible
process, the amount of the catalyst does not affect the
equilibrium concentration of peroxy acid, other condi-
tions being equal. However, some published data
contradict generally accepted views on the effect of
some factors on reversible reactions. For example,
Havel and Weigner [6] stated that the equilibrium
constant for the reaction under study is directly
proportional to the sulfuric acid concentration in solu-
tion (at a constant temperature) and that the heat effect
decreases as the catalyst concentration rises.
dx/dt = k1[c0(H2O2)
x][c0(AcOH)
x]
k2x[c0(H2O) + x].
(1)
According to the data of [5, 6, 10, 11], the
maximal equilibrium concentration of peroxyacetic
acid depends on the concentration and molar ratio of
the initial reactants. However, these data are contra-
dictory, and the corresponding studies were performed
under different conditions (reactant ratio, temperature,
range of variation of the catalyst concentration); there-
fore, it is difficult to estimate on a quantitative level
the effect of the above factor on the yield of peroxy-
acetic acid. Some studies were carried out in non-
aqueous solvents [12], but the solvent effect was not
taken into account; therefore, these data cannot be
used.
Here, x is the current concentration of peroxyacetic
acid, M; c0(H2O2), c0(AcOH), and c0(H2O) are the
initial concentrations of hydrogen peroxide, acetic
acid, and water, respectively, M; and k1 and k2 are the
second-order rate constants of the forward and reverse
1
reactions, respectively, l mol 1 s .
In order to calculate the rate constants k1 and k2, it
was necessary to determine the equilibrium constant
K. For this purpose, we measured the equilibrium
concentrations of peroxyacetic acid at various molar
ratios of the initial reactants at 20 C, the catalyst
concentration remaining unchanged, c(H2SO4) =
0.057 M. Kinetic experiments showed that the con-
centration of peroxyacetic acid reached its maximal
value in 36 h after mixing the reactants and that it
then remained almost unchanged. Just these values
were taken as equilibrium, and the equilibrium
constant was calculated by Eq. (2).
The goal of the present work was to estimate the
effect of the initial AcOH H2O2 molar ratio, sulfuric
acid (catalyst) concentration, and temperature on the
rate of formation and concentration of peroxyacetic
acid in the equilibrium mixture. Experiments were
performed in an aqueous solution.
It should be noted that peroxyacetic acid is an un-
stable compound. Its decomposition is known to
follow two paths, catalytic and noncatalytic. Trace
amounts of transition metals, dust, and reactor surface
are capable of acting as catalysts of decomposition.
Among the decomposition products, CO2, CO, and
CH3OH were detected. Addition of stabilizers, e.g.,
complexones [13 15], phosphates, or stannates [16]
suppresses the catalytic decomposition. To prevent
catalytic decomposition of peroxyacetic acid, solu-
tions were stabilized by adding orthophosphoric acid;
its concentration in all experiments was 0.057 M
(5 wt%). In the absence of catalysts, spontaneous
decomposition of peroxyacetic acid occurs according
to the following equation:
x1[c0(H2O) + x1]
K =
.
(2)
[c0(H2O) x1][c0(AcOH) x1]
Here, x1 is the equilibrium concentration of peroxy-
acetic acid, M.
Table 1 contains the equilibrium constants deter-
mined at 20 C for different initial reactant ratios.
Obviously, the equilibrium constant should depend
neither on the initial reactant ratio nor on the amount
of the catalyst. In the given system, it should depend
only on the temperature. Therefore, from the data in
Table 1 we calculated the average value of K at 20 C
(K = 2.1).
According to published data, the equilibrium
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 75 No. 7 2005

KINETICS OF FORMATION OF PEROXYACETIC ACID
1127
Table 1. Initial reactant concentrations, equilibrium compositions of the reaction mixtures, and equilibrium constants at
20 C, c(H2SO4) = 0.057 M
Initial reactant concentations, c0, M
Equilibrium concentations ,c0, M
Molar ratio
H2O2 : AcOH,
molmol
K
1
H2O2
AcOH
H2O
AcOOH
H2O2
AcOH
H2O
1: 6
1: 5
1: 4
1: 3
1: 2.5
1: 2
1: 1
1: 0.5
1: 0.4
1: 0.33
1: 0.25
1: 0.2
1: 0.167
2.42
2.79
3.29
4.00
4.48
5.10
7.05
8.71
9.14
9.46
9.88
10.2
10.3
14.5
13.9
13.1
12.0
11.2
10.2
7.05
4.36
3.66
3.15
2.47
2.03
1.72
8.57
9.85
11.6
14.1
15.8
18.0
24.8
30.6
32.1
33.2
34.7
35.7
36.3
1.75
1.90
2.06
2.24
2.29
2.26
1.97
1.42
1.23
1.08
0.84
0.71
0.63
0.673
0.889
1.23
1.76
2.19
2.84
5.08
7.29
7.91
8.38
9.04
9.44
9.71
12.8
12.0
11.1
9.75
8.91
7.94
5.08
2.94
2.43
2.07
1.63
1.32
1.09
10.3
11.8
13.7
16.3
18.1
20.2
26.8
32.0
33.4
34.3
35.6
36.4
37.0
2.10
2.09
2.07
2.14
2.12
2.03
2.04
2.13
2.14
2.14
2.03
2.07
2.19
Average 2.10 0.05
constant K2 of the process under study has the fol-
lowing values: 3.27 (35 C) and 2.87 (50 C) [7]; 3.7
(20 C), 4.0 (30 C), 4.3 (35 C) [17]; 1.21 (0 C), 1.2
(5 C), 1.29 (35 C) [18]. These data are contradictory
with respect to both values of K2 and its temperature
dependence. Therefore, in the subsequent calculations
of k1 and k2 at 20 C we used our value of the equilib-
rium constant at that temperature. In addition, our
results allowed us to determine the optimal initial
molar ratio of acetic acid and hydrogen peroxide,
which ensured the maximal equilibrium concentration
of peroxyacetic acid (see figure); this ratio was 1:2.5.
Integration of Eq. (4) gave Eq. (5).
ln[(x2 x)/(x1 x)] = ln(x2/x1) + (x2 x1)(k1 k2)t. (5)
From Eq. (5) it follows that the time dependence
of ln[(x2 x)/(x1 x)] is linear with the slope b =
(x2 x1)(k1 k2), where k1 and k2 are unknown. These
parameters can readily be found with account taken
of known expression (6). The results of calculations
are summarized in Table 2.
K = k1/k2.
(6)
Insofar as the reaction under study is catalyzed by
acids, we examined the effect of sulfuric acid con-
It should be noted that Eq. (2) is second-order
with respect to peroxyacetic acid concentration x. It
has two solutions: x1 and x2. Among these, only that
c(AcOH), M
satisfying the condition x1 < c0(H2O2) and x1
<
c0(AcOH) has physical sense. The second solution, x2
makes no physical sense. However, both parameters,
x1 and x2, are necessary to calculate the rate constants
k1 and k2. The values of x1 and x2 are given in Table 2.
The parameters x1 and x2 fit Eq. (3).
2.0
1.5
1.0
0.5
1
x1 + x2 =
{K[c (H O ) + c (AcOH] + c (H O)}.
(3)
0
2
2
0
0
2
K
1
According to [19], kinetic equation (1) was trans-
formed into Eq. (4).
0
1
2
3
4
5
6
1
H2O2/AcOH, mol mol
dx/dt = k1(K
1)(x
x1)(x
x)(x2
x2)
Dependence of the equilibrium concentration of peroxy-
acetic acid on the initial reactant ratio.
= (k1 k2)(x1
x).
(4)
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 75 No. 7 2005

1128
DUL’NEVA, MOSKVIN
Table 2. Calculated rate constants of the forward (k1) and reverse reaction (k2) of hydrogen peroxide with acetic acid
at 20 C, c(H2SO4) = 0.057 M
H2O2 : AcOH molar ratio,
x1,a
M
(k1
k2) 105,
k1 105,
k2 105,
x2
1
1
1
1
molmol
l mol 1 s
l mol 1 s
l mol 1 s
1: 6
1: 4
1: 3
1: 2.5
1: 2
1.75
2.07
2.23
2.28
2.30
2.00
1.41
1.22
1.07
0.86
38.5
39.9
41.2
42.1
43.3
47.5
51.5
52.5
53.3
54.4
3.43
4.02
4.65
4.95
3.61
3.89
2.96
3.51
2.28
6.56
7.68
8.89
9.46
6.90
7.43
5.65
6.70
4.35
8.72
3.13
3.66
4.24
4.51
3.29
3.54
2.69
3.20
2.08
4.15
1: 1
1: 0.5
1: 0.4
1: 0.33
1: 0.25
4.56
Average
7.23 2.42
3.45 0.55
a
x
is the equilibrium concentration of peroxyacetic acid.
1
Table 3. Calculated rate constants of the forward (k1) and reverse reaction (k2) of hydrogen peroxide with acetic acid
at different concentrations of the catalyst
w(H2SO4),
c(H2SO4),
(k1
k2) 105,
k1 105,
k2 105,
x1
x2
1
1
1
wt%
M
l mol 1 s
l mol 1 s
l mol 1 s
0
1
2
3
4
5
6
7
8
9
0
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.22
1.23
1.24
52.8
52.7
52.7
52.6
52.6
52.5
52.4
52.4
53.0
53.1
0.12
0.23
044
0.66
2.16
3.57
3.56
3.60
3.54
3.57
0.23
0.44
0.85
1.26
4.13
6.82
6.79
6.87
6.76
6.82
0.11
0.21
0.40
0.60
1.97
3.25
3.24
3.27
3.22
3.25
0.011
0.023
0.034
0.046
0.057
0.069
0.080
0.091
0.103
centration on the kinetic parameters of the process.
For this purpose, we measured the concentration of
AcOOH as time elapsed at various sulfuric acid con-
centrations. The initial mixture was prepared with an
H2O2 AcOH molar ratio of 2.5:1. Orthophosphoric
acid was added as stabilizer of peroxyacetic acid; in
all experiments, the concentration of orthophosphoric
acid was 0.057 M. The rate constants were calculated
according to the above-described mathematical model.
The results are presented in Table 3.
means that there are no reasons to raise the catalyst
concentration above 5 wt%. Presumably, the rate-
determining stage in the forward reaction is elimina-
tion of water molecule from oxonium ion C which
occurs in dynamic equilibrium with neutral inter-
mediate B. When the sulfuric acid concentration
exceeds 5 wt%, the equilibrium B
C is com-
pletely displaced to the right, the concentration of ion
C reaches is maximal value under the given condi-
tions, and the rate constant of the forward reaction no
longer changes. Analogous considerations are also
valid for the reverse reaction where the rate-determin-
ing stage is elimination of hydrogen peroxide from
ion A.
It is seen that increase in the catalyst concentration
from 0 to 5 wt% leads to increase in the rate constants
and that further raising the catalyst concentration
from 5 to 9 wt% almost does not affects the rate
constants; the average values of k1 and k2 are 6.81
The temperature effect on the reaction rate and
equilibrium constant was studied by measuring the
5
5
1
10 and 3.25 10 l mol 1 s , respectively. This
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 75 No. 7 2005

KINETICS OF FORMATION OF PEROXYACETIC ACID
1129
Table 4. Compositions of the reaction mixture in the initial moment and in the equiblirium state at different temperatures
and equilibrium constants
Equilibration Initial reactant concentrations, c0, M
Equilibrium concentrations, M
Temperature,
C
time, h
K
H2O2
AcOH
H2O
AcOOH
H2O2
H2O
AcOH
20
40
60
36
28
22
9.88
9.88
9.88
2.47
2.47
2.47
34.7
34.7
34.7
0.840
0.678
0.544
9.04
9.20
9.33
35.6
35.4
35.3
1.63
1.80
1.93
2.10
1.46
1.07
1
kinetic dependences for peroxyacetic acid at 20, 40,
and 60 C. The initial molar ratio H2O2 AcOH was
1:0.25. The concetrations of the catalyst (H2SO4) and
stabilizer (H3PO4) were maintained constant
(0.057 M). The initial and equilibrium compositions
of the reaction mixture and the equilibrium constant
are given in Table 4. It is seen that increase in
temperature shortens the time necessary for the equi-
librium to establish. The concentration of AcOOH in
the equilibrium mixture decreases in parallel, since the
equilibrium constant decreases as the temperature
rises (Table 4). The obtained data were used to
calculate thermodynamic parameters of the reaction
according to Eq. (7).
(69.135 [17], 6.20 [7], 42.61 to 56.65 kJ mol at
various catalyst concentrations [9]) and high negative
entropies of activation. In particular, this means that
the transition states in both forward and reverse reac-
tions should be much less ordered than the correspond-
ing initial state. On the other hand, this statement
contradicts the above hypothesis implying such rate-
determining stages of the forward and reverse pro-
cesses, for which the entropy of activation should be
positive. Presumably, the activation parameters
determined in the present study are apparent quantities
characterizing the entire fairly intricate process rather
than a particular reaction stage. Nevertheless, these
values may be used to predict the rate of the process
as a whole.
lnK =
rH0/RT + rS0/R,
(7)
By special experiments we showed that decomposi-
tion of peroxyacetic acid and hydrogen peroxide in the
presence of orthophosphoric acid as stabilizer
(0.057 M) occurred (on the average) by 10% in
330 days at 20 + 3 C. Therefore, the change in the
concentrations of peroxyacetic acid and hydrogen
peroxide as the result of their decomposition during
our kinetic experiments was assumed to be negligible.
1
1
rH0 13.7 0.1 kJ mol , rS0 40.5 0.4 J mol 1 K ;
r 0.99996, s 0.00407, n 3.
Using these data, we calculated (as described
above) the rate constants of the forward and reverse
reactions at different temperatures [c(H2SO4) =
0.057 M] and activation parameters of the forward and
reverse processes according to the Arrhenius and
Eyring equations [Eqs. (8) and (9), respectively].
EXPERIMENTAL
Procedure of kinetic experiments. A reactor (a 2-l
glass three-necked flask) equipped with a thermometer
and a stirrer (operating at a speed of 100 rpm) was
placed in a temperature-controlled unit and charged
with a 35 wt% aqueous solution of hydrogen peroxide,
and 85% orthophosphoric acid was added to a con-
Temperature, K
293
313
333
k1 105, l mol 1 s
k2 105, l mol 1 s
6.81
3.25
8.55
5.85
13.82
12.92
1
1
Ea/RT
k = Ae
kBT
,
(8)
(9)
1
centration of 0.057 mol l . Specified amounts of
S /R
glacial acetic acid and sulfuric acid (catalyst) were
added under stirring. Samples were withdrawn from
the reaction mixture at definite time intervals, and the
concentrations of hydrogen peroxide and peroxyacetic
acid were measured. The experiment was assumed to
be finished than the composition of the mixture
almost no longer changed. While studying the effect
of the temperature on the rate of formation of peroxy-
acetic acid, the mixture was maintained at 40 and
60 C for 8 h.
k =
e
H /RT e
.
h
Forward reaction Reverse reaction
1
Ea, kJ mol
14.22 3.49
3.804 1.35
11.62 3.45
285.24 11.05
27.90 3.39
1.067 1.31
25.29 3.34
244.73 10.72
lnA
1
H , kJ mol
S , J mol 1 K
1
Both forward and reverse reactions are characte-
rized by fairly low energies (enthalpies) of activation
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 75 No. 7 2005

1130
DUL’NEVA, MOSKVIN
The following reagents were used: 35% hydrogen
5. Parker, W.E., Wetnauer, L.E., and Swern, D., J. Am.
Chem. Soc., 1958, vol. 80, no. 2, p. 323.
peroxide of medical grade, glacial acetic acid of
chemically pure grade, 85% orthophosphoric acid, and
98% sulfuric acid of chemically pure or analytical
grade.
6. Havel, S. and Weigner, J.A., Chem. Prum., 1960,
vol. 10, p. 293.
7. Suzuki, T., Iwamoto, I., and Suzuki, S., J. Chem. Soc.
Jpn., Pure Chem. Sect., 1962, vol. 83, no. 11, p. 1212.
The concentration of hydrogen peroxide was
determined by permanganatometric titration [4, 20]
using a standard solution of potassium permanganate
(0.1 M; technical specification 2642-001-49415344-99
or 6-09-2540-87), sulfuric acid (chemically pure or
analytical grade, GOST 4204-77), and distilled water
(GOST 6709-72).
8. Dvorak, J., Chem. Prum., 1959, vol. 9, p. 524.
9. Havel, S., Sborn. Vedeckych praci. Vysoka Skola
Chemickotechnologicka, Pardubice, 1967, pp. 1, 79.
10. Agnihotri, V.G. and Parikk, D.V., Res. Ind., 1965,
vol. 10, no. 6, p. 170.
11. Karetnikova, N.V., Pen, R.Z., and Pen, V.R., Khim.
rastit. syr’ya, 1999, no. 2, p. 41.
The concentration of peroxyacetic acid was deter-
mined iodometric titration [4, 21] using sodium
carbonate (chemically pure or analytical grade, GOST
83-79) or sodium hydrogen carbonate (chemically
pure or analytical grade, GOST 4201-79); potassium
iodide (chemically pure grade, GOST 4232-74; 10%
aqueous solution prepared according to GOST 4517-
87, p. 2.67), a standard solution of sodium thiosulfate
pentahydrate (0.1 M, technical specification 6-09-
2540-87), soluble starch (GOST 10163-76; a 0.5%
aqueous solution prepared according to GOST 4517-
87, p. 2.90), and distilled water (GOST 6709-72).
12. Ogata, Y. and Sawaki, Y., Tetrahedron, 1965, vol. 21,
no. 12, p. 3381.
13. Koubek, E., Haggett, M.L., and Battaglia, C.J., J. Am.
Chem. Soc., 1963, vol. 85, no. 5, p. 2263.
14. Dorofeikov, V.V., Shcherbak, I.G., Zemchen-
kov, A.Yu., and Timokhovskaya, G.Yu., RU Patent
no. 2077890, 1997; Byull. Izobret., 1997, no. 12.
15. Meloun, D.U.D., RU Patent no. 2145879, 2000;
Byull. Izobret., 2000, no. 6.
16. Lunenok-Burmakina, V.A., Miroshnichenko, A.G.,
Kolyadenko, V.G., Mikhno, I.L., Anisimova, I.G.,
Taran, V.V., Blonskaya, L.F., Emel’yanova, O.B.,
and Limanov, V.E., USSR Inventor’s Certificate
no. 1683763, 1991; Byull. Izobret., 1991, no. 38.
The overall absolute error in the determination of
hydrogen peroxide and peroxyacetic acid was 0.15%
at a confidence probability of 0.95.
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