Kinetics and mechanism of addition of parabanic acid (imidazolidine-2,4,5-trione) to oxiranes

Article abstract of DOI:10.1002/kin.10104

The results of studies on the kinetics of reaction of 1 mol of parabanic acid (imidazolidine-2,4,5-trione) with 1 mol of ethylene oxide (oxirane) or propylene oxide (2-methyloxirane) carried out in the presence of triethylamine catalyst in dimethylsulfoxide solution are presented. A rate equation describing the reaction is presented and the mechanism proposed. The validity of the proposed mechanism is proved by instrumental analytical methods. The effect of temperature is also presented and the thermodynamic parameters of the reaction evaluated.

Full text of DOI:10.1002/kin.10104

Kinetics and Mechanism of
Addition of Parabanic Acid
(Imidazolidine-2,4,5-trione)
to Oxiranes
IWONA ZARZYKA-NIEMIEC, JACEK LUBCZAK
Faculty of Chemistry, Rzeszo´w University of Technology, 35-959 Rzeszo´w, Poland
Received 5 March 2002; accepted 16 October 2002
DOI 10.1002/kin.10104
ABSTRACT: The results of studies on the kinetics of reaction of 1 mol of parabanic acid
(imidazolidine-2,4,5-trione) with 1 mol of ethylene oxide (oxirane) or propylene oxide (2-
methyloxirane) carried out in the presence of triethylamine catalyst in dimethylsulfoxide solu-
tion are presented. A rate equation describing the reaction is presented and the mechanism
proposed. The validity of the proposed mechanism is proved by instrumental analytical meth-
ods. The effect of temperature is also presented and the thermodynamic parameters of the
reaction evaluated. ꢀ 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 73–80, 2003
C
amount of unreacted oxirane by measuring the partial
pressure of ethylene oxide (oxirane) or propylene oxide
(2-methyloxirane) over reacting mixture [19]. The sec-
ond method involves chemical determination (usually
by titration) of unreacted oxirane [20,21], and the third
consists in following the volume contraction in reaction
mixture [22]. The first method is not frequently used
and because of technical problems can be applied only
to systems where a large excess of oxirane is used.
The chemical methods are not too accurate, particu-
larlyforsystemswithaminecatalysts. Thesimplestand
most convenient seems to be the dilatometric method,
which is particularly useful for the imide–oxirane sys-
tem studied in this work.
INTRODUCTION
Informationonthekineticsofreactionsofcyclicimides
with oxiranes is rather scarce in literature as opposed
to that on reactions of oxiranes with other active
hydrogen-containing organic compounds, such as al-
cohols [1–3], thiols [4,5], phenols [6], carboxylic acids
[7–11], and amines or amides [12–14], that are car-
ried out in the presence of various catalysts and in dif-
ferent solvents [15–18]. The methodology of studying
the kinetics of these reactions comprises three differ-
ent approaches. One of them consists in following the
We used parabanic acid containing two imide
groups. It reacts with oxiranes in two steps. First,
N-hydroxyalkyl hydroparabanate (I) is formed and
then N,Nꢁ-bis(hydroxyalkyl) parabanate (II) [23],
Correspondence to: Jacek Lubczak; e-mail: jml@prz.rzeszow.pl.
Contract grant sponsor: Polish Committee of Scientific Research.
Contract grant number: 4T09 B 010 22.
2002 Wiley Periodicals, Inc.
c
ꢀ

74
ZARZYKA-NIEMIEC AND LUBCZAK
according to the following reaction:
O
C
O
C
O
C
O
C
O
C
O
C
CH R
CH2
CH R
CH2
O
O
H-N
N-H
HO-CHR-CH2-N
N-CH2-CHR-OH
H-N
N-CH2-CHR-OH
C
O
C
O
C
O
(I)
(II)
with R = H, CH3.
sulphoxide by placing the flask in a warm water bath.
The solution was then brought to a desired tempera-
ture (30, 35, 40, 45, or 50◦C ( 0.05◦C)) and a calcu-
lated amount of triethylamine was added to the flask.
Thevolumewasthenadjustedusingproperlypreheated
dimethyl sulphoxide.
It was found that the presence of triethylamine con-
siderably reduces the reaction time. The optimal tem-
perature for the reaction was 25–50◦C. Further eleva-
tion of temperature leads to formation of polymeric
products of the following structure [23]:
The effect of parabanic acid concentration on the
rate of reaction was determined at constant oxi-
rane concentration equal to 0.25 mol/dm3, changing
the acid concentration in the range 1.0–2.0 mol/dm3 at
0.5 mol/dm3 intervals.
The effect of catalyst concentration was studied at
the constant parabanic acid (1.0 mol/dm3) and oxirane
(1.0 mol/dm3) concentrations. The catalyst concentra-
tion was changed in the range 0.1–0.5 mol/dm3 at 0.1
mol/dm3 intervals.
The effect of temperature was studied at the constant
parabanic acid (1.0 mol/dm3), oxirane (1.0 mol/dm3),
and triethylamine (0.5 mol/dm3) concentrations. Tem-
perature was changed in the range 30–45◦C in the case
of ethylene oxide or 35–50◦C for propylene oxide at
5◦C intervals.
O
C
O
C
CH2 CH
R
O
N
C
2
n
O
HN CH2 CH OH
R
(III)
with R = H, CH3.
In this work we have studied the kinetics of of reac-
tion of 1 mol of parabanic acid with 1 mol of ethylene
oxide or propylene oxide. The reaction products are
the respective N-hydroxyalkyl hydroparabanates. We
have limited ourselves to this molar ratio because in the
presence of an excess of oxiranes, a more complex re-
action mixture is obtained because of side reactions of
oxirane with hydroxy groups and, at an even higher ex-
cess, to an opening ofparabanic acid ring and formation
of the earlier mentioned polymeric products (III). A re-
port on the reaction of parabanic acid with an excess
of oxiranes will be the subject of a forthcoming paper.
A dilatometer of total volume of ca. 45 cm3 was
used, equipped with a 40-cm long capillary of inner di-
ameter 1 mm. Before it was filled it was kept at reaction
temperature for at least 15 min. The reaction time was
measured from the moment of mixing the reactants.
The first reading of meniscus level was usually made
after 10 min, which was needed to fill in the dilatometer
and bring the mixture to reaction temperature. The next
readings were made after constantly increasing time in-
tervals until the meniscus level stabilized. The initial
level of meniscus was calculated by extrapolating the
readouts to the time t = 0. The values from the con-
version range of oxirane 0.2–0.8 taken from smoothed
readout curves at conversion intervals 0.05 were used
to obtain rate equations.
EXPERIMENTAL
Materials
Parabanic acid was obtained as described elsewhere
[24]. Ethylene oxide and propylene oxide were reagent
grade products supplied by Fluka (Switzerland).
Triethylamine was a regent grade product of Avocado
(Germany). Dimethyl sulfoxide (pure, Avocado) was
dried on molecular sieves A4, a product of POCh
(Poland).
The system with ethylene oxide (EO) was the refer-
ence one. The relative activity of propylene oxide, rPO
,
was calculated as the ratio of rate constants kPO and
kEO determined at the same temperature:
Rate Measurements
In a 50-cm3 measuring flask, a predetermined amount
of parabanic acid was weighed (to within 0.1 mg). The
content was then dissolved in ca. 30 cm3 of dimethyl
kPO
rPO
=
(1)
kEO

ADDITION OF PARABANIC ACID TO OXIRANES
75
1H NMR and IR Spectra
The Gibbs activation energy was calculated using the
equation
1H NMR spectra were recorded using a BS-586A 80
MHz spectrometer (Tesla, Czechoslovakia). The sol-
vent was d6-DMSO, and hexamethyldisiloxane was
the internal standard. IR spectra were recorded using
a Paragon 1000 FT spectrometer (Perkin-Elmer). The
samples were prepared in the form of KBr tablets.
ꢀ
ꢁ
k
ꢀG= = RT · 23.764 − ln
(2)
T
By plotting ꢀG= vs. T a straight line was obtained
with activation enthalpy and entropy of the reaction as
the coefficients of the line:
RESULTS AND DISCUSSION
ꢀG= = ꢀH= − T · ꢀS=
(3)
The study aimed at finding
In Eqs. (2) and (3) T is the temperature of addition, k
is the rate constant, R is the gas constant, and ꢀG=,
ꢀH=, and ꢀS= are the Gibbs free energy, enthalpy,
and entropy of activation, respectively.
•
a general rate equation describing the reaction of
addition of parabanic acid to ethylene oxide or
propylene oxide;
•
•
activation parameters of the reactions; and
possible mechanism of the reactions.
Analytical Methods
Conductometry. The conductivity of the solutions of
parabanic acid and triethylamine was measured at 20◦C
( 0.1◦C) using a Radelkis OK-102/1 conductometer
(Hungary). Solutions of parabanic acid, triethylamine,
and mixtures thereof in water were prepared with the
same total concentrations 0.5 mol/dm3. A 20-cm3 sam-
ple of each solution was placed in the measuring cell
and its conductivity measured. Then the sample was di-
luted with another 20 cm3 of water and the conductivity
measured again. The procedure was continued until the
system reached conductivity close to that of pure water.
Conductivity of aqueous solutions of mixtures of para-
banic acid and triethylamine in which molar ratios of
components changed in the range from 0 to 1 in 0.1 in-
tervals were also measured. The total concentration of
the solutions was constant and equal to 0.25 mol/dm3.
The temperature range of the experiments was lim-
ited by the relatively low reaction rate, on one hand,
and a danger of quick evaporation of volatile oxirane
(boiling points 14 and 34◦C for EO and PO, respec-
tively) on the other. The study was carried out in DMSO
solutions. The solvent dissolves parabanic acid very
well.
Parabanic acid has been found to react with ethy-
lene oxide (subscript B) following the first-order rate
equation with respect to oxirane (Table I):
−dcB
V =
= k · cB
(4)
dt
The relation is correct provided no subsequent re-
actions take place in the system, i.e., reactions of
Table I The Rate Constants kn of the Reaction of Imide Groups of Parabanic Acid (AH) with Ethylene Oxide (B) in the
Presence of Triethylamine Catalyst at 40◦C as Calculated Assuming Reaction Order n with Respect to Ethylene Oxide
No. t (min) Oxirane Conversion, p k1/2 (10−5
s
−1mol1/2 dm−3/2
)
k1 (10−5 s−1
)
k3/2 (10−5
s
−1mol−1/2 dm3/2
)
1
2
3
4
5
6
7
8
9
10
11
12
13
140
180
225
285
330
405
480
560
660
750
900
1050
1320
0.204
0.246
0.295
0.350
0.390
0.449
0.500
0.549
0.600
0.640
0.698
0.740
0.798
2.18
2.18
2.23
2.18
2.15
2.13
2.06
2.02
1.97
1.90
1.82
1.74
1.61
4.55
4.63
4.80
4.79
4.80
4.87
4.81
4.84
4.85
4.81
4.78
4.76
4.60
0.955
0.981
1.04
1.06
1.08
1.12
1.13
1.18
1.22
1.25
1.30
1.35
1.38
The initial concentrations were c0AH = 2.0001 mol/dm3; c0B = 0.2557 mol/dm3; ccat = 0.5112 mol/dm3.

76
ZARZYKA-NIEMIEC AND LUBCZAK
N-hydroxyalkyl groups with unreacted oxirane:
Thus, by integrating rate equation (8) one obtains
ꢂ
1
1
kꢁ =
√
+
N CH2 CH2 OH
CH2 CH2
O
t
c0AH − c0B
ꢃ
ꢃ
ꢃ
ꢃ
ꢃ
√
√
ꢀ
√
ꢃ
ꢃ
ꢃ
− c0AH − pc0B
−
+
c0AH − c0B
c0AH − c0B
×
ln
√
N CH2 CH2 O CH2 CH2 OH (5)
− c0AH − pc0B
ꢃ
ꢃ
ꢃ
ꢃ
√
√
ꢁꢄ
ꢃ
− c0AH
−
c0AH − c0B
To eliminate an effect of these reactions, a large
excess of imide groups (subscript AH) with respect to
oxirane was applied. Their concentration enter into the
rate equation hidden in the rate constant k, according
to equation
ꢃ
− ln
√
(9)
√
ꢃ
ꢃ
− c0AH
+
c0AH − c0B
From the data in Table II it follows that the values of
kꢁ calculated using the two methods are very close to
each other. A difference becomes apparent only when
there is a relatively small (eightfold) excess of imide
groups with respect to oxirane. At this ratio of reagents,
the effect of subsequent reactions of ethylene oxide
with hydroxyethyl groups, that are slower than reac-
tions of imide groups, starts to show up.
The effect of catalyst concentration was studied at
the twofold excess of the active imide (AH) groups of
parabanic acid with respect to ethylene oxide. The re-
lation between catalyst concentration and the rate con-
stant calculated according to Eq. (9) is
k = kꢁ · cAmH
(6)
By applying 8-, 12-, and 16-fold excess of imide groups
with respect to ethylene oxide, the values of m and kꢁ
have been evaluated by the least-squares method (cor-
relationcoefficientr = 0.9986). ByintroducingEq. (6)
into Eq. (4) with m = 1/2 one obtains:
V = kꢁ · cA1/H2 · cB
(7)
kꢁ = kꢁꢁ · cczat
(10)
If Eq. (7) well described the reaction of addition of
parabanic acid to ethylene oxide, the value of kꢁ would
have been the same as that of the same constant in
Eq. (9) (later in the text), where no constancy of imide
group concentration was assumed and correction was
made according to
that can be used to calculate exponent z and the value of
kꢁꢁ. The best fit was obtained for z = 0.5 (r = 0.9992).
Hence, the general rate equation describing the re-
action of addition of parabanic acid to ethylene oxide
reads
V = kꢁ(c0AH − pc0B)1/2(1 − p)c0B
(8)
V = kꢁꢁ · cK1/2 · c1/2 · cB
(11)
AH
(one should bear in mind that cAH is twice the concen-
tration of parabanic acid).
The reaction mechanism that is consistent with the
rate equation (11) might read as follows:
where “0” in the subscript denotes the initial concen-
tration of reagents and p is the conversion of oxirane
measured dilatometrically.
O
C
O
C
O
C
O
C
_
+
:
+
+
:
N
:
+
+
HN(CH2CH3)3
N(CH2CH3)3
H-N
H-N
N-H
C
O
C
O
k1
_
+
AH
A
K
KH
k −1
O
O
C
O
O
C
C
C
_
_
..
:
:
+
CH2 CH2
O
H-N
N
H-N
:
N-CH -CH -O
..
2
2
C
O
C
O
k2
_
_
+
B
AB
A

ADDITION OF PARABANIC ACID TO OXIRANES
77
O
C
O
C
O
C
O
C
_
+
..
:
+
N(CH2CH3)3
:
H-N
H-N
N-CH2-CH2-OH
+
N-CH -CH -O
..
HN(CH2CH3)3
2
2
C
O
C
O
k3
_
+
+
+
KH
K
AB
ABH
k−3
The mechanism consists of three elementary reactions:
From the assumption on the slowest, rate-
determining step, one has
•
formation of an adduct of parabanic acid with tri-
ethylamine that occurs in ionized form
attack of parabanic ion upon oxirane molecule
catalyst recovery
k22 · cB2 ꢃ 4k1 · k−1 · cAH · cK
(17)
(18)
(19)
(20)
(21)
•
•
and
1/2
AH
cA = K11/2 · c · cK1/2
Assuming that the rate-limiting step is the reaction
between anion and oxirane (the other two are quick
since they involve proton exchange), the general rate
equation should read
−
By substituting Eq. (18) into Eq. (12) one obtains
Vgeneral = k2 · K1/2 · cK1/2 · c1/2 · cB
1
AH
−
Vgeneral = V2 = k2 · cB · cA
(12)
with
From the Bodenstein stationary rule it follows that
−
dcA
kꢁꢁ = k2 · K11/2
+
−
= k1 · cAH · cK − k−1 · cA · cHK
dt
−
− k2 · cA · cB = 0
(13)
(14)
which finally gives
Since
Vgeneral = kꢁꢁ · cK1/2 · c1/2 · cB
AH
+
−
cA = cHK
The rate equation (21) is the same as found in exper-
iment, thus confirming the assumption on the mecha-
nism of reaction.
The mechanism has been verified by using instru-
mental methods. The adduct, which is in fact a salt,
triethylammonium hydroparabanate, was prepared by
reacting parabanic acid with triethylamine in tetrahy-
drofurane at room temperature.
Triethylammonium hydroparabanate is a crystalline
substance of mp 149–150◦C. Its structure has been
confirmed by 1H NMR and IR. In the 1H NMR spec-
trum, the chemical shift of protons at NH groups
of parabanic acid (Fig. 1a) is 11.7 ppm, whereas in
the spectra of its adduct with triethylamine the shift is
10.2 ppm (Fig. 1b). This suggests the presence of ion
pair or free ions. Furthermore, in IR spectrum of the
adduct, bands of medium intensity appear at around
2500 cm−1 (cf. Figs. 2a and 2b) usually ascribed to tri-
ethylammonium cation. The conductometric measure-
mentsalsoindicatethationsappearinsolutionsofpara-
banic acid and triethylamine in water. For mixtures of
parabanic acid and triethylamine the conductivity has
one gets
−k−1 · cA2 − − k2 · cB · cA + k1 · cAH · cK = 0 (15)
−
Hence,
ꢅ
k2 · cB − k22 · cB2 + 4k−1 · k1 · cAH · cK
−
cA
=
(16)
−2k
−1
Table II The Rate Constants of the Reaction of
Parabanic Acid with Ethylene Oxide at 40◦C as
Calculated from Rate Equations (7) and (9)
Imide to
Oxirane
kꢁ
kꢁ
(10−5 s−1
c0AH
(10−5 s−1
(mol/dm3) Molar Ratio mol−1/2 dm3/2) mol−1/2 dm3/2
)
4.000
3.000
2.000
16:1
12:1
8:1
4.77
4.09
2.96
4.80
4.09
3.31
c0B = 0.2500 mol/dm3, ccat = 0.5000 mol/dm3.

78
ZARZYKA-NIEMIEC AND LUBCZAK
Figure 1 1H NMR spectra of parabanic acid (a) and triethylammonium hydroparabanate (b).
been found to be higher than the sum of conductivi-
ties of solutions of individual components. The highest
conductivity was measured for equimolar mixtures of
the components (cf. Fig. 3). Evidently, 1:1 salt was
formed.
character of carbon atom 1 in oxirane molecules:
+
2
3
3
2
+CH2 CH CH3
CH2
CH2
O
O
-
-
1
1
Equation (21) describing the rate of reaction of
parabanic acid with ethylene oxide applies to the
parabanic acid–propylene oxide system as well.
By comparing the respective rate constants, one
concludes that ethylene oxide is much more reactive in
addition of parabanic acid than propylene oxide. The
average relative activity of the second is only 0.55. By
analyzing electron shifts one may also conclude that
the reactivity depends primarily on the electropositive
According to the induction effects shown in the scheme
above, the electrophilic character of carbon atom 1 in
propylene oxide is diminished by the donor action of
methyl group. This may explain the reduced reactiv-
ity of propylene oxide as compared to that of ethy-
lene oxide. It has been shown in Ref. [25] that para-
banate anion attacks carbon C-3 of 2-methyoxirane

ADDITION OF PARABANIC ACID TO OXIRANES
79
Figure 2 IR spectra of parabanic acid (a) and triethylammonium hydroparabanate (b).
and the resulting alcoholate has the structure
N CH2 CH(CH3) O−.
10
9
8
7
6
5
4
3
2
1
0
From the temperature effect on reactions of para-
banic acid with oxiranes, the Gibbs free energy, ꢀG#,
as well as enthalpy, ꢀH#, and entropy of activation,
ꢀS#, have been evaluated (Fig. 4). The results of cal-
culations are presented in Table III. The values of
activation entropy suggest that the transition state of
reaction consists of two components, in accord with
the proposed mechanism of addition. Somewhat lower
Table III Activation Parameters of the Addition of
Parabanic Acid to Ethylene Oxide or Propylene Oxide
0,0 0,1
TEA
0,2 0,3
0,4 0,5
0,6 0,7
0,8 0,9
1,0
PA
Activation Parameter
EO
PO
molar fraction
ꢀG# (kJ mol−1
)
)
103.75
71.4
−107.9
105.80
68.9
−120.7
Figure 3 The conductivity of water solutions of mixtures of
triethylamine (TEA) and parabanic acid (PA) vs. molar frac-
tion of the components. Total concentration: 0.25 mol/dm3.
ꢀH# (kJ mol−1
ꢀS# (J mol−1 K−1
)

80
ZARZYKA-NIEMIEC AND LUBCZAK
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ꢀ
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•
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