Kinetics of the synthesis of 1-alkyl-3-methylimidazolium ionic liquids in dilute and concentrated solutions

Article abstract of DOI:10.1002/kin.20812

The kinetics of the reactions of 1-methylimidazole with iodoethane, 1-iodobutane, 1-bromobutane, 1-bromohexane, 1-bromooctane resulting in the formation of corresponding 1-alkyl-3-methylimidazolium halide ionic liquids in acetonitrile and cyclopentanone solutions has been studied in a wide range of concentrations and degrees of conversion. The studied reactions were found to follow the S_N2 rate law in the dilute solutions. The significant deviations from the simple S_N2 rate law observed at higher concentrations of the reactants were assigned to the concentration dependence of activity coefficients for the reactants and the transition states. The experimental data were processed with the conductor-like screening model-segment activity coefficient (COSMO-SAC) model and the Scatchard-Hildebrand equation. The latter was found to provide somewhat better description of the experimental results; however, the former has a wider predictive ability. The Arrhenius activation energies and the activation enthalpies were calculated for the investigated systems. The rate constants at infinite dilution were obtained for a large number of 1-haloalkane + 1-methylimidazole + solvent systems with the use of the COSMO-SAC model. It was demonstrated that the rate constants of the studied reactions in various non-hydrogen-bonding solvents can be estimated from a correlation with the Hildebrand solubility parameter.

Full text of DOI:10.1002/kin.20812

Kinetics of the Synthesis
of 1-Alkyl-3-
methylimidazolium Ionic
Liquids in Dilute and
Concentrated Solutions
DZMITRY S. FIRAHA, YAUHENI U. PAULECHKA
Chemistry Faculty, Belarusian State University, Leningradskaya 14, Minsk 220030, Belarus
Received 6 August 2012; revised 2 April 2013; 15 June 2013; accepted 11 July 2013
DOI 10.1002/kin.20812
Published online in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The kinetics of the reactions of 1-methylimidazole with iodoethane, 1-iodobutane,
1-bromobutane, 1-bromohexane, 1-bromooctane resulting in the formation of corresponding
1-alkyl-3-methylimidazolium halide ionic liquids in acetonitrile and cyclopentanone solutions
has been studied in a wide range of concentrations and degrees of conversion. The stud-
ied reactions were found to follow the SN2 rate law in the dilute solutions. The significant
deviations from the simple SN2 rate law observed at higher concentrations of the reactants
were assigned to the concentration dependence of activity coefficients for the reactants and
the transition states. The experimental data were processed with the conductor-like screening
model–segment activity coefficient (COSMO-SAC) model and the Scatchard–Hildebrand equa-
tion. The latter was found to provide somewhat better description of the experimental results;
however, the former has a wider predictive ability. The Arrhenius activation energies and the
activation enthalpies were calculated for the investigated systems. The rate constants at infi-
nite dilution were obtained for a large number of 1-haloalkane + 1-methylimidazole + solvent
systems with the use of the COSMO-SAC model. It was demonstrated that the rate constants
of the studied reactions in various non-hydrogen-bonding solvents can be estimated from a
ꢀC
correlation with the Hildebrand solubility parameter. 2013 Wiley Periodicals, Inc. Int J Chem
Kinet 1–9, 2013
INTRODUCTION
chemical properties of these liquids can be easily tai-
lored by changing their structure: nature of the cations
and the anions or the alkyl substituents in the cations,
andit is possibletofindILpossessingthe requiredchar-
acteristics. A large number of potential applications of
these compounds both in science and technology are
considered nowadays [2].
Room temperature ionic liquids (ILs) are salts with
melting temperatures below T = 373 K [1]. Physico-
Correspondence to: Yauheni U. Paulechka; e-mail:
paulechka@bsu.by.
Supporting Information is available in the online issue at
www.wileyonlinelibrary.com.
Imidazolium ILs are among the most studied com-
pounds of this class. They can be synthesized by
C
ꢀ
2013 Wiley Periodicals, Inc.

2
FIRAHA AND PAULECHKA
quaternization of 1-methylimidazole (MeIm) with es-
ters, such as diakyl sulfates, carbonates, and methyl
triflate. However, in most cases imidazolium ILs are
obtained in two stages through corresponding halides:
and Scurto [10] obtained kinetic characteristics of
the reaction between HexBr and MeIm in various
solvents. Groβe Bo¨wing and Jess [11] studied
homogeneous and heterogeneous reaction between
(R1)
(R2)
A chloride, bromide or iodide IL is obtained at the
first stage (R1), and the anion is changed to the desired
one at the second stage (R2). The highly exothermic
stage (R1) [3,4] can be realized by either continuous or
periodic methods. In the continuous method, the reac-
tants are mixed in a microreactor and then the reaction
proceeds in a flow mode [5–9]. At the beginning, the
rate of the process is rather high; however, it may take
a few days to achieve the degree of conversion of more
than 99%. High quality of the obtained product due to
the good temperature control is the advantage of this
method. The second method is normally used if a small
amount of ILs is required. The possibilities of scaling
up for this method are limited due to problems with
temperature control. These problems are partly solved
if the solvent is used.
1-chlorobutane and MeIm in the presence of ethanol
and without it. Alkylation of MeIm with 1-
bromobutane BuBr without solvent in the temperature
range 348–363 K was considered by Hu et al. [13]. The
energy of activation of reaction (R1) for R = 1-butyl
and Hal = Br was reported [3].
The aim of this work is to study the kinetics of the
reactions between MeIm and haloalkanes including io-
doethane EtI, 1-iodobutane BuI, 1-bromobutane BuBr,
1-bromohexane HexBr, and 1-bromooctane OctBr in
acetonitrile and cyclopentanone media in a wide range
of concentrations and degrees of conversion and to
evaluate the performance of theoretical methods to-
ward quantitative description of the observed kinetic
dependences.
The existing methods of the synthesis should be im-
proved for further promotion and wide usage of ILs.
The quantitative description of kinetics and thermody-
namics of the IL synthesis is one of important steps
in this process. The reaction rate constants and acti-
vation energies as well as the enthalpies of the pro-
ceeding reactions are necessary for the development
of new production units. These data can also be used
for development of procedures quantifying the effect
of various factors on the rate of these reactions.
In this work, the systems with a solvent were chosen
for the kinetic study of the reaction (R1) with a number
of haloalkanes. The solvent allowed us to keep the re-
action mixture homogeneous in the course of the reac-
tion and perform the process isothermally. Acetonitrile
and cyclopentanone were used as solvents since the
rate constants for the reactions between MeIm and 1-
bromohexane HexBr in these solvents were found to be
higher than those in other conventional solvents [10].
The kinetics of the synthesis of other 1-alkyl-
3-methylimidazolium ILs has been considered in a
number of studies [5–13]. The kinetics of forma-
tion of 1-ethyl-3-methylimidazolium ethylsulfate
[C2mim]EtSO4 was studied in [8] and [9]. Schleicher
EXPERIMENTAL
Commercial samples of MeIm (99%; Fluka, Switzer-
land), BuBr (99%; Acros Organics, Belgium), and
acetonitrile (>99.99%; Khimmed, Russia) were used
without further purification. Commercial samples
of EtI (99%; Sigma-Aldrich, Germany), BuI (98%;
Fluka), HexBr (pure grade; Reakhim, Russia), and
OctBr (pure grade; Reakhim) were washed with the so-
lutions of Na2S2O3 and NaCl, then dried over P2O5 and
distilled. Cyclopentanone (pure grade; Reakhim) was
dried over K2CO3 and distilled twice. The mixtures
of 1-butyl-3-methylimidazolium halides [C4mim]Hal
with MeIm were obtained by mixing BuHal and the
1.1 to 1.2-fold excess of MeIm and keeping the solu-
tion at T = 338 K for 8 h.
A 4–25 cm3 amount of acetonitrile or cyclopen-
tanone and 0.5–15 cm3 of RHal were mixed in a round-
bottomed flask. The amount of RHal was adjusted in
such a way as to get its initial concentration within
0.3–3.6 mol·dm−3. The flask was thermostated within
0.1 K for 30 min in a liquid thermostat. 0.3–4.0 mL
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

SYNTHESIS OF 1-ALKYL-3-METHYLIMIDAZOLIUM IONIC LIQUIDS
3
Table I Values of Parameters in COSMO-SAC (CA)
of MeIm or MeIm + IL solution in a syringe was ther-
mostated within 2 K in an air thermostat for 30 min.
The amount of MeIm was adjusted to get its initial
concentration in the range 0.3–3.6 mol·dm−3. After
that, MeIm or MeIm + IL solution was introduced
into the flask held in the liquid thermostat. During
the experiment, the reaction mixture was continuously
stirred. Periodically, samples of 0.2–5.0 cm3 volume
were taken and immediately poured into cold water to
stop the reaction. The amount of MeIm in the sam-
ples was determined by titration with a 0.1 mol·dm−3
acid solution. The equivalent point was found potentio-
metrically using a glass electrode. The uncertainty of
the titration was evaluated from the titration of MeIm
aqueous solutions to be 0.3%. All the reported uncer-
tainties correspond to the confidence interval of 95%.
The amounts and concentrations of components in
the solutions were calculated from the mass of the
components determined with the maximum error of
5 × 10−4 g. Based on the experimental data, the
amount of substances at the initial points and at the time
of sampling was calculated. The volume of the so-
lutions was assumed to be equal to the sum of vol-
umes of pure components. In the calculations, the
molar volumes of molecular liquids [14] were used.
The molar volume of 1-ethyl-3-methylimidazolium io-
dide [C2mim]I was found from the linear extrapola-
tion of the molar volumes of [Cnmim]I (n = 4, 6,
8) [15] to n = 2. The molar volumes of 1-alkyl-3-
methylimidazolium bromides [C4mim]Br, [C6mim]Br,
and [C8mim]Br were found from the molar volume of
[C3mim]Br [16] increased by the contribution to the
molar volume per the CH2 group evaluated from the
recommended data for 1-alkyl-3-methylimidazolium
bis(trifluoromethanesulfonyl)imides [Cnmim]NTf2 (n
= 2, 4, 6, 8) [14].
Parameter
Value
2
˚
˚
aeff (A )
7.25
0.804
0.007
66.69
79.53
10
rav (A)
−2
˚
σ0 (e·A
)
3
˚
˚
r (A )
2
q (A )
Z
αꢁ (kJ·mol−1·A ·e
84,282.5
11,702.7
4
−2
)
˚
Chb (kJ·mol−1·A ·e
)
4
−2
˚
˚
1.96 and 2.20 A [21] by 15%. The solvent radius was
˚
set to 1.2 A. The latter value was found to provide good
agreement for the σ profiles obtained with GAMESS
and those obtained with D-Mol3 package [19]. The
most stable TT conformation was considered for BuI
and the GT conformation for BuBr [22]. For HexBr,
calculations for the similar GTTT conformation were
carried out. These conformations were also adopted as
the starting points for the transition state geometry
optimizations. σ profiles for the most stable conform-
ers of the particles and their geometries are presented
in the Supporting Information. COSMO-SAC calcula-
tions for the MeIm + OctBr + acetonitrile systems were
not performed since the number of surface segments in
MeIm···Oct···Br particles exceeded the software limi-
tations.
The σ profiles were generated from the GAMESS
output files using the homemade software based on the
program source codes provided by the Virginia Tech
group [23] and equations from [20]. Each calculated
σ profile was divided into non-hydrogen-bonding and
hydrogen-bonding σ profile. The σhb profile was found
based on the segments that belong to fluorine, oxy-
gen, and nitrogen atoms having a nonbonding electron
pair and hydrogen atoms attached to these atoms. The
In the conductor-like screening model–segment ac-
tivity coefficient (COSMO-SAC) [17], properties of
molecules or ions in solution are found from the re-
sults of quantum mechanical COSMO calculations.
The activity coefficients are determined by molec-
ular surface interactions, which are supposed to be
dominated by local electrostatic interactions. Sur-
face charge distribution in the species is character-
ized by their hydrogen-bonding σhb profiles and non-
hydrogen-bonding σnhb profiles. In the COSMO calcu-
lations, the GAMESS (US) quantum chemistry pack-
age (version 24, March 2007 (R1)) [18] was used. The
source code of this program was modified according
to Wang et al. [19]. The calculations were performed
at the B3LYP/6–311G(d,p) theory level. The atomic
radii [20] were used. The radii for the bromide and
σ
nhb profile was calculated as a difference between the
σ and the σhb profiles. The empirical parameters used
in these calculations (Table I) were obtained from the
COSMO-SAC (CA) version [17,20,24].
The methods for calculation of activity coefficient
used in this work provide the rational activity coeffi-
cients based on the symmetric convention of normal-
ization γ x,sym. The transformation of the activity coef-
ficients to the asymmetric convention was performed
using the equation [25]
γx,sym
γx∞,sym
γx =
(1)
˚
iodide ions were assumed to be 2.25 and 2.53 A, re-
where γx∞,sym is the activity coefficient at infinite di-
lution based on the symmetric convention. γ x were
spectively, which exceed their crystallographic radii of
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

4
FIRAHA AND PAULECHKA
converted into γ c, with the use of the equation
x · γx
γc =
(2)
Vm,sol
C
where C and x are the concentration and the mole
fraction of the solute and Vm,sol is the molar volume
of the solvent.
EXPERIMENTAL
Formal Kinetics. One would expect that the studied
reactions follow the SN2 kinetics, since this mechanism
is typical for similar reactions [10,26]. The differential
kinetic equation for this mechanism is
dn (MeIm)
dt
n (MeIm) .n (RHal)
−
= k
(3)
Figure 1 Typical kinetic curves for the reaction MeIm
+ BuI → [C4mim]I at T = 318.2 K in acetonitrile me-
dia: ◦, C0(MeIm) = 0.605 mol·dm−3, C0(BuI) = 0.626
mol·dm−3; ꢀ, C0(MeIm) = 1.105 mol·dm−3, C0(BuI) =
0.485 mol·dm−3; ꢁ, C0(MeIm) = 0.550 mol·dm−3, C0(BuI)
V
where k is the reaction rate constant, V is the volume
of the reaction mixture, and n(MeIm) and n(RHal) are
the current amount of the reactants. If the volume of
the mixture remains unchanged in the course of the
reaction andtheamount of reagents is not equal, Eq. (3)
corresponds to the integral kinetic equation
= 0.964 mol·dm−3; ꢂ, C0(MeIm) = 3.078 mol·dm−3
,
C0(BuI) = 0.555 mol·dm−3; ♦, C0(MeIm) = 0.575
mol·dm−3, C0(BuI) = 2.951 mol·dm−3; •, C0(Melm) =
0.875 mol·dm−3
,
C0(BuI)
=
1.042 mol·dm−3
, and
C0([C4mim]I) = 1.316 mol·dm−3
.
1
C (MeIm) · C0 (RHal)
θ =
ln
C0 (MeIm) − C0 (RHal) C0 (MeIm) · C (RHal)
= kt (4)
respect to t and combines the results with Eq. (3),
it becomes clear that at a moment of time k(t) =
dθ/dt. To provide further processing of the experimen-
tal data, the experimental θ(t) points for each exper-
iment were smoothed by a second-order polynomial
and the apparent rate constants were calculated for each
point.
It was found that the k(0) values for the same sys-
tem could differ more than twice at different concen-
trations of the participants (Fig. 1 for the MeIm + BuI +
CH3CN system and Figs. S12, S14, S20, S24, and S28
in the Supporting Information). In some experiments,
the apparent rate constants doubled in the course of the
reaction.
Transition State Theory. For the SN2 reaction,
where the reactants are uncharged but the transition
state has built up a charge, the polarity of media has
strong influence on the reaction rate [26]. The strong
dependence k on the composition of the reaction mix-
ture can be quantitatively described by changes in the
activity coefficients for the reactants and the transition
state in the course of the reaction. The following equa-
tion relates the apparent rate constant and the true rate
where C0(MeIm), C0(RHal) and C(MeIm), C(RHal)
are the initial and current concentrations of the reac-
tants.
Taking into account Eq. (4), one would expect that
θ versus t dependence is linear for all concentration
ranges. This behavior was observed at low degrees of
conversion if the concentration of the reactants was
about 0.5 M in all the studied systems (Fig. 1 for the
MeIm + BuI + CH3CN system and Figs. S12, S14,
S20, and S24 in the Supporting Information for other
systems). However, the systematic deviations from the
line occurred at higher concentrations of the reactants,
in the presence of the products in the initial reac-
tion mixture, and at high degrees of conversion. At
a given moment of time, the increase in the RHal
concentration leads to the decrease in the θ values
and the rate of the reactions. The opposite trend was
observed when the concentration of MeIm increased
or the product was introduced to the initial reaction
mixture.
If k varies in the course of the reaction, then θ is
not equal to kt. However, if one differentiates θ with
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

SYNTHESIS OF 1-ALKYL-3-METHYLIMIDAZOLIUM IONIC LIQUIDS
5
SHE. This equation, the basic equation of the theory
of regular solutions [27], has the following form:
⎛
ꢀ
⎞
2
xj Vm,j δj
Vm,i ⎜
j
⎟
⎠
ꢀ
ln γi,x
=
δ −
(6)
⎝
i
RT
xkVm,k
k
where R is the gas constant, Т is the temperature, δi
is the Hildebrand solubility parameter, and xi is the
mole fraction of the ith component. The mole fraction
of the transition state was assumed to be zero. The
δi parameters for the reactants and the solvent were
calculated from the follwing equation:
ꢁ
ꢀvapHmo,i − RT
Vm,i
δi =
(7)
Figure 2 Typical kinetic curves for the reaction MeIm +
BuI → [C4mim]I at T = 318.2 K in acetonitrile media after
COSMO-SAC processing. For symbols, see Fig. 1.
where ꢀvapHm°,i is the standard molar vaporization en-
thalpy of the component. In the calculations, we used
the recommended values of the enthalpies of vaporiza-
tion for molecular compounds [14].
constant k0:
The δi parameters for the product and the transi-
tion state were determined from the nonlinear fit of
the experimental kinetic data. First, the δIL and δTS
values were determined individually for each system.
SHE provides better description of the obtained exper-
imental data than COSMO-SAC (Table II) that can be
explained by the presence of two adjustable parame-
ters for each system in this approach. With individual
parameters for each system, SHE can be used only for
interpolation of the experimental kinetic data for the
studied systems. To improve the predictive ability of
this approach, we assumed that the δIL and δTS param-
eters for different systems are related by the following
equations:
γc (MeIm) · γc (RHal)
k = k0
(5)
γc (MeIm · · · R · · · Hal)
where γ c(MeIm) and γ c(RHal) are the activity coef-
ficients of the reactants and γ c(MeIm···R···Hal) is the
activity coefficient of the transition state.
Different models are used for the prediction of ac-
tivity coefficients in solution. However, most of them
cannot be applied to calculation of activity coeffi-
cients for the transition state because of either un-
developed computational procedures or the absence
of the required empirical parameters. The two meth-
ods used in this work are free from these draw-
backs. The COSMO-SAC model [17] does not use the
system-specific adjustable parameters. The Scatchard–
Hildebrand equation (SHE) [27] has some adjustable
parameters, which, however, can be found from the
obtained experimental data.
δIL = δ[C mim]Hal + n − 1 · δCH
(
)
(8)
1
2
δTS = δMeIm···CH ···Hal + (n − 1) · δCH
(9)
3
2
COSMO-SAC. The processing with COSMO-SAC,
whose typical results are presented in Fig. 2 for the
MeIm + BuI + CH3CN system and Figs. S13, S17,
S21, and S25 in the Supporting Information for the
other systems, improved convergence of the curves,
which are expected to coincide in the ideal case. How-
ever, at high concentrations of the reactants or high
degrees of conversion the rate constants significantly
deviated from the average value. The statistical char-
acteristics of the solutions are reported in Table II. The
results of this processing may be further improved by
reparameterization of COSMO-SAC.
where δ[C1mim]Hal, δMeIm···CH3···Hal, and δCH2 are
the Hildebrand parameters for [C1mim]Hal,
MeIm···CH3···Hal, and CH2 fragments, n is the
number of carbon atoms in RHal. Equations (8) and
(9) allow one to use only three adjustable parameters
for description of the kinetics of all the studied
systems as well as the systems with other bromo- and
iodoalkanes. The following parameters were found
to provide the best description of the experimental
data: δMeIm···CH3···Hal = 24.1 MPa1/2, δ[C1mim]Hal
=
28.4 MPa1/2, and δCH2 = −0.38 MPa1/2
.
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

6
FIRAHA AND PAULECHKA
Table II Results of Experimental Data Processing with COSMO-SAC and SHE
RHal
EtI
BuI
BuI
BuBr
HexBr
OctBr
Solvent
Acetonitrile Acetonitrile Cyclopentanone Acetonitrile Acetonitrile Acetonitrile
T (K)
318.6
318.2
318.6
328.4
328.4
328.2
Experimental data
k (× 105 dm−3·mol·s−1
)
30.7 1.7
6.0
12.0 0.5
2.8
13.1 1.0
3.8
8.9 0.5
2.9
10.1
6.8 0.6
2.1
5.9 0.6
1.9
RMS (× 105 dm−3·mol·s−1
)
)
ME (× 105 dm−3·mol·s−1
)
13.0
7.1
7.9
4.3
3.1
COSMO-SAC
k0 (× 105 dm−3·mol·s−1
)
28.8 1.5
5.3
10.6 0.2
0.9
8.2 0.4
1.3
7.2 0.2
1.5
6.9 0.3
1.1
–
–
–
RMS (× 105 dm−3·mol·s−1
ME (× 105 dm−3·mol·s−1
)
13.0
3.2
2.6
6.8
2.3
SHE
Individual parameters for each system
δIL ( MPa1/2
δTS ( MPa1/2
)
)
31.3
23.6
26.2 0.7
2.5
26.3
22.8
10.0 0.1
0.5
24.4
24.3
10.5 0.2
0.7
29.5
22.4
6.7 0.1
0.6
26.9
22.1
7.0 0.1
0.2
23.9
21.7
6.7 0.1
0.2
k0 (× 105 dm−3·mol·s−1
)
RMS (× 105 dm−3·mol·s−1
)
)
ME (× 105 dm−3·mol·s−1
)
6.1
1.3
1.5
2.5
0.4
0.5
General parameters
k0 (× 105 dm−3·mol·s−1
)
27.3 0.8
2.6
9.8 0.1
0.7
10.8 0.4
1.4
7.3 0.1
0.7
7.2 0.1
0.3
6.4 0.1
0.4
RMS (× 105 dm−3·mol·s−1
ME (× 105 dm−3·mol·s−1
)
4.9
2.2
3.1
2.1
0.6
0.9
The δ values for [Cnmim]Hal ILs determined in
both case and δCH2 value are close to the values for
[Cnmim]NTf2 and [Cnmim]PF6 (n = 2,4,6,8), which
were determined by the intrinsic viscosity method [28].
This fact can be used for estimation of the δ values for
other 1-alkyl-3-methylimidazolium ILs. It should also
be mentioned that the δ values for reagents, transition
state, and products are consistent with overall charac-
teristic of the SN2 reaction with uncharged reactant and
ionic product [26] since the δ values for the transition
state are lower than those for products and higher than
those for reactants.
It is seen from the results presented in Table II
that statistical characteristics of the solution with three
adjustable parameters are similar to those obtained
for individual processing of each system, whereas the
predictive ability of the former is higher. The kinetic
curves after processing with SHE are demonstrated in
Figs. 3 and 4 for the MeIm + BuI + CH3CN system
and in the Supporting Information for other systems.
Temperature Dependence of Rate Constants. A se-
ries of experiments at different temperatures with the
initial reagent concentration of 0.3–0.6 mol·dm−3 was
carried out for each system. The temperature depen-
dence of the rate constant in dilute solution, k was
described by the Arrhenius equation:
Figure 3 Typical kinetic curves for the reaction MeIm +
BuI → [C4mim]I at T = 318.2 K in acetonitrile media after
SHE processing with individual parameters. For symbols,
see Fig. 1.
where А is the preexponential factor and EA is the
energy of activation in the dilute solution. The obtained
EA values (Table III) are in good agreement with the
values obtained for similar systems with the solvent
[10] and without it [3,10].
EA
ln k = −
+ A
(10)
RT
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

SYNTHESIS OF 1-ALKYL-3-METHYLIMIDAZOLIUM IONIC LIQUIDS
7
Table III Activation Energy and Enthalpies of Activation for Different Systems
RHal
Solvent
Temperature Range (K) EA (kJ·mol −1
)
ꢀ‡H°COSMO-SAC (kJ·mol −1
)
ꢀ‡H°SHE (kJ·mol −1
)
EtI
BuI
BuI
BuBr
HexBr
HexBra
OctBr
Acetonitrile
Acetonitrile
Cyclopentanone
Acetonitrile
Acetonitrile
Acetonitrile
Acetonitrile
308–338
298–338
308–338
321–343
321–343
298–333
321–343
76
70
67
72
72
70
70
4
1
3
3
2
3
1
72
67
64
68
69
68
2
1
1
2
2
3
69
67
64
65
66
69
68
1
1
3
1
1
3
1
–
aActivation parameters were calculated using the data from [10].
enthalpy of activation ꢀ‡H° by the equation
ꢂ
ꢃ
ꢂ
ꢃ
kBT
h
ꢀ‡S◦
R
ꢀ‡H◦
RT
k0 = χ
exp
exp −
(11)
where χ is the transmission coefficient, kB is the Boltz-
mann constant, and h is the Planck constant. The en-
thalpy of activation can be found from a slope of a line
obtained from the experimental results in the ln(k0·T−1
)
against T−1 coordinates. The δIL and δTS parameters
were assumed to be independent of temperature. The
values of ꢀ‡H° for the same system found using both
COSMO-SAC and SHE agreed within the uncertain-
ties of their determination (Table III). The enthalpy of
activation obtained for the HexBr + MeIm + acetoni-
trile system is in a good agreement with the previously
reported value [10].
Figure 4 Typical kinetic curves for the reaction MeIm +
BuI → [C4mim]I at T = 318.2 K in acetonitrile media after
SHE processing with general parameters. For symbols, see
Fig. 1.
Rate Constants in Different Solvents. Both
COSMO-SAC and SHE can be used to calculate the
rate constants at different concentrations. However, if
one needs to obtain the rate constants in an arbitrary
solvent, COSMO-SAC should be used. To do this,
only one experiment, preferably in dilute solutions,
is required to evaluate k0, which will then be used to
calculate the apparent rate constants at different con-
centrations:
According to the transition-state theory, the k0 rate
constant for a bimolecular reaction is related to the
standard entropy of activation ꢀ‡S° and the standard
Experimental k
Δ
vapH°, Vm of reagents
QC calculations
σ-profiles
k0(COSMO-SAC)
k0(SHE),δIL, δTS
k at any composition
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

8
FIRAHA AND PAULECHKA
Table IV Rate Constant for Different Systems at T = 328.2 K Obtained with COSMO-SAC
RHal
Solvent
kdilute (×105 dm3·mol·s−1
)
k0(COSMO) (× 105 dm3·mol·s−1
)
EtI
BuI
BuI
Acetonitrile
Acetonitrile
Cyclopentanone
Acetonitrile
Acetonitrile
Acetonitrile
Dimethyl sulfoxide
Cyclopentanone
Acetone
2-Butanone
Ethyl lactate
Methanol
Dichloromethane
Ethyl formate
57.6
23.4
24.0
6.26
7.47
6.79
22.9
5.30
4.34
3.73
1.28
1.05
2.80
3.42
3.0
1.0
1.5
55.2
22.6
19.6
6.01
7.40
6.40
22.6
4.69
4.12
3.40
1.30
1.06
4.03
3.46
2.2
0.4
0.3
BuBr
HexBr
HexBr
HexBr
HexBr
HexBr
HexBr
HexBr
HexBr
HexBr
HexBr
0.19
0.80
0.19
1.7
0.45
0.39
0.54
0.13
0.18
0.21
0.32
0.12
0.79a
0.07
1.7 a
0.40 a
0.37 a
0.49 a
0.13 a
0.18 a
0.31 a
0.32 a
aCalculated using the data from [10].
The values of rate constant in dilute solution (kdilute
)
and k0 obtained for different systems in this work and
those from [10] and adjusted to a common temperature
of 328.2 K are presented in Table IV. The k0 rate
constants for the HexBr + MeIm + acetonitrile system
obtained in this work and in [10] agree very well. A
good agreement between k0 and kdilute is observed for
most systems. However, k0 should be used instead of
of kdilute for theoretical analysis.
As expected, the iodides react more rapidly than
the bromides, because iodide is a better leaving group
than bromide due to its lower basiсity. The increase in
the alkyl chain from EtI to BuI significantly affects the
rate constant, but only minor differences are observed
for the BuBr–HexBr–OctBr series. This fact can be ex-
plained if one considers two circumstances. The alkyl
group is an electron-releasing group (+I effect), which
directly affects reactivity of RHal. The +I effect in-
creases with the size of the alkyl group. At the same
time, the inductive effect rapidly dies out and is signif-
icant only at short distances. As a result, changes in the
inductive effect in the pair Et-Bu are more pronounced
than in the Bu to Oct series.
Figure 5 Correlation of rate constants in dilute solutions
with solvent Hildebrand parameters for the reaction MeIm +
HexBr → [C6mim]Br at T = 328.2 K.
The k0(acetonitrile)/k0(cyclopentanone) quotient is
very close for the systems with BuI and HexBr where
it is available (Table IV). The constancy of these quo-
tients for the reactions with similar transition states
may be useful for the estimation of the rate constants
in various solvents. The data from Table IV, which
contains the information on the reactions with different
RHals in acetonitrile and for the reaction with HexBr
in various solvents, can be used for this purpose.
Stefani [29] demonstrated that the rate constant for
the Menshutkin reaction correlates with the Hildebrand
solubility parameters for the solvent. The linear depen-
dence in the ln k versus δ coordinates was found for
the non-hydrogen-bonding solvents. To check applica-
bility of this correlation to the reactions studied in this
work, we used the kdilute rate constants for the HexBr
+ MeIm system from Table IV. The δ parameters for
the solvents except methanol and ethyl lactate were
calculated from the recommended data [14]. One can
see (Fig. 5) that this correlation works satisfactory for
the studied system, and the dependence is described by
International Journal of Chemical Kinetics DOI 10.1002/kin.20812

SYNTHESIS OF 1-ALKYL-3-METHYLIMIDAZOLIUM IONIC LIQUIDS
9
the equation
8. Renken, A.; Hessel, V.; Lo¨b, P.; Miszczuk, R.; Uerdin-
gen, M.; Kiwi-Minsker, L. Chem Eng Proc 2007, 46,
840–845.
9. Groβe Bo¨wing, A.; Jess, A. Chem Eng Sci 2007, 62,
1760–1769.
ꢄ
ꢅ
ꢆ
ln kdilute · 105 dm3 · mol · s−1
ꢄ ꢅ
ꢆ
= − 2.785 + 0.220 δ MPa1/2
(12)
10. Schleicher, J. C.; Scurto, A. M. Green Chem 2009, 11,
694–703.
11. Groβe Bo¨wing, A.; Jess, A. Green Chem 2005, 7, 230–
235.
CONCLUSIONS
12. Jess, A; Groβe Bo¨wing, A.; Wasserscheid, P. Chem Ing
Tech 2005, 77, 1430–1438.
Experimental investigation of kinetics of quaterniza-
tion of MeIm with different RHals demonstrated that
this reaction follows the expected SN2 kinetic rate law
only in the dilute solutions. Deviations from the sim-
ple dependence are caused by changes in the activity
coefficients of the reactants and the transition state. It
was demonstrated that both the COSMO-SAC model
and SHE can be used for the description of the kinetic
results over the whole studied range of concentrations.
Moreover, these approaches allowed estimating the
rate constants at any concentration of reagents and
products. SHE provides better description of the ex-
perimental data but uses adjustable parameters. The
COSMO-SAC model also performs satisfactorily and
does not need system-specific adjustable parameters
thus demonstrating wider predictive ability. The rate
constants at infinite dilution were obtained for a large
number of haloalkane + 1-methylimidazole + solvent
systems with the use of the COSMO-SAC model.
13. Hu, S.; Wang A.; Lo¨we, H.; Li, X.; Wang, Y.; Li, C.;
Yang, D. Chem Eng J 2010, 162, 350–354.
14. Frenkel, M.; Chirico, R. D.; Diky, V.; Muzny, C. D.;
Lemmon, E. W.; Kazakov, A. NIST ThermoData En-
gine. NIST Standard Reference Database 103b–Pure
compounds, Version 4.0; NIST: Boulder, CO, 2009.
Available at http://www.nist.gov/srd/nist103b.cfm (ac-
cessed July 30, 2013).
15. Ghatee, M. H.; Zare, M.; Moosavi, F.; Zolghadr, A. R.
J Chem Eng Data 2010, 55, 3084–3088.
16. Paulechka, Y. U.; Kabo, G. J.; Blokhin, A. V.; Shaplov,
A. S.; Lozinskata, E. I.; Vygodskii, Ya. S. J Chem Ther-
modyn 2007, 39, 158–166.
17. Lin, S.-T.; Sandler, S. I. Ind Eng Chem Res 2002, 41,
899–913.
18. Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S.
T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga,
N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.;
Montgomery, J. A., Jr. J Comput Chem 1993, 14, 1347–
1363.
19. Wang, S.; Lin, S.-T.; Watanasiri, S.; Chen, C.-C. Fluid
Phase Equil 2009, 276, 37–45.
SUPPORTING INFORMATION
20. Wang, S.; Sandler, S. I.; Chen, C.-C. Ind Eng Chem Res
2007, 46, 7275–7288.
σ
hb and σnhb profiles for the studied species (Figs. S1–
S11), optimized geometries of species for GAMESS/
COSMO calculations, tables of experimental kinetic
data (Tables S1–S6), and typical kinetics curves (Figs.
S12–S30) are available as the Supporting Information.
21. Lide, D. R. ed. CRC Handbook of Chemistry and
Physics, 90th ed. (CD-ROM version); CRC Press/Taylor
and Francis: Boca Raton, FL, 2010.
22. Ogawa, Y.; Imazeki, S.; Yamaguchi, H.; Matsuura, H.;
Harada, I.; Shimanouchi, T. Bull Chem Soc Jpn 1978,
51, 748–767.
BIBLIOGRAPHY
23. Mullins, E.; Oldland, R.; Liu, Y. A.; Wang, S.; Sandler,
S. I.; Chen, C.-C.; Zwolak, M.; Seavey, K. Ind Eng Chem
Res 2006, 45, 4389–4415.
24. Yang, L.; Sandler, S. I.; Peng, C.; Liu, H.; Hu, Y. Ind
Eng Chem Res 2010, 49, 12596–12604.
25. Prausnitz, J. M.; Liechtenthaler R. N.; Gomes de
Azevedo, E. Molecular Thermodynamics of Fluid-Phase
Equilibria, 3rd ed.; Prentice Hall PTR: Upper Saddle
River, NJ, 1999.
26. Smith, M. B.; March, J. March’s Advanced Organic
Chemistry: Reactions, Mechanisms, and Structure, 6th
ed.; Wiley: Hoboken, NJ, 2007.
27. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular
and Related Solutions; Van Nostrand–Reinhold: New
York, 1970.
28. Sang, H. L.; Sun B. L. Chem Commun 2005, 27, 3469–
3471.
1. Welton, T. Chem Rev 1999, 99, 2071–2083.
2. Wasserscheid, P. In Ionic Liquids in Synthesis, 2nd
ed.; Welton, T. Eds.; Wiley VCH: Weinheim, Germany,
2008.
3. Paulechka, Y. U.; Kabo, A. G.; Blokhin, A. V. J Phys
Chem B 2009, 113, 14742–14746.
4. Kabo, G. J.; Paulechka, Y. U.; Kabo, A. G.; Blokhin,
A. V. J Chem Thermodyn 2010, 42, 1292–1297.
5. Lo¨we, H.; Axinte, R. D.; Breuch, D.; Hofmann, C.; Pe-
tersen, J. H.; Pommersheim, R.; Wang, A. Chem Eng J
2010, 163, 429–437.
6. Waterkamp, D. A.; Heiland, M.; Schlu¨ter, M.;
Sauvageau, J. C.; Beyersdorff, T.; Tho¨ming, J. Green
Chem 2007, 9, 1084–1090.
7. Minnich, C. B.; Ku¨pper, L.; Liauw, M. A.; Greiner, L.
Catal Today 2007, 126, 191–195.
29. Stefani, A. P. J Am Chem Soc 1968, 90, 1694–1700.
International Journal of Chemical Kinetics DOI 10.1002/kin.20812