Predicting the Solvent Effect on Esterification Kinetics

Article abstract of DOI:10.1002/cphc.201700507

It is well known that solvents influence reaction kinetics. The classical concentration-based kinetic modeling is unable to describe these effects. In this work, the reaction kinetics was studied for the esterifications of acetic acid and propionic acid with ethanol at 303.15 K. It was found that the reactant ratio as well as the applied solvents (acetonitrile, tetrahydrofurane, dimethylformamide) significantly affect the reaction rate. The thermodynamic model PC-SAFT was applied to account for the interactions between the reacting species and the solvents via activity coefficients. This allowed the identification of solvent-independent kinetic constants and the prediction of the solvent effect on reaction kinetics in almost quantitative agreement with experimental data. The presented approach shows the importance of taking into account thermodynamic non-idealities and significantly reduces experimental effort for finding the best solvent candidate for a given target reaction.

Full text of DOI:10.1002/cphc.201700507

Accepted Article
Title: Predicting the solvent effect on esterification kinetics
Authors: Max Lemberg and Gabriele Sadowski
This manuscript has been accepted after peer review and appears as an
Accepted Article online prior to editing, proofing, and formal publication
of the final Version of Record (VoR). This work is currently citable by
using the Digital Object Identifier (DOI) given below. The VoR will be
published online in Early View as soon as possible and may be different
to this Accepted Article as a result of editing. Readers should obtain
the VoR from the journal website shown below when it is published
to ensure accuracy of information. The authors are responsible for the
content of this Accepted Article.
To be cited as: ChemPhysChem 10.1002/cphc.201700507
Link to VoR: http://dx.doi.org/10.1002/cphc.201700507
A Journal of
www.chemphyschem.org

10.1002/cphc.201700507
ChemPhysChem
COMMUNICATION
Predicting the solvent effect on esterification kinetics
Max Lemberg and Gabriele Sadowski*
Abstract: It is well-known that solvents influence reaction kinetics.
The classical concentration-based kinetic modeling is unable to
describe these effects. In this work, the reaction kinetics was studied
for the esterifications of acetic acid and of propionic acid with ethanol
at 303.15 K. It was found that the reactant ratio as well as the
applied solvents (acetonitrile, tetrahydrofurane, dimethylformamide)
significantly affect the reaction rate. The thermodynamic model PC-
SAFT was applied to account for the interactions between the
reacting species and the solvents via activity coefficients. This
allowed the identification of solvent-independent kinetic constants
and the prediction of the solvent effect on reaction kinetics in almost
quantitative agreement with the experimental data. The presented
approach shows the importance of taking into account
thermodynamic non-idealities and significantly reduces experimental
any solvents effects.
Jannsen et al.[6] investigated an enzyme-catalyzed esterification
reaction in different solvents and modeled the experimental data
comparing the performance of two different kinetic models.
Thereby one of the models accounted for the activity coefficients
of reactants/products and the other did not. As they observed a
significant solvent effect, they fitted a completely new set of
kinetic parameters for every solvent. They found that the model
parameters obtained when accounting for the activity
coefficients were less solvent-dependent than the ones obtained
when not accounting for the activity coefficients. This shows that
the solvent effect on the kinetics of enzyme reactions can at
least partly be explained by the solvent-influenced activity
coefficients of the reactants/products. For those reactions, the
effort for finding the best solvent candidate for a given target reaction. solvent effect is usually also partly attributed to solvent-enzyme
interactions which cannot be accounted for by the activity
coefficients for the reactants/products.
Solvents are known to have a significant influence on both,
Kiviranta-Pääkkönen et al.[7] investigated the kinetics of the
reaction equilibria and reaction kinetics.
A comprehensive
tertiary amyl methyl ether (TAME) synthesis and also applied
two models for the correlation of the experimental data. They
found that the model which accounted for the activity coefficients
was able to describe the experimental data over a wider range
of conditions than the other model which did not.
overview of related studies was given by Reichardt and Welton[1].
Besides experimental results, they presented a theoretical
framework based on the Gibbs energy of solvation that allowed
for correlating experimentally-obtained apparent equilibrium
constants and rate constants with the solvent polarity scale
ET(30). However, as these correlations are empirical and
specific for a given reaction, they cannot be used to predict
solvent effects on other reactions than the ones used for
obtaining the correlations.
In this work we investigated the reaction kinetics of the
esterification of HAc with EtOH (R1) and of HProp with EtOH
(R2) at 303.15 K using Raman spectroscopy. The reactions
were performed in solvent-free reaction mixtures at different
initial mole ratios ꢀꢁ0ꢂꢃꢄ: ꢀꢅ0ꢆꢇꢈ (1:1, 3:1, 1:3) on the one hand and
in the solvents acetonitrile (ACN), tetrahydrofurane (THF) and
N,N-dimethylformamide (DMF) at an initial reactant
concentration of ꢉꢁ0ꢂꢃꢄ =ꢉꢅ0ꢆꢇꢈ =3.5188 mol/L on the other hand.
Fuming hydrochloric acid (HCl) was used as catalyst at constant
concentration of ꢉꢈꢊꢋ =0.1506 mol/L in all reaction mixtures.
Further details for the reaction-kinetics measurements are
presented in the supporting information S4.
A predictive approach for describing solvent effects on reaction
equilibria was presented in a previous work of our group by
Riechert et al.[2] who investigated the esterification equilibrium of
acetic acid (HAc) and of propionic acid (HProp) with ethanol
(EtOH) at different reactant ratios and in different solvents. The
proposed thermodynamic approach considers the interactions
between the reacting species and the different solvents via
activity coefficients predicted using the Perturbed-Chain
Statistical Associating Fluid Theory (PC-SAFT). This allowed
predicting the solvent effects once the thermodynamic
equilibrium constants were determined from experimental data
for the solvent-free reaction equilibrium.
Works that account for activity coefficients of reactants/products
when modeling the kinetics of liquid-phase reactions were
published by several groups applying gE-models like UNIFAC[3],
UNIQUAC[4] and NRTL[5]. These works mostly investigated the
effects of temperature, catalyst concentration and reactant ratio
on the reaction kinetics whereas the effect of solvents on the
reaction kinetics has not been examined. The parameters of the
kinetic models were fitted to the entire experimental data
obtained in these works and there was no focus on predicting
The experimental data of the solvent-free systems with
equimolar reactant ratio was modeled by fitting the intrinsic rate
constants while accounting for the activity coefficients of the
reactants/products using PC-SAFT. Based on this, the
esterification kinetics at the other reactant ratios and in the
different solvents were purely predicted via PC-SAFT using the
solvent–dependent activity coefficients of the reactants/products
and compared with the experimental data. Details concerning
the PC-SAFT model and the used model parameters are
presented in the supporting information S1.
For an equilibrium reaction of the type ꢌ + ꢍ ⇌ ꢎ + ꢏ , the
reaction rate ꢐ can be expressed as
ꢄꢂ
ꢑ
ꢐ =
= ꢒ1 ∙ ꢉꢓꢔꢓ ∙ ꢉꢕꢔꢕ − ꢒ−1 ∙ ꢉꢊꢔꢊ ∙ ꢉꢖꢔꢖ (1)
M. Lemberg, Prof. Dr. Gabriele Sadowski
Laboratory for Thermodynamics
ꢄꢆ
whereby ꢉꢃ denotes the concentration of component ꢗ in mol/L
and ꢔꢃ is the activity coefficient of component ꢗ. ꢒ1 and ꢒ−1 are
the intrinsic rate constants of the forward and backward reaction,
respectively. The activity coefficients ꢔꢃ account for the
interactions of the reacting agents among themselves and with
other components present in the reaction mixture (e.g. solvents).
Department Biochemical & Chemical Engineering
TU Dortmund University
Emil-Figge-Str. 70, D-44227 Dortmund
E-mail: gabriele.sadowski@bci.tu-dortmund.de
Supporting information for this article is given via a link at the end of
the document.
This article is protected by copyright. All rights reserved.

10.1002/cphc.201700507
ChemPhysChem
COMMUNICATION
In contrast to the intrinsic rate constants ꢒ1 and ꢒ−1 which
depend on temperature only, the activity coefficients ꢔꢃ depend
on reactant concentrations as well as on the solvent. Using them
in Eq.(1) thus allows for predicting the effects of reactant ratio
and solvents on the reaction kinetics.
Comparing the experimental results for R1 and R2, it can be
seen that R1 is approximately twice as fast as R2. For both, R1
and R2, the reaction with an initial reactant-ratio 1:1 and the
highest initial reactant concentrations was the fastest one. This
was expected according to Eq. 1 even when neglecting the
activity coefficients ꢔꢃ. What was unexpected is the difference in
the reaction rates of the 1:3 and the 3:1 reactions as the rate law
(Eq. 1) is symmetric with respect to the concentrations of the two
reactants when not accounting for their activity coefficients. This
discrepancy is obviously caused by the (concentration
dependent) activity coefficients of the reactants/products and
could never be accounted for when they were neglected.
As the reaction kinetics leads to the reaction equilibrium (eq) at
infinite time (where ꢐ = 0), ꢒ1 and ꢒ−1 are connected via the
thermodynamic equilibrium constant ꢘꢁ according to:
ꢂ
ꢜ
∙ꢂ
ꢜ
ꢙ
ꢑ,ꢚꢛ ꢑ,ꢚꢛ ꢝ,ꢚꢛ ꢝ,ꢚꢛ
1
= ꢘꢁ =
(2)
ꢙ
ꢂ
ꢜ ∙ꢂ ꢜ
−1
ꢞ,ꢚꢛ ꢞ,ꢚꢛ ꢟ,ꢚꢛ ꢟ,ꢚꢛ
This means, that once the thermodynamic equilibrium constant
ꢘꢁ is known, only one kinetic parameter ꢒ1- or ꢒ−1 - needs to be
adjusted for modeling the reaction kinetics.
Thus, using the activity coefficients of the reactants/products in
Eq. 1 obtained from the thermodynamic model PC-SAFT and
the intrinsic rate constants ꢒ1, fitted to the reaction kinetics of the
solvent-free 1:1 systems, the reaction kinetics of the 1:3 and 3:1
systems were purely predicted as shown in Fig. 1. In case of R1
(Fig. 1 left) it can be seen that the reaction kinetics for the 3:1
system was predicted to be much faster than the one for the 1:3
system which is in very good agreement with the experimental
findings. Only for longer times, the prediction slightly
overestimates the concentration of ethyl acetate (EtAc) for the
1:3 system. For R2, the effect of the reactant ratio on the
reaction rate is predicted to be opposite to the one of R1 as the
1:3 system reacts faster than the 3:1 system, which is again in
very good agreement with the experimental data (Fig.1 right).
The concentration of ethyl propionate (EtProp) is slightly
underestimated for the 3:1 system at the beginning of the
reaction but again in very good agreement with the experiment
at longer times.
The ꢘꢁ-values for the reactions R1 and R2 at 303.15 K were
determined from literature data to 20.4 and 10.0, respectively.
Details can be found in the supporting information S5. The rate
constants ꢒ1,ꢠ1 and ꢒ1,ꢠ2 were fitted to the reaction kinetics of the
solvent-free system with equimolar reactants (1:1 system) of the
respective reaction. The resulting values are ꢒ1,ꢠ1 =2.45⋅10-5
L/(mol⋅s) and ꢒ1,ꢠ2=1.45⋅10-5 L/(mol⋅s). Using ꢘꢁ and ꢒ1 for both
reactions, the reaction kinetics of the remaining solvent-free
systems (1:3, 3:1) and for the reactions in different solvents
were predicted via Eqs. 1 and 2. The activity coefficients ꢔꢃ were
predicted using PC-SAFT without fitting any model parameters
to reaction data.
The experimental and modeling/prediction results for the
reaction kinetics of the solvent-free reactions R1 and R2 are
presented in Figure 1.
For a qualitative prediction
of the solvents effect on the
reaction kinetics, binary
vapor-liquid
(VLE)
equilibrium
from
data
reactant/solvent
systems
was used. This VLE data
allows to identify and to
evaluate the interactions
between a reactant and a
solvent and therewith to
determine
coefficients ꢔꢃ of
reactants in
the
activity
the
different
solvents. These activity coefficients are of particular interest for
a qualitative prediction of the solvent effect on the initial part of
the reaction kinetics as at this point the concentration of the
products is still small (Eq. 1).
The equilibrium pressure ꢡ of a binary mixture is related to the
activity coefficients ꢔꢃ of the components in the mixture as
described in Eq. 3:
Figure 1. Concentration of EtAc (left) and EtProp (right) for R1 (left) and R2
(right) at 303.15 K over time. The symbols are experimental data for the
solvent-free systems with initial reactant ratios ꢀꢁ0ꢂꢃꢄ: ꢀꢅ0ꢆꢇꢈ 1:1 (circles), 3:1
(triangles) and 1:3 (squares). The error bars for the experimental data lie
within the symbols and are therefore not shown. The solid lines for the
reactant-ratio 1:1 were modeled with PC-SAFT by fitting the rate constants
ꢒ1,ꢠ1 (left) and ꢒ1,ꢠ2 (right). The other lines were purely predicted for the
reactant ratios 3:1 (dashed) and 1:3 (dotted).
ꢣꢤ
ꢣꢤ
02
ꢡ = ꢢ1ꢔ1ꢡ + ꢢ2ꢔ2ꢡ
(3)
01
This article is protected by copyright. All rights reserved.

10.1002/cphc.201700507
ChemPhysChem
COMMUNICATION
Thereby ꢢꢃ denotes the
ꢣꢤ
mole fraction and ꢡ
0ꢃ
the vapor pressure of
component
Neglecting the activity
coefficients ꢔꢃ , Eq.
ꢗ
.
3
becomes the Raoult’s
law. If the activity
coefficients are not unity,
a system has either a
positive deviation (ꢔꢃ>1)
or a negative deviation
(ꢔꢃ<1) from Raoult’s law.
This
deviation
is
associated
with
repulsive and attractive interactions between the components.
Deviations from the Raoult’s law may also lead to the formation
of azeotropes with a pressure maximum (ꢡꢥꢁꢦ ) or pressure
minimum (ꢡꢥꢃꢧ ), corresponding to activity coefficients greater
than one (repulsion) or smaller than one (attraction), respectively.
Table 1 gives an overview of binary azeotropes of the reactants
and solvents of the two reactions considered in this work. This
already allows to qualitatively estimate the solvent effect on the
esterification kinetics.
Figure 2. Concentration of EtAc (left) and EtProp (right) for R1 (left) and R2
(right) at 303.15 K over time. The symbols are experimental data for systems
with an initial reactant concentration of ꢉꢁ0ꢂꢃꢄ = ꢉꢅ0ꢆꢇꢈ =3.5188 mol/L in the
solvents ACN (circles), THF (triangles) and DMF (squares). The error bars lie
within the symbols and are therefore not shown. The lines are purely predicted
with PC-SAFT for the solvents ACN (drawn through), THF (dashed) and DMF
(dotted).
It can be seen that the reaction rate strongly depends on the
solvent, whereby the effects of the solvents on R1 and R2 are
comparable. Both reactions are fast in ACN and slow in DMF.
This is in agreement with the qualitative discussion above
without using any calculation based on VLE data only.
Table 1. Binary ꢡꢥꢃꢧ/ꢡꢥꢁꢦ azeotropes of HAc, HProp, EtOH with the solvents
used in this work
azeotrope
HAc
ACN
no[8]
no[8]
ꢡꢥꢁꢦ
THF
no[9]
no[a]
no[12]
DMF
Concerning the quantitative prediction, it has to be mentioned
that the solvent effect in principle cannot be predicted using
concentration-based kinetic model as the initial reactant
concentration did not change. Thus, using the same rate
constants would lead to exactly the same reaction rates for
every solvent. However, by accounting for the activity
coefficients for the reactants/products which strongly depend on
the solvent, the solvent effect on the reaction rate of R1 could be
predicted using the above-determined intrinsic rate constant in
very good agreement with the experimental data (Fig. 2 left). For
R2, the prediction is also in good agreement with the
experimental data for the solvents ACN and DMF, whereby the
concentration of the ester is slightly underestimated in both
cases (Fig. 2 right). The prediction for R2 in THF is still
qualitatively correct as it lies between the predictions for R2 in
DMF and in ACN.
[10]
ꢡꢥꢃꢧ
[a]
HProp
EtOH
ꢡꢥꢃꢧ
no[13]
[11]
[a] VLE data measured within this work. Details are provided in the supporting
information S3
As it can be seen from Table 1, the carboxylic acids HAc and
HProp behave similarly as they both only show a pressure-
minimum azeotrope with the solvent DMF. This corresponds to
attractive interactions and acid activity coefficients in DMF
smaller than one. EtOH on the other hand shows a pressure-
maximum azeotrope with the solvent ACN, which corresponds to
repulsive interactions and EtOH activity coefficients greater than
one. As can be seen in Eq. 1, the product ꢔꢁꢂꢃꢄꢔꢅꢆꢇꢈ determines
the solvent effect on the reaction rate. It can therefore be
qualitatively concluded from Table 1 that the reaction rates
Concluding, it was shown that the reactant concentration/ratio
and solvents can affect the rate of reactions significantly due to
interactions of the reactants/products among themselves as well
as with the solvent(s). For a quick assessment of different
solvents, a strategy was presented solely based on binary
reactant/solvent VLE data. Using a kinetic model accounting for
the interactions between reactants/products and the presence of
solvents via activity coefficients even allowed for quantitatively
predicting the influence of solvents and reactant concentrations
on the reaction kinetics in very good agreement with the
ꢐ
in a solvent are expected in the order ꢐꢓꢊꢬ>ꢐꢭꢈꢮ>ꢐꢖꢯꢮ for
ꢨꢩꢋꢪꢫꢧꢆ
both, R1 and R2.
Quantitative predictions of the reaction kinetics of the systems
with equimolar reactants in ACN, THF and DMF were performed
in the same way as for the solvent-free 1:3 and 3:1 systems
using Eq. 1 and the same intrinsic rate constants as before while
accounting for the reactant/product activity coefficients in the
reaction mixtures obtained from PC-SAFT. The predicted results
compare with experimental data as shown in Figure 2.
This article is protected by copyright. All rights reserved.

10.1002/cphc.201700507
ChemPhysChem
COMMUNICATION
J. Wang, Chin. J. Chem. Eng. 2009, 17, 773-780; e) M. T. Sanz, R.
Murga, S. Beltrán, J. L. Cabezas, J. Coca, Ind. Eng. Chem. Res. 2002,
41, 512-517.
experimental data. This significantly reduces the experimental
effort for finding the best solvent candidate for a given reaction.
[4]
[5]
a) P. Delgado, M. T. Sanz, S. Beltrán, Chem. Eng. J. 2007, 126, 111-
118; b) P. Patidar, S. M. Mahajani, Chem. Eng. J. 2012, 207–208, 377-
387; c) A. K. Kolah, N. S. Asthana, D. T. Vu, C. T. Lira, D. J. Miller, Ind.
Eng. Chem. Res. 2007, 46, 3180-3187; d) J. Gangadwala, S. Mankar,
S. Mahajani, A. Kienle, E. Stein, Ind. Eng. Chem. Res. 2003, 42, 2146-
2155; e) L. K. Rihko, P. K. Kiviranta-Pääkkönen, A. O. I. Krause, Ind.
Eng. Chem. Res. 1997, 36, 614-621.
Acknowledgements
This work is part of the Collaborative Research Center/
Transregio 63 “Integrated Chemical Processes in Liquid
Multiphase Systems” (subproject A4). Financial support by the
Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) is gratefully acknowledged (TRR 63). The authors
thank Dr. Ole Riechert for valuable discussions on this subject.
a) A. Orjuela, A. J. Yanez, A. Santhanakrishnan, C. T. Lira, D. J. Miller,
Chem. Eng. J. 2012, 188, 98-107; b) W.-T. Liu, C.-S. Tan, Ind. Eng.
Chem. Res. 2001, 40, 3281-3286.
[6]
[7]
A. E. M. Janssen, B. J. Sjursnes, A. V. Vakurov, P. J. Halling, Enzyme
Microb. Technol. 1999, 24, 463-470.
P. Kiviranta-Pääkkönen, L. Struckmann, A. O. I. Krause, Chem. Eng.
Technol. 1998, 21, 321-326.
Keywords: Esterification • Reaction kinetics • Solvent effects •
PC-SAFT • Activity coefficients
[8]
[9]
T. S. Banipal, B. S. Lark, S. Singh, Can. J. Chem. 1991, 69, 2117-2121.
H. E. Kalali, A. M. Demiriz, J. Budde, F. Kohler, A. Dallos, F. Ratkovics,
Fluid Phase Equilib. 1990, 54, 111-120.
[1]
[2]
[3]
C. Reichardt, T. Welton, Solvents and Solvent Effects in Organic
Chemistry, VCH, Weinheim, 2010.
[10] G. S. Shealy, S. I. Sandler, J. Chem. Eng. Data 1985, 30, 455-459.
[11] V. N. Davydova, V. V. Beregovykh, S. V. L'vov, Pharm. Chem. J. 1982,
16, 699-703.
O. Riechert, M. Husham, G. Sadowski, T. Zeiner, AIChE J. 2015, 61,
3000-3011.
a) R. Rönnback, T. Salmi, A. Vuori, H. Haario, J. Lehtonen, A.
Sundqvist, E. Tirronen, Chem. Eng. Sci. 1997, 52, 3369-3381; b) H. T.
R. Teo, B. Saha, J. Catal. 2004, 228, 174-182; c) V. K. S. Pappu, A. J.
Yanez, L. Peereboom, E. Muller, C. T. Lira, D. J. Miller, Bioresour.
Technol. 2011, 102, 4270-4272; d) Y. Qu, S. Peng, S. Wang, Z. Zhang,
[12] L. Bernshtein, T. Generalova, Y. Zelvenskii, V. Shalygin, Russ. J. Appl.
Chem. 1980, 53, 1577-1579.
[13] V. A. Shalygin, Y. G. Zelinskii, G. E. Smirnova, Pharm. Chem. J. 1987,
570-575.
This article is protected by copyright. All rights reserved.

10.1002/cphc.201700507
ChemPhysChem
COMMUNICATION
COMMUNICATION
Max Lemberg and Gabriele Sadowski*
Page No. 1– Page No. 4
Predict the best reaction solvent.
For the esterifications of acetic acid and of propionic acid with ethanol in different solvents, a thermodynamic model was applied to
account for solvent/reactant interactions. Using only one intrinsic kinetic constant for all solvent systems, the proposed new activity-
based kinetic modeling approach allowed for predicting the solvent effects on reaction kinetics in very good agreement with the
experimental data.
This article is protected by copyright. All rights reserved.