Online reaction monitoring and evaluation of kinetic parameters for dilute reactions using refractive index measurements

Article abstract of DOI:10.1021/op9001388

This work demonstrates the utility of an online refractometer technique as a simple and accurate tool for monitoring the progress of a reaction and determining its end-point. It is also shown that, for a dilute reaction, the change of refractive index due to reaction is proportional to the extent of reaction. The corresponding kinetic rate coefficient can also be evaluated, provided the kinetic model is known. This proposed methodology was subsequently applied to monitor and study the kinetics of two different model reactions, namely alkaline hydrolysis of methyl paraben and hydrolysis of acetic anhydride. Both reactions were performed in dilute solution and under pseudo-first-order reaction conditions. The rate coefficients determined from the present refractive index measurements were in agreement with those independently determined using calorimetric and spectroscopic methods. Replicate kinetic experiments were also performed in order to confirm the reliability of the present refractive index measurements. For known simple reactions which are repetitively performed, or for continuous online process monitoring of simple reactions, the present approach provides a convenient alternative to spectroscopic and/or calorimetric monitoring.

Full text of DOI:10.1021/op9001388

Organic Process Research & Development 2009, 13, 1209–1213
Technology Reports
Online Reaction Monitoring and Evaluation of Kinetic Parameters for Dilute
Reactions Using Refractive Index Measurements
Martin Tjahjono,* Effendi Widjaja, and Marc Garland
Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research (ASTAR), 1 Pesek Road, Jurong
Island, Singapore 627833, Singapore
volume, surface tension,4,5 conductivity, viscosity, heat-
flow,
3
,4
3
6
Abstract:
7
-11
etc. can also be used to monitor a reaction. The
This work demonstrates the utility of an online refractometer
technique as a simple and accurate tool for monitoring the progress
of a reaction and determining its end-point. It is also shown that,
for a dilute reaction, the change of refractive index due to reaction
is proportional to the extent of reaction. The corresponding kinetic
rate coefficient can also be evaluated, provided the kinetic model
is known. This proposed methodology was subsequently applied
to monitor and study the kinetics of two different model reactions,
namely alkaline hydrolysis of methyl paraben and hydrolysis of
acetic anhydride. Both reactions were performed in dilute solution
and under pseudo-first-order reaction conditions. The rate coef-
ficients determined from the present refractive index measure-
ments were in agreement with those independently determined
using calorimetric and spectroscopic methods. Replicate kinetic
experiments were also performed in order to confirm the reliability
of the present refractive index measurements. For known simple
reactions which are repetitively performed, or for continuous
online process monitoring of simple reactions, the present ap-
proach provides a convenient alternative to spectroscopic and/or
calorimetric monitoring.
changes in the bulk physico-chemical properties of solution
mixtures at fixed temperature and pressure are directly correlated
to the reaction progress. Compared to spectroscopic techniques,
the measurement and subsequent numerical evaluation of these
bulk physico-chemical property measurements are rather simple
and quite straightforward, at least for simple reactions.
In the current study, the use of a bulk physico-chemical
measurement, namely refractive index, to monitor reaction
progress is investigated. This technique certainly deserves more
attention since it has several practical features, i.e., ease of use,
sensitivity to composition changes, nondestructiveness, rapid
data acquisition times, applicability to online measurements,
etc. In this regard, an online refractometer is employed in the
present study to provide continuous refractive index measure-
ments during reactions. In addition, this study also proposes a
novel and rather simple methodology to derive kinetic param-
eters from the refractive index measurements for dilute reaction
systems. The relationship between the changes of refractive
index monitored during reaction to the corresponding extent
of reaction is provided. Accordingly, given a kinetic reaction
model, the kinetic rate coefficient can be directly evaluated from
the online refractive index measurements.
Introduction
In order to demonstrate the present methodology, two
different reactions with considerably different reaction times,
namely alkaline hydrolysis of methyl paraben and hydrolysis
of acetic anhydride, were studied with an online refractometer.
These were selected as model reactions since they could be
conveniently performed in dilute solution under typically
Online process analytical tools have been increasingly
utilized to monitor chemical reactions. In comparison to off-
line analytical tools, online measurements are generally able to
collect much more information on the reaction progress, and
as such, they can greatly improve the efficiency as well as the
accuracy of the process reaction monitoring. Simple, fast, and
nondestructive techniques are certainly some of the preferred
criteria to monitor most reactions. On the basis of this
consideration, many spectroscopic tools, such as IR (near-IR,
mid-IR, and far-IR), UV/vis, and Raman have been developed
and are widely utilized as online process analytical techniques.
In addition to spectroscopic measurements, several physico-
(3) Cristallini, C.; Villani, A.; Lazzeri, L.; Ciardelli, G.; Rubino, A. S.
Polym. Int. 1999, 48, 63–68.
(
(
4) Schork, F. J.; Ray, W. H. J. Appl. Polym. Sci. 1983, 28, 407–430.
5) Tauer, K.; Dessy, C.; Corkery, S.; Bures, K.-D. Colloid Polym. Sci.
1999, 277, 805–811.
(
(
6) Vega, M. P.; Lima, E. L.; Pinto, J. C. Polymer 2001, 42, 3909–3914.
7) Andr e´ , R.; Bou-Diab, L.; Lerena, P.; Stoessel, F.; Giordano, M.;
Mathonat, C. Org. Process Res. DeV. 2002, 6, 915–921.
1,2
(8) Tjahjono, M.; Widjaja, E.; Garland, M. ChemPhysChem 2009, 10,
chemical property measurements such as refractive index,
1
274–1283.
(
9) Ferretti, A. C.; Mathew, J. S.; Blackmond, D. G. Ind. Eng. Chem.
Res. 2007, 46, 8584–8589.
*
Corresponding author. Telephone: (65) 6796-3960. Fax: (65) 6316-6185.
E-mail: martin_tjahjono@ices.a-star.edu.sg.
(10) O’Neill, M. A. A.; Beezer, A. E.; Labetoulle, C.; Nicolaides, L.;
Mitchell, J. C.; Orchard, J. A.; Connor, J. A.; Kemp, R. B.; Olomolaiye,
D. Thermochim. Acta 2003, 399, 63–71.
(
(
1) Zald ´ı var, C.; Iglesias, G.; del Sol, O.; Pinto, J. C. Polymer 1997, 39,
47–251.
2) Weng, L.; Zhou, X.; Zhang, X.; Xu, J.; Zhang, L. Polymer 2002, 43,
761–6765.
2
(11) De Domenico, G.; Lister, D. G.; Maschio, G.; Stassi, A. J. Therm.
Anal. Calorim. 2001, 66, 815–826.
6
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0.1021/op9001388 CCC: $40.75  2009 American Chemical Society
Vol. 13, No. 6, 2009 / Organic Process Research & Development
•
1209
Published on Web 09/08/2009

pseudo-first-order reaction conditions. The kinetic rate constants
determined using the present technique were found to be in
good agreement with those determined using other more
established techniques, namely spectroscopy and calorimetry.
Consequently, the present study indicates that for known simple
reactions which are repetitively performed, or for continuous
online process monitoring of simple reactions, the present
approach provides a potential alternative to spectroscopic and/
or calorimetric monitoring.
b
a
t
0
A
0
B
n ) n + R (y - ꢀ) + R y - ꢀ +
S
(
A
B
(
)
0
C
c
a
0
D
d
a
0
R y + ꢀ + R y + ꢀ /y
(5)
C
(
)
D
(
)) total
Equation 5 can be factored. The simplified expression is
0
shown in eq 6. In this equation, n is the refractive index of the
solution at t ) 0, and ꢁ is the lumped-parameter which takes
into account the stoichiometric reaction coefficients, the coef-
i
ficients R and the initial total moles of reaction mixture. It can
be noted that the lumped parameter ꢁ may not be exactly
constant due to the mass balance approximation used as well
as possible small changes in the individual refractive indices
during reaction.
Methodology
The numerical procedure for obtaining the kinetic rate
coefficient from the refractive index measurement of a single
reaction performed in a dilute range of concentration is outlined
below.
t
0
n ) n + ꢁꢀ
(6)
In dilute solution, the refractive index n of a solution can be
0
0
A A
0
B B
0
C C
0
0
total
n ) n + (R y + R y + R y + R y )/y
related to the refractive index of the solvent n
fraction of the individual solutes x
is the corresponding coefficient for each individual solute.
s
and the mole
S
D D
(7)
(8)
i
, as shown in eq 1, where R
i
c
a
d
a
b
a
0
total
ꢁ
)
R + R - R - R /y
(
C
D
A
B
)
n ) n +
R x
i i
(1)
s
∑
solute-i
The evaluation of the parameters in eq 6 from experimental
data requires a few steps. First, the initial refractive index of
A rather general stoichiometric reaction with stoichiometric
coefficients a, b, c, and d can be written as shown in eq 2.
Accordingly, the bulk refractive index of the solution at any
reaction time t can be related to the mole fractions of the
individual reactive substances as shown in eq 3. In this equation,
mole fractions are expressed in terms of y
to the initial moles of substance-i, the total moles of the reaction
solution at reaction time t, and the extent of reaction, respec-
tively. The total mole of the reaction solution ytotal is given in
eq 4 as a summation of the total initial moles ytotal (i.e., from
all the reactive substances y
change of moles due to reaction.
0
t
the solution n is most easily obtained by extrapolation of n to
the initial reaction time (i.e., ꢀ f 0). Second, the lumped
parameter ꢁ can only be evaluated after the reaction model and
the extent of reaction as a function of time is defined.
In the case of a first-order reaction or a pseudo-first-order
0
t
i
, ytotal, ꢀ which refer
reaction, the fractional conversion X
time as given in eq 9. Furthermore, the fractional conversion
can be related to the extent of reaction ꢀ and the change of
A
is related to the reaction
X
A
t
refractive index ∆n as provided in eq 10. Finally, substitution
of these two expressions provides the direct relationship between
the change of refractive index and the reaction time eq 11.
0
0
0
i
as well as the solvent y
S
) and the
-
ln(1 - X ) ) kt
(9)
A
aA + bB f cC + dD
(2)
t
0
ꢀ
(n - n )
∆n
XA )
)
)
(10)
0
0
0
t
0
A
0
B
b
a
y
ꢁy
ꢁy
A
A
A
n ) n + R (y - ꢀ) + R y - ꢀ +
S
(
A
B
(
)
∆
n
0
C
c
0
D
d
a
t
-
ln 1 -
) kt
(11)
R y + ꢀ + R y + ꢀ /y
(3)
C
(
)
D
(
)) total
0
A
(
)
a
ꢁy
Both the kinetic rate constant k and lumped parameter ꢁ
can be simultaneously evaluated using a nonlinear minimization
procedure. In this work, numerical calculations were performed
using Matlab (v. R2007b), with an in-house written algorithm.
t
0
A
0
B
0
C
0
D
0
S
y
) y + y + y + y + y + ꢀ ×
total
(
c + d) - (a + b)
0
total
(c + d) - (a + b)
)
y
+ ꢀ
(
)
(
)
a
a
(
4)
Experimental Section
For dilute reactions, the change of moles due to reaction is
Materials. Acetic anhydride (J.T. Baker, Baker analyzed for
HPLC solvent, 99.8%+), methyl 4-hydroxybenzoate or methyl
paraben (Sigma Aldrich, Sigma Ultra, 99%+), and sodium
hydroxide pellets (Merck, pro analysi, >99%) were used directly
without further purification. Deionized ultrapure water was used
in this study (Young Lin Instrument, Aquamax - Basic 321
Water Purification System).
always small compared to the total initial moles of the reaction
solution. Furthermore, since dilute reaction is considered, the
total moles y tt otal can be assumed to be nearly constant, and
therefore substituted by the total initial moles of the reaction
solution ytotal. This results in the new expression eq 5. Note that
eq 5 is exact when the sum-total stoichiometric coefficients
0
before and after reaction are equal (i.e., (c + d) - (a + b) )
The purity of the substrate methyl paraben was checked by
H NMR after dissolution in CDCl (Bruker Avance 400 MHz
3
1
0).
1
210
•
Vol. 13, No. 6, 2009 / Organic Process Research & Development

with 0.5 WB, equipped with a 5 mm TBI probe with z gradient,
running a standard Bruker supplied pulse sequence). The
measurements of the spectra showed that only very minor levels
of impurities were found. Integration of the proton resonances
provided lower bounds for the purity of methyl paraben
Scheme 1. Alkaline hydrolysis reaction of methyl paraben
deprotonated)
(
(>99.5%).
Equipment. The reactions were carried out in a 50 mL
jacketed glass reactor equipped with a magnetic stirrer. The fluid
was pumped continuously in a closed loop system from the
reactor through a Teflon membrane pump (Cole-Parmer) to the
refractometer and recycled back to the reactor. A temperature
bath recirculator (Polyscience model 9105, with temperature
stability (0.05 K) was used to maintain the temperature of the
reactor. The flow-rate of the pump used in this study was set
to ∼1 mL/min.
Scheme 2. Hydrolysis reaction of acetic anhydride
Refractive index measurements were performed with a flow-
through Abbemat-HP automatic refractometer using the sodi-
um-D line at 589.3 nm. This refractometer has an accuracy of
pump and flow-through refractometer and back to the reactor.
A certain amount of acetic anhydride (∼0.54 g) was directly
injected into the reactor using a gas-tight syringe. The time when
acetic anhydride was transferred into the reactor was noted as
-
5
-6
(
2 × 10
D D
n , a resolution of ( 10 n , and is thermostatically
controlled to within (0.01 K. Continuous measurements of the
refractive index can be automatically recorded every second.
The amount of solid reagents methyl paraben and sodium
hydroxide used for the reactions were measured using a balance
reaction time t . The total time for homogeneous mixing in the
0
present closed-loop experimental setup was ∼5 min. Afterwards,
good quality data could be acquired. This mixing time can be
compared to the typical total reaction times of ∼45 min. Since
the water concentration is ∼520 times greater than the acetic
anhydride concentration, pseudo-first-order conditions can be
assumed. The overall reaction for the hydrolysis of acetic
anhydride is shown in Scheme 2.
(
GR-200, A&D, Japan) with a precision of (10-4 g. The
amount of liquid acetic anhydride used in the reaction was
determined from the difference in the masses of the gas-tight
syringe before and after its injections.
Hydrolysis of Methyl Paraben. An aqueous solution of
sodium hydroxide (0.5 M in 50 mL solution) was prepared.
Approximately 25 mL of this solution was first transferred into
the reactor. The reactor was kept isothermal at the reaction
temperature. The stirrer and pump were turned on, and the
solution was circulated through the pump, flow-through refrac-
tometer and back to the reactor. A certain amount of methyl
paraben (∼0.38 g) was transferred into the reactor using a
funnel, while the pump was turned off. Subsequently, another
Results and Discussion
Hydrolysis of Methyl Paraben. Refractive index measure-
ments were carried out in order to monitor and evaluate the
kinetic rate coefficient for the hydrolysis reaction of methyl
25 mL of sodium hydroxide solution was quickly added to the
reactor to ensure that no reagents were left in the funnel. The
time when methyl paraben was transferred into the reactor was
noted as reaction time t . After methyl paraben was fully
0
dissolved into solution in the 50 mL jacketed glass reactor, the
pump was turned on again. Methyl paraben is only slightly
soluble in pure water, but becomes highly soluble in aqueous
sodium hydroxide since it is very rapidly transformed into its
deprotonated form. Since the sodium hydroxide concentration
used is ∼10 times greater than the methyl paraben concentration,
pseudo-first-order condition can be assumed. The overall
reaction for the alkaline hydrolysis of methyl paraben is shown
in Scheme 1.
The total time for (1) dissolution of methyl paraben and (2)
homogeneous mixing in the present closed-loop experimental
setup was ∼7 min. Afterwards, good quality and representative
data could be acquired. This mixing time can be compared to
the typical total reaction times of ∼3 h and more.
Figure 1. Changes of refractive index during the hydrolysis
reaction of methyl paraben at 298 K (•), 308 K (1), and 318 K
(
9). A good fit of the data was obtained with a third-order
Hydrolysis of Acetic Anhydride. Approximately 50 mL
of water was first transferred into the reactor. The reactor was
kept isothermal at the reaction temperature. The stirrer and pump
were turned on, and the solution was circulated through the
polynomial. Outlier measurements due to bubble formation
have been omitted. The interval data of changes of refractive
index used for subsequent kinetic analysis are indicated by the
dotted lines.
Vol. 13, No. 6, 2009 / Organic Process Research & Development
•
1211

Table 1. Summary of pseudo-first-order rate constants for
hydrolysis of methyl paraben, obtained from on-line
refractometer method as well as other techniques of
measurements
k (10- s )
4
-1 a
refractometer
(this study)
T (K)
FTIR spectroscopy
calorimetry
3.08 ( 0.01b
3.35 ( 0.03
c
2
98
3.3 ( 0.1
d
e
e
3
.15 ( 0.22
3
3
08
18
6.9 ( 0.1
13.5 ( 0.3
6.78 ( 0.03
13.9 ( 0.19
a
b
Standard deviations are reported as 2σ.
Evaluated directly from
concentration data (obtained using FTIR spectroscopy) as reported in ref 8.
Evaluated directly from heat flow data (obtained using flow-through Thermal
Activity Monitor (TAM) III microcalorimeter) as reported in ref 8. Reference 10.
Independently measured using TAM III microcalorimeter with ampoule
c
d
e
measurements. Detailed procedure can be found in ref 10.
paraben. Reactions at three different temperatures (298.15,
308.15, and 318.15 K) were performed in order to demonstrate
the utility of the present online refractive index measurement.
The changes of refractive index observed during reactions in
these three different experimental runs are shown in Figure 1.
An initial period of ∼400 s was typically needed to ensure
the homogeneity of the reaction solution in the present online
setup. The measurements obtained from this initial period are
not representative of the intrinsic reaction kinetics and, hence,
were omitted from further analysis. The refractive index changes
presented in Figure 1 clearly show the progress of the reaction.
Since the hydrolysis reaction of methyl paraben in the
presence of excess sodium hydroxide can be represented by
Figure 2. Kinetic plot of methyl paraben hydrolysis at 298 K
).
The pseudo-first-order reaction constants are provided by the
slopes of the regression lines (solid line).
(
•), 308 K (1), and 318 K (9) using eq 11 where f ) (∆n)/(ꢀy0
A
10
pseudo-first-order kinetics, eq 11 can be readily used to
simultaneously evaluate both the pseudo-first-order rate constant
k and the lumped parameter ꢁ. Only intermediate reaction times
(indicated by dotted lines in Figure 1) which ensure solution
homogeneity and have relatively higher signal-to-noise ratios
were used in the kinetic analysis. The pseudo-first-order rate
constants obtained are reported in Table 1. These values are
also compared to those previously and independently determined
8,10
using FTIR spectroscopy as well as calorimetric measurements.
The results show that the rate constants determined from the
present refractive index method are in good agreement with
those determined from other techniques. It is also noted,
however, that the standard deviations of the rate constants
determined from the present refractive index measurements are
typically greater than those determined from both spectroscopic
and calorimetric measurements.
A comparison of the experimental data and the pseudo-first-
order model (eq 11) is shown in Figure 2. The consistency of
the results confirms that a pseudo-first-order kinetic model is
appropriate for this hydrolysis reaction.
Figure 3. Refractive index changes during the hydrolysis
reaction of acetic anhydride at 293 K (•) and 298 K (1).
Smoothing lines are shown. A good fit of the data was obtained
with a third-order polynomial. Outlier measurements due to
bubble formation have been omitted. The interval data of
changes of refractive index used for subsequent kinetic analysis
are indicated by the dotted lines.
The refractive index changes in Figure 3 clearly reflect both
the extent of reaction as well as the approach to a reaction end-
point. The initial period of time (i.e., t < 300 s) before the
reaction solution has attained homogeneity is not shown.
The hydrolysis reaction of acetic anhydride in the presence
of excess water can be approximated by a pseudo-first-order
Hydrolysis of Acetic Anhydride. Refractive index mea-
surements were carried out in order to monitor and
evaluate the kinetic rate coefficient for the hydrolysis
reaction of acetic anhydride at 293.15 and 298.15 K. It
can be noted that this reaction is faster than the hydrolysis
reaction of methyl paraben and also provides a smaller
8,11
kinetic model. Accordingly, eq 11 can be readily used. Using
the smoothed refractive index changes, both the pseudo-first-
order rate constant k and the lumped parameter ꢁ were
simultaneously determined. Only intermediate reaction times
(indicated by dotted lines in Figure 3) which ensure solution
-
4
change of refractive index (i.e., ∼1 × 10
D
n ). The
changes of refractive index due to reaction performed at
two different temperatures are shown in Figure 3.
1
212
•
Vol. 13, No. 6, 2009 / Organic Process Research & Development

Table 2. Summary of pseudo-first-order rate constants for
hydrolysis of acetic anhydride, obtained from on-line
refractometer method as well as other measurement
techniques
k (10- s )
3
-1 a
refractometer
(this study)
T (K)
Raman spectroscopy calorimetery
2
93 1.6 ( 0.07 (run 1)
1
.5 ( 0.08 (run 2)
2.13 ( 0.03a
2.24 ( 0.01
b
2
2
98 2.1 ( 0.2 (run 1)
98 2.2 ( 0.3 (run 2)
c
2.23
a
Standard deviations are reported as 2σ. Calculated directly from the
concentration profile data (obtained using Raman spectroscopy) as reported in ref
b
8
. Evaluated directly from the heat flow data (obtained using flow-through TAM
c
III microcalorimeter) as reported in ref 8. ref 11.
homogeneity and have relatively higher signal-to-noise ratios
were used in the kinetic analysis. The pseudo-first-order rate
constants obtained are reported in Table 2.
The presently obtained pseudo-first-order rate constants can
be compared to those previously determined using Raman
spectroscopy and calorimetric measurements. The results show
that the rate constants determined using the refractive index
method are in good agreement with those evaluated from other
measurement techniques. Replicate measurements were also
carried out for each temperature in order to validate the present
approach. The kinetic rate coefficients determined from replicate
measurements compare favorably. In Table 2, the standard
deviations of the kinetic rate constants obtained from the
refractive index measurement are greater than those obtained
from Raman and TAM microcalorimeter measurements. This
indicates that the accuracy of the refractometer method is
somewhat less than that of the other techniques used to monitor
the present reaction. A comparison of the experimental data
and the pseudo-first-order model (eq 11) is shown in Figure 4.
The consistency of the results confirms that a pseudo-first-order
kinetic model is appropriate for the acetic anhydride reaction.
Additional Comments. It should be noted that the present
mathematical treatment relies on additivity of refractive indices
Figure 4. Kinetic plot of acetic anhydride hydrolysis at 293 K
0
(
A
•) and 298 K (1) using eq 11 where f ) (∆n)/(ꢀy ). The pseudo-
first-order reaction constants are provided by the slopes of the
regression lines (solid line).
On a more practical level, it is also important to ensure as
far as possible that bubble formation during the online refractive
index measurements are avoided or at least minimized. In
addition, it is useful to minimize temperature and/or flow-rate
fluctuations during measurements.
Conclusions
This work demonstrates the utility of an online refractometer
technique as a simple and accurate tool to monitor the progress
of reactions as well as to determine the end-point of reactions.
For known reactions, the present approach represents a more
economical method compared to using online spectroscopic or
calorimetric determinations. Therefore, for reactions which are
repetitively performed, or for continuous online processes, this
approach provides an attractive alternative to spectroscopic/
calorimetric determinations. Although the present study focused
on hydrolysis reactions, the proposed methodology is certainly
applicable to much wider range of liquid-phase reactions.
(eq 1) and hence a linear dependence between change of
refractive index and extent of reaction (eq 6) and that this can
only be guaranteed in the case of dilute reactions. Extension to
more concentrated reactive solutions is potentially more com-
plex, and the relationship between refractive index and extent
of reaction would have to be clarified on a case-by-case basis.
In practice, this could be further investigated by performing
independent but simultaneous online spectroscopic or calori-
metric measurements and comparing the resulting extents of
reactions obtained by the various methods. If the extents of
reactions are not consistent, a calibration involving the con-
centration dependence of refractive indices could be included
in the mathematical model.
Acknowledgment
This work was supported by the Agency for Science,
Technology and Research (A*STAR), Singapore. We thank Dr.
Chacko Jacob for assistance in the NMR measurements.
Received for review June 4, 2009.
OP9001388
Vol. 13, No. 6, 2009 / Organic Process Research & Development
•
1213