PAPER
www.rsc.org/pccp | Physical Chemistry Chemical Physics
Comparative solubilisation of potassium carbonate, sodium bicarbonate
and sodium carbonate in hot dimethylformamide: application of
cylindrical particle surface-controlled dissolution theory
Claire L. Forryan,a Richard G. Compton,*a Oleksiy V. Klymenko,b
Colin M. Brennan,c Catherine L. Taylorc and Martin Lennonc
Received 5th September 2005, Accepted 8th November 2005
First published as an Advance Article on the web 17th November 2005
DOI: 10.1039/b512463h
A surface-controlled dissolution of cylindrical solid particles model is applied to potassium
carbonate, sodium bicarbonate and sodium carbonate in dimethylformamide at elevated
temperatures. Previously published data for the dissolution of potassium carbonate is interpreted
assuming a cylindrical rather than a spherical shape of the particles, the former representing a
closer approximation to the true shape of the particles as revealed by scanning electron
microscopy. The dissolution kinetics of sodium carbonate and sodium bicarbonate in
dimethylformamide at 100 1C were investigated via monitoring of the deprotonation of
2-cyanophenol with dissolved solid to form the 2-cyanophenolate anion that was detected with UV
–visible spectroscopy. From fitting of experimental results to theory, the dissolution rate constant,
k, for the dissolutions of potassium carbonate, sodium bicarbonate and sodium carbonate in
dimethylformamide at 100 1C were found to have the values of (1.0 0.1) 107 mol cm2 s1,
(5.5 0.3) 109 mol cm2 s1 and (9.7 0.8) 109 mol cm2 s1, respectively.
1
Introduction
Reactions between solids and liquids are of widespread synthetic, industrial and environmental importance; for example
in heterogeneous catalysis,1 drug dissolution2,3 dyeing4 and
geological weathering.5 Processes at the solid/liquid interface
typically involve a complex sequence of mass transport,
adsorption/desorption processes, surface diffusion, heterogeneous reaction/electron transfer and chemical transformation
of intermediates. The identification and kinetic quantification
of which have posed difficulties in fully understanding mechanisms. Understanding the dissolution kinetics of solid
particles is important in natural processes and in industry,6
particularly in the development and operation of processes for
the production of agrochemicals and pharmaceuticals. Surprisingly, whilst heterogeneous systems are widely used in the
production of fine chemicals, there is little literature information on the dissolution of solid particles in organic solvents.
Formerly, studies of the dissolutions of inorganic solids have
been in aqueous solutions,7–11 such as the dissolution of
limestone in aqueous electrolyte,10,12–15 and only particles of
sizes in a small diameter fraction or single crystals have been
selected.
In previous papers we reported the surface-controlled dissolutions of KHCO3 and K2CO3 in dimethylformamide
a
Physical and Theoretical Chemistry Laboratory, University of
Oxford, South Parks Road, Oxford, UK OX1 3QZ. E-mail:
[email protected]; Fax: +44 1865 275410;
Tel: +44 1865 275413
b
Mathematical and Computer Laboratory, Kharkov National
University of Radioelectronics, 14 Lenin Avenue, Kharkov, 61166,
Ukraine
c
Syngenta, Leeds Road, Huddersfield, UK HD2 1FF
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(DMF) at elevated temperatures. Two theoretical models have
been developed, the first for the dissolution of spherical solid
particles16,17 and secondly for the dissolution of cylindrical
particles18 A comparison between the theories was used to
show the influence of particle shape on the dissolution kinetics
of a solid and hence the importance of knowing the shape of
the individual solid particles for realistic modelling of their
dissolution. Both surface-controlled dissolution models were
successfully applied to experimental results for the dissolution
of KHCO3 in DMF and values for the dissolution rate
constant, k, determined. However, it was found that results
obtained from the cylindrical model gave improved fits between theory and experiment, from which a refined and more
precise value of k was determined. These findings were consistent with scanning electron microscopy imaging of the
inorganic solid, which showed that a closer approximation
to the true shape of the particles was that of cylinders.
Attention is now focused on modelling the dissolution kinetics
in turn of K2CO3 and then NaHCO3 and Na2CO3 in hot
DMF.
In this paper, the cylindrical particle surface-controlled
dissolution theory is applied to re-examine the previously
published data on the dissolution kinetics of K2CO3 in
DMF at elevated temperatures. Scanning electron microscopy
was employed in this report to expose the true ‘rod like’ rather
then spherical shape of the K2CO3 solid sample used in the
previous experiments. Thus, the experimental results found
from monitoring the loss of 2-cyanophenol by deprotonation
with dissolved solid,17 can be re-modelled assuming a cylindrical particle shape distribution of the solid. A further SEM
study of the K2CO3 solid particles with dissolution time gives
insight into the surface-controlled dissolution process.
Phys. Chem. Chem. Phys., 2006, 8, 633–641 | 633
Heterogeneous systems, frequently the inorganic base
K2CO3 in the organic solvent DMF, are widely used in organic
synthesis and the production of agrochemicals and pharmaceuticals.19–24 The carbonate facilitates the formation of a
required anionic organic nucleophile for coupling with a
dissolved electrophile to give the product. The importance of
K2CO3 dissolution in controlling such reactions has been
reported,17 with the fast dissolution, as compared to KHCO3,
allowing for a swift production of the nucleophile anion and
subsequent reaction with the electrophile, which leads to a
shorter overall processing time. Consider an inorganic base
which dissolves at an even slower rate and hence gives a slower
formation of the required nucleophile, then the electrophile is
given opportunities to participate in further unwanted reactions and potentially extent the time of product formation.
Even though Na2CO3 is cheap, it is not used as the inorganic
base in heterogeneous systems for the production of fine
chemicals. It is thought that this is not due to differences in
base strength, but rather a slower rate of dissolution into polar
aprotic solvents as compared to K2CO3. This is investigated in
this paper, by monitoring in turn the dissolution of NaHCO3
and then Na2CO3 in DMF at 100 1C via the homogeneous
deprotonation of 2-cyanophenol. Akin to K2CO3, the scheme
for the reaction of Na2CO3 with 2-cyanophenol is given in
Scheme 1, where the dissolved inorganic solids deprotonate
the 2-cyanophenol to produce the 2-cyanophenolate anion.
Experimentally, the NaHCO3/DMF and Na2CO3/DMF
solutions were heated via the heated microdisk method developed by Coles et al.,25 which utilizes an electronically controlled heat gun that allows for greater precision in controlling
the solution temperature. Power ultrasound was incorporated
into the system to induce mixing, which has been shown to
facilitate reproducible microelectrode responses in heterogeneous systems.26 The 2-cyanophenolate anion produced was
detected by UV–visible spectroscopic analysis of samples
removed from the reaction vessel over time.
The results reported below show that for the reaction with
2-cyanophenol both NaHCO3 and Na2CO3 display similar
behaviour to their potassium counterparts. There is initial rapid
deprotonation of the 2-cyanophenol via predissolved inorganic
solid in the DMF solutions, followed over longer time by the
slower loss of 2-cyanophenol as controlled by the rate of solid
dissolution. The dissolution kinetics of both NaHCO3 and
Na2CO3 in DMF at 100 1C were then analysed using the
surface-controlled dissolution model for cylindrical particles,
this shape approximation confirmed from the SEM analysis.
2
Experimental
2.1 Chemical reagents
All experiments were carried out in N,N-dimethylformamide
(DMF, Aldrich, 99.9+%, HPLC grade). The DMF was
carefully treated by drying over Linde 5 Å molecular sieves
(Aldrich) for a minimum of 48 hours, and then prior to use,
shaken with ICN alumina N-super 1 (ICN Biomedicals
GmbH, Germany) and the solvent decanted off. The water
content of the solvent was determined by Karl-Fischer titration (Metrohm, 758 KFD Titrino),27 and it was found that the
DMF drying procedure outlined above yielded DMF with a
water content of ca. 0.04% by weight (2.3 102 mol L1),
compared to DMF as supplied, which has a water content of
ca. 0.15% by weight (8.6 102 mol L1).
2-cyanophenol (Aldrich), sodium bicarbonate (AnalaR) and
sodium carbonate (AnalaR) were obtained of the highest
commercially available grade and used without further
purification.
2.2 Instrumentation
2.2.1 High temperature and ultrasound apparatus. The
ultrasonic generator used was a model VCX 5000 (Sonics
and Materials, USA) horn equipped with 3 mm diameter
titanium microtip, emitting 25 kHz ultrasound. The power
output of the transducer was calorimetrically calculated in
DMF28,29 for which an amplitude of 5% was found to
correspond to 8 W cm2 and employed for all experiments.
The high temperature experiments were carried out in a cell
with a solution volume of 15 cm3 by hot air circulation from
an electronically controlled heat gun within a small box of
insulating material with a front glass wall25 A Pt resistance
thermometer controlled the air temperature and a thermocouple in contact with the solution was used to read the
temperature. The ultrasound horn was inserted from above
into the cell, through a precision bored aperture in the teflon
cell lid, which was manufactured in house to minimise heat
losses. Temperature control was most important, and care was
taken to ensure that all experiments were carried out at the
required temperature to 1 1C. In order to maintain the
solution temperatured of 80 1C and 100 1C under the application of the power ultrasound, external heating required hot air
circulation of ca. 65 1C and 86 1C, respectively.
The solutions of K2CO3/DMF, NaHCO3/DMF and
Na2CO3/DMF were heated under ultrasound at the desired
elevated temperatures for 2 hour time periods before the
addition of 2-cyanophenol. The solutions were thoroughly
degassed with nitrogen (BOC gases) throughout their initial
heating and a continuous flow of nitrogen over the solution
was maintained throughout the experiments to ensure that no
oxygen was in contact, and to exclude and drive-off carbon
dioxide.
2.2.2 UV–visible spectroscopy. UV–visible spectra were
recorded on a Unicam UV2 series UV–visible spectrophotometer (Unicam, Cambridge, UK), using a quartz cuvette of
pathlength 1 cm, scanning over a wavelength of 275 nm to 400
nm. Small volume samples (ca. 50 ml) were removed at regular
Scheme 1 Scheme for the reaction of Na2CO3 with 2-cyanophenol in DMF.
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time intervals from the ultrasound-heated solutions, over a
one hour period, and allowed to cool to room temperature.
These were diluted with DMF by a known factor and their
UV–visible spectra recorded. Each spectrum was background
subtracted from that of blank DMF.
2.2.3 Scanning electron microscopy. Scanning electron microscopy (SEM) images were recorded using a Leica 430i
instrument. The samples were adhered to a 0.500 aluminium
stub with double sided tape and quickly coated with gold to
avoid adsorption of water. They were examined under the
SEM at an accelerating voltage of 10 keV, 15 mm working
distance and magnifications of 50 to 1000 times. The samples
were examined under the secondary electron detector.
3
Theoretical model
In the kinetic treatment of the dissolution of cylindrical solid
particles developed in a previous paper,18 the number of moles
of solid remaining undissolved in solution over time is modelled.
In summary, let us consider a sample of cylindrical particles
of mass m and density r, initially with the circular end having
diameter d0 and with cylindrical length of l0. As the particle
dissolves the diameter and cylindrical length are denoted l and
d, respectively, where l = zd and l0 = z0d0. After being placed
into the solution the particles start to dissolve with the rate
constant k. The rate of change of the number of moles of the
species in a particle is proportional to the rate constant k and
the particle surface area, S = pdl + pd2/2. Hence, the
following differential equation can be written for a single
particle of diameter d:
h
dn
p i
¼ kS ¼ k pdl þ d 2
ð1Þ
dt
2
For a sample of particles described by a number distribution
function, f(d), and assuming all cylindrical particles have the
same initial z0 value, we obtain the time dependence of the
total number of moles of the species in the particle mixture:
Z1
pr
nðtÞ ¼
4M
2Mk
r
2Mk 2
d0 t
r
Hðz0 1þz1 Hð1z0 ÞÞ
0
ð2Þ
2Mk
t f ðd0 Þdd0
z0 d0 r
where a Heaviside step function (H) is utilised, in order to
avoid negative values of the equation after a particle has been
fully dissolved.
For a more detailed derivation ref. 18 should be consulted.
Fig. 1 (a) SEM image of K2CO3 and (b) the cylindrical diameter
number distribution function, f(d), (—) for the K2CO3 sample.
cylindrical approximation is more valid than a spherical one.
A large number of particles were examined and the cylindrical
dimensions d and l of individual particles measured from the
SEM images. Inspection of the images gave the mean values
of; cylindrical diameter d = 135 62 mm, cylindrical length
l = 388 153 mm, z = 3.2 1.3, and the distribution
functions f(d) in Fig. 1b.
Fig. 2 display SEM images for samples of NaHCO3 and
Na2CO3, respectively, used in the experiments of this paper.
These show that overall the shapes of the individual NaHCO3
and Na2CO3 particles are rod like and hence a cylindrical, as
opposed to spherical, approximation gives a more realistic
representation of the solids. Again, analysis by measurement
of individual particles in the SEM images gave mean values for
the cylindrical diameter, d, and the cylindrical length, l. For
NaHCO3, d = 64 30 mm, cylindrical length l = 120 44 mm
and a mean z value of 2.0 0.5. For Na2CO3, d = 62 45
mm, cylindrical length l = 143 83 mm and a mean z value of
2.6 0.8. The number distribution function, f(d) was developed from the SEM images and is given in Fig. 2c and 3c for
NaHCO3 and Na2CO3, respectively. The Na2CO3 sample
shows a much broader cylindrical diameter distribution than
that for NaHCO3.
4.2 The dissolution of cylindrical K2CO3 particles in DMF
4
Results and discussions
4.1 Scanning electron microscopy imaging of the inorganic
solids
Fig. 1a displays an SEM image for a sample of the K2CO3
used in the previous experiments.17 It can be seen that the
individual K2CO3 particles are rod like in shape; hence a
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The dissolution of K2CO3 in DMF at elevated temperatures
was followed experimentally in ref. 17 by employing the
previously described strategy, whereby the dissolved solid
deprotonates the 2-cyanophenol to produce the 2-cyanophenolate anion that is detected spectroscopically.16,17 The concentration of 2-cyanophenolate formed at each reaction time
was determined from the Beer–Lambert Law.30 Taking a 1 : 1
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Fig. 2 SEM images at magnifications of (a) 25 and (b) 125 of NaHCO3 and (c) the cylindrical diameter number distribution function, f(d), (—)
for the NaHCO3 sample.
mole ratio of 2-cyanophenolate produced to K2CO3 reacted,
as it has been shown that for an excess of initial K2CO3 the
formation of the anion is predominantly via the left-hand side
of Scheme 1, the number of moles of K2CO3 remaining in
solution at each time was calculated.
4.2.1 Determination of the dissolution rate constant, k. The
UV–visible spectroscopic experimental results from ref. 17 are
analysed using the model developed for the surface-controlled
dissolution of cylindrical particles model.18 Eqn (2) was solved
numerically to develop plots of the number of moles of
undissolved solid, n(t)/mol against time/s to compare the
cylinder theory with experiment. The following parameters
were used: mass of the inorganic solid/g, density of the solid/g
cm3, molecular weight of the solid/g mol1, time/s, k/mol
cm2 s1, cylindrical particle diameter number distribution
function, f(d), (Fig. 1b) with all particles having the same
initial z0 of 3.2. It has been found electrochemically and
spectroscopically that initially the 2-cyanophenol deprotonation is via pre-dissolved K2CO3 in the DMF solution, followed
over longer time by the slower surface-controlled dissolution
of solid.17 Hence, the mass of solid used was calculated via
subtraction of the mass pre-dissolved in solution from the
initial mass of solid added and the first minute of reaction not
included in the fits.
Solutions of DMF with K2CO3 of masses 0.020 g and
0.050 g were heated at 100 1C, with the addition of 10 mM
and 25 mM 2-cyanophenol, respectively. The corresponding
plots of the n(t) against time are given in Fig. 4. Overlaid are
the theoretical fits from the cylinder model. Good fit to the
experimental data can be seen, hence supporting the dissolution model for cylindrical particles. The mean value determined for the dissolution rate constant, k, for the dissolution
636 | Phys. Chem. Chem. Phys., 2006, 8, 633–641
of K2CO3 in DMF at 100 1C is (1.0 0.1) 107 mol
cm2 s1.
The effect of temperature on the dissolution rate controlled
constant for K2CO3 in DMF was examined. The addition of
25 mM 2-cyanophenol to solutions of 0.062 g K2CO3/DMF at
70 1C, 80 1C and 90 1C are shown in Fig. 5. The successful fits
to the theoretical model are overlaid from which the values of
k are found to be (3.6 0.1) 109 mol cm2 s1 at 70 1C,
(4.3 0.3) 108 mol cm2 s1 at 80 1C and (7.9 0.3) 108 mol cm2 s1 at 90 1C. A graph of ln k against 1/T over
the temperature range of 70 1C to 100 1C studies, inset Fig. 5,
yields a straight line with R2 value of 0.952. From analysis in
terms of an Arrhenius type relation, the activation energy for
the dissolution of K2CO3 in DMF was calculated to be 39.3 0.3 kJ mol1.
Table 1 gives the mean values of k for the dissolution of
K2CO3 in DMF at elevated temperatures, found previously
employing the surface-controlled dissolution of spherical solid
particles model6 and those values determined above using the
surface-controlled dissolution of cylindrical solid particles
approach. The values of k found for cylindrical and spherical
theory over the temperature range of 70 to 100 1C studied give
broadly similar values at each temperature. However, a comparison of the standard deviations from the mean values of k
shows that the cylindrical modelling gives a somewhat improved fit to the experimental data over the entire temperature
range. Hence, the surface-controlled dissolution of cylindrical
particles theory gives a more refined value for k, more
consistent with the SEM findings of the true K2CO3 particle
shapes.
4.2.2 SEM analysis of K2CO3 particles with dissolution
time. The K2CO3 solid was examined by SEM after dissolution
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Fig. 3 SEM images at magnifications of (a) 25 and (b) 125 of Na2CO3 and (c) the cylindrical diameter number distribution function, f(d), (—)
for the Na2CO3 sample.
in DMF at elevated temperatures to gain a quantitative insight
into the changes in the cylindrical particle shape and sizes with
dissolution time. Solutions of DMF with 1.00 g of K2CO3
(assuming hypothetically that the complete dissolution of the
solid was possible, this mass would correspond to a concentration of 472 mM) were heated under ultrasound for 2 h at
80 1C with subsequent addition of 500 mM of 2-cyanophenol.
The solid was then removed, dried under vacuum and analysed
by SEM; (a) after the 2 h pre-ultrasound period, (b) 1 h after
the 2-cyanophenol addition and (c) 2 h after the 2-cyanophenol addition. Fig. 6a–c show the corresponding images of the
K2CO3 solid at magnifications of 50 and 250.
Fig. 4 Plots of n(t)/mmol against time/s for theoretical (—) and UV–
visible spectroscopic experimental results at 100 1C for the dissolutionrate-controlled-process of the addition of (K) 10 mM 2-cyanophenol
to 0.020 g K2CO3 in DMF and (J) 25 mM 2-cyanophenol to 0.050 g
K2CO3 in DMF.
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The K2CO3 solid after the pre-ultrasound time in Fig. 6a,
before addition of the 2-cyanophenol, bears excellent resemblance to the SEM image of the starting sample of solid given
previously in Fig. 2b. This affirms that the presence of ultrasound in the experiments of this thesis serves solely to agitate
and stir the solutions, with no breakdown of the solid from the
cavitational and acoustic streaming effects of sonication.31–34
The pre-ultrasound period gives the amount of K2CO3 dissolved in DMF at elevated temperatures and this shall be
Fig. 5 Plots of n(t)/mmol against time/s for theoretical (—) and UV–
visible spectroscopic experimental results for the dissolution-ratecontrolled-process of the addition of 25 mM 2-cyanophenol to 0.062
g K2CO3 in DMF at (J) 70 1C, (K) 80 1C and (m) 90 1C. Inset shows
a graph of ln(k/mol cm2 s1) against 1/(T/K) over the temperature
range of 70 1C to 100 1C.
Phys. Chem. Chem. Phys., 2006, 8, 633–641 | 637
Table 1 Values of the dissolution rate constant, k, determined from
employing the surface-controlled dissolution of spherical solid particles theory and the surface-controlled dissolution of cylindrical solid
particles theory to model the dissolution of K2CO3 in DMF at 70 1C,
80 1C, 90 1C and 100 1C
K2CO3 with particle size distribution f(d)
T/1C
Cylindersa k/mol cm2 s1
70
80
90
100
(3.6
(4.3
(7.9
(1.0
0.1)
0.3)
0.3)
0.1)
108
108
108
107
Spheresb k/mol cm2 s1
(3.9
(5.5
(9.5
(1.3
0.1)
0.4)
0.5)
0.2)
108
108
108
107
a
Values deduced using eqn (2), in which f(d) is that given in
Fig. 1b. b Values deduced in ref. 17.
address later in the report. Fig. 6b and 6c shows that the loss
of 2-cyanophenol from solution is controlled by the solid
dissolution, as both d and l dimensions of the particles have
decreased with time after the addition of the 2-cyanophenol to
the solutions. After 2 h of the surface-controlled dissolution it
appears that the smaller sized particles have completely dis-
solved. It is observed from Fig. 6a–c that the edges of the
larger particles become more rounded during the dissolution
process, and hence the curvature of the particles plays a role in
the dissolution. This underlines that both the spherical and
cylindrical dissolution models adopted in our studies are only
primitive models that rely on an approximation of the real
particle shapes.
4.3 The dissolution of cylindrical NaHCO3 and Na2CO3
particles in DMF
4.3.1 UV–visible spectroscopic analysis. UV–visible spectroscopy was employed as a strategy to follow the dissolutions
of solids NaHCO3 and Na2CO3, whereby the dissolved solid
deprotonates the 2-cyanophenol, as shown in Scheme 1, to
form the 2-cyanophenolate anion which can be detected
spectroscopically. It is known that the UV–visible spectrum
of a 0.1 mM solution of potassium 2-cyanophenolate in DMF
displays the phenolate absorption peak at 359 nm with an
absorbance of 0.898.35 The molar extiction coefficient, e, for
Fig. 6 SEM images at magnifications of 50 and 250 of K2CO3; (a) after the 2 h pre-ultrasound period, (b) 1 h after the 2-cyanophenol addition
and (c) 2 h after the 2-cyanophenol addition.
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Fig. 7 Plots of 2-cyanophenolate concentration/mM against reaction
time/s for the addition of (’) 20 mM 2-cyanophenol to 0.025 g
NaHCO3, and (K) 30 mM 2-cyanophenol to 0.035 g NaHCO3 in
DMF heated under ultrasound for 2 h at 100 1C.
Fig. 8 Plots of 2-cyanophenolate concentration/mM against reaction
time/s for the addition of (’) 10 mM 2-cyanophenol to 0.025 g
Na2CO3, and (K) 20 mM 2-cyanophenol to 0.050 g Na2CO3 in DMF
heated under ultrasound for 2 h at 100 1C.
this peak was calculated by using the Beer–Lambert law to be
8980 mol1 dm3 cm1.30 The absorbance of this peak was
analysed over time after the addition of 2-cyanophenol to
NaHCO3/DMF and Na2CO3/DMF solutions after predissolution ultrasound times of 2 hours at 100 1C. The concentration of 2-cyanophenolate formed at each reaction time was
then determined.
Solutions of DMF with 0.025 g and 0.035 g of NaHCO3
were heated under ultrasound at 100 1C, followed by the
addition of 20 mM and 30 mM 2-cyanophenol, respectively.
Assuming hypothetically that the complete dissolution of the
solid was possible, these masses correspond to NaHCO3
concentrations of ca. 20 mM and 28 mM. The corresponding
plots of the concentration of 2-cyanophenolate formed against
time are given in Fig. 7. In each case, there is an initial rapid
formation of 2-cyanophenolate, followed over longer time by
a gradual increase in 2-cyanophenolate concentrations. These
results are consistent with those found for KHCO3;16 initially
predissolved solid in the DMF solution deprotonates the 2cyanophenol, and at longer time the loss of 2-cyanophenol
being controlled by the slower surface-controlled dissolution
of solid into the DMF solutions.
From the initial homogeneous reaction of predissolved
solid, the formation in 2-cyanophenolate over the first minute
enabled the amounts of NaHCO3 dissolved in DMF to be
estimated. Taking a 1 : 1 mole ratio of 2-cyanophenolate to
NaHCO3 (right-hand side of Scheme 1) allowed the determination of the number of moles of dissolved solid, from which
the consentration of NaHCO3 in DMF at 100 1C can be
approximated. For the additions of 25 mg and 35 mg NaHCO3 to 15 mL solutions of DMF, it was estimated that after an
ultrasound time of 2 hours at the temperature of 100 1C the
masses of NaHCO3 dissolved in solution were 8.9 and 15.0 mg,
respectively. These correspond to concentrations of 7.1 103
mol L1 and 1.2 102 mol L1. This can be compared to the
results from an analogous experiment for KHCO3 in ref. 16,
where 25 mg of the inorganic solid was heated in DMF with
the predissolution time of 2 hours at 100 1C. It was calculated
that the mass of solid dissolved in the DMF solution was 2.5
mg, corresponding to a concentration of 1.7 103 mol L1.
Hence a larger mass of NaHCO3 than KHCO3 is dissolved in
the DMF solutions under analogous conditions, and conse-
quently NaHCO3 is relatively more dissolved than KHCO3 in
DMF at 100 1C.
Fig. 8 displays the results for the additions of 10 mM and
20 mM 2-cyanophenol to solutions of 0.025 g and 0.050 g
Na2CO3 in DMF heated under ultrasound at 100 1C. Assuming hypothetically that the complete dissolution of the solid
was possible, these masses correspond to Na2CO3 concentrations of ca. 16 mM and 31 mM, and hence an excess of solid
was added in each case. As expected, the initial rapid formation of 2-cyanophenol via the homogeneous deprotonation of
2-cyanophenol with predissolved solid is seen. Over longer
times, the gradual formation of the 2-cyanophenolate is again
observed, with the loss of 2-cyanophenol being controlled by
the rate of dissolution of solid Na2CO3 into the DMF solutions.
From these results the amounts of Na2CO3 predissolved in
DMF at the elevated temperature of 100 1C can again be
estimated. For the additions of 25 mg and 50 mg Na2CO3 to
15 mL solutions of DMF, it was estimated that after an
ultrasound time of 2 hours at 100 1C the masses of Na2CO3
dissolved in solution were 4.6 mg and 6.2 mg, equivalent to
concentration of 2.9 103 mol L1 and 3.9 103 mol L1,
respectively. Comparison to NaHCO3, where 8.9 mg of solid
was dissolved after the initial mass addition of 25 mg solid,
show that a smaller mass of Na2CO3 solid is dissolved in the
solution, with the concentration of Na2CO3 being ca. one half
that of NaHCO3. The Na2CO3 results can also be compared to
those from an analogous experiment for K2CO3 in ref. 17,
where 50 mg of the inorganic solid was heated in DMF with
the predissolution time of 2 hours at 100 1C. It was calculated
that the mass of solid dissolved in the DMF solution was 6.3
mg, corresponding to a concentration of 3.0 103 mol L1.
This is comparable to the amount of Na2CO3 dissolved, and
hence the concentration of Na2CO3 and that of K2CO3 in
DMF at 100 1C are similar. Overall, the relative amounts of
dissolution of the four inorganic solids in hot DMF have the
order, NaHCO3 > Na2CO3, K2CO3 > KHCO3.
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4.3.2 Determination of the dissolution rate constant, k. The
UV–visible spectroscopic experimental results are analysed
using the model developed above for the surface-controlled
dissolution of cylindrical particles model. eqn (2) was solved
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Table 2 Table of the dissolution rate constant, k, determined from
the surface-controlled dissolution of cylindrical solid particles model,
for the dissolution of KHCO3, NaHCO3, K2CO3 and Na2CO3 in
DMF at 100 1C
Inorganic solid
Dissolution rate constant, k/mol cm2 s1
KHCO3
NaHCO3
K2CO3
Na2CO3
(9.6
(5.5
(1.0
(9.7
a
Fig. 9 Plots of n(t)/mmol against time/s for theoretical (—)and UV–
visible experimental results at 100 1C for the dissolutions in DMF of
(’) 0.035 g NaHCO3 and (m) 0.025 g Na2CO3.
numerically to develop plots of the number of moles of
undissolved solid, n(t)/mols against time/seconds to compare
the cylinder theory with experiment. The following parameters
were used: mass of the inorganic solid/g, density of the solid/g
cm3, molecular weight of the solid/g mol1, time/s, k/mol
cm2 s1. In the theoretical modelling, as concern is with the
dissolution-rate-controlled kinetics the mass of inorganic solid
was calculated via subtraction of the mass predissolved in
solution from the initial mass added in the experiments. The
diameter number distribution functions describing all particles
in the inorganic solids, f(d), incorporated into eqn (2) were
those given in Fig. 2c and 3c, and the initial z0 values were 2.0
and 2.6 for NaHCO3 and Na2CO3, respectively.
The experimental plots of the number of moles of solid
remaining undissolved in solution with time were calculated
assuming a 1 : 1 mole ratio of 2-cyanophenolate produced to
both NaHCO3 (right-hand side of Scheme 1) and Na2CO3
(left-hand side of Scheme 1). Overlaying of the theoretical
plots of n(t) against time and the experimental data allowed
values of the dissolution rate constant, k, to be determined for
NaHCO3 and then Na2CO3 in DMF at 100 1C.
Results for NaHCO3. Fig. 9 shows the plots of theoretical
and experimental data for the dissolution of 0.035 g NaHCO3
in DMF at 100 1C. There is a good fit between experimental
and theoretical data, as was also observed in the modelling of
the dissolution of 0.025 g NaHCO3. The mean value determined for the dissolution rate constant, k, for the dissolution
of NaHCO3 in DMF at 100 1C is (5.5 0.3) 109 mol
cm2 s1.
Results for Na2CO3. The theoretical and experimental plots
for the dissolution of 0.025 g Na2CO3 in DMF at a temperature of 100 1C are also shown in Fig. 9. Again good concurrence between experiment and theory developed from the
surface-controlled dissolution of cylindrical particles is seen.
The mean value determined for the dissolution rate constant,
k, for the dissolution of Na2CO3 in DMF at 100 1C is (9.7 0.8) 109 mol cm2 s1.
4.4 Comparison of inorganic solids
Table 2 displays the mean values of the dissolution rate
constant, k, determined, employing the surface-controlled
640 | Phys. Chem. Chem. Phys., 2006, 8, 633–641
1.6)
0.3)
0.1)
0.8)
109a
109
107
109
Value deduced in ref. 18.
dissolution of cylindrical particles model, for the dissolution
in DMF at 100 1C of the inorganic solids; KHCO3, NaHCO3,
K2CO3 and Na2CO3. As originally defined18 for the surfacecontrolled dissolution of the inorganic solids in solution, the
rate of change of the number of moles of solid particle
remaining undisssolved in solution with time is proportional
to the dissolution rate constant, k, and the particle surface
area. Clearly the dissolution of K2CO3 is faster, approximately
by a factor of ten, than that for the other inorganic solids
studied. These findings are consistent with the principal use of
K2CO3 in the polar aprotic solvent, DMF, as the inorganic
base of choice in solid–liquid systems.
5 Conclusions
The surface-controlled dissolution of cylindrical sold particles
model is effectively applied to interpret previous experimental
data for the dissolution of K2CO3 in DMF at elevated
temperatures. SEM images of the experimental K2CO3 sample
showed the more ‘rod like’ as opposed to spherical shape of
the individual particles. Hence, the cylindrical dissolution
theory was applied to give more precise values of the dissolution rate constant, k, over the temperature range investigated.
From this refinement, k was found to be (1.0 0.1) 107
mol cm2 s1 for the dissolution of K2CO3 at 100 1C and the
activation energy for the dissolution was 39.3 0.3 kJ mol1
over the temperature range of 70 1C to 100 1C. A visual survey
of the solid particles with dissolution time, as revealed by SEM
imagery, showed decreases in the cylindrical dimensions, d and
l, during the surface-controlled dissolution process.
The dissolutions of both NaHCO3 and Na2CO3 in hot
DMF were studied by following the deprotonation of 2cyanophenol via dissolved solid over time, with the subsequent
formation of 2-cyanophenolate being detected spectroscopically. In each case it was shown that initially the 2-cyanophenol deprotonation is by predissolved inorganic solid in the
DMF solution, and at longer times the observed kinetics are
controlled by the rate of solid dissolution. This is analogous
behaviour to that observed for KHCO3 and K2CO3. The
surface-controlled dissolution of cylindrical sold particles
model is applied to successfully model the experimental results. The mean value determined for the dissolution rate
constant, k, for the dissolutions of NaHCO3 and Na2CO3
in DMF at 100 1C were (5.5 0.3) 109 mol cm2 s1 and
(9.7 0.8) 109 mol cm2 s1, respectively.
This journal is
c
the Owner Societies 2006
Acknowledgements
CLF expresses her gratitude to the EPSRC for a DTA
studentship and Syngenta for a CASE award. We also thank
Syngenta for the use of their facilities for carrying out
the Karl-Fischer titrations and the SEM analysis of the
inorganic solids. OVK thanks the Clarendon fund for partial
support.
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