Interpreting Freezing Point Depression of Stearic Acid and Methyl Stearate
By
M. J. Goff, G. J. Suppes*, and M. A. Dasari
Department of Chemical Engineering
The University of Missouri-Columbia
Columbia, MO 65211
(Revised, Submitted, Fluid Phase Equilibrium)
ABSTRACT
Freezing point depressions of binary systems including either stearic acid (SA) or methyl
stearate (MES) were evaluated based on differential scanning calorimetry melting scans . The
second binary component included a solvent from the group acetic acid, acetone, 2-butanone, and
hexane. Vapor pressure as a function of liquid composition and temperature was used to measure
vapor/liquid equilibrium. Activity coefficients were calculated from this data and models fit to the
data to determine how well the models fit the solid-liquid equilibrium.
The Gibbs/Duhem equation and polymorphism of the melt transitions indicated that
freezing point depressions were due to a combination of 1) a reduction of activity of the triglyceride
derivative in solution albeit with activity coefficients >1.0, 2) incorporation of the solvent into the
solid matrix for at least some of the mixtures, and 3) substantially different physical properties
between the solid and liquid phases of the SA and MES. Different melting phenomena were
observed in differential scanning calorimetry (DSC) scans depending upon the heteroatom
functionality of the solvent.
The empirical Margules, NRTL, and Wilson activity coefficient models fit data for the
solvent activity coefficients well, while the UNIQUAC model combined with the predictive abilities of
UNIFAC could not accurately predict activity coefficients. Despite questions on the fundamental
interpretation of the data, modeling the activity coefficients for the solvent is sufficient to
approximate the effect the solvent will have on the melting point depression. Relatively simple
experiments following the total pressure of mixtures as a function of composition and temperature
can be used to obtain activity coefficient model parameters for the Margules, NRTL, UNIQUAC,
and Wilson.
Keywords: activity coefficient modeling, crystallization, fatty acid esters, fatty acids, freezing point
depression, phase change, phase change materials, and phase equilibria
1
1 INTRODUCTION
The ability to predict solid-liquid equilibrium data is extremely important when designing
crystallizers and understanding fluid properties. Solid-liquid equilibrium (SLE) data is scarce, and
accurate methods of predicting equilibrium are needed. Vapor-liquid equilibrium (VLE) data is
readily available for a large number of binary systems. By correlating VLE data with activity
coefficient models and using the correlations to predict solid-liquid equilibria (SLE), available VLE
data can be used to compensate for the shortfall in SLE data. This paper evaluates the utility of
activity coefficients obtained from VLE to predict SLE and the fundamental understanding of SLE of
SA and MES using solvents for freezing point depression. The performance of solvents on the
freezing point depression of SA and MES is then compared to established freezing point
depression theory.
Freezing point depression of SA and MES in solvents is an important fundamental
parameters in many areas of research and practical applications. The ability to accurately predict
the effect of varying concentrations of solvents is needed to control cold flow properties of diesel
fuels[1,2], vary the freezing points of mixtures for use as phase change materials, and for purifying
substances both in the laboratory and in industry. For phase change materials it is important to
know the correct amount of solvent required to achieve the desired freezing point depression. For
solid-liquid separations using low concentrations of solvent, accurate knowledge of activity
coefficients of the components can be used to develop separation schemes.
Solid-liquid equilibrium systems are often characterized by high activity coefficients, the
formation of new intermolecular compounds between two SA or two MES molecules, and
components with significantly different molecular properties. The size and volume of the molecular
species, whether they be SA or MES crystallizing as single molecules or as multiple molecules that
form intermolecular compounds often differ significantly, resulting in large deviations from ideality.
2
Due to this non-ideal behavior, data for predicting activity coefficients are necessary to reduce
uncertainties in experimental design.
The most convenient method for predicting activity coefficient data is to use physically or
empirically derived models. Group contribution models such as UNIFAC and analytical solution of
groups (ASOG) have been used to predict VLE and SLE for components of similar size.[3,4,5]
Successful prediction of SLE from VLE for components containing similar groups and sizes has
been accomplished by adjusting the interaction of the structural groups on the activity coefficient
using the ASOG method.[6,7] The lack of a free volume contribution to the phase behavior of
liquid mixtures has limited the success of these models for mixtures with significant size differences
between components. The Wilson equation has been shown to model SLE when large differences
in size are present and group contribution methods are inadequate.[8,9,10]
SLE phase diagrams for a large number of binary systems other than those involving SA
and MES have been constructed using a new method employing DSC.[8,11] Construction of SLE
curves directly from DSC requires the mixture be immiscible in the solid phase. The SLE data
obtained from the DSC can then be used to calculate the activity coefficient of the SA and MES.
The Wilson and UNIFAC models have been used to adequately model SLE data obtained from
DSC[12] while others have investigated the UNIFAC and DISQUAC models on fitting SLE.[9,13,14]
A more detailed description of obtaining accurate SLE is given elsewhere.[15]
2 EXPERIMENTAL
2.1 Materials
Stearic acid 99% Aldrich (St. Louis, MO), MES 99% Aldrich, acetone 99% Fisher, acetic
acid glacial ACS grade 99.7% Fisher, 2-butanone certified reagent Fisher, and hexane were all
99% pure from Aldrich.
3
2.2 Methods
2.2.1 DSC Procedure
Samples were prepared by mixing components 1 and 2 at the desired concentration and
sealing them in vials. The vials were then placed in the oven to melt the sample and shaken to
ensure adequate mixing of the mixture. Vial contents were then allowed to cool completely before
opening the vial to limit the amount of solvent lost by evaporation. Samples were weighed into
aluminum hermetic DSC pans and hermetically sealed to prevent solvent from evaporating during
the analysis. Samples of ~5 mg provided an optimal combination of mass accuracy and response
to the instrument. The samples were analyzed by twice cycling the sample from a temperature
about 10°C above the melting point of the mixture to a temperature about 40°C below the melting
point of the mixture.
2.2.2 Method of Analysis
A TA Instruments (New Castle, DE) Q100 Series DSC with TA5000 Advantage Software
Suite provided transition temperatures and latent heats. The refrigerated cooling system provided
cooling and a 50 mL/min nitrogen purge preserved sample quality. A Denver Instrument A-200DS
balance was used to measure the mass of components added to the 5 mm diameter aluminum
hermetic pans. Measured masses had standard deviations of 0.094 mg.
2.2.3 SA and MES Activity Coefficient Procedure
Results for the freezing point depression were analyzed using the melting onset
temperature and extrapolating these results to a scan rate of zero. This procedure is described in
more detail in a previous paper[16] and by others.[9,17] The effect of different scan rates on the
melting point tangent line and how this can be extrapolated to a scan rate of 0°C/min is shown in
Figure 1. The extrapolated onset point was reported as the freezing point for purposes of
discussion and modeling. This improves the accuracy for determination of the melting points of the
4
samples. Activity coefficients were calculated using the classic freezing point depression equation
(1).[18]
γi =
− ∆H mi (Tmi − T )
1
(1)
exp
xi
RTmi T
where ∆Hmi is the molar heat of fusion of pure component i,Tmi is the absolute melting temperature
of pure component i, T is the absolute melting temperature of the mixture, and xi is the mole
fraction of component i.
2.2.4 Solvent Activity Coefficient Procedure
Activity coefficients for solvent were determined by placing 2 mL samples into 2 mL brass
capped tubes fitted with a Hamilton pressure gauge capable of reading pressure to the nearest 1.4
kPa (0.2 psi). The pressure gauge apparatus was placed into a pre-heated Fisher Isotemp® muffle
furnace. Samples were left in the oven for one hour to allow the temperature inside the pressure
gauge apparatus to reach equilibrium. Each composition was prepared at least twice and the
average vapor pressure used to calculate the activity coefficient. At least 10 samples were
prepared at mole compositions of less than 10 (mol)% solvent to obtain more data at near infinite
solvent dilution. Pressure readings were taken at two temperatures for each sample. Samples
with acetic acid, 2-butanone, and hexane were taken at 120°C and 140°C while samples with
acetone were taken at 100°C and 120°C. Activity coefficients were determined assuming activity
coefficients of one for MES and SA. This assumption provides for accurate estimates because all
the vapor pressure data was collected at high concentrations of MES and SA, where the activity
coefficients approximate one and because the vapor pressure of MES and SA are over two orders
of magnitude less than solvent. Vapor pressures were calculated from the total pressure reading,
allowing for calculation of solvent activity coefficients.
coefficients are about 0.1.
5
Standard deviations for the activity
2.2.5 Activity Coefficient Modeling
Experimental activity coefficients obtained from freezing point depression and vapor
pressure data were regressed using the Margules, NRTL, Wilson and UNIQUAC models.[19] The
Margules, NRTL, and Wilson were regressed in Excel through a least-squares algorithm, while
UNIQUAC was regressed using UNIFAC in ChemCad version 5.3.1.
3 RESULTS AND DISCUSSION
Activity coefficients for SA and MES were calculated from the SLE results obtained by
DSC. Solvent activity coefficients were calculated from VLE obtained through vapor pressure data.
The activity coefficient data were fit to the Margules, NRTL, UNIQUAC, and Wilson activity
coefficient models.
The models were then used to predict the activity coefficients of the
components to construct SLE curves.
SLE and VLE binary mixtures of SA and MES methyl stearate and stearic acid
(components 1) with solvents acetic acid, acetone, 2-butanone, and hexane were evaluated. All
solvents led to freezing point depression. For the more volatile solvents, it took considerable
experimental procedure development to prevent the solvent from evaporating from the small
sample sizes prior to measurement of the freezing point depression. DSC pans and lids were
tared on the balance together, the fatty acid derivative and solvent mixture were added to the
sample pan, and the lid immediately placed on top of the sample pan to prevent any evaporative
loss during the weighing process.
3.1 Activity of MES and SA
Activity coefficients for SA and MES at different compositions are provided in Figure 2.
The activity coefficients of SA and MES increase with decreasing compositions of the other
component, as expected. Activity coefficients increase at about the same rate for both SA and
MES, and the activity coefficients for SA are consistently higher than those for MES in the same
6
solvent. Activity coefficients for SA and MES at infinite dilution and at a composition of 50%mol are
provided in Table 1. The data at 50%mol were calculated from DSC measurements, and the
infinite dilution values were extrapolated from experimental data using the model that had the best
fit with the data. These data suggest that the carboxylic acid group of SA lead to greater positive
deviations from ideal behavior for the solvents of this study.
3.2 Activity of Solvents
Activity coefficients for the solvents at infinite dilution (extrapolated values from Wilson
equation) and at a composition of 50% mol are provided in Table 1. Table 2 contains the complete
set of activity coefficient as calculated from VLE experimental data.
The dipole moments of the solvents are: hexane = 0, acetic acid=1.7, acetone=2.88, and
2-butanone=2.78 debye.[20] Stearic acid has a dipole moment of 1.76 debye, while the value for
MES is based on extrapolated values from lower molecular weight fatty acids and methyl esters
(e.g., hexanoic acid at 1.13 debye and methyl hexanoate at 1.7 debye), the dipole moment of MES
is about 1.99 debye. The dipole moment of MES is closer to that of acetic acid and acetone which
explains the lower activity coefficients of these solvents in the MES binaries relative to the SA
binaries. The dipole moment of stearic acid is smaller than that of MES and therefore closer to that
of hexaneand explains the lower activity coefficient of SA in hexane compared with MES in
hexane. The high activity coefficients of acetic acid in the SA and MES is not fully understood, but
could be caused by the fact that acetic acid has a greater density than the other solvents.
Also, the impact of local compositions is believed to impact the data. Stearic acid and
MES are known to crystallize with their polar groups aligned, so if the solvent molecules are
preferentially attracted to the polar groups, greater localized solvent concentrations different from
the bulk concentration will impact the SLE data.
Acetic acid showed the highest activity
coefficients of all the solvents with infinite dilution activity coefficients in excess of 4. However,
7
even at 50mol%, the activity coefficients of acetic acid were about 1.2 for both systems. This
relatively low activity coefficient could be explained by the like-like interactions of acetic acid next to
the carboxylate group (or methyl ester group) of the SA and MES. At higher concentrations of
acetic acid, the like-dislike interactions of the acid group with the aliphatic tails of the SA and MES
leads to much higher activity coefficients. The large size and complexity of the SA and MES leads
to interactions that tend to be a strong function of composition.
3.3 Activity Coefficient Modeling
Binary interaction parameters were calculated for the Margules, NRTL, and Wilson models
based on the activity coefficients obtained from VLE data and are summarized in Table 3.
Experimental solvent activity coefficient data used for model fitting are summarized in Table 2.
Figure 3 shows the four models fit to the SA/acetone system and represents the fit obtained for the
other seven binary pairs. The models fit the data for the activity coefficients of solvent well, but
could not accurately model the activity coefficients for SA and MES.
UNIQUAC regression using ChemCad tended to underestimate the activity coefficient of
both components, giving activity coefficients less than one. UNIQUAC has difficulties modeling the
phase behavior of two components with such large differences in size and physical properties
using group contribution methods.
One of the greatest limitations is caused by the difference in polarity for SA and MES
between the solid and liquid phases. Stearic acid[21] and methyl stearate[22] crystallize as dimers
by forming hydrogen bonds in the case of stearic acid and the interaction of the polar ester groups
in methyl stearate. This makes the molecules larger in the solid state, resulting in decreased
polarity for the dimers because the polar groups are protected by the long aliphatic chain of the
fatty acid. A small molecule such as acetic acid can disrupt the crystallization process more than a
larger molecule. Such a large difference in apparent size and polarity of the molecules between
8
the solid and liquid states accounts for the discrepancy when attempting to model activity
coefficients.
Activity coefficients of SA and MES are close to one, except at near infinite dilutions where
they increase slightly. This poses a problem when modeling because these commonly used
models are not effective at fitting data with high activity coefficients for one component with an
activity coefficient near one for the other component over most of the composition range. This is
due to the mathematical limitations of the models and does not allow these models to fit data with
great differences in activity coefficients.
To better understand the difficulties encountered in modeling the data the thermodynamic
consistency of the data was evaluated using the Gibbs/Duhem equation. For a binary system the
Gibbs/Duhem equation reduces to
x1
d ln γ 1
d ln γ 2
+ x2
= 0.
dx1
dx1
Rearranging the equation yields:
d ln γ 2
x d ln γ 1
=− 1
dx1
x 2 dx1
The slope of the ln γ1 curve at every composition is of opposite sign to the slope of the ln
γ2 curve. For the case when two components are present in equal amounts, the slopes of the two
curves will have the same slope, but opposite sign. This explains why the models have a difficult
time fitting data from binary mixtures when one component has high activity coefficients and the
other component has relatively low activity coefficients close to one. The inability of the activity
coefficient models to accurately fit SA and MES data does not adversely impact the predicted SLE,
and will be discussed later.
9
For these binary systems, the Gibb's/Duhem equation will not allow the activity coefficient
of both components to simultaneously decrease or increase. This creates a modeling problem
when a SA and MES has an activity coefficient < 1.0 over some composition range while the
solvent always has an activity coefficient >1.0. Further discussion on this topic is provided after a
discussion of the solid-liquid equilibrium and the certainty of the activity coefficients obtained from
that data.
3.4 Freezing Point Depression
All of the solvents depressed the freezing points of SA and MES. The melting point is
interpreted as the intercept of the inflection tangent with the base line. For example, the freezing
point of stearic acid is 66.98°C. Table 1 summarizes the freezing point depressions for 50%mol
SA and MES in solvent. The greatest impact on freezing point depression was observed for
solvents in MES. Figure 4 shows the effect of different solvents on the decrease in melting point
for SA.
Acetone caused the least freezing point depression while maintaining the sharpest DSC
peak. Solvents with the greatest impact on freezing point depression tended to broaden the DSC
peak the most. Acetic acid caused the greatest freezing point depression as well as broadening of
the endotherm peak.
The two endotherms (two peaks) for the acetic acid system of Figure 4 provide evidence
that acetic acid is interacting directly with the acid group in the solid matrix. Different crystalline
structures of the hetero-atom groups in a TG derivative are typically a source of polymorphism.
Sato has measure three polymorphs and two polytypes for stearic acid in n-hexane, with the least
soluble form being favored at temperatures above 23°C.[23]
This explains why only one
endotherm is present when hexane is used as the solvent. Methyl stearate is also known to be
10
polymorphous with the transition temperatures being so close together that it is nearly impossible
to distinguish the two from each other using a DSC.[24]
The DSC scans highlight an important aspect of SLE for large molecules; namely, complex
molecules can undergo polymorphism with different parts of the large molecule responding
differently to changing environments (e.g. a changing solvent matrix). While the SA and MESsolvent systems are binary systems, certain aspects of the phase behavior are more consistent
with a ternary systems. Specifically, the ability of a solvent to interact differently with the
heteroatom groups of the SA and MES as compared to the aliphatic chain.
In these systems, VLE (especially the smaller molecules) tends to behave like a binary
system. However, the SLE (especially the larger molecule solid phases) tends to behave like
ternary systems due to polymorphism, differences in polarity between the solid and liquid phases,
and large differences in size that result in localized concentration of the polar solvents near the
polar end of the SA and MES. It is this complex behavior of the solid phase that makes
interpretation of the data difficult and makes interpretation of the Gibbs/Duhem equation less than
straight forward.
The actual activity coefficients (as opposed to those calculated from freezing point
depression) are believed to be consistent with the Gibbs/Duhem equation. At least part of the
freezing point depressions reported in Table 1 are due to a modification of the solid structure due
to incorporation of the solvent into the solid matrix (as evidenced by the different shapes of the
DSC peaks of Figure 4). In the calculation of the activity coefficients of Figure 2, the freezing point
depression was incorrectly interpreted as a solution phenomenon when it was actually a solid-state
phenomenon.
11
3.5 SLE Phase Diagrams
VLE data were obtained and modeled for binary systems to determine if these systems
follow freezing point depression theory (equation 1) and to better understand how VLE data can be
used to predict freezing point depression.
Figure 5 summarizes the SLE for the SA / acetone system. The model curves of Figure 5
are constructed using activity coefficients obtained from their respective model.
Standard
deviations for the temperature in the T-x diagram arising from errors in activity coefficient
measurements are about 0.5°C. At a standard deviation of +/-0.21ºC for DSC measurements, the
data have a standard deviation far less than their variance from the model prediction. The
UNIQUAC model fits the solid/liquid equilibrium data very well, however, the activity coefficients
predicted by the model are not physically possible, as there should be no maximum or minimum in
the activity coefficient curves.
UNIQUAC did not predict the correct solid/liquid equilibrium for the other binary systems,
and provided a prediction between those of the ideal prediction that of the other three models
(Margules, NRTL, and Wilson). Use of the Margules, NRTL, and Wilson activity coefficient models
improved accuracy of SLE calculations over ideal behavior.
The UNIQUAC model predicts activity coefficients less than one, predicting that the
temperature at which pure SA and MES begins to freeze out of solution is less than that predicted
for the ideal case. The experimental data and models are above the temperature predicted using
ideal freezing point depression theory because the activity coefficients are greater than unity. For
mixtures containing more than about 5% mol SA and MES, corresponding to the eutectic
composition, freezing point depression is only influenced by the activity coefficient of SA and MES.
As long as the concentration range of interest is with a mole concentration of more than this
composition, it is only necessary to obtain activity coefficients of the SA and MES. Therefore,
12
increases in the activity coefficients of SA and MES increase the freezing point and the activity
coefficient of the solvent does not directly impact the freezing point. Mixtures composed of
components with similar functional groups have lower activity coefficients (in this case, close to 1)
and provide the greatest freezing point depression.
3.6 Mixtures with Larger Molecules
The DSC of Figure 6 summarizes the solid-liquid transition for a mixture of 70wt.% MES
and citric acid as compared to these pure components. Whereas all the solvents provides a
freezing point depression, this mixture of two larger molecules provided no freezing point
depression.
This behavior is consistent with a mechanism of freezing point depression for SA and MES
where localized interaction of a small molecule on a TG derivative leads to a substantially different
SLE transition. Two larger molecules are less susceptible to this type of behavior and thus have a
greater tendency to have substantially separate freezing phenomenon.
3.7 Application of Freezing Point Depression
Modeling of activity coefficient data provides insight into trends and can be used as an
effective tool to screen possible solvents for use in determining the solvent and quantity required to
obtain a certain freezing point depression. This allows a single SA and MES to meet a range of
PCM temperature requirements, and more importantly, the amount of solvent required to achieve
the desired operating temperature.
4 CONCLUSION
Freezing point depression can be achieved by mixing solvents with SA and MES. DSC of
the melt transition indicate that the freezing point depression is due in part to incorporation of the
solvent into the solid matrix leading to a solid that has a lower freezing point. The activity
coefficients of the SA and MES in solution are greater than 1.0, and it can be difficult to achieve
significant freezing point depression without selecting solvents that actually modify the solid
13
crystalline structure.
This is especially the case for mixtures with larger molecules where
substantial similarity in molecular structure is needed to provide freezing point depression.
The Margules, NRTL, and Wilson activity coefficient models fit data for the solvent activity
coefficients well, while the UNIQUAC model could not accurately predict activity coefficients.
Because of the difficulty of distinguishing between “solution” and “solid-state” phenomena for
mixtures with SA and MES, activity coefficients calculated from depressions in freezing points may
readily be lower than the actually activity coefficients of the SA and MES in solution. Inaccuracies
in the calculation of the activity coefficients can lead to erroneous interpretations that the
Gibbs/Duhem equation is being violated.
Despite questions on the fundamental interpretation of the data, modeling the activity
coefficients for the solvent is sufficient to approximate the effect the solvent will have on the
depression. Relatively simple experiments following the total pressure of mixtures as a function of
composition and temperature can be used to obtain activity coefficient model parameters.
14
List of Figures
Figure 1. Effect of different scan rates on the melting tangent point. .............................................16
Figure 2. Activity coefficients of SA and MES (component 1) in solvent at the melting point of the
mixture....................................................................................................................................17
Figure 3. Modeling of activity coefficient data for SA/Acetone system at 140°C. ...........................18
Figure 4. Freezing point depression of 85%wt. SA in solvent. .......................................................19
Figure 5 Solid-Liquid equilibrium for SA/Acetone. ..........................................................................20
15
List of Tables
Table 1. Freezing depression for 50%mol SA and MES (component 1) and activity coefficients...22
Table 2. Activity coefficient data of solvents (component 2) at 120°C for acetone systems and
140°C for all others. ...............................................................................................................23
Table 3. Model parameters. ...........................................................................................................24
4
25.82°C
140.0J/g
3
2 C/min
31.57°C
Heat Flow (W/g)
2
25.16°C
147.9J/g
5 C/min
1
0
31.94°C
10 C/min
24.73°C
148.4J/g
-1
-2
-3
32.59°C
-4
Exo Up
0
10
20
30
Temperature (°C)
Figure 1. Effect of different scan rates on the melting tangent point.
16
40
50
Universal V3.1E TA Instruments
2.0
Activity Coefficient
MES/AA
MES/ACE
1.5
MES/HEX
MES/MEK
1.0
SA/AA
SA/ACE
SA/HEX
0.5
0.0
0.00
SA/MEK
0.20
0.40
0.60
0.80
1.00
x (Mol Fraction Component 1)
Figure 2. Activity coefficients of SA and MES (component 1) in solvent at the melting point
of the mixture.
17
Margules
Wilson
NRTL
UNIQUAC
Comp. 1 Exp.
Comp. 2 Exp.
3.0
Activity Coefficient
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
SA (mol %)
Figure 3. Modeling of activity coefficient data for SA/Acetone system at 140°C.
18
7
50mol% SA/Acetic Acid
6
53.48°C
162.3J/g
5
60.61°C
4
50mol% SA/Acetone
60.37°C
180.5J/g
3
Heat Flow (W/g)
2
65.28°C
50mol% SA/2-Butanone
1
60.97°C
176.0J/g
0
66.35°C
50mol% SA/Hexane
-1
61.04°C
220.4J/g
-2
66.37°C
-3
Stearic Acid
66.98°C
214.6J/g
-4
-5
-6
69.12°C
-7
Exo Up
0
20
40
60
Temperature (°C)
Figure 4. Freezing point depression of 85%wt. SA in solvent.
19
80
100
Universal V4.0C TA Instruments
70
T (C)
60
Ideal
50
Margules
Wilson
40
NRTL
UNIQUAC
30
Experimental
20
0
0.2
0.4
0.6
0.8
1
SA (mol %)
Figure 5 Solid-Liquid Equilibrium Predicted and Experimental Values for SA/Acetone.
20
Sample: BK3P287E
Size: 3.6700 mg
Method: Cyclic
Comment: 70% MES/Citric Acid
File: C:\DSC\Jan '04\013004.001
Operator: M. Goff
Run Date: 30-Jan-2004 16:08
Instrument: DSC Q100 V6.19 Build 227
DSC
8
34.04°C
6
Heat Flow (W/g)
4
2
168.3J/g
0
36.81°C
169.4J/g
-2
38.18°C
-4
Exo Up
0
10
20
30
Temperature (°C)
Figure 6. Mixture of 70wt.% MES/Citric Acid.
21
40
50
60
Universal V4.0C TA Instruments
Table 1. Freezing depression for 50%mol SA and MES (component 1) and activity
coefficients.
x1 Mole
Component 1 Component 2 Fraction
MES
SA
Freezing
x1 Volume Depression
Fraction
γ1
T (C)
∞
∞
γ2
γ1
0.5
γ2
0.5
Acetic Acid
Acetone
0.50
0.51
0.87
0.83
12.47
7.85
1.69
1.47
4.94
1.65
0.70
1.03
1.06
1.00
2-Butanone
Hexane
Acetic Acid
Acetone
2-Butanone
Hexane
0.50
0.50
0.50
0.50
0.50
0.50
0.83
0.73
0.85
0.82
0.77
0.70
10.54
10.28
12.24
6.35
8.96
9.02
1.47
1.84
1.84
1.36
1.79
1.82
2.43
2.63
4.36
2.14
2.58
2.64
0.90
0.93
0.84
1.25
1.11
1.10
1.07
1.09
1.06
1.01
1.07
1.07
22
Table 2. Activity coefficient data of solvents (component 2) at 120°C for acetone systems
and 140°C for all others.
MES/Acetic Acid
γ2
x1 mol
0.00
0.05
0.05
0.12
0.23
0.44
0.80
0.82
0.94
0.95
0.97
MES/Acetone
γ2
x1 mol
1.00
1.06
1.06
1.11
1.17
1.18
1.79
1.97
3.67
4.02
3.83
SA/Acetic Acid
γ2
x1 mol
0.00
0.16
0.33
0.58
0.85
0.85
0.88
0.89
0.92
0.93
0.94
0.95
0.00
0.44
0.43
0.86
0.90
0.90
0.91
0.93
0.95
0.95
MES/2-Butanone
γ2
x1 mol
1.00
1.00
1.08
1.23
1.26
1.28
1.30
1.27
1.26
1.21
SA/Acetone
γ2
x1 mol
1.00
1.04
1.11
1.26
1.45
1.48
2.35
2.21
3.60
3.19
3.78
3.16
0.00
0.21
0.45
0.75
0.81
0.85
0.91
0.91
0.94
0.95
0.97
0.99
0.00
0.30
0.53
0.53
0.80
0.84
0.90
0.94
0.95
0.95
0.97
MES/Hexane
γ2
x1 mol
1.00
1.02
1.16
1.04
1.62
1.80
1.86
1.81
1.89
1.90
2.10
SA/2-Butanone
γ2
x1 mol
1.00
1.09
1.16
1.22
1.19
1.30
1.33
1.57
1.65
1.48
1.87
1.98
0.00
0.54
0.70
0.88
0.89
0.93
0.93
0.93
0.95
0.95
23
0.00
0.58
0.64
0.70
0.76
0.80
0.84
0.93
0.94
0.94
0.95
0.96
1.00
1.01
1.07
1.14
1.22
1.32
1.44
1.51
1.60
1.97
2.88
2.81
SA/Hexane
γ2
x1 mol
1.00
1.00
1.01
1.03
1.26
1.33
1.55
1.62
2.36
1.69
0.00
0.59
0.85
0.89
0.91
0.92
0.93
0.95
0.95
0.96
0.98
0.99
1.00
1.01
1.97
2.28
2.27
2.01
2.08
2.10
2.36
2.42
2.91
3.06
Table 3. Model parameters.
MES/
MES/
MES/
MES/
Model
Acetic Acid Acetone 2-butanone Hexane
Margules
A12
0.83
0.26
0.39
0.46
A21
Wilson
λ12
λ21
NRTL
δg12
δg21
α12
1.49
0.34
0.86
0.80
5032
476
2100
1900
3058
311
3329
215
4461
673
2643
2719
1084
447
437
874
0.70
1.20
0.55
1.47
SA/
SA/
SA/
SA/
Model
Acetic Acid Acetone 2-butanone Hexane
Margules
A12
0.73
0.54
0.61
1.10
A21
Wilson
λ12
λ21
NRTL
δg12
δg21
α12
1.24
0.63
0.89
1.00
3974
2041
2537
1628
3034
503
2748
1797
4258
2106
2778
3058
1394
935
602
1483
1.36
2.3
1.32
0.92
24
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25