Indirect Analysis of a Homogeneous Ternary Mixture - ACS Publications

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Indirect Analysis of a Homogeneous Ternary Mixture Cristina-Silvia Stoicescu and Gabriel Munteanu* “Ilie Murgulescu” Institute of Physical Chemistry, 202 Splaiul Independentei Street, P.O. Box 12-194, 060021 Bucharest, Romania S Supporting Information *

ABSTRACT: When there is a saturated homogeneous ternary mixture, composed by two immiscible liquids and an amphiphilic one, it is possible to prepare a second one starting from the first. The compositions of the two mixtures are uniquely determined if their solubility curve is known. In this work, one describes a new procedure to determine these compositions. The procedure is applied to a ternary system known in literature: water + n-propanol + n-butanol at 294.15 K and atmospheric pressure. Comparing the results obtained by the new procedure to those determined by measuring the refractive index one concludes that the two analysis methods have similar accuracies.

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INTRODUCTION

has to be analyzed is rich in liquid 1, the second SHTM can be prepared in one of the following ways: (A) One adds a small amount from the liquid 3, making the mixture heterogeneous; one then adds liquid 2 with stirring, little by little, until the turbidity desappearsthe cloud point method.11 (B) One adds a small amount from the amphiphilic liquid 2 obtaining in this way an unsuturated homogeneous mixture; one then adds liquid 3 with stirring, little by little, until the mixture becames turbid. In both cases, component 1 remains unchanged, with only components 2 and 3 being changed in a known way; see Figure 1a and b. Many years ago Smith9 elaborated a method to evaluate the compositions of the two SHTMs. He considered that all the compositions corresponding to the solubility curve satisfy an equation of the type

1

In the LLE studies of the type I ternary mixtures composed by two imiscible liquids and an amphiphilic one, the binodal curve and tie lines have to be determined. To determine tie lines, one prepares several heterogeneous ternary mixtures that, after a vigurous stirring, are allowed to separate into pairs of saturated homogeneous mixtures. After analyzing these mixtures, one computes the distribution coefficients and separation factors or one correlates the experimental data with the theoretical models like NRTL or UNIQUAC.2,3 In many cases, the analysis of these mixtures is performed directly, usually by gas chromatography.4,5 In some cases, the analysis is performed measuring a physical property of the binodal mixtures that depends on composition. One can determine the density,6,7 viscosity7,8 or refractive index.6,8 The compositions of the binodal mixtures are determined knowing the corresponding calibration curves, that is, the dependence of the physical property on the concentration of the imiscible liquids in the saturated homogeneous ternary mixtures. From the above, we conclude that the determination of a calibration curve practically implies the knowledge of the solubility curve. However, this knowledge is enough to determine9,10 the composition of a saturated homogeneous ternary mixture (SHTM). To do this, it is enough to prepare a second SHTM starting from the SHTM that must be analyzed. In case that the ternary mixture is composed by two imiscible liquids, 1 and 3, and an amphiphilic one, 2, and the SHTM that © 2016 American Chemical Society

⎛w ⎞ ⎛ w2 ⎞α ⎜ ⎟ = K·⎜ 1 ⎟ ⎝ w1 ⎠ ⎝ w3 ⎠

(1)

In eq 1, α and K are constants, w1 and w3 being the mass fractions of the two immiscible liquids and w2 the mass fraction of the amphiphilic liquid. Taking into account the fact that in Received: December 2, 2015 Accepted: July 12, 2016 Published: July 22, 2016 2954

DOI: 10.1021/acs.jced.5b01024 J. Chem. Eng. Data 2016, 61, 2954−2959

Journal of Chemical & Engineering Data

Article

Figure 1. Preparation of a second SHTM starting from a given one, B, rich in liquid 1. (a) Preparing first a heterogeneous mixture, S, by adding of small amount of liquid 3; the second SHTM, Q, is obtained adding 2 with stirring, drop by drop, until the turbidity disappears. (b) Preparing first an unsaturated homogeneous mixture, T, by adding a small amount of liquid 2; the second SHTM, Q, is obtained adding 3, drop by drop, until the mixture becomes turbid.

temperature determining then their compositions by the new analysis procedure. We shall compute then the values of Hand’s coefficients14 and we shall compare these values to those already known.13 In this way, we shall be able to appreciate the accuracy of this new analysis method. To more accurately assess the errors, the binodal mixtures will be also analyzed by measuring their refractive indexes. Finally, we shall compare the compositions determined in the two ways.

the procedure of the preparation of the new SHTM, one component remains unchanged, the other two being modified in a known way, one obtains two algebraic equations that allow determination of the unknown components. The method is simple but has significant errors because eq 1 does not fit well a real solubility curve. Another method that uses the same experimental procedure (A, in the above) and has a very good theoretical basis has been elaborated by Newsham and Ng.10 Taking into account the connection between the material balance and metrical relationships in the ternary phase diagram (see Figure 1a)

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EXPERIMENTAL SECTION Chemicals. n-Butanol and n-propanol were supplied by Merck and were used without further purification; see Table 1. Bidistilled water was used in all the experiments, its electrical conductivity, measured with a CDM230 conductivity meter, being of 2 μS/cm.

S3 m = B3 (m + m 3) and m2 SQ = Q2 (m + m 3)

Table 1. Sample Description (2) chemical name

they elaborated an ingenious graphical method to determine the point S, that corresponds to the heterogeneous mixture. After that, B is immediately determined together with its corresponding composition. In eq 2, m is the mass of the homogeneous saturated mixture, B, m3 is the mass of the immiscible liquid 3 added to obtain the heterogeneous mixture, S and m2 is the mass of the amphiphilic liquid added to obtain the new homogeneous saturated mixture, Q. Although the method is laborious, Newsham and Ng obtained good results in the analysis of the binodal mixtures of the water−n-butanol−npropanol system at various temperatures.10 In this work, we shall show that having a SHTM and preparing a second one by using the way A, described above, the compositions of the two mixtures are uniquely determined if their solubility curve is known. Although the second SHTM can be prepared, as we showed above in two different ways, in our study, we shall use the experimental procedure used both by Smith and by Newsham and Ng. In this work, we will show by using a new algorithm that any of the three points, B, Q, and S (see Figure 1a), can be determined in a fast and accurate way. Although the new analysis procedure can be applied to any ternary system, in our exemplification we shall apply it to a well-known10,12,13 system: water−n-butanol−n-propanol. The solubility curve of this system at 294.15 K is known.12,13 Due to this fact, we shall prepare only several binodal mixtures at this

1propanol 1-butanol water a

final mole fraction purity

source

initial mole fraction purity

Merck

0.995

none

GCa

Merck

0.995

none double distilation

GCa CMb

purification method

>0.9999

analysis method

Gas chromatography. bConductivity measurements.

Apparatus and Procedure. The heterogeneous mixtures that were used to obtain the binodal compositions have been prepared by weighing, using a cell (about 40 cm3) equipped with an isothermal fluid jacketed vessel to keep the temperature constant. The temperature was measured with an accuracy of ±0.1 K, the masses being weighed with ±0.1 mg accuracy. Each of these mixtures was stirred for 1 h under isothermal conditions and set for around 24 h at constant temperature to separate into binodal mixtures. Three heterogeneous mixtures were prepared, keeping the ratio of alcohol/water constant. The refractive index was measured with an Anton Paar (Abbemat RXA 170) refractometer, with the temperature being kept constant during measurements: 294.15 K. To determine the calibration curve, there were prepared six ternary compositions lying on the binodal curve established before.12,13 2955



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THEORETICAL According to those described above starting from B with a mass m, adding then a mass m3 of the liquid 3 and finally a mass m2 of the liquid 2 one obtains the point Q, located also on the binodal curve. Denoting the compositions of B and Q with w1B, w2B, w3B and w1Q, w2Q, w3Q, respectively, we have the following relationships: w ·m w1Q = 1B Σm w ·m + m2 w2Q = 2B Σm w3B·m + m3 w3Q = (3) Σm

curve that is the locus of the points corresponding to those located on the binodal curve between M and E. As can be seen in Figure 2, this curve crosses the binodal curve in Q. Knowing the location of this point, one can evaluate its composition: w1Q, w2Q, w3Q. Finally from eq 2, we have w1B = w2B = w3B =

w1Q ·∑ m m w2Q ·∑ m − m2 m w3Q ·∑ m − m3 m

(4)

that is, the composition of the mass m (as well as the location of B). According to those presented above, both B and Q are uniquely located on the solubility curve. The point S is also uniquely located. The description of the complementary algorithms used to locate B and S is available in Supporting Information.

where Σm means m + m2 + m3. Similar relationships are obtained when we start from a mass m rich in liquid 3. The composition of the mass m is not known. We only know that point B is located on the binodal curve and that preparing the Q mixture, in the way described above, Q is located on the binodal curve too. The location of B can be randomly chosen on the binodal curve. This means to choose randomly the composition for the mass m (in agreement with the location of B). Using eq 2, one can compute which would have to be the composition of the resulting mixture if we add a mass m3 of the liquid 3 and m2 of the liquid 2. One must remark that this point, Q, corresponding to this mixture is located on the binodal curve only if the location of the point B was correctly chosen. Otherwise its location is either below or above the binodal curve. For example, if we choose as the location of the point B one of the extreme points of the binodal curve, either M, the lowest point on the binodal curve, or F, the highest point on the binodal curve, the corresponding points, computed by eq 2, are N or F, respectively. In Figure 2, one can see that N is located below the binodal curve and F above it. Choosing several points located on the binodal curve, between M and E, we determine, by eq 2, their corresponding points, located between N and F. These points determine a

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ERRORS In the estimation of the errors, we would have to consider all of the experimental errors inherent both in determining the binodal curve as well as those specific to this method. We would have to take into account the errors due to weighing, volume measurements, evaporation, and titration. In the following, we will consider only the errors due to procedures involved in this method. More exactly, we shall consider the errors of titration as well as those made in graphical estimation of the concentrations, which correspond to a point from the ternary phase diagram. In titration, the error in measuring the propanol volume is ±0.05 mL, that is, the error in determining m2 is δm = ±0.04 g. The values of w1Q, w2Q, w3Q are also evaluated with errors. They are graphicaly evaluated in the ternary phase diagram. The error in location of a point on paper is ±0.5 mm. Because the ternary phase diagram usually is plotted on A4 paper size, the side of the triangle being 20 cm, the errors in determining wiQ, i = 1, 2, 3, are 0.0025. Taking into account the usual values of m, m2, and m3 as well as the errors mentioned above we determined that the standard uncertainties of u(wi), i = 1, 2, 3, are 0.0035.

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RESULTS AND DISCUSSION Water−n-Propanol−n-Butanol System at 294.15 K and Atmospheric Pressure. The binodal curve for water−nbutanol−n-propanol system at 294.15 K was determined before.12,13 Following the procedure described above, we prepared, by weighing, four heterogeneous water−n-butanol− n-propanol mixtures. Their compositions are given in Table 2. Each of these mixtures has been kept at 294.15 K for 24 h. In these conditions, there were obtained, for each mixture, two very clear separated phases: one water-rich and one butanolrich. From each phase, 5 mL was taken and these were put into the cell and then weighed. Depending on whether the phase is water-rich or butanol-rich, either 1 mL of butanol or 1 mL of water was added into the cell. After weighing the cell, it was again connected to thermostat. After fixing the temperature at 294.15 K, n-propanol was added drop by drop, under continuous stirring, until the turbidity disappeared. In other

Figure 2. Graphical determination of the point Q: moving B along the solubility curve one determine the locus, NF, of the points computed by eq 2. The curve NF crosses the solubility curve in Q. 2956



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Table 2. Mass Fractions of the Heterogeneous Mixtures at 294.15 K and 101325 Pa: w1, Water, w2, n-Propanol, w3, nButanola w1

w2

w3

0.5286 0.4952 0.4618

0.1121 0.1682 0.2243

0.3593 0.3366 0.3139

a

The standard uncertainties are u(T) = 0.05 K, u(p) = 10 kPa, u(w) = 0.0001.

words, starting from point B, located on the binodal curve, we obtained the point Q, located also on the binodal curve. In Table 3, we present the masses added to the homogeneous phases to obtain new homogeneous mixtures. Table 3. Masses Added to the Homogeneous Phases to Obtain New Homogeneous Mixtures at 294.15 K and 101325 Pa: Aq. Ph., Aqueous Phase, Alc. Ph., Alcoholic Phasea aq. ph.

butanol

propanol

alc. ph.

water

propanol

4.851 4.802 4.750

0.812 0.815 0.806

1.124 1.007 0.901

4.264 4.296 4.349

0.996 0.998 1.013

1.000 0.762 0.535

Figure 3. Heterogeneous mixtures, the solubility curve, and tie lines.

Testing the above values in connection with their consistency, that is, determining the values of a and b coefficients from the Hand14 equation ⎛w ⎞ ⎛w ⎞ ln⎜ 23 ⎟ = a + b·ln⎜ 21 ⎟ ⎝ w11 ⎠ ⎝ w33 ⎠

a

Standard uncertainties are u(T) = 0.05 K, u(p) = 10 kPa, u(m) = 0.0001 g.

we found a = 1.517 and b = 1.898 (with a correlation coefficient r = 0.988) values which are very close to those determined before:13 a = 1.499 and b = 1.904. In eq 5, we denoted by w23 and w33 the content of n-propanol and n-butanol respectively in the alcoholic phase. Similarly, we denoted by w21 and w11 the content of n-propanol and water, respectively, in the aqueous phase. The two pairs of Hand coefficients were obtained using two series of LLE data determined by two different analysis methods of the binodal mixtures. The fact that the values of these coefficients are very close means that the two analysis methods have similar accuracies, that both methods give good results. LLE literature data for the system water−n-propanol− n-butanol at various temperatures and atmospheric pressure is availabe in Supporting Information. Refractive Index Measurements. To confirm the validity of the results obtained by the new procedure, we evaluated the compositions of the binodal mixtures by measuring their refractive indexes. The calibration curves were determined measuring the refractive indexes of six SHTMs. The values of the mass fractions of these saturated homogeneous ternary mixtures together with their measured refractive indexes are shown in Table 6. There were also measured the refractive

Following the procedure suggested in Figure 2, we determined the corresponding Q points. Their corresponding compositions are given in Table 4. Table 4. Mass Fractions of the Q Points at 294.15 K and 101325 Pa: w1, Water; w2, n-Propanol; w3, n-Butanola w1

w2

w3

0.6150 0.5800 0.5550 0.4125 0.3550 0.3175

0.2275 0.2425 0.2525 0.2800 0.2700 0.2500

0.1575 0.1775 0.1925 0.3075 0.3750 0.4325

(5)

a

The standard uncertainties are u(T) = 0.05 K, u(p) = 10 kPa, u(wi) = 0.0025.

Knowing the compositions of the Q points and using the relationships in eq 4, we determined the compositions of the binodal phases, shown in Table 5. All these results are presented in Figure 3.

Table 6. Mass Fractions of the SHTMs Used To Establish the Calibration Curves and the Refractive Indexes, nD, of These SHTMs Measured at 294.15 K and 101325 Paa

Table 5. Mass Fractions of the Binodal Phases at 294.15 K and 101325 Pa: w1, Water; w2, n-Propanol; w3, n-Butanola w1

w2

w3

w1

w2

w3

nD

0.860 0.800 0.754 0.326 0.268 0.232

0.087 0.125 0.154 0.257 0.203 0.132

0.053 0.075 0.092 0.417 0.529 0.635

0.8494 0.7350 0.3648 0.2840 0.2382 0.2063

0.0936 0.1645 0.2727 0.2225 0.1459 0.0361

0.0570 0.1005 0.3625 0.4935 0.6159 0.7576

1.346934 1.355307 1.376892 1.382232 1.386174 1.389408

a

a

The standard uncertainties are u(T) = 0.05 K, u(p) = 10 kPa, u(wi) = 0.0035

The standard uncertainties are u(T) = 0.03 K, u(p) = 10 kPa, u(wi) = 0.0001, u(nD) = 0.00004.

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(i.) The mass fractions of water and n-butanol were evaluated with some errors because we considered that the refractive index linearly depends on both mass fractions. (ii.) The n-propanol mass fraction is computed according to the assumption that w1 + w2 + w3 = 1, and due to this fact, the values of w2 have cumulated both errors, of w1 and w3. Computing the distribution coefficients of n-propanol, using data both from Table 5 as well as from Table 7, one obtained the results presented in Figure 5. In spite of those mentioned

indexes of the three constituent liquids: nwater = 1.33285, npropanol = 1.38460 and nbutanol = 1.39782. All of the measurements were performed at 294.15 K and 101325 Pa. The above values of the refractive indexes were plotted as functions of the mass fractions of water, w1, and n-butanol, w3 (see Figure 4), obtaining in this way the calibration curves.

Figure 5. Distribution coefficients of n-propanol vs w21 computed using data from Tables 5 and 7. Figure 4. Calibration curves: refractive index, nD, as functions of w1, water mass fraction, and w2, n-butanol mass fraction.

above, we note that the values of the two series of distribution coefficients are similar. One can say that the values of the mass fractions presented in both tables characterize well the studied system. Consequently, one concludes that the two analysis methods have close accuracies. Refractive index measurements for the system water−n-propanol−n-butanol at various temperatures and atmospheric pressure−literature data is available in Supporting Information.

After measuring the refractive indexes of those six binodal mixtures the mass fractions of water and n-butanol have been determined. One considered that between two consecutive values of the mass fractions used for calibration the refractive index linearly depends on the mass fraction. The mass fraction of n-propanol was calculated taking into account that w1 + w2 + w3 = 1. The values of the refractive indexes of those six binodal mixtures as well as the corresponding mass fractions of the three constituent liquids are shown in Table 7.

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CONCLUSIONS Having a SHTM, composed by two immiscible liquids and an amphiphilic one, and knowing its solubility curve one can prepare a second SHTM. Both mixtures are uniquely located on the solubility curve. The locations of both mixtures are determined by a fast and accurate procedure, determining in this way the compositions of both mixtures. The accuracy of this indirect analysis method is similar to that of the determinations by measuring the refractive index. In other words, one can say that a saturated homogeneous ternary mixture, composed by two immiscible liquids and an amphiphilic one, can be accurately analyzed knowing only its solubility curve.

Table 7. Refractive Indexes, nD, of the Binodal Phases and the Determined Mass Fractions of the Constituent Liquids at 294.15 K and 101325 Pa: w1, Water; w2, n-Propanol; w3, nButanola nD

w1

w2

w3

1.34579 1.35079 1.35401 1.37923 1.38286 1.38663

0.862 0.791 0.753 0.330 0.276 0.234

0.085 0.132 0.153 0.251 0.211 0.131

0.053 0.077 0.094 0.419 0.513 0.635

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a

The standard uncertainties are u(T) = 0.03 K, u(p) = 10 kPa, u(nD) = 0.00004, u(w) = 0.001

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b01024. Algorithms for determining points B and S, LLE literature data for the water−n-propanol−n-butanol system at 294.14 K and atmospheric pressure, refractive index measurements literature data for water−n-propanol−n-butanol system, and additional references. (PDF)

Comparing Tables 5 and 7, it is possible to note that the differences between the values of the water mass fractions are below 1%. In the case of the n-butanol mass fractions, the differences vary between 2 and 3% in water-rich mixtures, being below 1% in n-butanol-rich mixtures. The differences are important in the case of n-propanol mass fractions, especially for the water-rich mixtures as well as when their values are small. These differences are small enough, below 1%, when the mass fractions are large but increase when the n-propanol mass fraction decreases. These large differences are due to two cumulative reasons

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +4021.312.1147. Funding

This paper was done within the research program “Chemical Thermodynamics and Kinetics. Quantum chemistry” of the 2958



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“Ilie Murgulescu” Institute of Physical Chemistry, financed by the Romanian Academy. The Anton Paar refractometer (Abbemat RXA 170) was purchased from POS-CCE O 2.2.1, INFRANANOCHEM project, no. 19/01.03.2009. Notes

The authors declare no competing financial interest.

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REFERENCES

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Indirect Analysis of a Homogeneous Ternary Mixture - ACS Publications

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