Experimental and Correlational Study of Phase Equilibria in Aqueous

Article pubs.acs.org/jced

Experimental and Correlational Study of Phase Equilibria in Aqueous Solutions of Formic and Butyric Acids with Isoamyl Acetate and Methyl Isoamyl Ketone at T = 298.15 K Hossein Ghanadzadeh Gilani,† Ali Ghanadzadeh Gilani,*,‡ and S. Laleh Seyed Saadat‡ †

Department of Chemical Engineering, University of Guilan, Rasht, Iran Department of Chemistry, Faculty of Science, University of Guilan, Rasht, Iran

‡

ABSTRACT: This study demonstrates the experimental solubility and tie-line data for {water + formic acid or butyric acid + solvents} ternary systems at T = 298.15 K and p = 101.32 kPa for the first time. The selected organic solvents were isoamyl acetate and methyl isoamyl ketone. Despite structural similarity, however, they belong to two different C7 chemical classifications. The phase diagrams for all of the studied ternary systems are of type-1. Solubility curves were experimentally determined using the cloud point method. The experimental tie-line data were determined by acidimetric titration, the Karl−Fischer technique, and refractive index measurements. The experimental tie-line data were correlated using the UNIQUAC and NRTL models. The quality of the experimental tie-line data was determined through the Othmer−Tobias and Hand correlation plots. From the experimental equilibrium data, distribution coefficients and separation factors were obtained through the regions of immiscibility.

1. INTRODUCTION Precise liquid−liquid equilibrium (LLE) data of the ternary aqueous mixtures of carboxylic acids are always needed in the design of many chemical and fermentation processes. Up to now, many valuable investigations have been carried out on the thermodynamic and LLE behavior of this group of acids by many researchers.1−9 Carboxylic acids are important organic chemicals that have a large range of applications in various chemical, biochemical, and pharmaceutical industries.10 Certain carboxylic acids are used as reagents or chemical intermediates in many chemical syntheses. Among the most widely used carboxylic acids are formic acid (FA) and butyric acid (BA). Both FA and BA are colorless, watersoluble liquids and have unpleasant odors. These acids can be produced by chemical synthetic or fermentation methods.11−13 Thus, separation of these acids from aqueous solutions is chemically and industrially important. One of the earliest publications of LLE measurement for the ternary systems consisting of FA or BA was that of Leung and Badakhshan.14 Subsequently, important studies have been carried out on LLE measurements by several researchers.15−17 To the best of our knowledge, heavy alcohols,18−23 esters,24−30 and hydrocarbons31,32 have mainly been used as the extractant in © 2014 American Chemical Society

recovery of these acids from water. However, further LLE studies are still needed for various industrial purposes. More equilibrium data for the aqueous solutions of FA or BA with various organic solvents, mainly heavy alcohols have been reported in our previous publications.33−36 In this work, we present the solubility and tie-line data for (water + FA or BA + solvents) ternary systems at 298.15 K and 101.32 kPa. The selected organic solvents were isoamyl acetate (IAA) and methyl isoamyl ketone (MIAK), where their molecular structures are similar to each other. The quality of the experimental tie-line data was determined by the Othmer−Tobias37 and Hand38 correlation equations for the studied systems. The LLE data were correlated using the universal quasi-chemical (UNIQUAC) method of Abrams and Prausnitz39 and the nonrandom two-liquid (NRTL) model of Renon and Prausnitz.40,41 For these equilibrium models, the binary interaction parameters were obtained. Moreover, in order to establish the possibility of the solvents used in this study for the separation process, experimental distribution coefficients (D) and separation factors (S) were determined. Received: December 18, 2013 Accepted: February 20, 2014 Published: March 4, 2014 917

dx.doi.org/10.1021/je401095k | J. Chem. Eng. Data 2014, 59, 917−925

Journal of Chemical & Engineering Data

Article

Formic acid (stated mass fraction purity > 0.99) was obtained from Chemlab. The stated purity of the chemicals was checked by the refractive index and density measurements. The chemicals were used as received, without any purification. The chemical structures of the solvents used in this work are given in Figure 1. Deionized and redistilled water with an electrical conductivity less than 5 μS·cm−1 at T = 298.15 K was used throughout all experiments. The refractive index and density data of the chemicals along with their literature values are listed in Table 1. 2.2. Apparatus and Experimental Procedure. Refractive index and density values of the pure liquids were measured at 298.15 K using an Abbe refractometer (model CETI) and a DA210 (Kyoto electronic) density meter, respectively. The instruments were initially calibrated before being used. The uncertainty in refractive index and density measurements were ± 0.0002 and 0.03 kg·m−3, respectively. The temperature of the

Figure 1. Molecular structures of the solvents used in this study: (a) isoamyl acetate (IAA) and (b) methyl isoamyl ketone (MIAK).

2. EXPERIMENTAL SECTION 2.1. Materials. The chemicalsbutyric acid (butanoic acid), isoamyl acetate (3-methylbut-1-yl ethanoate), and methyl isoamyl ketone (5-methyl-2-hexanone)with stated mass fraction purity higher than 0.99 were supplied from Merck.

Table 1. Source, Purity, Refractive Index (nD), and Density (ρ) of the Pure Componentsa ρ/(kg·m−3)

nD chemical name

CAS no.

supplier

mass fraction purity

exp.

lit.

exp.

lit.

formic acid (FA) butyric acid (BA) isoamyl acetate (IAA) methyl isoamyl ketone (MIAK) water (W)

64-18−6 107-92-6 123-92-2 110-12-3

Chemlab Merck Merck Merck

> 0.99 > 0.99 > 0.99 > 0.99 deionized and bidistilled

1.3710 1.3977 1.3976 1.4051e 1.3324

1.3712b 1.3975c 1.398d 1.4062e 1.3325f

1219.50 952.68 866.71 887.92e 997.01

1219.85b 952.80c 867.1d 887.5e 997.05f

a Uncertainties u are u(nD) = 0.0002, and u(ρ) = 0.03 kg·m−3. bTaken from ref 20. cTaken from ref 11. dTaken from ref 42. eTaken from ref 26 at T = 293.2 K. fTaken from ref 46.

Table 2. Solubility Curve Data in Mass Fraction (wi) For {Water (1) + Carboxylic Acid (2) + Organic Solvent (3)} at T = 298.15 K and p = 101.32 kPa for the Investigated Systemsa water (1) + FA (2) + IAA (3)

a

water (1) + FA (2) + MIAK (3)

water (1) + BA (2) + IAA (3)

water (1) + BA (2) + MIAK (3)

w1

w2

w1

w2

w1

w2

w1

w2

0.9477 0.8967 0.8439 0.7940 0.7375 0.6938 0.6407 0.5904 0.5394 0.4816 0.4265 0.3719 0.2755 0.3169 0.2561 0.2351 0.2149 0.1899 0.1695 0.1485 0.1300 0.1147 0.1034 0.0853 0.0773 0.0632 0.0473 0.0361

0.0501 0.1000 0.1507 0.1995 0.2539 0.2955 0.3465 0.3946 0.4413 0.4931 0.5217 0.5559 0.5423 0.5881 0.5207 0.4984 0.4705 0.4406 0.4192 0.3831 0.3533 0.3103 0.2719 0.2309 0.1930 0.1406 0.0984 0.0485

0.9442 0.8926 0.8435 0.7921 0.7358 0.6861 0.6307 0.5822 0.5219 0.3360 0.4760 0.3154 0.4075 0.3730 0.2916 0.2675 0.2354 0.2126 0.1894 0.1698 0.1412 0.1201 0.0991 0.0839 0.0725 0.0588 0.0372 0.0265

0.0498 0.0994 0.1478 0.1982 0.2485 0.2945 0.3460 0.3870 0.4344 0.4663 0.4661 0.4392 0.4950 0.4935 0.4252 0.4076 0.3783 0.3543 0.3233 0.2972 0.2659 0.2223 0.1803 0.1527 0.1256 0.0942 0.0500 0.0341

0.9418 0.8914 0.8340 0.7815 0.7311 0.6897 0.6421 0.5856 0.5288 0.4860 0.4335 0.3860 0.3262 0.2734 0.2106 0.1648 0.1540 0.1316 0.1085 0.0877 0.0706 0.0615 0.0542 0.0468 0.0347 0.0303 0.0261 0.0218

0.0571 0.1065 0.1628 0.2143 0.2604 0.2997 0.3430 0.3937 0.4445 0.4830 0.5242 0.5620 0.5984 0.6144 0.6220 0.6038 0.5927 0.5696 0.5400 0.4970 0.4155 0.3842 0.3315 0.2867 0.2056 0.1556 0.1074 0.0560

0.9472 0.8832 0.8444 0.7932 0.7420 0.6902 0.6346 0.5868 0.5326 0.4839 0.4338 0.3780 0.3266 0.2674 0.2051 0.1637 0.1414 0.1244 0.1115 0.1001 0.0936 0.0812 0.0704 0.0619 0.0558 0.0471 0.0385 0.0333

0.0499 0.1130 0.1507 0.2009 0.2492 0.2981 0.3488 0.3927 0.4404 0.4841 0.5262 0.5657 0.5979 0.6178 0.6117 0.5886 0.5572 0.5238 0.4919 0.4521 0.4127 0.3739 0.3275 0.2910 0.2431 0.1991 0.0962 0.0522

Standard uncertainties u are u(T) = 0.01 K, u(p) = ± 0.40 kPa, and u(w) = 0.0007. 918



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Table 3. Experimental Refractive Indices (nD) As a Function of Water Mass Fraction (w1) in the Aqueous Phase and the Solvent Mass Fraction in the Organic Phase (w3) at T = 298.15 K and p = 101.32 kPa for the Investigated Systemsa aqueous phase mass fraction system water (1) + formic acid (2) + isoamyl acetate (3)

water (1) + formic acid (2) + methyl isoamyl ketone (3)

water (1) + butyric acid (2) + isoamyl acetate (3)

water (1) + butyric acid (2) + methyl isoamyl ketone (3)

organic phase mass fraction

w1

nD

w3

nD

0.8439 0.7940 0.7375 0.6407 0.5904 0.5394 0.4816 0.9442 0.8926 0.8435 0.7921 0.7358 0.6861 0.5822 0.9418 0.8914 0.8339 0.7807 0.7310 0.6899 0.6421 0.9472 0.9150 0.8832 0.8444 0.7932 0.7420 0.6902

1.3377 1.3404 1.3424 1.3477 1.3492 1.3523 1.3543 1.3323 1.3354 1.3378 1.3398 1.3428 1.3454 1.3512 1.3335 1.3362 1.3412 1.3441 1.3486 1.3509 1.3538 1.3337 1.3368 1.3405 1.3441 1.3498 1.3543 1.3606

0.5750 0.6246 0.6838 0.7296 0.7962 0.8543 0.9154 0.5930 0.6576 0.7207 0.7633 0.8470 0.9128 0.9394 0.6143 0.6666 0.7098 0.7597 0.8141 0.8665 0.9223 0.6021 0.6471 0.7011 0.7750 0.7538 0.8087 0.8654

1.3815 1.3833 1.3848 1.3866 1.3887 1.3904 1.3918 1.3838 1.3896 1.3930 1.3954 1.4022 1.4056 1.4075 1.3920 1.3924 1.3927 1.3930 1.3934 1.3939 1.3942 1.399 1.3996 1.4008 1.4021 1.4015 1.4029 1.4037

Standard uncertainties u are u(T) = 0.01 K, u(p) = ± 0.40 kPa, u(nD) = 0.0002, and u(w) = 0.0007.

a

Figure 2. Refractive index standard curves for (a) {Water (1) + FA (2) + IAA (3)}; and (b) {water (1) + BA (2) + MIAK (3)} in aqueous phase (w11) at T = 298.15 K; blue circle, IAA; red square, MIAK.

instruments was controlled by circulation of water and was measured with a copper−constantan thermocouple. The temperature of the samples was measured with a precision digital thermometer (Lutron TM-917) with an accuracy of ± 0.01 K. All weighting was carried out with an AND electronic analytical balance (HR-200) with an accuracy of ± 0.0001 g. The Karl Fischer titration was carried out using a Metrohm-870 KF Titrino plus Karl−Fisher titrator. The titrator was calibrated with a standard solution of sodium tartrate. 2.2.1. Solubility Data Measurements. Solubility data of the ternary systems {water + FA or BA + IAA} and {water + FA or BA + MIAK} were experimentally determined at T = 298.15 K by the cloud point method.42 Feed binary liquids mixtures of different known compositions were prepared gravimetrically and were introduced to a glass cell with a volume of about 20 mL. The third component (solvent or water) was progressively added into the cell using a Brand Transferpette micropipet with an accuracy of ± 0.001 mL. The resulting mixture was agitated continuously with a magnetic stirrer. The titration end point was determined visually by observing the transition from a clear to a turbid mixture. All of the visual measurements were repeated at least three times. The average of these readings was taken for the component compositions. The temperature of the cell was controlled by a water jacket and maintained with an accuracy of

within ± 0.01 K. The average uncertainty in the mass fraction of the solubility data was within ±0.0007. The measured solubility data for the ternary systems are given in Table 2. 2.2.2. Tie-Line Data Measurements. The tie-line data were determined for the ternary systems at 298.15 K. Experiments were carried out in a jacketed 250 mL glass cell. The temperature was estimated to be accurate to within ±0.01 K. The prepared mixtures with known compositions were placed in the glass cell and were vigorously agitated by a magnetic stirrer. For the studied systems, both the stirring and settle times were at least 4 h for complete phase separation. Preliminary tests showed that these times (stirring and resting times) are enough to achieve the phase equilibrium. The samples of organic-rich phase were taken by a glass syringe from the upper layer and that of water-rich phase from a sampling tap at the bottom of the cell. After separation, samples of both phases were transparent and were carefully weighed. 2.3. Analysis. The mass fractions of the acids (FA and BA) in both phases (w21 and w23) were measured by potentiometric NaOH titration. The evaluation of the potentiometric curve was performed according to the standard analytical procedure. The water content of the organic layer (w13) was measured by the Karl 919



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Table 4. Equations for Refractive Index (nD) As a Function of Water Mass Fraction (w11) in the Aqueous-Rich Phase and the Solvent Mass Fraction in the Organic-Rich Phase (w33) at T = 298.15 K and p = 101.32 kPa for the Investigated Systemsa eqb

system water (1) + formic acid (2) + isoamyl acetate (3)

water (1) + formic Acid (2) + methyl isoamyl ketone (3)



nD = −0.0462w11 + 1.3768 nD = 0.0307w33 + 1.3640 nD = −0.0510w11 + 1.3806 nD = 0.0672w33 + 1.3446 nD = −0.0696w11 + 1.3989 nD = 0.0072w33 + 1.3876 nD = −0.1036w11 + 1.4317 nD = 0.0182w33 + 1.3880

R2 0.9966 0.9965 0.9978 0.9958 0.9963 0.9969 0.9989 0.9920

a Standard uncertainties u are u(T) = 0.01 K, u(p) = ± 0.40 kPa, u(nD) = 0.0002, and u(w) = 0.001. bThe estimated standard error of slope and intercept coefficients of the linear plot are 0.0012 and 0.0001, respectively.

Table 5. Experimental Tie-Line Data in Mass Fraction for {Water (1) + Carboxylic Acid (2) + Organic Solvent (3)} at T = 298.15 K and p = 101.32 kPaa aqueous phase mass fraction w11 0.783 0.645 0.576 0.502 0.430 0.397 0.844 0.725 0.634 0.561 0.502 0.455 0.966 0.954 0.934 0.922 0.906 0.894 0.972 0.956 0.944 0.934 0.925 0.918

w21

w31

organic phase mass fraction w13

w23

Water (1) + Formic Acid (2) + Isoamyl Acetate (3) 0.210 0.007 0.039 0.057 0.343 0.013 0.053 0.108 0.408 0.016 0.071 0.169 0.476 0.022 0.080 0.200 0.525 0.045 0.096 0.262 0.541 0.062 0.113 0.302 Water (1) + Formic Acid (2) + Methyl Isoamyl Ketone (3) 0.148 0.009 0.055 0.090 0.259 0.016 0.080 0.145 0.343 0.023 0.100 0.185 0.407 0.032 0.110 0.214 0.451 0.047 0.125 0.236 0.476 0.069 0.142 0.265 Water (1) + Butyric Acid (2) + Isoamyl Acetate (3) 0.033 0.001 0.035 0.160 0.045 0.001 0.042 0.219 0.065 0.001 0.053 0.313 0.076 0.002 0.061 0.363 0.092 0.002 0.070 0.405 0.104 0.002 0.075 0.425 Water (1) + Butyric Acid (2) + Methyl Isoamyl Ketone (3) 0.025 0.003 0.046 0.186 0.041 0.003 0.063 0.297 0.053 0.003 0.084 0.380 0.062 0.003 0.097 0.439 0.072 0.004 0.109 0.486 0.078 0.004 0.124 0.524

w33 0.904 0.839 0.760 0.720 0.641 0.585 0.855 0.775 0.715 0.676 0.639 0.593

Figure 3. Ternary phase diagram for LLE of (a) {water (1) + FA (2) + IAA (3)} and (b) {water (1) + FA (2) + MIAK (3)} at T = 298.15 K; ●, experimental cloud points; ○, experimental tie-lines; blue square, UNIQUAC calculated points; red triangle, NRTL calculated points.

0.806 0.739 0.633 0.575 0.525 0.500

index measurements. In this way, the refractive indices of both phases at equilibrium (lying on the solubility curves) were measured and used for building standard curves. The experimental refractive indices of both the phases at equilibrium and their corresponding mass fractions are listed in Table 3. The typical standard curves for IAA and MIAK in the aqueous phase (w11) at T = 298.15 K are shown in Figures 2a and 2b. Equations for refractive index (nD) as a function of w11 and w33 at 298.15 K are given in Table 4. The uncertainty of all measured compositions was within ±0.001.

0.768 0.640 0.536 0.464 0.405 0.352

3. RESULTS AND DISCUSSION 3.1. Experimental Tie Line Data. Experimental tie-line data for the four ternary systems of {water + FA or BA + solvent (IAA and MIAK)} were determined at T = 298.15 K and p = 101.32 kPa. The experimental tie-line compositions of the equilibrium phases for these systems are listed in Table 5.

Standard uncertainties u are u(T) = 0.01 K, u(p) = ± 0.40 kPa, and u(w) = 0.001. a

Fischer method.43 The water and solvent contents in the aqueous (w11) and organic phases (w33) were performed using refractive 920



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Table 6. Experimental Separation Factors (S) and Distribution Coefficients of Carboxylic Acid (D2) and Water (D1) at T = 298.15 K and p = 101.32 kPaa T/K

D2

D1

S

water (1) + formic acid (2) + isoamyl acetate (3)

0.27 0.32 0.42 0.42 0.50 0.56 0.61 0.56 0.54 0.52 0.52 0.56 4.78 4.89 4.81 4.78 4.42 4.09 7.33 7.24 7.16 7.04 6.77 6.73

0.05 0.08 0.12 0.16 0.22 0.28 0.07 0.11 0.16 0.20 0.25 0.31 0.04 0.04 0.06 0.07 0.08 0.08 0.05 0.07 0.09 0.10 0.12 0.14

5.4 3.9 3.4 2.6 2.2 2.0 9.4 5.0 3.4 2.7 2.1 1.8 133.7 112.1 84.5 71.9 57.2 48.9 154.6 110.7 80.2 68.2 57.5 49.7

water (1) + formic acid (2) + methyl isoamyl ketone (3)



a Average uncertainties u are u(T) = 0.01 K, u(p) = 0.40 kPa, and u(S) = 0.1.

Table 7. Selection of Separation Factors (Highest Values) for the (Water + Carboxylic Acid + Solvents) Ternary Systems at T = 298.2 K and p = 101.32 kPa, Taken from the Literature

Figure 4. Ternary phase diagram for LLE of (a) {water (1) + BA (2) + IAA (3)} and (b) {water (1) + BA (2) + MIAK (3)} at T = 298.15 K; ●, experimental cloud points; ○, experimental tie-lines; blue square, UNIQUAC calculated points; red triangle, NRTL calculated points.

The LLE phase diagrams for the investigated ternary systems at T = 298.15 K were plotted and shown in Figures 3a,b and 4a,b. In order to evaluate the effectiveness of FA or BA extraction by the solvents (IAA or MIAK), distribution coefficients and separation factors were obtained. The separation factor, which is a measure of the ability of a solvent to separate the acid from water, is defined as the ratio of distribution coefficients of the acids (D2) to water (D1) as follows: S=

w23/w21 D = 2 w13/w11 D1

system

solvent type

S

water + FA + isoamyl actate water + BA + isoamyl actate water + FA + methyl isoamyl ketone water + BA + methyl isoamyl ketone water + FA + dimethyl maleate water + BA + dimethyl maleate water + FA + undecanol water + BA + undecanol water + FA + amyl alcohol water + BA + amyl alcohol water + FA + decanol water + BA + decanol

ester ester ketone ketone ester ester alcohol alcohol alcohol alcohol alcohol alcohol

5.4a 133.7a 9.4a 154.6a 15.46b 13.03b 5.03c 85.20c 7.5d 84.6e 3.2f 208g

a

This study. bTaken from ref 26. cTaken from ref 23. dTaken from ref 35. eTaken from ref 45. fTaken from ref 33. gTaken from ref 22.

A comparison of the extracting abilities of the solvents was made with respect to separation factor values. This factor was found to be greater than unity for the systems investigated, which means that extraction of these acids by these solvents is possible. As seen from the figures, a noticeable solvent effect on the separation factor can be observed. As a result, the ternary systems containing MIAK (ketone) display larger separation factors than that of other systems containing ester. This shows the superiority of the ketone as the preferred solvent for the extraction of both the acids from water.

(1)

w13 and w23 are the mass fractions of water and the acids in the organic-rich phase, respectively. w11 and w21 are the mass fractions of water and the acids in the aqueous phase, respectively. The experimental distribution coefficients and separation factors, for each system, are given in Table 6. The variation of experimental separation factor of the acids as a function of the mass fraction of FA or BA in aqueous phase for the studied systems are shown in Figure 5, panels a and b, respectively. 921



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Figure 5. Plot of the separation factor (S) of FA and BA as a function of mass fraction of the acids in the aqueous phase (w21) for (a) blue circle, {water + FA + IAA} and red triangle, {water + FA + MIAK}; (b) blue circle, {water + BA + IAA} and red triangle, {water + BA + MIAK} at T = 298.15 K.

Figure 6. Othmer−Tobias plot for the (a) blue circle, {water + FA + IAA} and red triangle, {water + FA + MIAK}; (b) blue circle, {water + BA + IAA} and red triangle, {water + BA + MIAK} at T = 298.15 K.

For comparison purpose, the highest values of the separation factor obtained in this work and some previously reported in the literature22,23,26,33,35,45 for similar ternary aqueous systems consisting of FA or BA are summarized in Table 7. As can be seen, it is possible to show differences between the extracting capabilities of the solvents. It is apparent that decanol offers a higher separation factor comparing to others quoted in this table. However, there is no regular relation between the separation factor values and the solvent chemical classifications. 3.2. Reliability of Tie-Line Data. For the studied systems, the quality of the experimental tie-line data was validated by

applying the Othmer−Tobias37 (eq 2) and the Hand38 (eq 3) equations. ⎛ 1 − w33 ⎞ ⎛ 1 − w11 ⎞ ln⎜ ⎟ = A + B ln⎜ ⎟ ⎝ w11 ⎠ ⎝ w33 ⎠

(2)

⎛w ⎞ ⎛w ⎞ ln⎜ 21 ⎟ = A′ + B′ ln⎜ 23 ⎟ ⎝ w11 ⎠ ⎝ w33 ⎠

(3)

where w11 is mass fraction of water in the aqueous phase, w23 and w21, are mass fractions of the acid in organic and aqueous phases,

Table 8. Othmer−Tobias and Hand Equations Constants (A, B, A′ and B′) and the Correlation Factor (R2) for the Ternary Systems at T = 298.15 K and p = 101.32 kPa Othmer−Tobias correlation

Hand correlation

system

A

B

R2

A′

B′

R2

water (1) + formic acid (2) + isoamyl acetate (3) water (1) + formic acid (2) + methyl isoamyl ketone (3) water (1) + butyric acid (2) + isoamyl acetate (3) water (1) + butyric acid (2) + methyl isoamyl ketone (3)

1.1133 0.7296 1.1991 1.5950

−0.877 −0.537 1.6087 4.4031

0.990 0.998 0.997 0.996

0.7734 1.2734 0.8159 0.6530

0.8737 1.1196 2.0714 2.6805

0.991 0.998 0.996 0.995

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Table 9. UNIQUAC Structural Parameters (r and q) for the Pure Components

a

component

r

q

watera formic acida butyric acidb isoamyl acetatec methyl isoamyl ketonec

0.920 1.528 3.55 5.27 4.73

1.40 1.53 3.15 4.49 5.50

was taken to be 0.3. The calculated LLE data for the ternary systems at T = 298.15 K are listed in Table 10. A comparison between the calculated and experimental tie-line data is shown in Figures 3 and 4 and shows that they agree well. The optimum UNIQUAC and NRTL binary interaction parameters were determined using the obtained LLE data. The interaction parameters describe the interactions between the i molecules and j molecules. The binary interaction parameters may be written as

Taken from ref 24. bTaken from ref 36. cTaken from ref 43.

aij = (uij − ujj)/R

respectively, w33 is mass fraction of the solvent in organic phase,and A, B, A′, and B′ are the Othmer−Tobias and the Hand parameters, which depend on type of system and equilibrium compositions. These parameters are given in Table 8. As seen in Figures 6a,b and 7a,b, the plots exhibit good linear fit and indicate the quality of the experimental LLE data in this work. 3.3. LLE Correlation. The thermodynamic models of NRTL and UNIQUAC were used to correlate the experimental tie-line data. For the investigated systems, the literature values were used for the UNIQUAC structural parameters r (van der Waals volume of molecule) and q (relative surface area per molecule)24,36,43 and are given in Table 9. The value of the nonrandomness (α) was fixed at 0.3. In the present work, the other values for α such as 0.1, 0.2, and regressed α were tested and finally the optimum value for the nonrandomness parameter

bij = (gij − gjj)/R

and

(4)

aij and bij are expressed in K. The parameters uij and gij characterizes the UNIQUAC and NRTL interaction energies, respectively. These interaction parameters can be correlated with the term τij. The adjustable parameter (τij) in the UNIQUAC and NRTL equations may be expressed as ⎛ Δuij ⎞ ⎛ aij ⎞ τij = ⎜ − ⎟ = exp⎜ − ⎟ ⎝ T⎠ ⎝ RT ⎠

and

⎛ Δgij ⎞ bij ⎟⎟ = τij = ⎜⎜ T ⎝ RT ⎠

(5)

These parameters were determined by minimizing the composition-based objective function. The iterative optimization procedure based on the average minimizes the difference

Table 10. Calculated UNIQUAC and NRTL Tie-Line Data in Mass Fraction for {Water + Carboxylic Acid + Organic Solvent} at T = 298.15 K and p = 101.32 kPaa aqueous phase

organic phase

w11 UNIQUAC

a

w21 NRTL

0.764 0.656 0.597 0.546 0.449 0.404

0.777 0.660 0.592 0.532 0.424 0.376

0.840 0.722 0.649 0.587 0.522 0.460

0.835 0.722 0.651 0.588 0.521 0.454

0.967 0.955 0.936 0.909 0.893 0.884

0.965 0.955 0.940 0.914 0.903 0.896

0.971 0.956 0.942 0.932 0.922 0.915

0.972 0.957 0.943 0.932 0.923 0.913

UNIQUAC

w13 NRTL

UNIQUAC

w21 NRTL

Water (1) + Formic Acid (2) + Isoamyl Acetate (3) 0.230 0.216 0.047 0.038 0.332 0.328 0.055 0.060 0.385 0.391 0.062 0.070 0.430 0.444 0.070 0.079 0.505 0.532 0.091 0.094 0.534 0.566 0.104 0.102 Water (1) + Formic Acid (2) + Methyl Isoamyl Ketone (3) 0.153 0.158 0.072 0.060 0.262 0.262 0.083 0.081 0.327 0.325 0.090 0.094 0.379 0.377 0.097 0.106 0.429 0.430 0.106 0.119 0.471 0.479 0.118 0.134 Water (1) + Butyric Acid (2) + Isoamyl Acetate (3) 0.032 0.034 0.035 0.035 0.044 0.044 0.042 0.043 0.062 0.058 0.050 0.052 0.090 0.084 0.061 0.064 0.105 0.095 0.067 0.068 0.115 0.102 0.070 0.071 Water (1) + Butyric Acid (2) + Methyl Isoamyl Ketone (3) 0.026 0.025 0.045 0.046 0.041 0.040 0.066 0.068 0.055 0.053 0.081 0.081 0.065 0.065 0.092 0.092 0.075 0.073 0.102 0.099 0.082 0.084 0.109 0.108

UNIQUAC

NRTL

0.058 0.113 0.152 0.194 0.290 0.340

0.058 0.113 0.151 0.190 0.277 0.324

0.095 0.143 0.175 0.206 0.242 0.282

0.089 0.142 0.177 0.211 0.251 0.298

0.168 0.215 0.269 0.328 0.357 0.373

0.171 0.217 0.276 0.368 0.404 0.426

0.183 0.287 0.350 0.387 0.420 0.442

0.188 0.297 0.363 0.412 0.443 0.477

Standard uncertainties u are u(T) = 0.01 K, u(p) = ± 0.40 kPa, and u(w) = 0.001. 923



Article

Table 11. Correlated Results from the UNIQUAC and NRTL Models and the Corresponding Binary Interaction Parameters (aij, aji, bij, and bji) for the Ternary Systems UNIQUAC i−j

aij /K

1−2 1−3 2−3

−75.20 −280.18 −221.61

1−2 1−3 2−3

−642.30 −296.82 7.77

1−2 1−3 2−3

88.86 −221.45 373.39

1−2 1−3 2−3

−269.50 −166.06 334.35

NRTL aji/K

i−j

rmsd %

bij /K

Water (1) + Formic Acid (2) + Isoamyl Acetate (3) 297.00 1−2 −196.42 −166.34 1.84 1−3 2074.13 207.88 2−3 998.99 Water (1) + Formic Acid (2) + Methyl Isoamyl Ketone (3) 274.46 1−2 963.87 −131.10 1.34 1−3 2230.64 −177.57 2−3 1424.08 Water (1) + Butyric Acid (2) + Isoamyl Acetate (3) −311.15 1−2 789.71 −647.72 2.27 1−3 2491.20 −1393.19 2−3 −182.46 Water (1) + Butyric Acid (2) + Methyl Isoamyl Ketone (3) 96.94 1−2 1014.753 −546.51 3.09 1−3 2109.773 −3019.22 2−3 −385.098

bji/K

rmsd %

−389.20 818.41 −848.33

1.35

−594.50 150.40 −653.15

1.27

183.84 826.40 137.41

0.99

−71.292 1064.679 2141.998

1.96

between measured and calculated values.44 The optimization results or the quality of correlation was tested by calculating the corresponding the root-mean square deviation (rmsd) data. The rmsd value was calculated from the difference between the experimental and calculated mass fractions according to the following equation: n

rmsd =

2

3

exp cal 2 ∑k = 1 ∑ j = 1 ∑i = 1 (wijk − wijk )

6n

(6)

where n is the number of tie-lines, wexp indicates the experimental mass fraction, wcal is the calculated mass fraction, the subscript i indexes components, and j indexes phases and k = 1, 2, ..., n (tie-lines). The NRTL and UNIQUAC binary interaction parameters for the ternary systems are shown in Table 11. As can be seen, both the models give good results and provide nearly the same rmsd values for the investigated systems.

4. CONCLUSIONS The tie-line data for the ternary systems of {water + formic or butyric acids + isoamyl acetate} and {water + formic or butyric acids + methyl isoamyl ketone} were measured at T = 298.15 K. The experimental LLE data were correlated using the UNIQUAC and NRTL (α = 0.3) models and the corresponding binary interaction parameters were determined. The thermodynamic models were fitted to experimental LLE data using an iterative computer program. Both of the models give acceptable results for the investigated systems. The separation factors and distribution coefficients for the solvents used in this work were calculated. The obtained separation factors confirm the ability of these solvents for extraction of these acids from their aqueous solutions. However, the ketone solvent (MIAK) has the advantage of a higher separation factor.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: +981313233262.

Figure 7. Hand plot for the (a) blue circle, {water + FA + IAA} and red triangle, {water + FA + MIAK}; (b) blue circle, {water + BA + IAA} and red triangle, {water + BA + MIAK} at T = 298.15 K.

Notes

The authors declare no competing financial interest. 924



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Article

(45) Ghanadzadeh Gilani, H.; Ghanadzadeh Gilani, A.; Amouzadeh, F. J. Chem. Thermodyn. 2014, 71, 103−111. (46) TRC Thermodynamic Tables-Nonhydrocarbons, Thermodynamic Research Centre, NIST/TRC Table Database, Win Table, 2004 version.

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Experimental and Correlational Study of Phase Equilibria in Aqueous

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