944
J. Chem. Eng. Data 2004, 49, 944-949
Activity of Water in Aqueous Solutions of Sodium Citrate and in Aqueous Solutions of (An Inorganic Salt and Citric Acid) at 298.15 K Andreas Schunk and Gerd Maurer* Chair of Applied Thermodynamics, University of Kaiserslautern, D-67653 Kaiserslautern, Germany
Modeling the reactive extraction of carboxylic acids in the presence of inorganic salts requires experimental data for the thermodynamic properties of aqueous solutions of the single salts as well as of aqueous solutions of (salt + carboxylic acid) mixtures. The activity of water in such solutions was determined by isopiestic measurements at 298.15 K for the binary mixture (water + sodium citrate) and the ternary mixtures of (water + citric acid + salt) for the salts sodium chloride, sodium nitrate, sodium sulfate, and sodium citrate. The experimental data are correlated with Pitzer’s Gibbs excess energy model for aqueous electrolyte solutions.
Introduction Carboxylic acids are commonly recovered from diluted aqueous solutions by reactive extraction with a waterinsoluble organic amine. The liquid-liquid phase equilibrium in such systems is strongly influenced by inorganic salts. The development and parametrization of a model for correlating and predicting such liquid-liquid phase equilibria requires not only experimental data for the partitioning of carboxylic acids to aqueous/organic two-phase systems in the presence of a chemical extractant and some inorganic salts, but also of the properties of subsystems. Here, experimental results are presented for the activity of water in aqueous solutions of a single salt (sodium citrate) as well as in aqueous solutions of citric acid which also contain a single sodium salt (chloride, nitrate, sulfate, citrate) at 298.15 K. The experimental results are used to determine parameters of Pitzer’s equation for the Gibbs excess energy of electrolyte solutions. Experimental Section The activity of water in aqueous solutions of nonvolatile solutes at 298.15 K was determined in isopiestic investigations using aqueous solutions of sodium chloride as references. The experimental techniques and the equipment are similar to those used in previous investigations on aqueous solutions of polymers (Groβmann et al.,1 Hasse et al.,2 Kany et al.3). Therefore, the experimental details are not repeated here. The experimental uncertainties are (0.1 K for the temperature and (0.35% in the molality of a solute. Aqueous solutions of sodium chloride were used as references. The correlation of Pitzer et al.4 was used to convert the experimental results for the molality of sodium chloride in the reference solution to the activity of water. The absolute uncertainty of the experimental results for the activity of water is estimated to (0.0005. However, that number does not include any contribution that might result from a bias of the correlation of Pitzer et al.4 (cf. Clark and Glew,5 Archer,6 and Archer and Carter7). Materials. Citric acid monohydrate (min. 99.8%), sodium nitrate, sodium chloride, and sodium sulfate (min. * To whom correspondence may be addressed. Tel.: +49-631-2052410. Fax: +49-631-205-3835. E-mail:
[email protected]. http://www.mv.uni-kl.de/TD.
Table 1. Survey of the Experimental Investigations (Minimum and Maximum Molalities of Solutes) salt Na3Cit Na3Cit NaCl NaNO3 Na2SO4
(m ˜ H3Cit)min 0.08 0.1 0.2 0.2
(m ˜ H3Cit)max
(m ˜ salt)min
(m ˜ salt)max
3.6 5.7 3.9 3.5
0.5 0.05 0.5 0.2 0.2
1.7 1.6 3.0 3.0 2.4
Table 2. Activity of Water in Aqueous Solutions of Sodium Citrate at 298.15 K m ˜ Na3Cit
(ref) mNaCl
mol‚kg-1
mol‚kg-1
aexp w
∆a(exp-corr) × 104 w
0.465 0.758 0.804 1.018 1.136 1.137 1.185 1.298 1.457 1.605 1.683
0.653 1.059 1.120 1.429 1.609 1.610 1.698 1.851 2.106 2.338 2.465
0.9785 0.9648 0.9627 0.9520 0.9457 0.9456 0.9425 0.9370 0.9277 0.9190 0.9142
1.6 -1.5 -0.7 0.5 0.8 0.8 -4.6 3.1 1.2 0.9 -1.0
99.5%) were purchased from Riedel-de Hae¨n, Seelze, Germany. Sodium citrate (min. 99%) was purchased from Merck, Darmstadt, Germany. Deionized water was used in all experiments. Experimental Results. Table 1 gives a summary of the compositions of the aqueous solutions. The stoichiometric molality of citric acid m ˜ H3Cit was typically varied between 0.1 and 4, while the stoichiometric molality of the salt m ˜ salt ranged from about 0.1 to 3.0. The activity of water aw was as low as 0.89. The experimental results are given in Table 2 (for aqueous solutions of sodium citrate), Table 3 (aqueous solutions of citric acid and sodium chloride), Table 4 (aqueous solutions of citric acid and sodium nitrate), Table 5 (aqueous solutions of citric acid and sodium citrate), and Table 6 (aqueous solutions of citric acid and sodium sulfate). The tables with the experimental results also contain the stoichiometric molality of sodium chloride (ref) m ˜ NaCl in the reference solution (used to determine the activity of water). Additionally, the experimental results for the activity of water in aqueous solutions of sodium
10.1021/je034258r CCC: $27.50 © 2004 American Chemical Society Published on Web 05/07/2004
Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004 945 Table 3. Activity of Water in Aqueous Solutions of Sodium Chloride and Citric Acid at 298.15 K m ˜ NaCl
m ˜ H3Cit
(ref) m ˜ NaCl
mol‚kg-1
mol‚kg-1
mol‚kg-1
aexp w
∆a(exp-corr) × 104 w
0.506 0.498 0.499 0.499 0.498 0.503 0.503 0.499 0.498 0.499 0.502 0.498 0.500 0.501 0.988 0.995 0.987 0.997 0.988 0.970 0.995 0.997 0.986 0.999 2.001 1.985 1.946 1.974 1.944 1.946 1.981 1.981 2.984 2.975 2.931 2.939 2.924
0.101 0.103 0.301 0.502 0.973 1.562 2.514 2.993 3.486 3.580 4.009 4.489 5.034 5.517 0.493 1.492 2.171 2.506 2.471 2.918 3.483 4.737 4.939 5.647 0.500 1.503 1.945 2.469 2.907 3.410 3.964 4.447 0.675 1.393 1.954 2.450 2.955
0.596 0.544 0.666 0.758 1.103 1.492 2.033 2.341 2.651 2.752 3.029 3.299 3.715 4.031 1.285 1.865 2.295 2.513 2.476 2.752 3.163 3.922 4.031 4.525 2.296 2.786 3.029 3.393 3.596 3.922 4.248 4.525 3.299 3.715 4.001 4.248 4.516
0.9804 0.9821 0.9779 0.9750 0.9633 0.9498 0.9303 0.9188 0.9070 0.9030 0.8921 0.8811 0.8639 0.8503 0.9571 0.9365 0.9206 0.9125 0.9137 0.9030 0.8895 0.8550 0.8503 0.8286 0.9206 0.9017 0.8921 0.8773 0.8689 0.8550 0.8409 0.8286 0.8811 0.8639 0.8513 0.8409 0.8290
-1.0 5.7 2.9 12 -9.3 -18 2.8 2.3 7.0 -7.8 -4.4 14 -4.9 -0.3 -3.3 3.0 -6.0 -4.0 -3.3 -8.2 7.9 1.0 7.2 0.4 -5.6 15 5.0 -8.6 3.1 -6.5 11 19 17 -3.2 -18 -1.0 -1.2
Figure 1. The activity of water in aqueous solution of sodium citrate at 298.15 K. O, experimental data; solid line, correlation results. Table 4. Activity of Water in Aqueous Solutions of Sodium Nitrate and Citric Acid at 298.15 K
citrate are shown in Figure 1. Figure 2 shows, as a typical example, the activity of water in aqueous solutions of sodium chloride and citric acid. As it is expected, the activity of water decreases with increasing concentration of sodium chloride as well as with increasing concentration of citric acid. Correlation Model. Pitzer’s equation8,9 for the excess Gibbs energy of an aqueous electrolyte solution is used to describe the experimental data. That equation gives for the activity of water (when pure liquid water is the reference state)
ln aw )
Mw 1000
[
2AφIm
(Im)1/2
S
1/2
(1 + b(Im) ) S
exp(-R(Im)1/2)
S
∑∑β
(0) i,j mimj
S
∑∑β
(1) i,j mimj
-
i)1 j)1
S
2
S
S
∑∑∑τ i)1 j)1 k)1
-
i)1 j)1
S
i,j,kmimjmk
-
∑m i)1
i
]
(1)
Aφ is the Debye-Hu¨ckel parameter of water (Aφ(25 °C) ) 0.392), b is a size parameter (b ) 1.2), R is a numerical (0) (1) value (R ) 2), mi is the molality of solute i, and βi,j , βi,j , and τi,j,k are parameters for interactions between solute species i, j, and k. These parameters are symmetric, e.g.,
m ˜ NaNO3
m ˜ H3Cit
(ref) m ˜ NaCl
mol‚kg-1
mol‚kg-1
mol‚kg-1
aexp w
∆a(exp-corr) × 104 w
0.194 0.296 0.379 0.447 0.542 0.620 0.782 0.840 0.907 1.001 1.105 1.203 0.519 0.602 0.719 0.928 1.136 1.226 1.335 1.410 1.631 1.815 2.030 0.506 0.711 0.903 1.107 1.312 1.500 1.915 2.094 2.290 2.480 2.715 2.906
1.742 1.599 1.507 1.389 1.250 1.134 0.892 0.807 0.706 0.561 0.399 0.247 2.663 2.560 2.419 2.155 1.884 1.768 1.623 1.521 1.221 0.962 0.658 3.861 3.638 3.420 3.203 2.975 2.758 2.261 2.043 1.796 1.552 1.257 1.005
1.223 1.223 1.223 1.223 1.223 1.223 1.223 1.223 1.223 1.223 1.223 1.223 2.102 2.102 2.102 2.102 2.102 2.102 2.102 2.102 2.102 2.102 2.102 2.870 2.870 2.870 2.870 2.870 2.870 2.870 2.870 2.870 2.870 2.870 2.870
0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9592 0.9287 0.9287 0.9287 0.9287 0.9287 0.9287 0.9287 0.9287 0.9287 0.9287 0.9287 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984 0.8984
5.5 6.2 12 7.1 6.5 5.9 4.4 4.5 3.7 2.4 1.0 0.1 7.0 7.2 8.4 8.2 6.9 6.6 5.9 5.1 3.2 0.5 -1.4 -4.2 -2.5 -3.1 0.2 1.4 0.6 2.4 3.8 -5.9 -8.1 -8.4 -9.7
(0) (0) ) βj,i . Mw is the molar mass of water; Im is the ionic βi,j strength
Im )
1 2
S
∑mz
2 i i
(2)
i)1
zi is the charge number of solute i, and S is the number of solute species in the aqueous phase. When citric acid and a salt (e.g., sodium citrate) are simultaneously dissolved
946
Journal of Chemical and Engineering Data, Vol. 49, No. 4, 2004
Table 5. Activity of Water in Aqueous Solutions of Sodium Citrate and Citric Acid at 298.15 K m ˜ NaCit
m ˜ H3Cit
(ref) m ˜ NaCl
mol‚kg-1
mol‚kg-1
mol‚kg-1
aexp. w
0.032 0.063 0.100 0.130 0.162 0.197 0.226 0.261 0.297 0.327 0.396 0.130 0.237 0.325 0.392 0.448 0.484 0.519 0.554 0.590 0.626 0.134 0.245 0.331 0.402 0.462 0.497 0.606 0.644 0.132 0.252 0.356 0.445 0.518 0.581 0.632 0.678 0.715 0.752 0.782 0.051 0.137 0.264 0.376 0.466 0.613 0.667 0.715 0.755 0.794 0.822 0.856 0.101
1.052 0.986 0.900 0.826 0.743 0.652 0.571 0.481 0.386 0.307 0.140 1.315 1.081 0.867 0.689 0.536 0.443 0.347 0.256 0.166 0.080 1.345 1.105 0.895 0.711 0.551 0.455 0.173 0.083 1.844 1.634 1.424 1.224 1.038 0.872 0.731 0.594 0.484 0.374 0.284 2.048 1.922 1.708 1.488 1.291 0.919 0.768 0.620 0.506 0.389 0.296 0.200 2.501
0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.919 0.919 0.919 0.919 0.919 0.919 0.919 0.919 0.919 0.919 0.948 0.948 0.948 0.948 0.948 0.948 0.948 0.948 1.226 1.226 1.226 1.226 1.226 1.226 1.226 1.226 1.226 1.226 1.226 1.284 1.284 1.284 1.284 1.284 1.284 1.284 1.284 1.284 1.284 1.284 1.284 1.609
0.9785 0.9785 0.9785 0.9785 0.9785 0.9785 0.9785 0.9785 0.9785 0.9785 0.9785 0.9696 0.9696 0.9696 0.9696 0.9696 0.9696 0.9696 0.9696 0.9696 0.9696 0.9686 0.9686 0.9686 0.9686 0.9686 0.9686 0.9686 0.9686 0.9591 0.9591 0.9591 0.9591 0.9591 0.9591 0.9591 0.9591 0.9591 0.9591 0.9591 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9571 0.9457
∆a(exp-corr) w
× 104
1.7 0.9 0.4 0.2 0.2 0.4 -0.7 -2.1 -6.0 -0.1 -8.4 1.5 2.5 3.9 1.2 -4.4 -8.7 -14 -13 -4.5
