Ind. Eng. Chem. Res. 1997, 36, 2445-2451
2445
Effect of NaCl and KCl on the Solubility of Amino Acids in Aqueous Solutions at 298.2 K: Measurements and Modeling Mohammad K. Khoshkbarchi and Juan H. Vera* Department of Chemical Engineering, McGill University, Montreal, Quebec, Canada H3A 2A7
Measurements were performed to determine the solubilities at 298.2 K of four amino acids in aqueous solutions of NaCl or KCl. The amino acids studied were glycine, DL-alanine, DL-valine, and DL-serine. The results show that the solubility of amino acids is affected by the concentration of electrolyte and by the nature of both the amino acid and the cation of the electrolyte. A model has been developed to correlate the solubilities of amino acids in aqueous electrolyte solutions. The activity coefficients of amino acids in electrolyte solutions required were represented by a perturbed hard-sphere model. The model can accurately correlate the solubility of amino acids in aqueous solutions containing an electrolyte. Introduction Biochemicals are of importance due to their applications in chemical, pharmaceutical, and food industries. Separation and concentration of biochemicals from dilute aqueous media are two important steps in their productions. The separation processes based on the precipitation and crystallization have proved to be useful techniques and have been widely used for the concentration and separation of biomolecules (Belter et al., 1988). It has been shown that the presence of electrolytes in solutions of biochemicals affects their solubilities (Cohn and Edsall, 1965). This phenomenon, which is a result of the interactions between the biomolecule and the electrolyte, has been exploited for salt-induced separation of proteins (Coen et al., 1995). Complex biomolecules such as peptides and proteins are made up of the sequences of various amino acids, which are the simplest biochemicals. Therefore, the study of the solubility of amino acids in aqueous electrolyte solutions may help in the understanding of the solubility behavior of other biomolecules. In addition, amino acids are valuable bioproducts. In this study we measure and model the solubility of amino acids in aqueous electrolyte solutions. Experimental measurement of the solubility of amino acids in aqueous electrolyte solutions has been the subject of few and rather old studies. The results of most of these studies were compiled by Cohn and Edsall (1965). The experimental measurements revealed that the presence of an electrolyte changes the solubility of an amino acid and usually increases it. This phenomenon is known as the salting-in effect. The reverse of this phenomenon in which the solubility of the amino acid decreases with an increase in the electrolyte concentration may also happen, and it is called the salting-out effect. As discussed by Cohn and Edsall (1965), the solubilities of glycine, cystine, and aspartic acid increase as the concentration of NaCl in the solution increases. It has been also shown that different electrolytes may have different effects on the solubilities of amino acids. For example, leucine shows a saltingin effect in the presence of NaCl and a salting-out effect in the presence of CaCl2 (Cohn and Edsall, 1965). To the best of our knowledge, the only modeling work for the solubility of amino acids in aqueous electrolyte solutions was performed by Chen et al. (1982). They * Author to whom correspondence should be addressed. S0888-5885(96)00639-2 CCC: $14.00
used their own version of the electrolyte NRTL model (Chen et al., 1982) to model the solubilities of four amino acids in electrolyte solutions. Their model contains a long-range interaction term represented by a PitzerDebye-Hu¨ckel form (Pitzer, 1980) and a short-range interaction term given by a modified form of the NRTL equation (Renon and Prausnitz, 1968). The modeling of the solubility of amino acids in aqueous solutions containing an electrolyte depends, to a large extent, on the accurate calculation of their activity coefficients. Lack of reliable models for the activity coefficients of amino acids in aqueous electrolyte solutions has been probably the main barrier for the development of solubility models. Despite its importance, very few studies have been conducted to develop models for the activity coefficients of amino acids in aqueous electrolyte solutions. Kirkwood (1934, 1939) developed two models which can qualitatively represent the behavior of the water-electrolyte-amino acid systems at low electrolyte and amino acid concentrations. Ferna´ndez-Me´rida et al. (1994) and Rodriguez-Raposo et al. (1994) applied the modified form of the Pitzer model (Pitzer, 1991) for aqueous solutions of an electrolyte and a nonelectrolyte to model the activity coefficients in water-electrolyte-amino acid systems. We have recently proposed two models for the activity coefficients of amino acids in aqueous solutions containing an electrolyte (Khoshkbarchi and Vera, 1996 a,b). The first model (Khoshkbarchi and Vera, 1996a) is a combination of a short-range interaction term represented by the NRTL model (Renon and Prausnitz, 1968) or the Wilson model (Wilson, 1964) and a long-range interaction term represented by the Bromley model (Bromley, 1973) or the K-V model (Khoshkbarchi and Vera, 1996c). The second model is based on the perturbation theory with a hard-sphere reference system (Khoshkbarchi and Vera, 1996b). Both models were applied to several water-electrolyte-amino acid systems and were shown to be able to correlate the experimental data accurately over a wide range of amino acid and electrolyte concentrations. In this study we have measured the solubility at 298.2 K of four amino acids in aqueous solutions of NaCl and KCl. The amino acids studied were glycine, DL-alanine, DL-valine, and DL-serine. A model has been developed to correlate the solubility of amino acids in aqueous electrolyte solutions. The activity coefficients have been calculated with a perturbed hard-sphere model recently proposed by Khoshkbarchi and Vera (1996b). It is © 1997 American Chemical Society
2446 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
shown that the model can accurately correlate the experimental data. Materials and Methods Sodium chloride and potassium chloride of 99.9% purity and glycine, DL-alanine, DL-serine, and DL-valine of 99.0% purity were obtained from A&C American Chemicals Ltd. (Montreal, Quebec, Canada). All amino acids were used as received. The salts were oven-dried for 72 h prior to use. During the drying period, each salt was taken out of the oven after 48 and 72 h, and, after cooling it in a vacuum desiccator, it was weighed. After 48 h, no change in its weight was observed. All the solutions were prepared based on molality, and the water was also weighed. The compositions of the initial solutions were accurate within (0.01 wt %. In all experiments deionized water with a conductivity of less than 0.8 µS cm-1 was used. Deionized water was prepared by passing the distilled water through ion-exchange columns of type Easy pure RF, Compact Ultrapure Water System, Barnstead Thermoline. Throughout the experiments, the temperature was kept constant at 298.2 ( 0.02 K using a thermostatic bath coupled with a bath cooler. The experiments were performed by preparing solutions with different molalities of NaCl or KCl and adding the amino acid, in an excess amount to that required for saturation. Jacketed glass containers containing 40 mL of solution were placed on top of magnetic stirrers and mixed continuously with a Tefloncoated stirring magnet. The temperature of the solution was first maintained for 3 h at 303.2 K, then it was lowered to 298.2 K, and the mixing was continued for 48 h to reach equilibrium. The mixing was then stopped for 7 h to settle the undissolved amino acid particles. The results of experiments with different mixing times showed that there was no difference in solubility after 24 h. Thus, a period of 48 h for mixing was employed to ensure that the equilibrium was attained. After settling the undissolved amino acid particles, a sample of the supernatant phase was withdrawn with a plastic syringe and filtered, through a 0.22 µm, HPLC, MSI disposable filter, into previously weighed aluminum dishes. These filters were previously tested with solutions of known concentration of amino acids and were found to have no adsorption toward amino acids. The aluminum dishes were then capped and weighed. The caps were also weighed. After removing the caps, the dishes were placed in an oven for 24 h at 323.2 K and for 72 h at 353.2 K to evaporate the water. After the evaporation, the aluminum dishes with the samples were weighed. The molality of dissolved amino acid was calculated from the knowledge of the initial concentration of the electrolyte present in the solution and the weights of the caps and of the aluminum dishes empty, with solution, and with dry sample. To test the effect of possible interfering parameters, known amounts of amino acid were dissolved to form unsaturated aqueous solutions with various NaCl or KCl concentrations and the amount of amino acid was measured by the dry weight method explained above. The measured concentrations were usually different by 0.1% and never by more than 0.4% from the initial known concentration of the solution. These experiments indicated that no detectable error was introduced due to sublimation of amino acid in the oven, retention of water by either the salt or the amino acid in the dry sample, or adsorption of the amino acid to the syringe or filter, respectively.
Figure 1. Solubility of glycine in aqueous solutions of NaCl and KCl: (b) experimental data for NaCl-glycine; (f) experimental data for glycine KCl; (s) results of modeling.
Figure 2. Solubility of DL-alanine in aqueous solutions of NaCl and KCl: (b) experimental data; (s) results of modeling.
For all water-electrolyte-amino acid systems four experiments were performed by adding amino acid by 10%, 30%, 50%, and 70% in excess to the solubility of the amino acid under investigation to the solutions of 1.0 and 1.5 m of NaCl or KCl. The solubilities of the amino acids in these systems were then measured by the method described above. The results showed that the measured solubilities were different by 0.5-1.3%. From these measurements it was concluded that no appreciable amount of electrolyte was adsorbed on the amino acid in the solid phase. Thus, the solid phase can be considered to be pure amino acid. All experiments were replicated at least four times and in most cases six times. The data reported are the average of the replicates. Sample variances were obtained from the replicates for each point, and a pooled standard deviation was calculated using these values. The calculated pooled standard deviations for a 95% confidence interval for the values of the solubilities of glycine, DL-alanine, DL-valine, and DL-serine in aqueous solutions of NaCl were calculated to be (0.7, (0.2, (0.2, and (0.4 g of amino acid/1000 g of water, respectively, and for the same amino acids in aqueous solutions of KCl were calculated to be (0.3, (0.1, (0.4, and (0.2 g of amino acid/1000 g of water, respectively. Experimental Results Figures 1-4 show the solubility of glycine, DL-alanine, and DL-serine, respectively, in aqueous solutions of NaCl or KCl at various electrolyte concentrations. The values of the solubilities measured are also presented in Tables 1 and 2. As shown in these figures the presence of NaCl and KCl has a drastic effect on the solubility of amino acids which may lead to either a salting-out or a salting-in effect. In order to show these effects more clearly, a horizontal line has been drawn in Figures 1-4 at the value of the solubility in the absence of salt. Notably, over the whole range of DL-valine,
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2447 Table 3. Chemical Structure of the Amino Acids Studied amino acid
chemical structure
Figure 3. Solubility of DL-valine in aqueous solutions of NaCl and KCl: (b) experimental data; (s) results of modeling.
Figure 4. Solubility of DL-serine in aqueous solutions of NaCl and KCl: (b) experimental data; (s) results of modeling. Table 1. Solubilities of Glycine in Aqueous Solutions of NaCl and KCl (of Amino Acid/1000 g of Water) glycine
electrolyte molality
NaCl
KCl
0.00 0.05 0.10 0.20 0.30 0.50 0.70 1.00 1.50
249.9 242.5 240.3 241.0 243.2 244.7 247.1 252.8 262.0
249.9 244.9 242.9 242.9 245.0 249.9 255.1 262.2 273.8
Table 2. Solubilities of DL-Alanine, DL-Valine, and DL-Serine in Aqueous Solutions of NaCl and KCl (g of Amino Acid/1000 g of Water) DL-alanine
DL-valine
DL-serine
electrolyte molality
NaCl
KCl
NaCl
KCl
NaCl
KCl
0.0 0.3 0.5 0.7 1.0 1.5
168.2 167.4 166.8 166.2 165.5 164.1
168.2 171.9 174.0 176.4 179.4 185.4
70.2 69.5 68.7 67.6 66.0 62.6
70.2 74.6 77.2 79.4 82.1 86.7
50.2 53.7 55.7 57.6 59.9 63.3
50.2 58.7 63.9 68.8 76.2 87.1
electrolyte concentration studied, and for all four amino acids, the solubility is larger in the presence of KCl than in the presence of NaCl. These effects are the result of the balance between the interactions of the ions and water molecules with the hydrocarbon backbones and the charged amino and carboxyl groups of the amino acids. Therefore, the chemical structure of amino acids plays an important role in their interactions with water molecules and different ions. Table 3 presents the chemical structure of the four amino acids studied here. As can be seen from Table 3, all four amino acids studied have in common an amino and a carboxyl group, but their hydrocarbon backbones are different. Glycine is the simplest amino acid with the smallest hydrocarbon backbone. The hydrocarbon backbone of DL-alanine has
one -CH2 group more than glycine and the hydrocarbon backbone of DL-valine has two -CH2 groups more than DL-alanine. The hydrocarbon backbones of DL-serine and DL-alanine have the same number of -CH2 groups. However, DL-serine has an -OH group in its hydrocarbon backbone. It should be mentioned that the amino acid carboxyl groups in aqueous solutions lose a proton and become negatively charged and their amino groups gain a proton and become positively charged. This form of an amino acid with a double charge is called a zwitterion. This results in the formation of a strong electrostatic field around the amino acid molecules, which gives rise to important ion-amino acid interactions. As is shown in Figure 1, at low electrolyte concentration the solubility of glycine, which is the simplest amino acid, decreases as the electrolyte concentration increases until it reaches a minimum solubility. After this point, the solubility of glycine increases with an increase in the electrolyte concentration. A reason for this anomalous behavior of glycine can be that, at low electrolyte concentrations, glycine molecules are surrounded by a strong electrostatic field which results in a long-range interaction between glycine molecules and charged ions. These kinds of interactions cause a salting-out effect. At higher electrolyte concentrations, however, glycine molecules may tend to form ion-pair complexes with the charged ions in the solution of the form:
AA+ + C+A- a C+(-AA+)A-
-
where -AA+ is the zwitterionic form of the amino acid and C+ and A- are the cation and the anion of the electrolyte, respectively. The formation of these complexes would suppress the long-range electrostatic forces, and, at the same time, the ion pairs would shield the hydrophobic interactions of the hydrocarbon backbone of glycine, thus producing a salting-in effect. Another reason for this behavior of glycine can be due to the formation of different crystalline forms of glycine in the solid phase at different electrolyte concentrations. This would affect the chemical potential of the solid phase, and hence the solubility of glycine. In fact, the
2448 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
formation of the different crystalline forms of the amino acids at different electrolyte concentrations can be visually observed by drying an electrolyte-amino acid aqueous solution. At low salt concentrations, precipitation occurs in the form of fine particles, and at higher salt concentrations, the crystals become rodlike and grow in size. At salt concentrations of about 1-1.5 m, the crystals grow up to 2-3 mm in length. From a modeling standpoint the occurrence of this phenomenon needs to be considered, and, at the present stage, it required the introduction of an empirical term in the model. Adsorption of the electrolyte on the solid amino acid, although in small quantity, may also affect the solubility behavior of an amino acid. Figure 1 shows that the trends of the solubility curves of glycine in the presence of both NaCl and KCl are similar. However, the solubility of glycine in the presence of KCl is higher than its solubility in the presence of NaCl, over the whole range of electrolyte concentration studied. From this figure, it can also be seen that at higher electrolyte concentrations the difference between the solubility of glycine in NaCl and in KCl solutions is larger. Once more, this effect can be related to the formation of ion-pair complexes between glycine and the ions in the solutions, and it can be inferred that ion-pair complexes formed by potassium ions and glycine screen more the hydrophobic and electrostatic interactions than the ion-pair complexes formed between sodium ions and glycine. From Figures 2 and 3 it can be seen that, in contrast to the solubility curves of glycine, the solubility curves of both DL-alanine and DL-valine in aqueous NaCl or KCl solutions do not pass through a minimum. For both amino acids, the presence of NaCl leads to a saltingout effect, whereas the presence of KCl results in a salting-in effect, over the whole range of electrolyte concentrations studied. As discussed before, these effects can be attributed to the difference between physicochemical properties of the ion-pair complexes formed between each amino acid and the sodium or the potassium ions. It should be noted that, in the case of DL-alanine and DL-valine, the hydrocarbon backbones are also larger than that of glycine, and this makes the effect of the hydrophobic interactions more pronounced. Figure 4 shows that the presence of NaCl or KCl has a salting-in effect on DL-serine over the whole range of electrolyte concentration studied. This can be due to the presence of an -OH group in the hydrocarbon backbone of DL-serine. This -OH group increases the polarity of the DL-serine hydrocarbon backbone and increases its tendency to dissolve in ionic solutions. As discussed before, the experimental data show that the interactions between hydrocarbon backbones of amino acids with the molecules of water and with the ions play an important role in the solubility behavior of amino acids. A comparison of the solubilities of glycine, DL-alanine, and DL-valine shows that a larger hydrocarbon backbone in the amino acid leads to a lower solubility in water (Fasman, 1976). Figure 5 compares the ratio of solubilities of DLalanine and DL-valine in the presence of NaCl or KCl to their solubilities in pure water, S/S0, as a function of electrolyte concentration. As can be seen from this figure, the presence of an electrolyte has a smaller effect on the ratio S/S0 of DL-alanine than on the ratio S/S0 of DL-valine. Since DL-valine has two -CH2 groups more than DL-alanine in the hydrocarbon backbone, it can be deduced that the interactions of the ions with the
Figure 5. Comparison of the ratio of the solubilities of DL-alanine and DL-valine in aqueous solutions of NaCl and KCl to their solubilities in pure water, S/S0: (b) experimental data for DLalanine; (f) experimental data for DL-valine.
Figure 6. Comparison of the ratio of the solubilities of DL-alanine and DL-serine in aqueous solutions of NaCl and KCl to their solubilities in pure water, S/S0: (b) experimental data for DLalanine; (f) experimental data for DL-serine.
hydrocarbon backbones of amino acids play a major role in their solubilities. Figure 6 compares the ratio of solubilities of DLalanine and DL-serine in the presence of NaCl or KCl to their solubilities in pure water, S/S0, as a function of electrolyte concentration. Both DL-alanine and DLserine have the same number of -CH2 groups and are only different by one -OH group in DL-serine. As can be seen from this figure, over the whole range of NaCl or KCl concentration studied, the presence of the electrolyte has a smaller effect on the ratio S/S0 of DLalanine than on that of DL-serine. As discussed before, this effect is probably due to the presence of an -OH group in the hydrocarbon backbone of DL-serine which increases its polarity. Since the solubility depends not only on the interactions in the liquid phase but also on the fugacity of the solid phase, other effects of the -OH group of DL-serine may also be important. For example, the -OH group in DL-serine, due to its highly polar nature, even when DL-serine is in the solid state, can easily become hydrated with different degrees of hydration, which, in turn, depends on the salt concentration. This, in turn, results in the formation of various crystalline forms and change of the chemical potential of the solid phase at different salt concentrations. Modeling The solubility of an amino acid, mAA, in an aqueous solution containing an electrolyte can be expressed in terms of its saturation molality in the absence of an electrolyte, mAA°, the ratio of its molality scale, unsymmetrically normalized, activity coefficients in the absence and in the presence of an electrolyte, γAA°/γAA, and the ratio of its solid-state fugacities in the presence and in the absence of an electrolyte, fAAS/fAA°S, by
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2449
mAA )
mAA°γAA° fAAS γAA f °S
(1)
Table 4. Values of the Pure Component Parameters of Amino Acids and Ions
AA
In both cases, the standard-state fugacity is chosen by considering the amino acid at infinite dilution in pure water as the reference state. For a pure solid phase in equilibrium with a solution, the fugacity of the solid phase is only a function of the temperature of the system. Thus, at constant temperature, if both solid phases are pure and have the same crystalline form, the ratio fAAS/fAA°S is equal to unity and is independent of the composition of the liquid phases in equilibrium with each amino acid solid phase. Hence, in this case, eq 1 simplifies to
mAA°γAA° mAA ) γAA
(2)
The values of γAA and γAA° can be calculated from a model based on the perturbation theory proposed by Khoshkbarchi and Vera (1996b) as
ln γAA(FAA) ) ln γAAHS -
{
4π 8 8 3 F σ 3 + F σ (1 + 2nFAA) + kT 9 AA AA AA 9 S AA,S x AA S FSR j SD h AA2
h AA2D h AA2 FAAD + 3
3(4π0r)2kTσAA,S
9(4π0r)2kTσAA3
+
FSzS2e2D h AA2 6(4π0r)2kTσAA,S
}
(3)
and
ln γAA°(FAA°) ) lim ln γAA(FAA)
(4)
FSf0
where F is the number density, 0 is the permittivity of vacuum, r is the relative dielectric constant of the medium, is the depth of the potential well, σ is the size parameter, D h is the dipole moment, R j is the polarizability, z is the charge number, e is the basic electric charge, k is the Boltzmann constant, and T is the absolute temperature. The binary interaction parameters l and n are the characteristic of each waterelectrolyte-amino acid system. It should be clearly mentioned that these parameters are not the adjustable parameters in this study, and their values can be evaluated from independent measurements of the activity coefficients of amino acids in aqueous electrolyte solutions. The contribution of the hard sphere to the activity coefficient, ln γAAHS is presented in the Appendix. From eq 2, once the solubility of the amino acid in pure water and its activity coefficient at saturation in pure water and in the water-electrolyte system are known, the solubility of the amino acid in an aqueous solution containing an electrolyte can be predicted. However, the derivation of eq 2 relies on the assumption that at various electrolyte concentrations the solid phase is pure amino acid and its crystalline form remains the same. In a general case this assumption does not hold and the ratio fAAS/fAA°S is a function of the electrolyte concentration. Even when no adsorption of salt in the solid phase amino acid was observed experimentally, the effect of salt in the crystallographic form of the solid phase of the amino acid was clearly observed. In order
glycine DL-alanine DL-valine DL-serine Na+ K+ Cl-
/k (K)
σ × 1010 (m)
D h (D)
165.40 86.40 8.30 189.33 96.00a 214.00a 336.00a
4.76 4.09 4.22 4.83 1.90b 2.66b 3.62b
11.50 9.53 10.68 10.34
R j ×1030 (m3)
0.158c 0.850c 3.940c
a Calculated from eq 12. b Reported in Lange’s Handbook of Chemistry (Dean, 1985). c Reported by Coker (1976). All values for amino acids are obtained from Khoshkbarchi and Vera (1996b).
to correlate the experimental results, a simple algebraic empirical form for the ratio fAAS/fAA°S, as a function of molality of the salt, is proposed in the next section. Evaluation of Parameters The parameters required by the model used in this work are the dipole moments, size parameters, and depths of potential wells of the amino acids and polarizabilities, and size parameters and depths of potential wells of both cation and anion of the electrolyte. The dipole moments of amino acids, which are not experimentally measurable (Greenstein and Winitz, 1961), have been previously calculated from a quantum mechanical approach using Hyperchem Molecular Modelling software (Khoshkbarchi and Vera, 1996b). The depths of potential wells and size parameters of the amino acids studied were also obtained previously (Khoshkbarchi and Vera, 1996b). These values together with the values of the dipole moments of amino acids are presented in Table 4. The size parameters of the electrolytes were considered to be the sum of the diameters of their cations and anions taken from their crystal lattice radii reported in Lange’s Handbook of Chemistry (Dean, 1985). The values of the ions polarizabilities are taken from Coker (1976). The electrolyte polarizability is considered to be the sum of its anion and cation polarizabilities. The total charge of the electrolyte is considered to be the sum of the net charges of its anions and cations. The ions depths of potential wells are calculated using the dispersion forces theory of Mavroyannis and Stephen (1962), with the pair potential written as
uijM-S(r) )
j iR jj 3a01/2e2R 2r6[(R j i/ηi)1/2 + (R j j/ηj)1/2]
(5)
where η is the total number of electrons in the particle, R j is the polarizability, and a0 ) 0.5292 Å is the Bohr radius. Following the method proposed by Shoor and Gubbins (1969), the depth of the potential well of each ion can be calculated by coupling eq 5 with the LennardJones equation (Maitland et al., 1981) as
j i1.5ηi0.5 i 2.2789 × 10-11R ) k σ6
(6)
i
The calculated values of the depths of potential wells for sodium, potassium, and chloride ions together with other parameters of the ions are presented in Table 4. The depth of the potential well for the electrolyte is calculated by the following mixing rule:
2450 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 Table 5. Values of the Parameters l and n for Equation 3, Obtained from Khoshkbarchi and Vera (1996b), and the Parameter a for Equation 9, Evaluated in This Work amino acid-electrolyte
l
n/NA
a
glycine + NaCl glycine + KCl DL-alanine + NaCl DL-alanine + KCl DL-valine + NaCl DL-valine + KCl DL-serine + NaCl DL-serine + KCl
0.73 0.66 0.83 0.71 1.00 1.40 0.71 0.42
0.015 0.020 -0.025 -0.037 -0.950 0.125 0.016 0.055
0.060 -0.053 0.021 -0.150 -0.134 -0.365 -0.104 -0.270
S ) x+-
(7)
where subscripts plus and minus indicate the depth of the potential well of the cation and the anion of the electrolyte, respectively. In eq 3 the following mixing rule for the size parameters is used:
1 σAA,S ) (σAA + σS) 2
(8)
The values of the binary interaction parameters l and n, for eq 3, were taken from a previous study (Khoshkbarchi and Vera, 1996b) and are reported in Table 5. These parameters were obtained from the modeling of the activity coefficients of amino acids in aqueous electrolyte solutions, obtained using an electrochemical method. Since the experimental data for the densities of the water-electrolyte-amino acid systems are not available in the literature, the number density values required in eq 3 were calculated using the densities of the water-electrolyte systems, at the same electrolyte concentration, as reported by Novotny and Soehnel (1988). For the fAAS/fAA°S ratio required by eq 1, after some preliminary trials, the following composition dependence was assumed:
fAAS fAA°S
)
1 1 + amSb
(9)
where a and b are adjustable parameters whose values can be determined by curve fitting of the solubility experimental data at various electrolyte concentrations. The use of this empirical form is the weakest point of the present treatment. Other expressions can be tested as more experimental information becomes available. The study of the nature of the solid phase and its evolution with a change in the concentration of electrolyte is a subject for a different study. It is important to mention that amino acids, when dissolved in aqueous media, undergo equilibrium ionization reactions and form different ionic species. As a result, they can lose a proton and form a negatively charged molecule or gain a proton and become a positively charged molecule. They can also have a positively charged amino group (NH3+) and a negatively charged carboxyl group (COO-) in the same molecule and become a zwitterion molecule. The zwitterionic nature of the amino acids is also reflected in their high dipole moments. In the absence of a strong proton donor (an acid) or a proton acceptor (a base), more than 99% of amino acid molecules stay in the zwitterionic form (Cohn and Edsall, 1965). Due to this fact, in this study, we assume that all the amino acid molecules in solutions are in their zwitterionic forms. As shown by Khoshk-
barchi and Vera (1996d), the activity coefficients of optical isomers of an amino acid in aqueous electrolyte solutions are equal. In this work, the parameters used in eq 3 were those obtained from the modeling of the experimental data of the DL-form of these amino acids. Results of Calculations The model proposed in this study was employed to correlate the solubility of four amino acids in aqueous solutions of NaCl or KCl, measured in this study. The solid lines in Figures 1-4 show the results of the correlation of the experimental data. As can be seen from these figures, the model can accurately correlate the solubility data over the whole range of electrolyte concentration studied. The values of the parameter a for eq 9, evaluated in this work, are presented in Table 5. Except for the systems containing glycine, only one adjustable parameter is enough to correlate the solubility of amino acids in aqueous electrolyte solutions measured in this work, and thus we set b ) 1. The reason for using two adjustable parameters for the systems containing glycine is the anomalous behavior of the solubility of glycine in electrolyte solutions discussed in detail in the previous sections. For glycine systems, the value of parameter b was obtained from a fit of the experimental data and was found to be equal to 0.150 for a water-NaCl-glycine system and 0.053 for a water-KCl-glycine system. It should be emphasized that eq 9 is an empirical form proposed to fit the experimental data within the range of salt concentration, up to 1.5 m studied in this work. For systems with a negative value of the parameter a, eq 9 will give erroneous results if used for salt molalities larger than (1/a)1/2. Conclusions The solubilities at 298.2 K of glycine, DL-alanine, DLvaline, and DL-serine in aqueous solutions with various NaCl and KCl concentrations up to 1.5 m were measured. The results showed that both the concentration of the electrolyte and the nature of its cation and of the amino acid affect the solubility of the amino acid in aqueous electrolyte solutions. It was shown that the model developed in this study can accurately correlate the solubilities of amino acids in aqueous electrolyte solutions over a wide range of electrolyte concentration. The model employs a perturbed hard-sphere model as proposed by Khoshkbarchi and Vera (1996b) to represent the activity coefficients of amino acids in electrolyte solutions. Acknowledgment The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for financial support. Notation a ) adjustable parameter b ) adjustable parameter D h ) dipole moment f ) fugacity I ) ionic strength k ) Boltzmann constant (1.381 × 10-23 J K-1) m ) molality l ) adjustable parameter NA ) Avogadro’s number
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2451 n ) adjustable parameter R ) universal gas constant T ) absolute temperature V h ) partial molar volume x ) mole fraction z ) charge number Greek Letters R j ) polarizability γ ) activity coefficient η ) number of electrons ) depth of the potential well 0 ) permittivity of vacuum (8.854 × 10-12 C V-1 m-1) r ) relative dielectric constant ξ ) packing factor F ) number density σ ) size parameter Superscripts HS ) hard sphere M-S ) Mavroyannis and Stephen S ) solid phase ° ) water-amino acid system θ ) standard state Subscripts AA ) amino acid S ) electrolyte + ) cation - ) anion
Appendix In this study the contribution of the hard sphere to the activity coefficient of the amino acid is represented by the model proposed by Mansoori et al. (1971). The mathematical expression for this model can be written as
ln γAA
HS
πPHSσi3 + E + 3F ) -ln(1 - ξ3) + 6kT
(A.1)
where
ξn )
E)
π
n
FkFkn ∑ 6k≈1
(n ) 0, 1, 2, 3)
(A.2)
3ξ2σi + 3ξ1σi2 9ξ22σi2 + 1 - ξ3 2(1 - ξ )2
[
ξ23σi3 3
F)
[
ξ22σi2 ξ32
PHS )
ξ3
2 ln(1 - ξ3) +
2 ln(1 - ξ3) +
[
3
]
ξ3(2 - ξ3) (A.3) 1 - ξ3
ξ3 ξ32 1 - ξ3 2(1 - ξ )2 3
]
3ξ1ξ2 ξ23(3 - ξ3) 6kT ξ0 + + π 1 - ξ3 (1 - ξ )2 (1 - ξ )3 3
3
]
(A.4)
(A.5)
Chen, C. C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Local Composition Model for Excess Gibbs Energy of Electrolyte Systems, 1: Single-Solvent, Single Completely Dissociated Electrolyte Systems. AIChE J. 1982, 32, 444. Coen, C. J.; Blanch, H. W.; Prausnitz, J. M. Salting Out of Aqueous Proteins: Phase Equilibria and Intermolecular Potentials. AIChE J. 1995, 41, 996. Cohn, E. J.; Edsall, J. T. Proteins, Amino Acids and Peptides as Ions and Dipolar Ions; Hafner Publisher Company: New York, 1965. Coker, H. Empirical Free-Ion Polarizabilities of the Alkali Metal, Alkaline Earth Metal, and Halide Ions. J. Phys. Chem. 1976, 80, 2078. Dean, J. A. Lange’s Handbook of Chemistry; McGraw-Hill: New York, 1985. Fasman, G. D. Handbook of Biochemistry and Molecular Biology, Physical and Chemical Data, 3rd ed.; CRC Press: Cleveland, 1976. Ferna´ndez-Me´rida, L.; Rodrı´guez-Raposo, R.; Garcı´a-Garcı´a, G. E.; Esteso, A. Modification of the Pitzer Equations for Application to Electrolyte + Polar Non-electrolyte Mixtures. J. Electroanal. Chem. 1994, 379, 63. Greenstein, J. P.; Winitz, M. Chemistry of Amino Acids; John Wiley & Sons: New York, 1961; Vol. 1. Khoshkbarchi, M. K.; Vera, J. H. Measurement and Modelling of Activities of Amino Acids in Aqueous Salt Systems. AIChE J. 1996a, 42, 2354. Khoshkbarchi, M. K.; Vera, J. H. A Perturbed Hard Sphere Model with Mean Spherical Approximation for the Activity Coefficient Amino Acids in Aqueous Electrolyte Solutions. Ind. Eng. Chem. Res. 1996b, 35, 4755. Khoshkbarchi, M. K.; Vera, J. H. Measurement and Correlation of Ion Activity Coefficients in Aqueous Single Electrolyte Solutions. AIChE J. 1996c, 42, 249. Khoshkbarchi, M. K.; Vera, J. H. Measurement of Activity Coefficients of Amino Acids in Aqueous Electrolyte Solutions: Experimental Data for the Systems H2O + NaCl + Glycine and H2O + NaCl + DL-Alanine at 25 °C. Ind. Eng. Chem. Res. 1996d, 35, 2735. Kirkwood, J. G. Theory of Solutions of Molecules Containing Widely Separated Charges with Spherical Application to Zwitterions. Chem. Phys. 1934, 2, 351. Kirkwood, J. G. Theoretical Studies Upon Dipolar Ions. Chem. Rev. 1939, 24, 233. Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A. Intermolecular Forces; Clarendon Press: Oxford, U.K., 1981. Mansoori, G. A.; Carnahan, N. F.; Starling, K. E.; Leland, T. W. Equilibrium Thermodynamic Properties of Mixtures of Hard Spheres. J. Chem. Phys. 1971, 54, 1523. Mavroyannis, C.; Stephen, M. J. Dispersion Forces. Mol. Phys. 1962, 5, 629. Novotny, P.; Soehnel, O. Density of Binary Aqueous Solutions 306 Inorganic Substances. J. Chem. Eng. Data 1988, 33, 49. Pitzer, K. S. Electrolytes. From Dilute Solutions to Fused Salts. J. Am. Chem. Soc. 1980, 102, 2902. Pitzer, K. S. Activity Coefficients in Electrolyte Solutions; Pitkowicz, M. R., Ed.; CRC Press: Boca Raton, FL, 1991. Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135. Rodrı´guez-Raposo, R.; Ferna´ndez-Me´rida, L.; Esteso, M. A. Activity Coefficients in (Electrolyte + Amino Acid) (aq), the Dependence of the Ion-Zwitterion Interactions on the Ionic Strength and on the Molality of the Amino Acid Analyzed in Terms of Pitzer’s Equations. J. Chem. Thermodyn. 1994, 26, 1121. Shoor, S. K.; Gubbins, K. E. Solubility of Nonpolar Gases in Concentrated Electrolyte Solutions. J. Phys. Chem. 1969, 73, 498. Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127.
where σ is the size parameter of the hard spheres and F is the number density of the components.
Received for review October 11, 1996 Accepted February 26, 1997X
Literature Cited Belter, P. A.; Cussler, E. L.; Hu, W.-S. Bioseparation; John Wiley & Sons Inc.: New York, 1988. Bromley, L. A. Thermodynamic Properties of Strong Electrolytes in Aqueous Solutions. AIChE J. 1973, 19, 313.
IE9606395
Abstract published in Advance ACS Abstracts, April 15, 1997. X
