Ind. Eng. Chem. Res. 1991,30, 1040-1045
1040
Correlation of Amino Acid Solubilities in Aqueous Aliphatic Alcohol Solutions C h a r l e s J. Orellat and Donald J. K i r w a n * Center for Bioprocess Development, Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903-2442
T h e successful description of separation process performance rests on the ability to describe the relevant thermodynamic and rate parameters. An investigation into the correlation of the solubility behavior of amino acids in mixed alcohol-water solvents a t 25 "C is reported here. The measured solubilities of glycine, L-alanine, L-isoleucine, L-phenylalanine, and L-asparagine monohydrate in aqueous solutions of methanol, ethanol, l-propanol, and 2-propanol were correlated with the use of an excess solubility approach and the Wilson activity coefficient formulation. Although the relative solubilities of these solutes changed as much as 3 orders of magnitude from water to pure alcohol, all solubility data were correlated with an average error of 15%. It was also noted that the excess solubility behavior of hydrocarbon gases in alcohol-water solvents was very similar to that of the amino acid solutes.
Introd uction The solubility behavior of amino acids in solutions of aqueous alcohol have been investigated as a prerequisite to crystallization studies. Even for solutes as common as the amino acids, solubility data are rarely available in the open literature. Cohn et al. (1934) measured the solubility of amino acids in mixtures of ethanol and water, but it was almost 40 years before the solubilities of amino acids in mixtures of methanol and water were reported (Gekko, 1981). These experimental data are shown in Figures 1 and 2 as the ratio of the solubility in the mixed solvent to that in water. The solubility of phenylalanine in ethanol solutions was reported by Verban (1986). The curves in Figures 1 and 2 represent correlations we have developed and will be discussed later. We have previously reported on the solubility measurements of various amino acids in binary aqueous solutions of l-propanol and 2-propanol (Orella and Kirwan, 1989). As a prelude to further crystallization studies, the object of this study was to correlate the measured solubility of several amino acids in solutions of water and alcohol. These data sets can then be used to gain an understanding of the solution thermodynamics of dilute solutions of amino acids in binary solutions of water and alcohol. Such thermodynamic information is not only relevant to separation systems for amino acids, but also provides fundamental information of the interactions of such molecules with mixed solvents. Literature Survey and Theory The amino acids are among the simplest biochemicals. In aqueous solutions at intermediate pH values an amino acid is doubly charged and is known as a zwitterion. The zwitterion carries no net charge but acts as a strong dipole. The zwitterion is also common to many other more complex biochemicals, such as the antibiotics. Thus,the amino acids share many similarities with more complex biochemicals. In discussing the solubility of a solute in a binary solvent solution, we will treat a ternary system for which the three components will be water (11, alcohol (2), and solute (3). In order to predict the solubility of an amino acid, we assume that the chemical potential of the solid phase is constant, so that at equilibrium the chemical potential of
* Author to whom correspondence should be addressed.
Current address: Merck Sharp and Dohme Research Laboratories, Merck and Co., Inc., West Point, PA 19486.
the solute in any saturated solution in contact with the solid is fixed. PLsolid
= Pref
+ RT In 73x3 = Pret + RT In 78x5
The last equality is valid for a saturated solution with a specified solvent composition. In this case the solvent is chosen to be pure water. If we choose the same reference chemical potential for all solvent compositions, then the activity of the solute in solution is also fixed. Therefore, the relative solubility varies inversely with the activity coefficient of the solute. x3/x3
= 73/73
,
(2)
The zwitterion must have a large effect on the solubility (activitycoefficient) of the amino acid in solution, although the nature of the side chain will also have considerable influence on it. The correlation or prediction of the solubility in a mixed solvent hinges directly upon the ability to correlate or predict the activity coefficient of the amino acids in mixed solutions. Since most of the amino acids are sparingly soluble in solution, the activity coefficient described above will be very nearly the infinite dilution value at each new solvent composition; that is, the activity coefficient will be insensitive to the concentration of the solute and will be most strongly impacted by the solvent composition. Even for the most soluble amino acids treated here, glycine and alanine, the activity coefficient of a saturated aqueous solution relative to infinite dilution in water is only slightly greater than unity (Sober, 1970), and so the contribution of finite solution concentration to the activity coefficient is small. Electrostatic Approaches One of the few theoretical attempts to consider amino acid solubilities was made by Kirkwood (1934). He used a statistical mechanical approach to determine the effect of a change in solvent on the activity coefficient of a spherical dipole. To derive his analytical solution, Kirkwood neglected dipole-dipole interactions, so that his solution is strictly valid only at infinite dilution. According to this approach, the solubility of a spherical dipole should decrease linearly with the reciprocal of the dielectric constant of the solvent. In x 3 / x $ = --
3P2
49kT
(1/D- l/DO)
(3)
This is the first term in an infinite series that represents
0888-588519112630-1040%02.50/0 , 0 1991 American Chemical Society I
(1)
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1041
x
c .-
2. The data for glycine and alanine examined in their article is that which comes closest to being monotonically decreasing on a semilog plot (see Figure 2). The data for leucine or phenylalanine, however, show an initial drop in solubility, followed by a wide region in which there is very little change in the solubility with changes in the solvent composition. It is difficult to discern how their model would fit this more complex behavior. Orella and Kirwan (19891, when reporting their measurements of the solubility of amino acids in aqueous propanol systems, also considered a correlation method based upon electrostatic and physical contributions. However, this method was not successful when the coefficient of the electrostatic term for a single solute was kept constant for different solvent systems.
0.1
0 -
-1
0
0
0.01
a
.->
. I -
m a
0 alanine
o valine
0.001
[r
A leucine + phenylalanine
0.0001 0
I
I
I
I
0.2
0.4
0.6
0.8
1.0
Mole Fraction Alcohol Figure 1. Comparison of amino acid solubilities in methanol-water solutions at 25 OC with the correlation based on Wilson's equation (data from Gekko (1981)).
I
O m
c
(4)
0.1
E3 0
a
0.01
> .c
m -
a
(I
Excess Approach Using an approach similar to that used for correlating the Henry's coefficient of a gas in a binary solvent solution (O'Connell and Prausnitz, 1963; O'Connell, 1971), it is possible to define the excess solubility of the solute in the mixed solvent.
0.001
+ phenylalanine 0.0001
0
I
I
I
I
0.2
0.4
0.6
0.8
1.0
Mole Fraction Alcohol Figure 2. Comparison of amino acid solubilities in ethanol-water solutions at 25 OC with the correlation based on Wilson's equation (data from Cohn et al. (1934) and Verban (1986)).
the interactions produced by the electric moments (i.e., dipole, quadrupole, etc.). At this same time in the early 19309 it was recognized that the presence of the amino acid in solution significantly increased the dielectric constant of the solution above that of the solvent. Thus, it was proposed that the dielectric constant of the solution should be used in place of the dielectric constant of the solvent. This would represent a first approximation to including the finite solute concentration. Cohn et al. (1934) found that their measurements of the solubility of amino acids in mixtures of ethanol and water did not conform to Kirkwood's prediction except for the case of glycine, using either the solvent or solution dielectric constant. There have been some attempts to combine electrostatic contributions with additional terms to account for physical interactions. Chen et al. (1989) proposed an electrostatic term that varies inversely with solvent dielectric constant. Unlike Kirkwood, Chen et al. allowed the coefficient of the electrostatic term to remain a parameter to be determined from experimental data. Therefore, the constant varied from one solvent system to another. The physical interactions in their model were represented by the NRTL equations. Unfortunately the only data correlated by them were for the amino acids glycine and alanine in aqueous ethanol solutions despite the additional data available (Cohn et al., 1934; Gekko, 1981) as shown in Figures 1and
When the excess solubility is unity, then the solubility in the mixed solvent would be represented by a straight line on a semilog plot of the solubility versus the alcohol mole fraction. In Figure 1 it can be seen that the solubilities in methanol nearly show this behavior. Thus, a first approximation to the solubility in mixed solvents can be obtained by assuming x f i= 1. For more complex solutes (e.g., phenylalanine in ethanol) and for higher alcohols this approximation is not valid quantitatively. The excess solubility then defines the deviations from linear behavior. Several well-known molecular models were utilized to represent the activity coefficient. The three models examined were the three suffix Margules, the Wilson, and the NRTL e uations (Prausnitz et al., 1986). The three suffix Margu es model can be written in the form In y3 = A31xI2(l - 2x3) + 2 A 1 3 ~ 1 ~ & - 1~ 3 +) A32xzZ(l- 2x3) + 2 A 2 3 ~ 2 ~ 3 (-1~ 3 -) 2 A 1 2 ~ 1 ~ - 22~A 2 1 ~ 1 ~ ~Q'X~XZ(I 2 -~ 3 (5) The Wilson model (Wilson, 1964) can be written in the form
'f
+
The NRTL model (Renon and Prausnitz, 1968) has the most complex form:
There are binary solvent-solvent interaction parameters for each of these three models available in the Dechema Chemistry Data Series (Gmehling et al., 1981) which we used without modification. In all three models, the optimum solute-solvent parameters were determined by minimization of an objective function, F, using the simplex routine first described by Nelder and Mead (1965).
)
(8)
)
1042 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 10 Om
..'
X
X"
c -x
0.1
B
3 0
fJ7
0.01
Q)
.->
o glycine
a¶
a:
asparagine H,O A isoleucine phenylalanine
0.0001
0
o glycine
4-
m -
0 alanine
0.2
0 alanine
asparagine H 2 0 A isoleucine phenylalanine
0.001
+
0.6
0.4
0.8
0.0001
1.0
0
0.2
Table I. Aqueous Solubility of Several Amino Acids at 25 O C ( d k a Water) solute present study Sober, 1970 256 250 glycine 169 167 L-alanine 32.0 34.0 L-isoleucine 26.7 29.6 L-phenylalanine L-asparagine monohydrate 28.1 29.9
The predicted values of the relative solubility were calculated from the excess solubility and the known solubilities in the pure solvents using eq 4. With the assumption of low solute concentration the three models for the excess solubility were simplified to Margules
XF =
4-431
+ A32 + Q?(W
~2')
+ 2Ai2xixz2 + 2A21xi2x2 (9)
Wilson In x f
In
[
x1
(: )I
+ x2
-
xix2A13(1
A32
x1 + XZAl2
+
xix&23(1
x1h1
0.8
1.0
Figure 4. Comparison of amino acid solubilities in l-propanolwater solutions at 25 "C with the correlation based on Wilson's equation (data from Orella and Kirwan (1989)).
t
o glycine a alanine 0 valine A leucine
I
OO
0.2
0.4
0.6
0.8
1 .O
Mole Fraction Alcohol Figure 5. Excess solubility of amino acids in aqueous methanol solutions.
- x 2 In - + - A12)
0.6
Mole Fraction Alcohol
Mole Fraction Alcohol Figure 3. Comparison of amino acid solubilities in 2-propanolwater solutions at 25 OC with the correlation based on Wilson's equation (data from Orella and Kirwan (1989)).
In
0.4
- 1121)
+ x2
(10)
NRTL In xF = Xl(713 + G31731) + d 7 2 3 + G32732) -
These three models were then tested for their ability to represent the experimental solubility data.
Results Qualitative Behavior. Our previously reported (Orella and Kirwan, 1989) measurements for the relative solubility of five amino acids at 25 OC in aqueous 1- and 2-propanol solutions are shown in Figures 3 and 4 with correlation lines to be discussed below. The Appendix contains the complete set of tabulated data of the measured solubilities for comparison to predicted values. Since Figures 1-4 indicate only the relative solubility, the measured aqueous solubilities of several amino acids are listed in Table I, along with the comparable literature values.
Examination of Figures 1-4 reveals many qualitative similarities. In each solvent system, glycine and alanine show the largest solubility decrease as the solvent is switched from water to alcohol. For the amino acids with an aliphatic side chain, the relative reduction in solubility decreases as the size of the amino acid side chain increases. Thus, the net interaction between the zwitterion and the solvent becomes less attractive as the alcohol content of the solvent increases. However, for phenylalanine with a nonpolar side chain, the attractive forces between the solute and the solvent increase, and the solubility change is smaller than that for glycine and alanine. Conversely, for asparagine monohydrate with an uncharged but polar side chain, the behavior is quite similar to that of a very small side chain. The effect of increasing the number of carbon atoms in the alcohol is to increase the attraction between the solute and solvent. This effect is small for glycine and alanine. Particularly for phenylalanine, there are dramatic differences between the solubility behavior in solutions containing the different alcohols. In fact, in solutions with 1-propanol, the solubility profile of phenylalanine exhibits a shallow minimum connected to a distinct maximum. Thus, on the basis of the experimental solubilities we surmise that there are multiple interactions that take place between the solute and solvent.
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1043 Table 11. Solubility of Glycine in Solutions Containing 2-Propanol" + re1 soly w2 CR x2 318 exp corr 0.0 256 0.00 0.0566 1.00 1.00 4.7 207 0.0139 0.0489 0.864 0.721 14.9 123 0.0483 0.0319 0.564 0.457 30.3 0.113 0.0173 0.306 0.259 57.6 45.2 0.0097 0.171 0.146 27.9 0.196 60.1 0.00396 0.070 0.0714 9.6 0.310 75.0 0.000857 0.0151 0.0244 1.7 0.473 90 0.000195 0.00344 0.0032 0.3 0.730
o glycine A isoleucine phenylalanine
r.
. I -
* *
::
*
A
A
A
W
*A
*
A
0
0
0
0
"A13
1 0 0 0 0
0.2
0.4
0.6
0.8
1.0
Mole Fraction Alcohol Figure 6. Excess solubility of amino acids in aqueous 2-propanol solutions.
Examples of the excess solubility are presented in Figures 5 and 6. Examination of these two figures shows that the excess solubility for each amino acid is unique, and the deviation of the excess from unity increases as the size of the nonpolar amino acid side chain increases. At very low alcohol concentrations, the excess solubilities of the different amino acids are nearly indistinguishable. In this range, the excess solubilities for all solutes are less than or about unity. Thus, the excess solubility of all amino acids appears as a skewed parabola, when plotted as a function of the mole fraction of alcohol in solution. The fact that the size of the amino acid seems to influence the excess solubility indicates that there are important interactions between the solute and solvent. If not, then we would expect that the excess solubility of all the amino acids would be quite similar. The excess solubility for all cases tested here, including those data presented in Figures 5 and 6, was below 5. Thus, even for solubility changes of 3 orders of magnitude, the excess model provides a qualitative description of the solubility behavior with the assumption of an excess solubility equal to 1. The same assumption allows a numerical estimate of the solubility of the amino acids that is within a factor of 5 of the correct value. This of course, requires the use of the pure component solubilities. However, as shown below, the numerical estimate can be improved significantly by using a molecular model to represent the excess solubility. Correlation and Modeling of Solubility Data. In testing all models, we have used the data base that consists of the solubilities of the amino acids in solutions containing methanol, ethanol, 2-propanol, and 1-propanol from the literature as well as from the experiments performed for this study. Since the relative solubility data of glycine and asparagine monohydrate are very nearly the same (see Figures 3 and 4),fitting the glycine data and the asparagine monohydrate data can be done with the same set of parameters for any given model. The model for the excess solubility based on the Margules activity coefficient form, eq 9, has only one unknown, lumped parameter, since the two solvent-dependent parameters are fixed at the values that represent their binary vapor-liquid equilibrium at that temperature. In all cases it was found that the Margules model did not quantitatively represent the solubility data as well as the Wilson model discussed below. The Wilson model, eq 10, contains three unknown parameters for each ternary system. These are the ratio
= 6.17; A32/A31 = 0.306.
A3, f A3i, A13, and A23. The value of A13 was required to be the same for all alcohol systems for a single solute, so that the solubility data for a single solute in all alcohol systems were regressed simultaneously. In addition, A,, was constrained in order to make the ratio of pure solvent activity coefficients inversely proportional to the ratio of the pure solvent solubilities. This led to an analytical constraint on the three parameters. A23
&2
x8
A31
x!
= AI3 = In - - In -
Thus, for an amino acid for which solubility data were available in n solvent mixtures containing water, the number of parameters to be determined was 1 n since there is a single value of A13 for all n systems. The results of these regressions are presented as the solid curves in Figures 1-4. The use of the Wilson model and the excess solubility gave the best quantitative fit of the experimental results for the available data. Average deviations were less than 15%. Tabulated comparisons of experimental and predicted values of the relative solubility are in the Appendix as are values of the Wilson equation parameters. Still, it is evident that there is a certain loss of detail in the region where the mole fraction of alcohol is below approximately 0.25. The NRTL model, eq 11, was employed to fit the experimental results in a manner similar to that used with the Wilson model. The fit for the solubility obtained was similar to that found by using the Wilson model. However, the NRTL model requires four parameters for each solvent system. Due to this added complexity, the Wilson model was chosen as the simpler of the two models to implement. The excess solubility data presented in Figures 5 and 6 appear to have deviations from parabolic behavior. These deviations appear larger than the estimate of the error in the solubility measurement (5%). In fact, they exhibit positive and negative deviations from an excess solubility of 1, especially in the higher alcohol systems. It was not clear whether this behavior was the result of solute interactions characteristic of the amino acids or was the result of the system alone. For this reason, it is interesting to compare the excess solubility behavior for the amino acids in solutions of water and alcohol with that for a gas in similar solutions. Zeck and Knapp (1985) reported the Henry's coefficient of several gases in binary solvent mixtures of methanol and water, methanol and acetone, and acetone and water (Figure 7). In mixtures of methanol and acetone the Henry's coefficient deviations are small and negative, indicating small positive deviations in the excess solubility. In mixtures of water and acetone the deviations are much larger, but still always positive in the excess solubility. However, in mixtures of water and methanol, the excess Henry's coefficient shows positive deviations from ideality
+
1044 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 10
Table 111. Solubility of Glycine in Solutions Containing 1-Propanola re1 soly corr X, exP c3 3/2 WZ 0.0 4.8 15.3 29.8 44.9 60.1 74.9 90.0
256 217 135 81.9 43.5 16.7 3.9 0.35
0.0566 0.0499 0.0351 0.0242 0.0150 0.00686 0.00197 0.00023
0.00 0.0142 0.0496 0.110 0.194 0.309 0.471 0.730
1.00 0.882 0.620 0.428 0.265 0.121 0.0348 0.00406
1.00 0.743 0.525 0.355 0.224 0.119 0.0448 0.0066
1
-C
0.01
a
A13 = 4.72;
0.0324 0.0287 0.0213 0.0119 0.00717 0.00350 0.00110 0.000015
0.0324 0.0254 0.0203 0.0146 0.00984 0.00529 0.00174 O.ooOo3
0.00 0.0145 0.0503 0.111 0.195 0.310 0.471 0.999
A32/Agl
U
1.00 0.870 0.645 0.361 0.217 0.106 0.0333 0.00046
1.00 0.768 0.520 0.321 0.199 0.109 0.0437 0.00046
1.00 0.784 0.626 0.451 0.303 0.163 0.0537 0.00093
1.00 0.784 0.576 0.410 0.276 0.160 0.0692 0.00093
= 0.194.
Table VI. Solubility of L-Isoleucine in Solutions Containing 2-Propanola re1 solv w2
c3
x2
0.0 4.7 14.9 30.3 45.2 60.1 75.0 90.0 100
32.0 28.1 19.5 13.1 10.2 5.1 2.8 0.8 0.032
0.00 0.0145 0.0497 0.115 0.198 0.311 0.473 0.730 0.999
a A13
x3 0.004 38 0.003 97 0.002 99 0.002 28 0.002 05 0.001 21 0.000 808 0.000 297 0.000019
exp
corr
1.00 0.906 0.683 0.521 0.468 0.276 0.184 0.0678 0.00434
1.00 0.891 0.731 0.569 0.438 0.311 0.181 0.0589 0.00434
= 1.94; A32/A31 = 0.0486.
Table VII. Solubility of L-Isoleucine in Solutions Containing 1-Propanola re1 soly W, C, X., X* exD corr 0 4.8 15.3 29.8 44.9 60.1 74.9 90.0 100 a '113
32.0 28.4 21.9 19.2 15.9 11.1 5.1 0.90 0.098
0 0 0
0.00 0.0142 0.0488 0.114 0.197 0.310 0.473 0.999
169 124 91.6 58.0 33.7 15.2 4.1 0.045
i
Water - Acetone ( 2 ) A Water - Methanol ( 2 )
0.001
Table V. Solubility of L-Alanine in Solutions Containing 1-Propanol" re1 soly exp corr w2 c3 x2 x3 0.0 4.8 15.3 29.8 44.9 60.1 74.9 100
i
I
Table IV. Solubility of L-Alanine in Solutions Containing 2-Pro~anol" re1 soly W, C, XP X!4 exp corr 169 141 96.5 46.9 24.4 10.1 2.6 0.022
i
0.1
UPY
A13 = 6.17; 832/A31 = 0.397.
0.0 4.7 14.9 30.3 45.2 60.1 75.0 100
I
o Methanol - Acetone ( 2 )
0 0.0148 0.0512 0.113 0.196 0.310 0.472 0.729 0.999
1.94; A32/A31 = 0.0699.
0.004 38 0.00403 0.00336 0.00331 0.00317 0.00262 0.00147 0.000336 0.000045
1 0.920 0.767 0.756 0.724 0.598 0.336 0.0767 0.0103
1 0.972 0.907 0.795 0.655 0.487 0.296 0.101 0.0103
0.0001
0
0
0.2
0
0.6
0.4
0.8
1.0
x2
Figure 7. Excess Henry's coefficient for ethylene in several binary solvents (data from Zeck and Knapp (1985)). Table VIII. Solubility of L-Phenylalanine in Solutions Containing 2-Propanol" re1 soly w2 c3 x2 x3 exP corr 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100
26.7 21.7 17.1 16.1 15.7 13.2 9.78 6.24 2.82 0.74 0.061
0.00 0.0322 0.0696 0.114 0.166 0.230 0.310 0.411 0.545 0.729 0.999
0.00290 0.00254 0.00216 0.00221 0.00237 0.00222 0.00184 0.00133 0.000699 0.000218 0.000022
1.00 0.886 0.754 0.772 0.827 0.774 0.641 0.465 0.244 0.076 0.00759
1.00 0.954 0.895 0.822 0.737 0.638 0.523 0.395 0.255 0.116 0.0076
"A13 = 1.64; A32/A31 = 0.0369.
Table IX. Solubility of L-Phenylalanine in Solutions Containing 1-Propanol' re1 soly exp corr w2 c3 x2 x3 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100
26.7 23.9 23.7 24.7 24.4 22.1 18.0 12.3 6.33 1.89 0.18
0.00 0.0322 0.0695 0.114 0.166 0.230 0.309 0.411 0.545 0.729 0.999
0.002 90 0.002 80 0.003 0 0.003 40 0.003 69 0.003 69 0.003 37 0.002 62 0.001 57 0.000 557 0.000 066
1.00 0.954 1.02 1.16 1.26 1.26 1.15 0.893 0.535 0.190 0.0223
1.00 1.28 1.36 1.34 1.25 1.12 0.943 0.727 0.481 0.227 0.0224
"A13 = 1.64; A32/A31 = 0.0583.
Table X. Solubility of L-Asparagine Monohydrate in Solutions Containing 2-Propanol W, C, Xl X2 0.0 15.0 30.0 40.0 50.0 60.0 70.0 90.0
28.7 12.4 5.98 3.78 2.27 1.19 0.577 0.0258
0.00 0.0502 0.114 0.167 0.231 0.310 0.412 0.730
0.003 43 0.001 65 O.OO0 908 O.OO0 630 0.000 419 0.000 246 0.000 136 0.000 008 4
at low alcohol concentrations and negative deviations from ideality at higher alcohol concentrations. These correspond to negative deviations in the excess solubility at low alcohol concentrations and positive excess solubility deviations at
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1045 Table XI. Solubility of L-Asparagine Monohydrate in Solutions Containing 1-Propanol
w2
C8
x2
X8
0.0 15.0 30.0 40.0 50.0 60.0 70.0
28.7 13.8 7.76 5.06 3.04 1.72 0.746 0.256 0.042
0.00 0.0502 0.114 0.167 0.231 0.310 0.412 0.545 0.730
0.00343 0.00185 0.001 18 O.OO0 843 O.OO0 561 O.OO0 356 O.OO0 176 O.OO0 0699 O.OO0 014
80.0 90.0
higher alcohol concentrations. This excess solubility behavior is similar to that exhibited by the amino acids in mixtures containing water and alcohol. This leads one to suspect that the deviation from parabolic behavior results primarily from the nature of the interactions between alcohol and water and are not due to the nature of the solute. There are, as well, important interactions that must involve the solute, since the excess solubility is significantly different for each of the different amino acids.
Conclusions 1. Although the relative solubilities of five different amino acid solutes in four alcohol-water solvent systems may change by over 3 orders of magnitude in going from water to pure alcohol, the excess solubility changes by less than a factor of 5. 2. Combination of a Wilson activity coefficient model with the excess solubility formulation permits correlation of all solubility data with an average deviation of 15%. 3. The qualitative behavior of the excess solubility of dilute solutions of amino acids in alcohol-water solvents is similar to that of hydrocarbon gases in these solvents, suggesting that details of the water-alcohol interactions are of great importance. Acknowledgment This project was supported by The National Science Foundation (CBT8810214) and The Virginia Center for Innovative Technology. Helpful discussions with J. P. O’Connell are gratefully acknowledged.
Nomenclature Aij = parameter in the Margules model C = concentration in gJkg solvent unless specified D = dielectric constant F = objective function for minimization in solubility models Gij = parameter in the NRTL equation k = Boltzmann’s constant Q = parameter in Margules model R = universal gas constant r = radius of a zwitterion T = temperature W = weight fraction x = mole fraction Greek Symbols y = thermodynamic activity coefficient A = parameter in the NRTL model
= chemical potential, or the dipole moment of an amino acid zwitterion in (3) qj = parameter in NRTL model
p
Subscripts
gly = glycine m = mixed 1 = water 2 = alcohol 3 = solute Superscripts a = saturated alcohol solution E = excess o = saturated aqueous solution
Appendix Tables 11-XI contain the complete set of tabulated data of the measured solubilities of glycine, L-alanine, L-isoleucine, L-phenylalanine, and L-asparagine monohydrate in 1- and 2-propanol solutions for comparison with experimental data. Literature Cited Chen, C.; Zhu, Y.; Evans, L. B. Phase Partitioning of Biomolecules: Solubilities of Amino Acids. Biotechnol. Prog. 1989,5,111-118. Cohn, E. J.; McMeekin, T. L.; Edsall, J. T.; Weare, J. H. The Solubility of a-Amino Acids in Alcohol-Water Mixtures. J. Am. Chem. SOC.1934,56,2270-2282. Gekko, K. J. Mechanism of Polyol-Induced Protein Stabilization: Solubility of Amino Acids and Diglycine in Aqueous Poly01 Solutions. J. Biochem. 1981,90,1633-1641. Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection; Chemistry Data Series; Dechema: Frankfurt/Main, Federal Republic of Germany, 1981;Vol. 1, Part la. Kirkwood, J. G. Theory of Solutions of Molecules Containing Widely Separated Charges with Special Applications to Zwitterions. J. Chem. Phys. 1934,2,351-361. Nelder, J. A,; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7,308-313. OConnell, J. P. Molecular Thermodynamics of Gases in Mixed Solvents. AIChE J. 1971,17,659-663. OConnell, J. P.; Prausnitz, J. M. Thermodynamics of Gas Solubility in Mixed Solvents. Ind. Eng. Chem. Fundam. 1963,3,347-353. Orella, C. J.; Kirwan, D. J. The Solubility of Amino Acids in Mixtures of Water and Aliphatic Alcohols. Biotechnol. Prog. 1989,5, 89-91. Prausnitz, J. M.; Lichtenthaler, R. N.; Gomez de Azevedo, E. Molecular Thermodynamics of Fluid Phase Equilibria, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1986;p 234. Renon, H.; Prausnitz, J. M. Local Compositionsin Thermodynamics Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135-143. Sober, H. A,, Ed. Handbook of Biochemistry, 2nd ed.; Chemical Rubber Co. (CRC): Cleveland, OH, 1970. Verban, G. Amino Acid Solubility in Alcohols. Master’s Thesis, University of Virginia, 1986. Wilson, G. M. Vapor Liquid Equilibrium X I Expression for the Excess Free Energy of Mixing. J. Am. Chem. SOC.1964,86, 127-134. Zeck, S.; Knapp, H. Solubilities of Ethylene, Ethane, and Carbon Dioxide in Mixed Solvents of Methanol, Acetone and Water. Znt. J. Thermophys. 1985,6,643-656.
Receiued for review June 7, 1990 Revised manuscript received January 23, 1991 Accepted January 28, 1991
