Znd. Eng. Chem. Res. 1994,33,1565-1573
1565
Amine Extraction of Hydroxycarboxylic Acids. 2. Comparison of Equilibria for Lactic, Malic, and Citric Acids J a r o s l a v ProchAzka,’*+Ale6 Heyberger, Vladislav Bizek, Michasla KouSovA, and E v a VolaufovA Institute of Chemical Process Fundamentals, Academy of Sciences of Czech Republic, Rozvojovci 135, 16502 Praha 6, Suchdol, Czech Republic
Lactic, malic, and citric acids are representatives of hydroxycarboxylic acids, and they are also important biotechnological products. Extraction equilibria of these acids in the system watersolution of trialkylamine in mixtures of l-octanolln-heptane a t temperatures 25,50, and 75 O C have been measured. Mathematical models of diverse complexity are presented, and their goodness of fit is tested and mutually compared. The best fits display the models comprising the formation of three acid-amine complexes and the nonideality of organic phase. In the cases of lactic and malic acids the acid-amine complexes ( l , l ) , (2,1), and (2,2) and in the case of citric acid the complexes ( l , l ) , (1,2), and (2,3) have been included. The incorporation of dissociation in the aqueous phase and of its nonideality has been found to have little effect on the model accuracy. The effects of temperature and solvent composition on the extraction equilibria have been studied, and exponential relations for their prediction have been derived. All the three systems display sensitivity to both temperature and solvent composition. Accordingly the principles of “temperature and diluent swings” are applicable to the processes of extractive recovery and purification of the acids investigated. Introduction Long-chain, aliphatic tertiary amines (TAA) with seven to nine carbon atoms in each alkyl group are effective extractants for carboxylic acids and their derivatives (Wardell and King, 1978; Kertes and King, 1986). For physical reasons they must be applied in solutions with suitable organic diluents. The diluents, however, may modify the extraction power of the amine for a particular acid (Tamada et al., 1990; Tamada and King, 1990; Yang et al., 1991; Bizek et al., 1993). For recoveringthe acid from the organic extract, various processes have been proposed (Baniel et al., 1981; Wennersten, 1983; Bauer et al., 1989; S t a n and King, 1992). A comprehensive survey of principles which can be exploited for this purpose, has been presented by King (1992). Within the scope of the present work the princples of “temperature swing” and “diluent swing” are of immediate interest. Both principles involve reextraction of the acid into pure water under conditions of equilibrium favoring the aqueous phase. The first principle comprises the reextraction under changed temperature; the second one is based on a change of solvent composition before reextraction. It has been shown (Tamada and King, 1990) that the reactions of formation of the acid-amine complexes are exothermic and therefore the apparent constants of complexformation and the respective extraction constants are generally decreasing functions of temperature. Hence low temperature will promote the extraction and elevated temperature the back-extraction. The diluent swing may comprise various effects connected both with formation of various acid-amine complexes in the organic phase and with their interaction with the diluent. The change in solvent composition may comprisean amine concentration change andlor a variation in diluent composition. It has been shown (Tamada et al., 1990; Bizek et al., 1992) that, except for the nonideality effect, the loading of amine with acid does not depend on the amine t
E-mail: ICECAS@CSEARN.
concentration, as long as only the acid-amine complexes of @,l)type are present. Accordingly, the existence of (p,q)complexes with q > 1is a prerequisite of an effective swing by changing the amine concentration. Mixed diluents consisting of an inert diluent and an active “modifier”have been proposed (Baniel et al., 19811, which allow changing the equilibrium in the extraction and reextraction steps by changing the diluent composition. The equilibria of citric acid in the system watersolution of TAA in l-octanolln-heptane at 25 “C were investigated by Bizek et al. (1992). In the present work the equilibria in the systems aqueous lactic, malic, or citric acid solution-solution of TAA in mixtures of l-octanolln-heptane at temperatures 25, 50, and 75 “Chave been investigated. Mathematical models of a common general form have been sought which would allow a satisfactorily accurate correlation and interpolation of experimental data. Simpler variants of the basic models have also been considered, and their goodness of fit has been compared. Theoretical Section Formation of various acid-amine complexes is a dominating feature of equilibria in the systems under consideration. Therefore the method of “chemical modeling” has been adopted as the main approach to the development of the respective mathematical models. Simultaneously other effects, e.g., the dissociation in the aqueous phase, its nonideality, and the specific and nonspecific interactions in the organic phase, have been taken into account. Chemical Reactions. In the present work it is assumed that the reactions between amine and acid molecules take place in the organic phase and that only undissociated acid molecules take part in them. The overall reaction of formation of the @,q) complex is 1”,A
+ jR3N = (HkA),(R3N)j;i = 1-p; j
= l-q; k = 1-3
(1) where the overbar denotes species in organic phase and k = 1, 2, 3 corresponds to lactic, malic, and citric acids,
0SSS-5SS5/94/2633-156~~04.50/0 0 1994 American Chemical Society
1566 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
respectively. The thermodynamic extraction constant, pi;, of reaction 1 is
Pi; = ((H,A)i(R3N)jJI(H,A)’(R3NJj; i = 1-p;j = 1-q; k = 1-3 (2) where the braces denote the activities. Coextraction of water has not been included in reaction 1. Equation 2 can be rewritten as
In the present case the highest value of k is 3 for citric acid. However, the value of the third-step dissociation constant is very low (4.02 X lo-’ a t 25 O C according to Weast and Astle (1981));therefore only k = 1,2 have been taken into account. From the balance of the total acid content in the aqueous phase, one obtains for the molality of its undissociated molecules
mo = mamH2/(mH2 + ~ l D l m H+ P’DZ)
(7)
where mais the total molality of the acid. For the molality of protons it follows from the balance of hydrogen atoms where m and y are the molality and the activity coefficient, respectively, the subscripts 0, e, and i j correspond to undissociated acid, amine and acid-amine complex, and p’i; is the conditioned overall extraction constant. The molalities in the organic phase refer to the diluent basis. The maximum number of reactions included in the model for a particular acid has been limited to three to keep the overall number of adjustable model parameters within reasonable limits. The choice of these reactions is a result of the following considerations. In cases in which overloading of the amine a t elevated acid concentrations in the aqueous phase has been observed, complexes with i > j have been included. When loading of the extractant has been found to depend on the molality of TAA, amine salts with j > 1have been assumed (Tamada et al., 1990; Bizek et al., 1993). Under some circumstances aggregation of simple complexes into larger adducts may occur. According to the stability of the individual aggregates this effect can be described as specific and nonspecific interactions, i.e., as chemical reactions and “physical” nonidealities (Marcus, 1973). The former case belongs to chemical modeling. In the present model the respective species have been described as products of formation from acid and amine molecules rather than as associates of simple complexes. Different sets of chemical reactions have been selected for the individual acids. Initially the (l,l), (2,1),and (2,2) complexes for lactic and malic acids, and (l,l), (1,2), and (2,3) complexes for citric acid, have been chosen. This choice reflects the fact that whereas lactic and malic acids display overloading, citric acid does not. The third complex in each group represents the products of specific aggregation processes. Aqueous Phase. It has been shown (Yang et al., 1991) that tertiary amines (Alamine 336) extract only undissociated molecules of carboxylic acids. Therefore, dissociation equilibria in the aqueous phase have been incorporated in the models. The stepwise dissociation constants are
mH3 + P’DlmH2- (B’Dlm,- P’D2ImH - 2P’Dzma = 0 (8) The activity coefficients of undissociated molecules of citric acid in aqueous solutions were calculated by Levien (1955) from the measurements of osmotic pressure. The data could be correlated as an exponential function of the acid molality. In the present work an empirical function of the form yo = exp[Blmo + B2(m1+ m,)l
(9)
has been used for approximating the activity coefficients of undissociated acid molecules for any of the acids investigated. Here B1 and B2 are empirical constants and ml and m2 are the molalities of the acid molecules dissociated to the first and second steps, respectively; the latter can be evaluated using eq 6:
mi = PfDimJrnHL
(6a)
Organic Phase. The equilibrium content of acid in the organic phase is the sum of contributions of the individual complexes
ml
where;, is the total acid molality in organic phase, the molality of the Ith complex, and j , the stoichiometric coefficient of acid in the complex. Physical solubility of the acids in the diluent has been neglected. For the (l,l), (2,1), and (2,2) stoichiometry eqs 3 and 10 yield
-
-
ma = Plfllaome+ 2(P”21a02-me + V z 2 a 2-,me21
From the balance of TAA me, can be determined: -
the molality of free amine,
-
meo = me + r l l a o m e+ p1121a02Ge + 2vzza,2me2
and the overall constants
(12)
Similarly for the (l,l), (1,2),and (2,3) stoichiometry holds -
i
/3Di
(11)
= (H+f(H,-iAi-)/(HkA)= n K D j ; i = 1-12 j=1
-
-
ma = pfllaome+ ~ f 1 2 a o m+e2pf23a02me3 2 (13)
(5)
and
where k is the number of carboxyl groups of the particular acid. As the acids in question are weak, the molalities of the ions can be substituted for their activities
pDi = m ~ m i / y o m opDi ; = mHimi/mo = yopDi; i = 1-k
Here the partially conditioned equilibrium constants
(6)
Here @ ’ ~ is i the conditioned overall dissociation constant and the subscripts H, i, and o denote the proton, the anion, and the undissociated acid, respectively.
have been used. The activity coefficients and in eq 3 incorporate the nonspecific interactions among the individual com-
Ti;
re
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1567 plexes, the free amine, and the modifier. However, the ratio in eq 3a is assumed to be independent of the acid concentration. It has been proposed to express these interactions as a linear dependence of the logarithm of the activity coefficient on various properties of the interacting species (Schmidt, 1980;Kojima and Fukutomi, 1987). For the system aqueous citric acid-solution of TAA in 1-octanolln-heptane,Bizek et al. (1992) have used the relation
-
+
-
p’.. il = p.. 51 exp(giim,O fijmwo)
(15)
-
where mwois the solubility of water in the acid-free organic phase and f and g are empirical constants. However,from their data it can be seen that the solubility of water is linearly dependent both on the molality of amine and on the mass fraction of octanol in the diluent. Therefore in the present work eq 15 has been modified to -
-
p’’, = pij exp(Aiim,O+ Bijx)
(16)
Effect of Temperature. Data on the temperature dependence of the dissociation constants at infinite dilution for the acids studied are available in the literature (Martell, 1964). For the dependence of the extraction equilibrium constants on temperature the relation l n @ = a / T +b
(17)
has been introduced, in accord with the van’t Hoff equation. In the range of temperatures considered, the empirical parameters a and b, as well as other parameters of the model, are supposed to be independent of temperature.
Experimental Section As trialkylamine a Russian commercial product was used, a mixture of straight-chaintertiary amines with seven to nine carbon atoms per chain containing 2.75 mollkg of active amines (M= 363.3 g/mol). It was conditioned by extracting with aqueous hydrochloric acid, stripping with aqueous sodium hydroxide, and washing with water. Citric acid monohydrate (Lachema Co., Brno), malic and lactic acids (Sigma Chem. Co.), as well as other reagents used, were of analytical grade purity. Lactic acid, a concentrated aqueous solution, was diluted to 15 mass % and depolymerized by boiling under reflux condenser for 6 h. The concentrations of amine in organic phase were determined by potentiometric titration with perchloric acid in acetic acid; the concentrations of acids in both phases were determined by potentiometric titration with sodium methanolate in a 3:l methanol/dimethylformamide mixture. The water content in organic phase was titrated using the Karl Fischer method. The variation of the amount of coextracted water was taken into account when the molalities in organic phase were calculated on the water-free diluent basis. The measurements of equilibria were performed by shaking equal volumes of initial aqueous and organic phases in a thermostated bath for 2 h. Thereafter the mixture was kept in the bath for another 2-5 h to reach full separation of phases. Experiments were carried out at three temperatures, 25, 50, and 75 “C, and at varying compositionsof the solvent. In the experiments at elevated temperature the initial phases were preheated under reflux before mixing to prevent pressurizing of the separation funnels during temperation. In each experiment the equilibrium acid concentrations were determined inde-
pendently in both phases and were checked by material balance. The desired solvent composition was prepared by weighing out the components and was assumed constant during the experiment. The solubilities of amine salts and of n-octanol in the aqueous phase were negligible in the range of variables investigated.
Results and Discussion The above introduced mathematical models consist of the relations 6-9, 16, and either 11 and 12 or 13 and 14, accordingto the acid considered. These equations contain 12 or 13 parameters (pDi, BI, B2, pij, Aij, Bij). The values of the dissociation constants of lactic, malic, and citric acids at the temperatures investigated have been taken from the literature (Bates and Pinching, 1949; Martin and Tartar, 1937;Martell, 1964). The values of the remaining 11parameters have to be determined from experimental data. Most of them are supposed to be temperature independent; the extraction equilibrium constants, pij, should obey eq 17. Two ways of evaluation of the model constants can be considered: either the evaluation from the subsets of data at constant temperature (isotherms), or the evaluation from the whole data set for one acid. In the former case for each subset the values of nine parameters of eq 16 and two parameters of eq 9 have to be determined. However, the values of Aij and Bij thus obtained may vary for different temperatures. In the latter case eqs 16 and 17 can be combined to
Tij= @,,(To)exp[Aij%,O+ B i j i + Cij(l/T- l/To)l (16a) where Tois the reference temperature. Thus the overall number of parameters to be evaluated is 14, but these parameter values are valid for the whole range of temperatures investigated. Model Variants. In view of the high parametricity of the complete models, various simpler models with fewer parameters were considered and their fit of experimental data was compared with that of a complete model. These models were as follows: 1. Models with ideal aqueous phase: yo = 1. 2. Models with the dissociation in aqueous phase neglected: p ~ =i 0; m, = ma. 3. Models with only two complexes considered. Thus in the simplets case models with only six parameters were examined. Evaluation and Comparison of Models. For optimizing the model parameters, the algorithm by Marquardt (1963) has been applied and the FORTRAN program BSOLVE (Kuester and Mize, 1973) has been adapted to this purpose. As an optimization criterion the sum of squares of relative deviations
has been used. The individual models have been compared according to their goodness of fit measured by the relative standard deviation
where n is the number of experiments minus the number of optimized parameters. The significance of the differences in the respective variance values has been assessed by means of the F-test. In what follows the maximum relative deviations
1568 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
are also indicated. Citric Acid. The measurements were performed a t 25 and 75 "C. For further treatment the data published by Bizek et al. (1992),at 25,50, and 75 "C (59 data) were also added. Thus a set of 150 measurements with aqueous 1.3), the molality of TAA acid molality ma E (3 X E (0.16,2.00),and the mass fraction in organic phase of octanol in the diluent E (0.14, 0.52) has been obtained. For the dissociation constants P D the ~ following values were taken (Bates and Pinching, 1949) (values at 75 "C are extrapolated):
Qe
0
U
.- 0,6
N
a X
W
N
-
0,4
1 - 2,0'
02 t ("C) 104PDl 104PD2
50 8.051 1.403
25 7.450 1.296
75 7.820 1.193
In Figures 1-3 some results of measurements at 25 "C are depicted in terms of the dependences of the extractant loading, Z, on the logarithm of acid molality in aqueous phase, log ma. Loading is defined as
d 1
- 1,5
1
I
-1.0
-
0,o
0.5 log ma
Figure 1. Citrgacid. Loading curves atvarying;:. T = 298.2 K; = 0.916 mol/kg; (0) rn: = 1.95 molikg.
x = 0.500; ( 0 )rn:
l
a
- -
I
i
Z = malm:
In Figure 1the effect of the amine molality is shown. The increase of loading with increasing amine molality indicates that complexes with q > 1 are present. In Figure 2 the effect of modifier, 1-octanol,is demonstrated. The increase of octanol content in the diluent promotes the extraction. The data for pure 1-octanol as the limiting case (Bizek et al., 1993) have also been included. Finally, Figure 3 shows a strong and complex effect of temperature on the extraction equilibrium of citric acid. The basic mathematical model for citric acid comprises eqs 6-9, 13, 14, and 16. Various variants of this model have been compared using a set of 105 data at 25 "C. The variants compared are indicated in Table 1;the results of the comparison are shown in Table 2. The last column of Table 2 contains the F-values for the 5 % confidence limit. It is evident that a very good fit has been obtained with the basic model I. The relative standard deviation of 6 % ' is comparable with the mean error of the experimental data, which has been estimated at about 4 % . The results in Table 2 show that there is no significant difference in the goodness of fit between models I, 11, and 111. Accordingly, for practical use both the nonideality and dissociation in the aqueous phase can be neglected and the simpler model I11 can be recommended. The values of the model parameters P i j , A+ and Bij, however, vary in the individual models, as shown in Table 3. This variation corresponds to the differences among the quantities a,, m,, and ma. As the values of -ya f (1.00, 1.07) calculated by means of model I for 25 "C are in good agreement with those found by Levien (1955), the parameter values obtained for this model can be expected to express most accurately the influence of the variables investigated. Using model I, the curves in Figures 1-3 have been calculated. A much lower goodness of fit can be observed when the number of complexes taken into account is reduced. Thus the F-value for model IV with only (1,l) and (1,2)complexes is significantly higher than the value for the 5 % confidence limit. This result supports the assumption that specific forms of aggregation of (1,l) and (1,2) complexes take place in the organic phase. The much higher F-value of model V shows that the role of the (1,2) complex in the models is essential.
0.2
1 -2.0
-3.0
J
0
-1.0
l o g m,
Figure 2. Citric acid. L_oading curves at varying i. T = 298.2 K; m: = 0.780 mol/kg; (0) n = 0.174; (+) n = 0.354; ( 0 )i= 1.000.
OS2
t
01
I
-2.0
I
I
I
-1.0
0 log ma
Figure 3. Citric acid. Loading curves a t varying temperature. rn: = 0.800 mol/kg; = 0.217; ( 0 )T = 298.2 K; (0)T = 323.2 K; (+) T = 348.2 K.
In this connection the effect of temperature is striking. In Table 4 the parameter values obtained for model I at temperatures 50 and 75 "C are compared with those a t 25 "C from Table 3. In this case the model with eq 16 has been used, so that the equilibrium constants Pi, are temperature dependent. The data in Table 4 show that P 2 3 disappears a t elevated temperatures. This finding can be interpreted as a weakening of hydrogen bonding between simple salts with increasing temperature. There-
Table 1. Citric Acid: Model Variants.
I
model I I1 I11 IV V a
/
D, A = dissociation and activity in aqueous phase accounted for.
Table 2. Citric Acid: Comparison of Models at 25 OC model I I1 I11 IV V
S
SI
0.375 0.378 0.396 0.545 2.029
0.062 0.063 0.064 0.074 0.143
% -15.9 -16.2 -16.1 21.9 -59.1
6mm
F
Fn nn
1.00 1.02 1.07 1.43 5.30
1.40 1.40 1.40 1.39 1.39
I
-\
\
11 0.15
.
I
\
I
I
0,175
-0
0.20
1
me
Table 3. Citric Acid: Variation of Parameter Values of Models I, 11, and I11 at 25 OC model
(id
Pij
Aij
4.187 45.84 70.19 4.403 48.78 77.21 4.299 41.81 48.77
-0.00676 -1.897 1.890 0.01638 -2.026 1.875 0.02079 -2.255 1.776
Bij 3.866 6.397 -0.3013 3.662 6.485 -0.3945 3.316 5.994 -0,2417
Figure 4. Citric acid. Effect of K t on equilibrium constants. T = 298.2 K; = 0.400; (-) V I I ; (- - -) ~ " I z (; * -) p 2 3 . 3
I
-.-.-.-.-
.-.-._.
Table 4. Citric Acid Model I: Variation of Parameter Values with Temperature
t = 25 "C; B1= 0.118; Bz = -0.265; sr = 0.0620 -0.00676 3.866 4.187 45.84 -1.897 6.397 1.890 -0.3013 70.19 t = 50 OC; B1 = 0.0462; Bz = 0.100; sr = 0.0580 (1,l) 0.431 1.821 4.167 (1,2) 6.268 -2.240 6.842 (23) 0.000 t = 75 OC; B1 = 0.0462; Bz = 0.100; S, = 0.0728 (1J) 0.146 1.821 4.167 (13 1.600 -2.240 6.842 (23) 0.000 (1J) (12) (23)
Table 5. Citric Acid Parameter Values of Model I with Temperature Term According to Eq 16a (To= 298.2 K)
(id
(1,U (1,2) (23)
Pii
Ai
Bi.i
S = 1.52; s, = 0.0852; 8,- = 20.9%; F = 1.88; Bi = 0.177; Bz = -0.958 4.620 0.0060 3.278 36.45 -1.790 6.767 31.15 1.987 -0.2276
1WCii
6.071 7.034 4.408
fore, at higher temperatures model I is reduced to a model IV type including the activity and dissociation in aqueous phase. As expected, the values of the other two equilibrium constants display a more than 1 order of magnitude decrease in the temperature range examined. I t has been assumed that the parameters B I ,Bz, Aij, and B;j should not depend on temperature. Without substantial loss in accuracy, this could be ensured only at temperatures 50 and 75 "C. Therefore an optimization experiment was undertaken with the whole body of 150 data for citric acid using model I with eq 16a containing the temperature term in the exponent. Its results are shown in Table 5. In this case @"23 does not disappear at higher temperatures, but decreases with increasing temperature similarly as the other two constants. Also the accuracy of the model with the temperature terms is
0.1
0.2
0,3
0,4
-
0.5
Figure 5. Citric acid. Effect of on equilibrium constants. T = 298.2 K; = 1.000 mol/kg; (-) p11; (- - -) ~ " I z ; (- -) 8"23.
somewhat lower than that of model I applied to the individual isotherms. Hence the general model including the temperature as parameter does not seem flexible enough for expressing the strong influence of temperature on specific interactions in the organic phase of the present system. On the other hand it allows simulation of mutual interactions between temperature and solvent composition with reasonable accuracy, using parameter values based on a manageable set of experimental data. Models of this type allow study of simultaneous effects of temperature and diluent swings. Therefore for correlation of data on malic and lactic acids the models incorporating the temperature terms have been used. The influence of nonspecific interactions in organic phase can be demonstrated on the dependence of the equilibrium constants pl', on the amine and octanol concentrations in the solvent according to eq 16. The course of the conditioned extraction equilibrium constants p", as functions of and at 25 "C is shown in Figures 4 and 5. According to Figure 4, the increase of the amine concentration at constant promotes formation of the (2,3) aggregates. This process proceeds apparently at the expense of the (1,l) and (1,2) complexes and is responsible for the overall increase of the acid distribution shown in Figure 1. A contraryeffect of the growing concentration of octanol at constant r n t can be seen in Figure 5. Apparently,
mt
x x
1570 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 t ("C)
104bD1 l W 3 ~ 2
7
z
'
I
-0.5
0
0 -2,0
-1.5
- 1.0
log ma
Figure 6. Citric acid. Components of o z r a l l loading. T = 298.2
K; x = 0.300; m l = 1.000 mol/kg, (-) Zi;m: = 2.000 mol/kg, (- - -)
zi.
N-
1
-2.0
-1.5
-l,o
-0.5
0
log m a
Figure 7. Citric acid. _Components of ovzall loading. T = 298.2 K; m,O = 2.000 molikg; x = 0.300, (-) 2,; x = 0.600, (- - -1 Z,.
1-octanol as a proton-donating solvent tends to form hydrogen-bonded solvates with the (1,l) and (1,2) complexes, thus stabilizing them and increasing the respective extraction constants. This process competes with the formation of hydrogen-bonded (2,3) aggregates. More information about the participation of individual reactions on the overall equilibrium is provided by Figures 6 and 7. Here the contributions - - - of acid molalities in individual complexes ( m L m2, m3) to the overall acid molality in organic phase maare depicted in terms of the respective components of loading (Z1,22,&). In Figure 6 the three isotherms are shown for two levels of amine concentration. It is apparent that higher TAA concentrations promote the (2,3)-complexformation at the expense of the other two complexes. Higher acid concentration, however, favors the (1,l)complex, so that maxima appear on the (1,2) and (2,3) isotherms. In Figure 7 the effect of octanol is shown. At higher octanol concentration the (2,3) isotherm drops and formation of the other two complexes is enhanced. This picture also indicates that the synergistic effect of octanol on the overall acid concentration in the organic phase depends on the acid concentration in the aqueous phase. Malic Acid. Equilibria were measured at 25, 50, and 75 " C in the following ranges: ma E ( 2 X 1.58); m: E (0.38,1.48); E (0.14,0.41). A set of 78 data was obtained. The values of used were (Martell, 1964) (values at 75 "C are extrapolated)
x
25 3.483 2.786
50 3.589 2.547
75 3.589 2.113
Examples of some equilibrium data at 25 and 75 "C are shown in Figures 8 and 9. The basic mathematical model I for malic acid comprises eqs 6-9,11, and 12. In this model, as well as in the simpler variants 11-V, the effect of temperature has been accounted for by including eq 16a instead of eq 16. Therefore the entire set of 78 data has been correlated simultaneously. The results of comparison of goodness of fit of the individual model variants are shown in Table 6. In this case models IV and V comprise the (l,l),(2,l) and (l,l), (2,2) salts, respectively. With the basic model I a similarly good fit has been obtained, as in the case of citric acid. However, it should be noted that in the present case also the effect of temperature variations has been included. Again there are no significant differences in the fit of models 1-111. The merits of including the complex (2,2), representing specific aggregation interactions, in the models are apparent from the fact that model V displays a fit almost as good as the first three models and is significantly better than model IV. The parameter values of model I are summarized in indicates a relatively Table 7. The very small value of small role of the (2,1)-complex formation, which is in correspondence with the good fit of model V. In Table 7 the values of extraction equilibrium constants shown are at the reference temperature 298.2 K. For expressing the effect of temperature on Pi,, eqs 16 and 17 can be combined to
The values of &j as functions of temperature are summarized in Table 8. From the steep drop of these values with increasing temperature, it can be concluded that the application of the temperature swing is promising in this case. In Figures 10 and 11the effects of and on loading calculated using model I are shown. The weak effect of meoand the moderate tendency to oversaturation confirm the choice of reactions included in the model. I t also means that changing the amine concentration alone would not contribute much to the efficiency of the extractionreextraction process. The comparatively strong influence of on the equilibrium, however, indicates that it is still possible to utilize the diluent swing principle for the process enhancement by employing the variation of diluent composition. Lactic Acid. Equilibria were measured at 25,50, and 75 "C in the following ranges: ma E ( 2 X 1.9); m: (0.18, 1.91); E (0.19, 0.53). A set of 70 measurements was obtained. For @ ~the i data published by Marin and Tartar (1937), were used (the value at 75 "C is extrapolated): t ("C) 104bD1
25 1.387
50 1.276
75 1.112
Similarly, as for malic acid, the basic mathematical model for lactic acid comprises eqs 6-9,11,12, and eq 16a including the effect of temperature. Some of the data (points) and their representations by model I (lines) are depicted in Figures 12 and 13. The results of comparison of the model variants are summarized in Table 9. As in the case of malic acid, a
Ind. Eng. Chem. Res., Vol. 33, No. 6,1994 1571
0
N"O' 8 ._ a X 0
I
//
N
0.4
01
I
- 2.0
1.5
- 0.5
-1.0
I
0,o
Figure 8. Malic acid. L o a d i s curves at T = 298.2-K. ( 0 )&" = 0.689 mol/kg, = 0,250; (0) m; = 1.178 mol/kg, x = 0.270; (+) meo = 1.447 mol/kg, x = 0.410.
J
01
-2.0
~ O Yma
-I5
-1.0
-0.5
0.5
0.0 LOP
ma
Figure 10. Malic acid. Effect of on loading. T = 298.2 K; = (-) r n t = 0.500 mol/kg; (-. -) = 1.OOO mol/kg; (- - -) rn; = 1.500 mol/kg.
m,"
0.500;
0,8
-2,o
Figure 9. Malic acid. Loadkg curves at T = 348,2 K. ( 0 )k : = m; = 0.981 mol/kg, x = 0.267. 0.376 mol/kg, = 0.136; (0)
S 0.329 0.382 0.387 0.657 0.452
I1 I11 IV V
Sr
0.072 0.076 0.077 0.097 0.080
,,6 7% -18.9 -20.2 -21.3 30.6 -23.1
F 1.00 1.11 1.14 1.82 1.23
-0,5
-1.0
log m,
0.5
0,o
Figure 11. Malic_acid. Effect of i o n loading. 2': 298.2 K; m,O = x = 0.200; (- - x = 0.300; (- - -) x = 0.400; (- -) x = 0.500.
-
-1.000 mol/kg; (-)
Table 6. Malic Acid Comparison of Models model I
-1,5
..
Fo.06 1.52 1.50 1.50 1.47 1.47
#
Table 7. Malic Acid Parameter Values of Model I ~~
~
(id
Pi] (To)
Aij
Bgj
10-3c,]
To= 298.2 K; B1 = 0.106; Bz = -0.637; S, = 0.0717 (1,l) (2,l) (2,2)
2.395 4.972 X 103 0.04564
-0.09969 2.704 4.510
4.870 5.917 0.6164
5.309 3.966 1.808
Table 8. Malic Acid Effect of TemDerature on 13;; T = 323.2 K T = 348.2 K (id T = 298.2 K 0.6042 0.1858 (171) 2.395 (291) 4.970 X 1.777 X le3 7.365 X lo4 (22) 4.560 X 2.855 X lo-* 1.911 x 10-2
~~~
~
good fit has been obtained with models 1-111. In contrast to the latter acid, however, model IV fits the data even better than the first three variants, whereas the results with model V are quite unsatisfactory. The pronounced deterioration of the results with model V testifies that in the case of lactic acid the existence of the (2,2) complex in organic phase is dubious. Apparently, the association of the (1,l)complex with free acid molecules is more likely
-2,0
-1.5
-1,o
-0,s
0,o
log m a
Figure 12. Lactic acid. Loadkg curves at T = 298.2 K. ( 0 )m,O = 1.130 mol/kg, = 0,384; (0) rn; = 1.210 mol/kg, x = 0.189; (+) m t = 1.910 mol/kg, x = 0.527.
than with another salt molecule. Incorporation of higher associates has not been considered in the present work. In Table 10 the parameter values of eq 16a for model I are summarized. Using these values, the values of extraction equilibrium constants in Table 11 have been calculated for the temperatures 25, 50, and 75 "C. The
1572 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
" 1
-
i c
I
0
-
N0,8 a X
a,
N
0,4
I
0 -1.5
- 0,5
0,o l o g ma
0.5
Figure 13. Lactic acid. Loading curves a t T = 34_8.2K. ( 0 )m t = 0.848mol/kg, I:= 0.225;(0) = 1.040 mol/kg, x = 0.284.
e,
Table 9. Lactic Acid: Comparison of Models S 0.340 0.358 0.327 0.326 2.858
model
I I1 I11 IV
v
01 -2.0
1
I
- l,o
SI
L
0.081 0.081 0.078 0.075 0.222
% -22.1 -21.4 -19.9 -20.0 -40.7 X
F
-1,5
-l,o
0.0
0,s
~ O Ym a
Figure 14. Lactic - acid. Effect of x-= 0.500;(-) r n t = 0.500 mol/kg; meo = 1.500 molikg.
Fn nR 1.52 1.50 1.50 1.47 1.47
1.00 1.00 0.93 0.86 7.51
- 0,s
m t on-loading. (-a
-)
T = 298.2 K; rnz = 1.000 mol/kg; (- - -)
'/
.,/,/
1
Table 10. Lactic Acid: Parameter Values of Model I
c
To = 298.2 K; B1 = 0.0981;Bz = 0.371;S? = 0.0809 (1,U (2,U (292)
2.057 0.5600 1.000
-0.6952 -0.3323 -10.00
5.806 6.552 -50.00
2.736 5.133 50.00
Table 11. Lactic Acid: Effect of Temperature on Bjj
(id
T = 298.2 K
T = 323.2 K
T = 348.2 K
(1,U (2,U (22)
2.057 0.5600 1.000
1.013 0.1480 2.388X lo4
0.5516 4.740 X 3.580X lo-"
m:
effect of and on the loading of extractant is shown in Figures 14 and 15. Similarly, as in the case of malic acid, there is little effect of the amine concentration, but the enhancement of extraction by increasing the octanol concentration is considerable. A strong tendency to oversaturation can be observed, especially at lower alcohol concentrations. The results in Table 11show a somewhat lesser effect of temperature on /311 and than in the cases of citric and malic acids. Nevertheless, it can be concluded that also in the case of lactic acid the application of both the temperature and the diluent swings seems feasible. Comparison of Acids. Comparing the values of the extraction equilibrium constants 011 a t 25 OC in Tables 3, 8, and 10, one can see a drop in the acid order citric > malic > lactic. In the same order decrease also the first dissociation constants, ( 3 ~ 1 , of these acids a t the same temperature. If the value of the equilibrium constant for the (2,1)-complexformation, is taken equal to zero for the citric acid, then these constants increase in the order citric C malic < lactic acid, which is the order of increasing tendency to oversaturation of amine. This finding is similar to that made by Tamada and King (19901, who compared acetic, succincic, lactic, malonic, and maleic acids. Their explanation of these phenomena can be applied to the present case as well. Similar conclusions have been arrived a t by Schmidt (1980) for a broad range of inorganic and organic acids.
I
01 -2.0
-1.5
Figure
15. Lactic acid. Effect of x = 0.200;(x = 0.500.
r n t = 1.000 molikg; (-) (-
** -)
-1.0
-0.5
log
0,0
ma
0,s
I:on- loading. -) x
T =-298.2 K; = 0.300; (- - -) x = 0.400;
Conclusions 1. The extraction equilibria in the systems aqueous solution of hydroxycarboxylic acid-solution of straightchain trialkylamines CT-C~in 1-octanolln-heptane mixtures were measured a t temperatures 25, 50, and 75 OC and in a wide range of solvent compositions. The equilibria of lactic, malic, and citric acids were investigated and mutually compared. 2. Basic mathematical models of a general form were derived, comprising formation of three acid-amine complexes in organic phase, nonideality of this phase, and dissociation and nonideality in the aqueous phase. The acid-amine complexes (l,l), (2,1), and (2,2) have been assumed in the cases of lactic and malic acids and (l,l), (1,2),and (2,3) in the case of citric acid. The basic models have been found to correlate the experimental data with a very good fit. The nonspecific interactions and nonideality in organic phase could be expressed in terms of the amine and alcohol concentrations. 3. The variation of values of the extraction equilibrium constants obtained for the individual acids could be explained in terms of variation of their acidity, consistent with the results for other acids reported in the literature. 4. Simulations performed with the basic models have demonstrated the sensitivity of the equilibria to changes in temperature and solvent composition, thus confirming
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1573 the feasibility of applying the temperature and diluent swing principles on the systems investigated. 5 . Simpler variants of the basic models have been considered and mutually compared according to their fit of experimental data. In all cases neglecting the dissociation and nonideality in aqueous phase had no effect on the model's fit. In the case of citric acid a t elevated temperatures formation of the (2,3) complex could be neglected. In the case of lactic acid neglecting the (2,2) complex in the whole temperature range considered has shown no effect on the model accuracy. Other model variants considered cannot be recommended for predicting equilibria in the respective systems.
Acknowledgment This work has been supported by the Grant Agency, Academy of Sciences of Czech Republic, under Contract No. 47202.
Nomenclature a = activity in aqueous phase, mol/kg of water a = constant in eq 17, K A,, = constant in eq 16, kg of diluent/mol
b = constant in eq 17 B,, = constant in eq 16 B1 = constant in eq 9, kg of water/mol Bz = constant in eq 9, kg of water/mol C, = constant in eq 16a, K f,, = constant in eq 15, kg of diluent/mol g,, = constant in eq 15, kg of diluent/mol j i = stoichiometric coefficient of Ith complex (eq 10) F = ( S , , ) ~ / ( S , # = ratio of variances in comparing ith model with model I Foo5 = value of 5% confidence limit of single-sided F-test k = number of acid carboxyl groups KD,= stepwise dissociation constant, mol/kg ma = total molality of acid in aqueous phase, mol/kg of water mH = molality of protons in aqueous phase, mol/kg of water m, = molality of anions due to dissociation to ith step, mol/kg of water m, = molality of undissociated acid molecules in aqueous - phase, mol/kg of water ma = total molality of acid in organic phase, mol/kg of diluent me = molality of free amine in organic phase, mol/kg of diluent m: = total molality of amine in organic phase, mol/kg of - dilutent = molality of ( i j ) complex in organic phase, mol/kg of mlhiluent mwo= solubility of water in acid-free organic phase, mol/kg of solvent M = effective molar mass of trialkylamine, g/mol n = number of degrees of freedom p = number of acid molecules in complex q = number of amine molecules in complex s, = relative standard deviation (eq 19) S = sum of squares of relative deviations (eq 18) T = temperature, K = mass fraction of 1-octanol in diluent, kg of octanol/(kg of octanol + heptane) 2 = loading of extractant, mol of acid/mol of amine PD, = overall dissociation constant, (mol/kg)I p ' ~= , conditioned overall dissociation constant, (mol/kg)l @,,= thermodynamic extraction equilibrium constant of (ij) complex, (kg/mol),+,-'
P,j= conditioned overall extraction constant of (ij)complex,
(kg/mol)'+j-l = partially conditioned overall extraction constant of ( i j )complex, (kg/mol)i+j-l yo = activity coefficient of undissociated molecules of acid in - aqueous phase ye = activity coefficient of amine in organic phase yij = activity coefficient of ( i j ) complex in organic phase HkA = hydroxycarboxylic acid R3N = trialkylamine @"ij
Literature Cited Baniel, A. M.; Blumberg, R.; Haidu, K. Recovery of acids from aqueous solutions. U.S. Pat. 4,275,234, 1981. Bates, R. G.; Pinching, G. D. Resolution of the dissociation constants of citric acid a t 0 to 50 OC, and determination of certain related thermodynamic functions. J . Am. Chem. SOC.1949, 71, 12741283. Bauer, U.; Marr, R.; Ruckl, W.; Siebenhofer, M. Reactive extraction of citric acid from aqueous fermentation broth. Ber. Bunsen-Ges. Phys. Chem. 1989,93,980-984. Bizek, V.; HorlEek, J.; Reficha, R.; KouBovl, M. Amine extraction of hydroxycarboxylic acids. 1. Extraction of citric acid with 1-octanolin-heptane solutions of trialkylamine. Znd. Eng. Chem. Res. 1992,31, 1554-1562. Bizek, V.; HorBEek, J.; KouBovl, M. Amine extraction of citric acid: Effect of diluent. Chem. Eng. Sci. 1993,48, 1447-1457. Kertes, A. S.;King, C. J. Extraction chemistry of fermentation product carboxylic acids. Biotechnol. Bioeng. 1986, 28, 269-282. Kuester, J. L.; Mize, J. H. Optimization techniques withFORTRAN McGraw-Hill: New York, 1973. King, C. J. Amine-based systems for carboxylic acid recovery. CHEMTECH 1992, May, 285-291. Kojima, T.; Fukutomi, H. Extraction equilibria of hydrochloric acid by trioctylamine in low-polar organic solvents. Bull. Chem. SOC. Jpn. 1987, 68, 1309-1320. Levien, B. A physicochemical study of aqueous citric acid solutions. J . Phys. Chem. 1955,59, 640-644. Marcus, Y. Nonstoichiometric interactions of long-chain ammonium salts in organic solvents. J . Phys. Chem. 1973, 77, 516-519. Marquardt, D. W. An algorithm for least-squares estimation of nonlinear parameters. J . SOC. Znd. Appl. Math. 1963, 11, 431441. Martell, A. E. In Stability constants of metal-ion complexes; The Chemical Society: London, 1964; Section 11, p 411. Martin, A. W.; Tartar, H. V. The ionization constants of lactic acid 0-50 OC, from conductivity measurements. J . Am. Chem. Soc. 1937,59, 2672-2675. Schmidt, V. S . Amine extraction;Atomizdat: Moscow, 1980; pp 4453, 82-84 (in Russian). Starr, J. N.; King, C. J. Water-enhanced solubility of carboxylic acids in organic solvents and its application to extraction processes. Znd. Eng. Chem. Res. 1992,31, 2572-2579. Tamada, J. A.; King, C. J. Extraction of carboxylic acids with amine extractants. 2. Chemical interactions and interpretation of data. Ind. Eng. Chem. Res. 1990,29,1327-1333. Tamada, J. A,; Kertes, A. S.; King, C. J. Extraction of carboxylic acids with amine extractants. 1. Equilibria and law of mass action modelling. Znd. Eng. Chem. Res. 1990,29, 1319-1326. Wardell, J. M.; King, C. J. Solvent equilibria for extraction of carboxylic acids from water. J . Chem. Eng. Data 1978,23, 144148. Weast, R. C.; Astle, M. J. Handbook of chemistry and physics, 62nd ed.; CRC Press: Boca Raton, FL, 1981. Wennersten, R. The extraction of citric acid from fermentation broth using a solution of tertiary amine. J . Chem. Technol. Biotechnol. 1983,33B, 85-94. Yang, S. T.; White, S. A.; Hsu, S. T. Extraction of carboxylic acids with tertiary and quaternary amines: Effect of pH. Znd. Eng. Chem. Res. 1991,30, 1335-1342.
Received for review December 2, 1993 Accepted March 17, 1994' Abstract published in Advance ACS Abstracts, April 15, 1994.
