Article pubs.acs.org/jced
Dissociation Constant and Solubility of (S)‑2-Hydroxy-4phenylbutyric Acid Fengxiang Tang, Zhongli Guo, Daqiang Li, Haoyu Chen, and Suying Zhao* College of Chemistry and Chemical Engineering, Fuzhou University, Fuzhou 350108, Fujian, China ABSTRACT: The dissociation constant (pKa) of (S)-2-hydroxy-4phenylbutyric acid ((S)-HPBA) was determined at 298.2 K by potentiometric titration. (S)-HPBA exhibits a pKa value of 3.81. The solubility of (S)-HPBA in toluene from (288.2 to 343.2) K, in water from (283.2 to 333.2) K, and in ethyl acetate from (278.2 to 313.2) K was measured by the steady-state method. The solubility in all selected solvents increases with the increase of temperature. The solubility of (S)-HPBA in ethyl acetate is much greater than that in water or toluene. Water was found to be a fine alternative to toluene for crystallizing (S)-HPBA and ethyl acetate to be a suitable extraction solvent of (S)-HPBA in the pharmaceutical industry. The experimental solubility data were correlated with the modified Apelblat, Redlich−Kister, Wilson, and universal quasichemical activity coefficient (UNIQUAC) equations, respectively. The Wilson, Redlich−Kister, and modified Apelblat equations show better agreement with the experimental solubility data of (S)-HPBA in toluene, water, and ethyl acetate, respectively. The solubility of (S)-HPBA in aqueous solutions over the pH range from 1.48 to 5.45 at 298.2 K was also determined by the steady-state method, and the corresponding solubility data were separately fitted well with a semi-Henderson−Hasselbalch equation (pH ≤ 4.0) and a linear equation (pH > 4.0).
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INTRODUCTION The production of optically pure intermediates is everincreasingly important to the pharmaceutical industry. (R)-2Hydroxy-4-phenylbutyric acid ((R)-HPBA) and its ethyl ester, ethyl (R)-2-hydroxy-4-phenylbutanoate, are important intermediates for production of various angiotensin-converting enzyme (ACE) inhibitors, such as cilazapril, enalapril, benazepril, ramipril, and quinapril.1−5 In the past three decades, their preparation routes has been intensively developed besides classical chemical resolution,6 such as kinetic resolution,7−10 chemical asymmetric synthesis,5,11−13 and biotransformation by microbe,14−18 plant cell,19 or enzyme20,21 of some prochiral precursors. However, classical chemical resolution is still popular in large-scale production due to its low cost and convenience in operation although the maximum theoretical yield of (R)-HPBA is 50 %. The undesired enantiomer, (S)HPBA, can be separated, racemized,22,23 and then reresolved or transformed into (R)-HPBA by configuration inversion.13 The purification process of (S)-HPBA contains dissociation from its N-octyl-D-glucamine salt, extraction, and crystallization. In order to design an optimum purification process, it is necessary to know its physiochemical data such as the pKa and solubility. However, a survey of the literature of (S)-HPBA indicates that little related data were reported. In the present work, the pKa constant of (S)-HPBA was measured at 298.2 K, and the solubility of (S)-HPBA in toluene from (288.2 to 343.2) K, in water from (283.2 to 333.2) K, and in ethyl acetate from (278.2 to 313.2) K, and in water over the pH range from 1.48 to 5.45 at 298.2 K was determined by the © XXXX American Chemical Society
steady-state method. The solubility data were correlated with different equations.
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EXPERIMENTAL SECTION
Materials. A detailed description of chemicals used in this paper is presented in Table 1. Double-distilled water was used in all experiments. (S)-HPBA with a mass fraction of 0.997 (determined by high-performance liquid chromatography, Table 1. Description of Materials Used in This Paper chemical name crude (S)HPBA toluene ethyl acetate methanol acetic acid sodium hydroxide hydrochloric acid
source Huitian Biological Medicine Industry Co. Ltd., Fujian, China Sinopharm Chemical Reagent Co., China Sinopharm Chemical Reagent Co., China Sinopharm Chemical Reagent Co., China Sinopharm Chemical Reagent Co., China Sinopharm Chemical Reagent Co., China Sinopharm Chemical Reagent Co., China
initial mass fraction purity 0.952 0.995 0.995 0.998 0.995 0.96 0.36−0.38
Received: January 13, 2013 Accepted: April 10, 2013
A
dx.doi.org/10.1021/je400053q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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vessel. The pH value of the aqueous solution containing excess solid (S)-HPBA was initially adjusted using 2 mol·L−1 NaOH or HCl. Then the solution was stirred for 24 h at 25.0 ± 0.1 °C and stood for 6 h. The stable pH value of the supernatant solution was measured using the same pH meter above. Three samples of supernatant solution (1 mL) were taken for HPLC analysis as mentioned above, respectively, and the average solubility (mol·kg−1) was thus obtained.
HPLC, as follows) was obtained from the crude (S)-HPBA shown in Table 1 by recrystallization from water three times. Dissociation Constant. The dissociation constant was measured by the potentiometric titration method.24,25 In a 100 mL cylindrical-jacketed glass vessel furnished with circulating water from a super thermostat water bath (501A, Shanghai Jinghong Laboratory Instrument Co., Ltd., uncertainty: ± 0.1 °C), the inner solution temperature was determined by a mercury-glass thermometer with an uncertainty of ± 0.1 °C and maintained within 25.0 °C ± 0.1 °C. The pH value was measured with a pH meter (FE20/LE438, Mettler-Toledo Instruments Co., Shanghai, uncertainty: 0.01). This pH meter was calibrated against standard buffers of pH 4.00 (phthalate buffer) and 9.20 (borate buffer) before each titration. Nitrogen was purged into the solution to maintain an inert atmosphere. The NaOH titrant was introduced into the system by a buret. Carbonate-free water was newly prepared for titration.25,26 The NaOH titrant was prepared at approximately 0.1 mol·L−1 and standardized by potassium acid phthalate. The accurate concentration was determined to be 0.09721 mol·L−1. A portion of 0.9860 g of (S)-HPBA was dissolved in 100 mL of carbonate-free water just prior to titration, and three 20 mL portions of this (S)-HPBA solution were withdrawn using a 20 mL glass pipet for titration. With continuous magnetic stirring, small increments of standardized NaOH titrant was added to the (S)-HPBA solution. Sufficient time (about (10 to 15) s) was allowed to reach a reasonably stable pH reading before the next NaOH addition was introduced. The stable pH value was recorded together with the volume of NaOH added. When the equivalence point was approached, only dropwise increments of NaOH were added until the equivalence point had been passed. In this way, three titration curves were obtained. (S)-HPBA Solubility in Different Solvents. In a 100 mL jacket glass vessel with circulating water from a super thermostat water bath mentioned above, excess solid (S)HPBA was added into the 50 mL of solvent (water, toluene, or ethyl acetate). A mercury-glass thermometer with an uncertainty of ± 0.1 °C was inserted into the inner solution to measure the temperature of the solution. A condenser was used to prevent the evaporation of the solvent. After being stirred for 24 h to reach equilibrium at a given temperature, the solution was allowed to stand for 6 h, and then 1 mL of supernatant solution was taken, filtered through a 0.45 μm micro membrane, and then appropriately diluted for HPLC analysis on a Shimadzu LC-2010A System equipped with a UV detector and a reversed-phase column (SinoChrom ODS-BP, 4.6 mm × 250 mm, 5 μm, Dalian Elite Analytical Instruments Co. Ltd.) at 254 nm. The column temperature was kept at 30 °C. The mobile phase was composed of CH3OH, H2O, and CH3COOH at a volume ratio of 70:30:1. At a certain temperature, three samples were taken and measured, and the average value is considered to be the solubility. The mole fraction solubility (x1) of the solute was calculated based on x1 =
m1/M1 m1/M1 + m2 /M 2
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RESULTS AND DISCUSSION Dissociation Constant. Figure 1 shows the resulting pH titration curves as a function of the volume of standard NaOH
Figure 1. Potentiometric pH titration curves and their first derivatives: +, titration curve 1; ○, titration curve 2; ×, titration curve 3; , first derivative 1; ---, first derivative 2; -·-·-·, first derivative 3.
added, VNaOH, and the first derivatives of these curves, d(pH)/ dVNaOH. On the first derivative curve 1, VNaOH corresponding to the maximum point, namely, the equivalence point,27 is 52.32 mL. Thus, the corresponding VNaOH of the half-equivalence point is 26.16 mL. At this VNaOH, the corresponding pH value should be 3.82 by interpolation. Therefore, the pKa value of (S)-HPBA is 3.82 according to titration curve 1. The other two groups of titration data gave the pKa value of 3.81 and 3.80, respectively. Hence, the average pKa value is 3.81, which is very similar to the calculated value 3.79.28 (S)-HPBA Solubility in Different Solvents. The solubility values of (S)-HPBA in three solvents at different temperatures are presented in Table 2 and Figures 2 and 3. As shown in Figure 2, the solubility of (S)-HPBA in both water and toluene increases slowly with the increase of temperature and shares the same order of magnitude at low temperatures, but the solubility of (S)-HPBA in water increases more rapidly than that in toluene when the temperature exceeds 323.2 K. From Figures 2 and 3, it is illustrated that the solubility of (S)-HPBA in ethyl acetate is much larger than that in water or toluene. This might be attributed to hydrophobic and hydrogen bond interactions [(S)-HPBA has three H acceptors and two H donors, and ethyl acetate has two H acceptors] taking place between (S)-HPBA and ethyl acetate. However, only the hydrogen bond interaction might account for the solubility of (S)-HPBA in water, and only hydrophobic interaction might contribute to the solubility of (S)-HPBA in toluene. Toluene is presently used as the solvent for recrystallization of (S)-HPBA in the pharmaceutical industry. From this study, water is elicited to be a good alternative to toluene from the view of industrial throughput and environmental friendliness. As for ethyl acetate, it can be used as an extraction solvent due to the large solubility of (S)HPBA in it at room temperature (about 200 kg·m−3).
(1)
where m1 and m2 denote the mass of (S)-HPBA and the solvent used in the experiment and M1 and M2 stand for the molecular weights, respectively. (S)-HPBA Solubility in Aqueous Solutions at Different pH Values. The solubility of (S)-HPBA in aqueous solutions at different pH values was determined in the same jacket glass B
dx.doi.org/10.1021/je400053q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. Mole Fraction Solubility of (S)-HPBA in Three Pure Solvents T/K
x1exp
x1cal,Apel
288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2 328.2 333.2 338.2 343.2
0.00130 0.00169 0.00235 0.00298 0.00407 0.00555 0.00729 0.00996 0.0127 0.0173 0.0238 0.0341
0.00152 0.00190 0.00241 0.00309 0.00401 0.00528 0.00703 0.00946 0.0128 0.0176 0.0243 0.0338
283.2 288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2 328.2 333.2
0.00071 0.00094 0.00107 0.00137 0.00172 0.00229 0.00311 0.00406 0.00701 0.0142 0.0440
278.2 283.2 288.2 293.2 298.2 303.2 308.2 313.2
0.107 0.117 0.128 0.140 0.150 0.160 0.174 0.182
x1cal,R‑K
Toluene 0.00161 0.00205 0.00262 0.00332 0.00426 0.00551 0.00715 0.00952 0.0125 0.0173 0.0241 0.0340 Water 0.00000 0.00069 0.00001 0.00089 0.00002 0.00112 0.00006 0.00144 0.00015 0.00184 0.00038 0.00239 0.00095 0.00316 0.00244 0.00420 0.00629 0.00668 0.0164 0.0143 0.0434 0.0440 Ethyl Acetate 0.107 0.106 0.117 0.119 0.128 0.129 0.139 0.138 0.150 0.150 0.161 0.163 0.172 0.168 0.182 0.185
x1cal,Wilson
x1cal,UNIQ
0.00132 0.00177 0.00236 0.00312 0.00414 0.00549 0.00725 0.00970 0.0128 0.0173 0.0239 0.0341
0.00144 0.00191 0.00251 0.00328 0.00429 0.00562 0.00735 0.00972 0.0127 0.0172 0.0237 0.0342
0.00038 0.00055 0.00076 0.00106 0.00148 0.00210 0.00302 0.00432 0.00721 0.0144 0.0439
0.00122 0.00147 0.00177 0.00214 0.00259 0.00316 0.00392 0.00488 0.00688 0.0121 0.0442
0.0924 0.104 0.116 0.129 0.146 0.166 0.186 0.214
0.103 0.112 0.121 0.133 0.146 0.162 0.179 0.201
Figure 3. Mole fraction solubility (x1) of (S)-HPBA in ethyl acetate. The solid fit line was from the calculated values based on the modified Apelblat equation.
Table 3. Molar Volumes and Structural Parameters component
molar volume/cm3·mol−1
ri
qi
(S)-HPBA toluene water ethyl acetate
147.7028 106.8536 18.0236 98.5036
7.1185 3.9228 0.9200 3.4786
5.582 2.968 1.400 3.116
ln x1 = A + B /(T /K) + C ln(T /K)
(2)
where A, B, and C are three adjustable model parameters and T is the absolute equilibrium temperature. Additionally, according to the classical thermodynamic method dealing with solid−liquid equilibrium, a universal equation describing the solubility of a solute can be expressed as30 ln x1γ1 =
ΔfusH1 ⎛ 1 1 ⎞ ΔfusCp ,1 ⎜⎜ − ⎟⎟ − R ⎝ Tfus,1 T⎠ R ⎛ Tfus,1 ⎞ Tfus,1 − + 1⎟ ⎜ln ⎝ ⎠ T T
(3)
where γ1 denotes the liquid-phase activity coefficient of the solute, ΔfusH1 denotes the enthalpy of fusion at the fusion temperature of the solute, Tfus,1 and ΔfusCp,1 are the difference of heat capacities of the solute at the liquid and solid states, and R is the universal gas constant (8.314 J·mol−1·K−1). The second term on the right-hand side in eq 3 is often minor and negligible as the heat capacities for the liquid and solid tend to compensate each other.31,32 Thus, eq 3 can be simplified as
a
x1exp is the experimentally determined solubility; x1cal,Apel, x1cal,R‑K, x1cal,Wilson, and x1cal,UNIQ are the calculated solubility from the modified Apelblat equation, the Redlich−Kister equation, the Wilson equation, and the UNIQUAC equation, respectively. bThe standard uncertainty u is u(T) = 0.1 K; the relative standard uncertainty u is ur(x1) = 0.02.
ln x1γ1 =
ΔfusH1 ⎛ 1 1⎞ ⎜⎜ − ⎟⎟ R ⎝ Tfus,1 T⎠
(4)
In this study, the Redlich−Kister (R-K) equation, the Wilson equation, and the universal quasichemical activity coefficient (UNIQUAC) equation were used to derive the solute activity coefficients from the experimental data, respectively. A fourorder R-K equation like eq 5 was used,33
Figure 2. Mole fraction solubility (x1) of (S)-HPBA in toluene and water: ■, toluene; ●, water. The solid line and dotted line were from the calculated values based on the Wilson model and the Redlich− Kister (R-K) equation, respectively.
ln γ1 = (1 − x1)2 [D + E(1 − x1) + F(1 − x1)2 ]
(5)
where D, E, and F are three adjustable model parameters. The Wilson equation34 and the UNIQUAC equation35 have been clearly described elsewhere and are not repeated here. The melting temperature of (S)-HPBA is 389.15 K.28 The fusion enthalpy of (S)-HPBA was determined as 31246.7 J·mol−1 on a simultaneous thermal analyzer (NETZSCH STA
The temperature dependence of the solubility values of (S)HPBA in toluene, water, and ethyl acetate was first correlated by the modified Apelblat equation (eq 2)29 C
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Table 4. Parameters of the Modified Apelblat Equation for (S)-HPBA in Three Solvents, r, rmsd, and δave solvent
A
B
C
r
103 rmsd
102 δave
toluene water ethyl acetate
−485.40 −1113.50 86.90
17540.26 35850.47 −5052.98
73.81 172.63 −12.61
0.9996 0.9966 0.9994
0.286 1.454 0.882
4.7 64.0 0.3
Table 5. Parameters of the R-K Equation for (S)-HPBA in Three Solvents, r, rmsd, and δave solvent
D
E
F
r
103 rmsd
102 δave
toluene water ethyl acetate
3.11 3.75 −2.89
−42.17 −104.19 4.80
486.36 1280.59 31.73
0.9997 0.9999 0.9937
0.260 0.125 2.795
6.9 3.6 1.5
Table 6. Parameters of the Wilson Equation for (S)-HPBA in Three Solvents, r, rmsd, and δave λ12 − λ11 solvent toluene water ethyl acetate
λ21 − λ22
−1
J·mol−1
r
103 rmsd
102 δave
6733.28 6102.89 51750.12
0.9999 0.9998 0.9870
0.0996 0.245 15.486
1.5 16.0 9.1
J·mol
1209.33 4329.27 −3452.90
Table 7. Parameters of the UNIQUAC Equation for (S)HPBA in Three Solvents, r, rmsd, and δave u12
u21
solvent
J·mol−1
J·mol−1
r
103 rmsd
102 δave
toluene water ethyl acetate
2894.94 3042.00 62725.23
−1125.56 −1935.24 −2912.01
0.9999 0.9980 0.9870
0.166 0.915 8.608
4.3 36.5 4.5
Figure 4. Molality of (S)-HPBA in aqueous solutions at different pH values: ■, pH ≤ 4.00; ●, pH > 4.00; , calculated solubility based on eqs 9 and 10; ---, calculated solubility from the HH equation.
Table 9. Parameters of eqs 9 and 10, r, rmsd, and δave
449 C, Germany). In addition, molar volumes of (S)-HPBA and three kinds of solvents (toluene, water, and ethyl acetate), and their structural parameters (ri and qi, calculated with group contribution method), which are required for using the Wilson equation and the UNIQUAC equation, respectively, are listed in Table 3. The model parameters of the modified Apelbat equation, the R-K equation, the Wilson equation, and the UNIQUAC equation were obtained by an optimization technique using Levenberg−Marquardt search method. The optimized parameters of the four equations, as well as the correlation coefficients
eq
A′
B′
r
rmsd
102 δave
eq 9 eq 10
0.0695 −0.542
3.73 0.185
0.9996 0.9993
0.00139 0.00311
1.38 0.73
(r), root-mean-square deviations (rmsd), and average relative deviations (δave) are presented in Tables 4, 5, 6, and 7, respectively. The rmsd and δave are defined as N
rmsd =
∑i = 1 (xexp ,i − xcal,i)2 N
(6)
Table 8. Solubility of (S)-HPBA in Water at Different pH Values (298.2 K) Sexp pH 1.48 2.18 2.27 2.41 2.63 2.82 2.98 3.18 3.39 3.48 3.64 3.76 3.86
mol·kg
Scal −1
0.0691 0.0696 0.0707 0.0716 0.0733 0.0788 0.0834 0.0912 0.101 0.110 0.127 0.144 0.164
mol·kg
Sexp −1
0.0699 0.0714 0.0719 0.0728 0.0750 0.0780 0.0818 0.0889 0.101 0.108 0.126 0.143 0.163
Scal −1
2
10 δ
pH
mol·kg
1.16 2.59 1.70 1.68 2.32 −1.02 −1.92 −2.52 0.00 −1.82 −0.79 −0.69 −0.61
3.96 4.00 4.21 4.38 4.51 4.61 4.76 4.82 5.07 5.15 5.26 5.35 5.45
0.185 0.197 0.235 0.269 0.293 0.314 0.335 0.349 0.390 0.407 0.434 0.444 0.47
mol·kg−1
102 δ
0.187 0.198 0.236 0.268 0.292 0.310 0.338 0.349 0.395 0.410 0.430 0.447 0.465
1.08 0.51 0.43 −0.37 −0.34 −1.27 0.90 0.00 1.28 0.74 −0.92 0.68 −1.06
a Sexp and Scal are the experimentally determined solubility and the calculated solubility from eq 9 or 10, respectively; δ is the relative deviation, δ = (Scal − Sexp)/Sexp. bThe standard uncertainty u is u(pH) = 0.01, relative standard uncertainty u is ur(S) = 0.02.
D
dx.doi.org/10.1021/je400053q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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N
δave =
∑i = 1 (xcal,i − xexp ,i)/xexp ,i N
δave =
(7)
where N is the number of experimental points, xexp,i is the experimental value of the solubility, and xcal,i is the solubility calculated from one of the four equations. Comparing the values of r, rmsd, and δave shown in Tables 4, 5, 6, and 7, one can conclude that the Wilson model, the R-K equation, and the modified Apelblat equation can provide the best simulation for the experimental solubility data of (S)HPBA in toluene, in water, and in ethyl acetate, respectively. (S)-HPBA Solubility in Aqueous Solutions at Different pH Values. The solubility of (S)-HPBA, S, at a particular pH value in the saturated aqueous solution is defined as the sum of the concentrations of its nonionized and ionized forms. The pH-dependent solubility data and curve of (S)-HPBA at 298.2 K are presented in Table 8 and Figure 4, respectively. As shown in Figure 4, over the pH range investigated, the solubility of (S)-HPBA increases with increasing pH value. The solubility rises slowly over the pH range from 2.0 to 4.0 and then increases linearly until the pH value reaches 5.45. It was observed experimentally that (S)-HPBA became fully miscible in water beyond pH 5.45. When the pH value decreases to less than 2.0, (S)-HPBA is all in its nonionized form with the intrinsic solubility, S0, at 0.0691 mol·kg−1. This tells us that, during the separation process of (S)-HPBA, after dissociation of (S)-HPBA from its N-octyl-D-glucamine salt by adding enough NaOH and subsequent filtration, the pH value of the filter should be adjusted to less than 2.0 so that all the (S)HPBA exists in nonionized form and then can be easily transferred into the extraction phase in the following extraction operation. Usually, when weak acid molecules exist only in the monomer state in aqueous solutions, its pH-dependent solubility, S, can be described by the Henderson−Hasselbalch (HH) equation:37 S = S0(10 pH − pKa + 1)
S = A′(10 pH − B ′ + 1)
pH > 4.0
S = A′ + B′pH
CONCLUSIONS The dissociation constant (pKa) of (S)-HPBA was determined as 3.81 at 298.2 K. The solubility of (S)-HPBA in three pure solvents (toluene, water, and ethyl acetate) increases with increasing temperature in the temperature range investigated. Water is proven to be a good alternative to toluene as a crystallization agent, and ethyl acetate is an ideal extraction agent. Among four models chosen for fitting the experimentally determined solubility in pure solvents, the Wilson equation can provide more reasonable solubility prediction for (S)-HPBA in toluene, the Redlich−Kister equation is superior to other models in the solubility simulation for (S)-HPBA in water, and the modified Apleblat equation can present a relatively accurate mathematical representation of the experimental solubility of (S)-HPBA in ethyl acetate. At 298.2 K, the solubility of (S)-HPBA in aqueous solutions increases slowly with an increase of the pH value in the pH range from 1.48 to 4.00 and then rises linearly with increasing pH value. The relationship between the solubility and pH value is well-correlated by a semi-HH equation (pH ≤ 4.00) and a linear equation (pH > 4.00), respectively. According to the pHdependent solubility curve, the pH value of the alkaline solution of (S)-HPBA produced from dissociating (S)-HPBA from its N-octyl-D-glucamine salt should be adjusted to less than 2.0 in order that all of the (S)-HPBA turns into its free acid and then can be extracted as much as possible by the extraction phase.
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(8)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Fax: 86- 0591-22866227. Funding
This project was financially supported by the National Science Foundation for Fostering Talents in Basic Research of the National Natural Science Foundation of China (No. J1103303). Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Watthey, J. W. H.; Stanton, J. L.; Desai, M.; Babiarz, J. E.; Finn, B. M. Synthesis and biological properties of (carboxyalkyl) aminosubstituted bicyclic lactam inhibitors of angiotensin converting enzyme. J. Med. Chem. 1985, 28, 1511−1516. (2) Yanagisawa, H.; Ishihara, S.; Ando, A.; Kanazaki, T.; Miyamoto, S.; Koike, H.; Iijima, Y.; Oizumi, K.; Matsushita, Y.; Hata, T. Angiotensin-converting enzyme inhibitors. 2. Perhydroazepin-2-one derivatives. J. Med. Chem. 1988, 31, 422−428. (3) Iwasaki, G.; Kimura, R.; Numao, N.; Kondo, K. A practical and diastereoselective synthesis of angiotensin converting enzymeinhibitors. Chem. Pharm. Bull. 1989, 37, 280−283. (4) Oda, S.; Inada, Y.; Kobayashi, A.; Ohta, H. Production of ethyl (R)-2-hydroxy-4-phenylbutanoate via reduction of ethyl 2-oxo-4phenylbutanoate in an interface bioreactor. Biosci. Biotechnol. Biochem. 1998, 62, 1762−1767.
(9) (10)
N
∑i = 1 (Sexp , i − Scal, i)2 N
(12)
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where A′ and B′ are adjustable parameters. Equation 9 is a semi-HH equation. The regressed values of A′ and B′ are shown in Table 9, together with corresponding r, rmsd, and δave, which are defined as eqs 11 and 12, respectively. rmsd =
N
where N, Sexp,i, and Scal,i are the number of experimental data points, the experimental solubility, and the solubility calculated from eq 9 or 10, respectively. As can be seen in Table 9 and Figure 4, the experimental determined solubility is wellcorrelated by eqs 9 and 10.
As shown in Figure 4, the experimentally determined solubility of (S)-HPBA obviously deviates from the theoretically estimated solubility by the HH equation (based on the experimentally determined intrinsic solubility and pKa mentioned above) when the pH value is greater than 4.0. This deviation might arise from molecule interactions such as aggregation.38 Since the HH equation failed to describe the relationship between the experimental solubility of (S)-HPBA and pH value, the solubility was correlated as a function of pH value as follows, pH ≤ 4.0
∑i = 1 (Scal,i − Sexp ,i)/Sexp ,i
(11) E
dx.doi.org/10.1021/je400053q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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dx.doi.org/10.1021/je400053q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
