In the Laboratory
Simultaneous Determination of the Ionization Constant and the Solubility of Sparingly Soluble Drug Substances
W
A Physical Chemistry Experiment Andria Aroti and Epameinondas Leontidis* Department of Chemistry, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus; *
[email protected] Objectives
Theory
In this experiment, students determine the ionization constant and solubility of the basic form of a sparingly soluble drug substance, using the inverse titration method with dissolution of a precipitate. Besides getting significant expertise in potentiometry and spectrophotometry, students are confronted with the requirements of controlling the temperature and excluding atmospheric CO2. They carry out three independent statistical analyses of the data and discuss their merits and complementary nature. The experiment is relevant for several areas of chemistry, in particular, physical chemistry (in Nicosia we use it in the 3rd-year advanced physical chemistry laboratory), pharmaceutical chemistry, analytical chemistry, and electrochemistry. It is important to establish such laboratory methods in the undergraduate physical chemistry laboratory and also to help students appreciate the difficulty of getting accurate pKa and solubility values and the general uncertainty of available published data.
Considering a weak base, carrying a positive charge in its acidic form, the neutralization process is
Background A large variety of methods are commonly used for determining dissociation constants of weak acids and bases (potentiometric titrations, spectrophotometry, conductimetry, etc.) (1). Of these, potentiometric titration methods are the most generally applicable (1, 2). In many cases, however— this being a rather common phenomenon for chemicals of pharmaceutical interest—the uncharged species produced upon neutralization are so insoluble that precipitation occurs during the titration, even if very low concentrations of acids and bases are used (on the order of 104 M or less). The titration is stopped at the precipitation point (3, 4), but the method often fails to provide an accurate pKa determination because it is difficult to determine the exact pH value (which strongly depends on the concentration) at which precipitation occurs. There are various ways to overcome this problem. Here we describe an advanced physical chemistry laboratory experiment based on the so-called “inverse” titration with dissolution of insoluble base (1). Many experimental titration methods for the determination of ionization constants have appeared in this Journal (e.g., 5–10) but, to our knowledge, none has addressed the inverse titration method. The applicability of the method is demonstrated using dibucaine, a tertiary amidoamine, which is a well-known local anesthetic. Determining the pKa of dibucaine is a difficult problem, as can be seen by the wide range of values found in the literature (pKa = 8.0 [11, 12], 8.31 [13], 8.50 [14], 8.72 [3], and 8.95 [15]). In addition to the pKa, the inverse titration experiment provides an estimate of the solubility of the basic form of dibucaine.
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BH+ + OH
B + H 2O
and the associated equilibrium constant is given by aB K K= = 1 = a a BH+ a OH K K b
(1)
(2)
w
The total solubility, S, of the substance increases with ionization and is the sum of the concentrations of the uncharged form, [B], and the ionized form, [BH+]: S = [B] + [BH+]
(3)
S0 is the limited solubility of the uncharged form in the solution and can be written as S0 = [B]
(4)
assuming that S0 does not depend on pH. Substituting So for [B] from eq 4 into eq 2 yields
Ka =
S0 S – S0
a H+ γBH+
(5)
γBH+ being the activity coefficient of the ionized form of the drug. Equation 5 can be transformed into a form suitable for linear regression analysis: S a H+ S = S0 + 0 γ + (6) K a BH
or can be written in the following logarithmic form: S0 pH = pK a – log γBH + + log S – S0
(7)
The inverse titration experiment provides the ratio S0/Ka in an alternative way, starting from the proton material balance in the system.W This is a useful way to check the consistency of the titration data. The Experiment
Equipment The pH measurements for the determination of pKa are made with a pH meter with an accuracy of ±0.01 pH units. Total solubility determination is made using a UV–visible recording spectrophotometer. The temperature of the titration vessel is maintained constant (25.0 ± 0.5 °C) using a constanttemperature water circulation bath.
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
In the Laboratory 7
Table 1. Nonlinear Regression Analysis of the Inverse Titration Experiment
6
7.20
Absorbance
5
4
T/°C
pKa
S0 /mol L1
Correlation Coefficient
25
8.87 ± 0.17 8.80 ± 0.19
(2.6 ± 0.9) × 105 (2.9 ± 0.9) × 105
.996 .995
35
8.28 ± 0.07 8.31 ± 0.08
(4.9 ± 0.6) × 105 (6.7 ± 0.9) × 105
— —
7.41
NOTE: Calculated according to eq 7. The uncertainties reported indicate the 90% confidence interval.
3
7.68
2
7.88
1
8.85
8.25
0 200
240
280
320
360
400
l / nm Figure 1. UV spectra of filtrate solutions, demonstrating increased dibucaine solubility upon pH lowering.
9.0
pH
8.5
chloric acid (0.1 N) is added using a 10-µL syringe, until a specific pH value is reached. Each titration is performed under nitrogen gas to avoid CO2 adsorption. Stirring is accomplished by a slow stream of nitrogen bubbles, introduced under the surface of the titrated solution (or with a magnetic stirring bar, if absolutely exact numbers are not required). pH equilibration after each addition of acid is slow, since it entails gradual dissolution of the precipitate. After a specific pH value is achieved, the content of the test tube is filtered and the UV spectrum of the filtrate is taken to determine total dibucaine solubility, S, using the Beer–Lambert equation. No HCl is added to the first test tube, which is used for the determination of the initial values, pHin and Sin. The total duration of an inverse titration experiment is 4–5 hours and the experiment can be completed in a single laboratory session. Hazards
8.0
7.5
7.0 0
50
100
5
150
200
1
S / (10 mol L) Figure 2. Nonlinear regression best-fit curves of two student experiments with experimental data superimposed.
Chemicals Dibucaine free base (Aldrich) is used as received. Potassium chloride 0.05–0.1 M is used as a constant ionic strength solvent. Standardized hydrochloric acid 0.1 N from an ampoule. Additions of hydrochloric acid are made with a microsyringe. Ion-free water from a reverse osmosis unit or at least doubly distilled water.
Procedure Equal weights (0.017 ± 0.001 g) of basic dibucaine are placed in each of seven test tubes, to which 10 mL of freshly prepared KCl (0.05–0.1 M) solution (alternatively 10 mL of pure deionized water) is added, so that the concentration of dibucaine, if it were freely soluble, would equal 5 × 103 mol L1. Hydro-
Dibucaine is highly toxic (toxicity index 3); it should not come in contact with the skin or the eyes and should not be inhaled. It produces skin, eye, and respiratory system irritation, and upon ingestion it produces nausea, vomiting, diarrhea, and cardiovascular and central nervous system effects. Students should always wear protective chemical-resistive gloves and safety goggles. See the lab documentation for more details related to the hazards from this compound, necessary safety measures and waste disposal information, and suggestions for alternative compounds to use in this kind of experiment.W Results Figure 1 shows a sequence of spectra of the filtrate solutions as a function of the pH. It can be seen that solubility increases steadily as the pH decreases and the substance is ionized. Because the ionized and neutral forms of dibucaine have identical UV spectra, total solubility analysis is achieved by measuring the absorbance at 327 nm. The equilibrium data can be analyzed in three ways: the full nonlinear curve fitting procedure suggested by eq 7, the linear plots suggested in eq 6, and a [H+] balance described in the lab documentation.W In every case, an expression for the activity coefficient is needed; this can be neglected at zero ionic strength and can be approximately evaluated by the extended Debye–Hückel formula (see ref 16 ) for constant ionic strength. For the sake of brevity we present here only the results of the nonlinear analysis of eq 7. Figure 2 shows the best-fit pH–S curves from two experiments, with experimental data superimposed. Table 1 contains the results (S0 and pKa) that were found from the nonlinear analysis.
JChemEd.chem.wisc.edu • Vol. 78 No. 6 June 2001 • Journal of Chemical Education
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In the Laboratory
Discussion The values for pKa are close to the more dependable literature estimates (8.72 [3] and 8.95 [15 ]). Direct precipitation titrations under nonoptimal conditions tend to provide significantly lower values for pKa (11, 12). The solubility of the neutral form of dibucaine calculated in this experiment is considerably smaller than that quoted in ref 3. In conclusion, we can say that the combination of spectrophotometry and potentiometry in the inverse titration method provides separate estimates of the solubility of the uncharged form, S0, and the acid dissociation constant, Ka, of the local anesthetic dibucaine. Both S0 and Ka are very important physical properties for all compounds of pharmaceutical interest. In fact, it is very interesting to determine these properties at 37 °C (3), and we find significant variations from the reported 25 °C values, which are often the only values that can be found in extensive literature tabulations. Results from a nonlinear analysis of two experiments performed by students at 35 °C are also contained in Table 1. The pKa decreases from ca. 8.80 to ca. 8.30 (in good agreement with the only literature value that we could find [3]), which shows the importance of measuring this property at temperatures other than 25 °C, especially for compounds of pharmaceutical interest that will be used under physiological conditions. The solubility increases considerably with temperature, as expected. W
Supplemental Material
The full text of this paper is available in this issue of JCE Online. It provides more extensive background and
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theoretical material, further information on safety and waste disposal and alternatives to use of dibucaine, details of the data analysis, and an expanded discussion. Literature Cited 1. Albert, A.; Serjeant, E. P. The Determination of Ionization Constants, A Laboratory Manual, 3rd ed.; Chapman and Hall: London, 1984. 2. Benet, L. Z.; Goyan, J. E. J. Pharm. Sci. 1967, 56, 665–680. 3. Kamaya, H.; Hayes, J. J. Jr.; Ueda, I. Anesth. Analg. 1983, 62, 1025–1030. 4. Levy, R. H.; Rowland, M. J. Pharm. Sci. 1971, 60, 1155–1159. 5. Tucker, S. A.; Amszi, V. L.; Acree, W. E. Jr. J. Chem. Educ. 1993, 70, 80–82. 6. Cawley, J. J. J. Chem. Educ. 1995, 72, 88–90. 7. Bada, J. L. J. Chem. Educ. 1969, 46, 689. 8. Baldwin, C. E.; Evans, J. S. J. Chem. Educ. 1974, 51, 205. 9. Partanen, J. I.; Kärki, M. H. J. Chem. Educ. 1994, 71, A120. 10. García-Doménech, R.; de Julián-Ortiz, J. V.; Antón-Fos, G. M.; Alvarez, J. G. J. Chem. Educ. 1996, 73, 792–793. 11. Ohki, S. Biochim. Biophys. Acta 1984, 777, 56–66. 12. Kuroda, Y.; Wakita, M.; Nakagawa, T. Chem. Pharm. Bull. 1994, 42, 2418–2425. 13. Padmanabhan, G. R. Anal. Profiles Drug Subst. 1983, 12, 105– 134. 14. Richie, J. M.; Greengard, P. J. Pharm. Exp. Ther. 1961, 133, 241–245. 15. Vanderkooi, G. Photochem. Photobiol. 1984, 39, 755–762. 16. Bockris, J. O’M.; Reddy, A. K. N. Modern Electrochemistry, Vol. 1, Ionics, 2nd ed.; Plenum: New York, 1998.
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
