Buffers, buffering agents, and ionic equilibria

INTROD UCTION It is well known that many dru gs are unstabl e when exposed to certa in acidi c or ba sic conditio ns, an d such informat ion is rou tinely gather ed during the prefor mu lation stage of developm ent. When such inst abiliti es are identifie d, one tool of the form ulation scienc es is to include a buffering agent (or agents ) in the dosage form with the hope that such excipie nts will impar t suf ficient stabili ty to en able the formulat ion. The proper ties that enable buffering agents to functi on as such is derived from their qualities as weak acids or bases, and have their ro ots in their respect ive ionic equilibria . AUTOIO NIZATIO N OF WA TER Even the purest grade of water contain s low concentra tions of ions that can be detect ed by means of ap pro priate cond uctivity measu rements. These ions aris e from the transfer of a proton from a water molecule to another: H2O þ H2O H3O þ þ OH
ð1Þ In Eq. (1), H3Oþ is known as the hydronium ion, and OH
is known as the hydroxide ion. This reaction is reversible, and the reactants are known to proceed only slightly on to the products. Approximating the activity of the various species by their concentrations, one can write the equilibrium constant for this reaction as KC ¼ ½H3Oþ½OH
 ½H2O 2 ð2Þ In aqueous solutions, the concentration of water is effectively a constant (55.55 M), and so Eq. (2) simpli fies to: KW ¼ ½H3Oþ½OH
 ð3Þ KW is known as the autoionization constant of water, and is sometimes identified as the ion product of water. The magnitude of KW is very small, being equal to 1.007  10
14 at a temperature of 25C.1 For the sake of convenience, Sørensen proposed the ‘‘p’’ scale, where numbers such as KW would be

Bio-V–Buffer Buffers, Buffering Agents, and Ionic Equilibria Harry G. Brittain Center for Pharmaceutical Physics, Milford, New Jersey, U.S.A. INTRODUCTION It is well known that many drugs are unstable when exposed to certain acidic or basic conditions, and such information is routinely gathered during the preformu- lation stage of development. When such instabilities are identified, one tool of the formulation sciences is to include a buffering agent (or agents) in the dosage form with the hope that such excipients will impart suf- ficient stability to enable the formulation. The proper- ties that enable buffering agents to function as such is derived from their qualities as weak acids or bases, and have their roots in their respective ionic equilibria. AUTOIONIZATION OF WATER Even the purest grade of water contains low concentra- tions of ions that can be detected by means of appro- priate conductivity measurements. These ions arise from the transfer of a proton from a water molecule to another: H 2 O þ H 2 O $ H 3 O þ þ OH À ð1Þ In Eq. (1), H 3 O þ is known as the hydronium ion, and OH À is known as the hydroxide ion. This reaction is reversible, and the reactants are known to proceed only slightly on to the products. Approximating the activity of the va rious species by their c o ncentrations, one can write the equilibrium constant for this reaction as K C ¼ ½H 3 O þ ½OH À  ½H 2 O 2 ð2Þ In aqueous solutions, the concentration of water is effectively a constant (55.55 M), and so Eq. (2) simpli- fies to: K W ¼½H 3 O þ ½OH À ð3Þ K W is known as the autoionization constant of water, and is sometimes identified as the ion product of water. The magnitude of K W is very small, being equal to 1.007  10 À14 at a temperature of 25  C. [1] For the sake of convenience, Sørensen proposed the ‘‘p’’ scale, where numbers such as K W would be expressed as the negative of their base10 logarithms. The value of pK W would then be calculated as pK W ¼ÀlogðK W Þð4Þ and would have a value equal to 13.997 at 25  C. Defining pH as pH ¼Àlog½H 3 O þ ð5Þ and pOH ¼Àlog½OH À ð6Þ then Eq. (3) can then be expressed as pK W ¼ pH þ pOH ð7Þ The autoionization of water is an endothermic reac- tion, so K W increases as the temperature is increased. [1] This temperature dep endence is plotted in Fig. 1. IONIC EQUILIBRIA OF ACIDIC AND BASIC SUBSTANCES Of the numerous definitions of acids and bases that have been employed over the years, the 1923 defini- tions of J. N. Brønsted and T. M. Lowry have proven to be the most useful for discussions of ionic equilibria in aqueous systems. According to the Brønsted–Lowry model, an acid is a substance capable of donating a proton to another substan ce, such as water: HA þ H 2 O $ H 3 O þ þ A À ð8Þ The acidic substance (HA) that originally donated the proton becomes the conjugate base (A À ) of that substance, because the conjugate base could conceiva- bly accept a proton from an even stronger acid than the original substance. One can write the equilibrium constant expression co rresponding to Eq. (8) as K C ¼ ½H 3 O þ ½A À  ½HA½H 2 O ð9Þ Encyclopedia of Pharmaceutical Technology DOI: 10.1081/E-EPT-120011975 Copyright # 2007 by Informa Healthcare USA, Inc. All rights reserved. 385 Bio-V–Buffer But because [H 2 O] is a constant, one can collect the constants on the left-hand side of the equation to derive the acid ionization constant expression: K A ¼ ½H 3 O þ ½A À  ½HA ð10Þ And, of course, one can define pK A as pK A ¼ÀlogðK A Þð11Þ A strong acid is a substance that react s completely with water, so that the acid ionization constant defined in Eq. (10) or (11) is effectively infinite. This situ ation can only be achieved if the conjugate base of the strong acid is very weak. A weak acid will be characterized by an acid ionization constant that is considerably less than unity, so that the position of equilibrium in the reaction represented in Eq. (8) favors the existence of unreacted free acid. A discussion of the ionic equilibria associated with basic substances parallels that just made for acidic sub- stances. A base is a substance capable of accepting a proton donated by another substance, such as water: B þ H 2 O $ BH þ þ OH À ð12Þ The basic substance (B) that originally accepted the proton becomes the conjugate acid (BH þ ) of that substance, b ecause the con jugate acid could con ceivably donate a proton to an even stronger base than the original substance. The equilibrium constant expression corresponding to Eq. (12) is: K C ¼ ½BH þ ½OH À  ½B½H 2 O ð13Þ Because [H 2 O] is a constant, the constants are col- lected on the left-hand side of the equation to derive the base ionization constant expression: K B ¼ ½BH þ ½OH À  ½B ð14Þ pK B is defined as pK B ¼ÀlogðK B Þð15Þ A strong base is a substance that reacts completely with water, so that the base ionization constant defined in Eq. (14) or (15) is effectively infinite. This situation can only be realized if the conjugate acid of the strong base is very weak. A weak base will be characterized by a base ionization constant that is considerably less than unity, so that the position of equilibrium in the reaction represented in Eq. (12) favors the existence of unreacted free base. IONIC EQUILIBRIA OF CONJUGATE ACIDS AND BASES Once formed, the conjugate base of an acidic substance (i.e., the anion of that acid) is also capable of reacting with water: A À þ H 2 O $ HA þ OH À ð16Þ Because aqueous solutions of anions are commonly prepared by the dissolution of a salt containing that anion, reactions of the type described by Eq. (16) are often termed hydrolysis reactions. Eq. (16) is necessa- rily characterized by its base ionization constant expression: K B ¼ ½HA½OH À  ½A À  ð17Þ and a corresponding pK B defined in the usual manner, but because ½OH À ¼K W =½H 3 O þ ð18Þ it follows that K B ¼ ½HAK W ½A À ½H 3 O þ  ð19Þ Temperature (°C) pK w Fig. 1 Temperature dependence of the autoionization con- stant of water. (From Ref. [1] .) 386 Buffers, Buffering Agents, and Ionic Equilibria Bio-V–Buffer Eq. (19) contains the right-hand side expression of Eq. (10), so one deduces that K B ¼ K W =K A ð20Þ or K W ¼ K A K B ð21Þ The same relation between ionization constants of a conjugate acid–base pair can be developed if one were to begin with the conjugate acid of a basic substance, so Eq. 21 is recognized as a general property of conju- gate acid–base pairs. IONIC EQUILIBRIA OF BUFFER SYSTEMS A buffer can be defined as a solution that maintains an approximately equal pH value even if small amounts of acidic or basic substances are added. To function in this manner, a buffer solution will necessarily contain either an acid and its conjugate base, or a base and its conjugate acid. The action of a buffer system can be understood through the use of a practical example. Consider acetic acid, for which K A ¼ 1.82  10 À5 (pK ¼ 4.74). The following pH values can be calculated (for solutions having a total acetate content of 1.0 M) using its acid ionization constant expression: Acetic acid, [HA] Acetate ion, [A À ] Calculated pH 0.4 0.6 4.92 0.5 0.5 4.74 0.6 0.4 4.56 When an acidic substance is added to a buffer sys- tem it would immediately react with the basic compo- nent, as a basic substance would react with the acidic component. One therefore concludes from the table that the addition of either 0.1 M acid or 0.1 M base to a buffer system consisting of 0.5 M acetic acid and 0.5 M acetate ion would cause the pH to change by only 0.18 pH units. This is to be contrasted with the pH changes that would result from the addition of 0.1 M acid to water (i.e., 7.0 to 1.0, for a change of 6.0 pH units), or from the addition of 0.1 M base to water (i.e., 13.0 to 1.0, also for a change of 6.0 pH units). A very useful expression for describing the proper- ties of buffer system can be derived from consideration of ionization constant expressions. For an acidic substance, Eq. (10) can be rearranged as ½H 3 O þ ¼ K A ½A À  ½HA ð22Þ Taking the negative of the base 10 logarithms of the various quantities yields the relation known as the Henderson–Hasselbach equation: pH ¼ pK A þ logf½A À =½HAg ð23Þ Eq. (23) indicates that when the concentration of acid and its conjugate base are equal (i.e., [HA] ¼ [A À ]), then the pH of the solution will equal the pK A value. Therefore, a buffer system is chosen so that the target pH is approximately equal to the pK A value. Viewed in this light, a buffer system can be envi- sioned as a partially completed neutralization reaction HA þ OH À $ A À þ H 2 O ð24Þ where comparable amounts of HA and A À are present in the solution. The buf fer region within a neutraliza- tion reaction is shown in Fig. 2, where the horizontal region in the graph of anion concentration and [acetate] pH Fig. 2 Neutralization curve obtained during the titration of 1.0 M acetic acid, plotted as a function of the acetate ion concentration. Buffers, Buffering Agents, and Ionic Equilibria 387 Bio-V–Buffer observed pH reveals the buffer region of the system. For practical purposes, the buffer region would extend over [HA]/[A À ] ratios of approximately 0.2 to 0.8. SELECTION OF AN APPROPRIATE BUFFER SYSTEM The selection of a buffer system for use in a pharma- ceutical dosage form is relatively straightforward. It is evident from the preceding discussion that the most important prerequisite for a buffer is the approxim ate equality of the pK A value of the buffer with the intended optimal pH value for the formulation. Knowledge of the pH stability profile of a drug sub- stance enables one to deduce the pH range for which formulation is desirable, and the basis for the most appropriate buffer system would be the weak acid or base whose pK A or pK B value was numerically equal to the midpoint of the pH range of stability. There are, of course, other considerations that need to be monitored, such as compatibility with the drug substance. Boylan [2] has provided a summary of the selection criteria for buffering agents: 1. The buffer must have adequate capacity in the desired pH range. 2. The buffer must be biologically safe for the intended use. 3. The buffer should have little or no deleterious effect on the stability of the final product. 4. The buffer should permit acceptable flavoring and coloring of the product. A practical consequence of Eq. (23) is that as long as the concentration of a buffer is not overcome by reac- tion demands, a buffer system will exhibit adequate capacity wi thin Æ1 pH unit with respect to its pK A or pK B value. The second criterion from the preceding list restricts buffering agents to those de emed to be pharmaceuti- cally acceptable. A list of appropriate buffer systems is provided in Table 1, along with values for their pK A or pK B values sourced from the compilations of Martell and Smith. [3–6] The use of buffering agents is most critical for parenteral formulations, and it has been noted over the years that phosphate, citrate, and acetate are most commonly used for such pur- poses. [7,8] Ethanolamine and diethanolamine are also used to adjust pH and form their corresponding salts, whereas lysine and glycine are often used to buffer pro- tein and peptide formulations. Akers [9] has reviewed the scope of drug–excipient interactions in parenteral formulations and has provided an overvi ew of the effect of buffers on drug substance stability. Table 1 Acids and bases suitable for use as buffer systems in pharmaceutical products Basis for buffering system pK 1 pK 2 pK 3 Martell and Smith reference Acetic acid 4.56 — — [5], p. 3 Adipic acid 5.03 4.26 — [5], p. 118 Arginine 9.01 2.05 — [3], p. 43 Benzoic acid 4.00 — — [5], p. 16 Boric acid 8.97 — — [6], p. 25 Carbonic acid 10.00 6.16 — [6], p. 37 Citric acid 5.69 4.35 2.87 [5], p. 161 Diethanolamine 8.90 — — [4], p. 80 Ethanolamine 9.52 — — [4], p. 15 Ethylenediamine 9.89 7.08 — [4], p. 36 Glutamic acid 9.59 4.20 — [3], p. 27 Glycine 9.57 2.36 — [3], p. 1 Lactic acid 3.66 — — [5], p. 28 Lysine 10.69 9.08 2.04 [3], p. 58 Maleic acid 5.83 1.75 — [5], p. 112 Phosphoric acid 11.74 6.72 2.00 [6], p. 56 Tartaric acid 3.95 2.82 — [5], p. 127 Triethanolamine 7.80 — — [4], p. 118 Tromethamine 8.09 — — [4], p. 20 388 Buffers, Buffering Agents, and Ionic Equilibria Bio-V–Buffer BUFFERS IN PHARMA CEUTICAL SYSTEMS It is well known that the stability of many active phar- maceutical substances can be strongly dependent on the degree of acidity or basicity to which they are exposed, and that a change in pH can cause significant changes in the rate of degradation reactions. For such compounds, formulators commonly include a buffer system to ensure the stability of the drug substance either during the shelf life of the product, or during the period associated with its administration. In addition, preformulation scientists routinely use buffer systems to set the pH of a medium in which they intend to perform experimentation. For instance, the pH stability profile of a drug substance is routinely obtained through the use of buffers, and the pH depen- dence of solubility is frequently measured using buffered systems. However, the possibility that the buf- fer system itself may influence or alter the results must be considered in these studies. Stabilization of Drug Substances in Formulations by Buffers As mentioned previously, the stability of parenteral formulations is often established through the use of buffer systems, and Table 2 contains a partial listing of such systems. [7,8] The inclusion of a phosphate buffer in homatropine hydrobromide ophthalmic solution enabled formula- tors to fix the solution pH at 6.8, enabling the product to be lyophilized. [10] This lyophilized product could be stored for extended periods without degradation. Tro- methamine was found to effect a stabilizing effect on N-nitrosoureas (such as lomustine, carmustine, and tauromustine) in aqueous solutions. [11] It has been reported that replacing succinate buffer with glycolate buffer improved the stability of lyophi- lized g-interferon. [12] In this work, it was found that the succinate buffer could crystallize in the frozen state, which limited its ability to maintain the appro- priate pH, and therefore led to degradation. On the other hand, use of the glycolate buffer appeared to minimize the freeze-induced pH shifting, and the lyophilized product exhibited superior solid-state stability. However, the use of buffers in parenterals is not always benign, and numerous instances have been summarized where buffers or other excipients have caused stability problems. [9] For instance, the com- plexation of Ca(II) and Al(III) with phosphate buffer solutions has been studied at great length, as well as the kinetic characteristics of the subsequent precipita- tion of calcium and aluminum phosphate salts. [13–17] The use of metal complexing excipients, such as citric acid or ethylenediaminetetraacetic acid, was found to be useful in delaying the onset of precipitation. The use of buffering agents in solid dose forms is not as widespread as the use in parenteral products. Nevertheless, the current Handbook of Pharmaceuti- cal Excipients lis ts calcium carbonate, monobasic and dibasic sodium phosphate, sodium and potassium citrates, and tribasic calcium phosphate as potential buffering agents. [18] In one study, the effect of 11 different compounds representing various classes of buffering agents were studied with respect to their effect on the dissolution kinetics of aspirin from tablet formulations. [19] It was found that buffering agents capable of reacting with acidic sub stances to evolve carbon dioxide (sodium bicarbonate, magnesium carbonate, or cal- cium carbonate) yielded the fastest dissolution rates, and hence were deduced to be more useful as tablet excipients. Less effective were water-soluble buffering agents (such as sodium ascorbate or sodium citrate), and least effective were water-insoluble buffering agents (such as magnesium oxide, magnesium trisili- cate, dihydroxyaluminum aminoa cetate, or aluminum hydroxide). In another study, the kinetics of aspirin, salicylic acid, and salicyluric acid were followed upon oral Table 2 Some of the buffer systems used to stabilize various parenteral products Basis for buffering system Product trade name Acetic acid Miacalcin injection Benzoic acid Valium injection Citric acid Aldomet injection Ceredase Cerezyme Duracillin A.S. Diethanolamine Bactrim IV Glycine Hep-B Gammagee Lactic acid Ergotrate maleate Fentenyl citrate and Droperidol Maleic acid Librium injection Monoethanolamine Terramycin solution Phosphoric acid Humegon Zantac injection Pregnyl Prolastin Synthroid Tartaric acid Compazine injection Methergine injection Priscoline injection Tromethamine Optiray From Refs. [7,8] . Buffers, Buffering Agents, and Ionic Equilibria 389 Bio-V–Buffer administration of aspirin as either an unbuffered tablet or two buffered solutions. [20] Significant differences in the absorption rates were observed, with the solution having 16 mEq of buffer being the fastest, the solution having 34 mEq of buffer being intermediate, and the unbuffered tablet being the slowest. These studies demonstrate that inclusion of a buffering agent in a tablet formulation of an acid-sensitive compound will lead to the generation of better dosage forms. Use of Buffers to Study the pH Stability Profile of Drug Subst ances The evaluation of the pH stability profile of a drug substance is an essential task within the scope of pre- formulation studies. Knowing the pH conditions under which a given compound will be stable is of vital importance to the chemists seeking to develop methods of synthesis, to analytical scientists seeking to develop methods for analysis, and to formulators seeking to develop a stable drug product. Typically, the prefor- mulation scientist will prepare solutions of the drug substance in a variety of buffer systems, and will then determine the amount of drug substance remaining after a predefined storage period. However, for the information to be useful, the investigator will also need to verify that the buffer itself does not have an effect on the observed reactions. The hydrolysis kinetics of vidarabine-5 0 -phosphate were studied at a variety of pH values that enabled the compound to exist as its protonated, neutral, and monoionized form. [21] It was found that the hydrolysis reaction followed first-order kinetics at the five pH conditions tested, and that the buffer system used did not influence the reaction rates. The pH–rate profile suggested that even though the compound was most stabile over pH 9.0 to 9.5, the stability at pH 7.4 (i.e., physiological pH) was more than adequate for development of a parenteral formulation. The degradation kinetics of phe ntolamine hy dro- chloride were studied over a pH range of 1.2 to 7.2 and in various glycol solutions. [22] The kinetics were determined to be first order over all pH values studied, and a consideration of the ionization constant of the compound indicated that only the protonated form of the compound had been studied. At relatively low acidities, a pH-independent region (pH 3.1–4.9) was noted for the hydrolysis, and the kinetics were not affected by the concentration of buffer used. However, the degradation reaction was found to proceed at a much faster rate at a pH of 7.2, and a small dependence of rate constant on the concentration of phosphate in the buffer system was noted. Other examples where buffers were successfully used to study the pH stability of drug substances (and where little or no effect could be ascribed to the buffer system used) include the chemi cal stability of diisoxazolyl- naphthoquinone [23] and metronidazole [24] in aqueous solution. In another detailed study, the effect of pH, buffer species, medium ionic strength, and temperature on the stability of azetazolamide was studied. [25] There are probably as many instances where buffer catalysis exerts a strong influence on pH stability studies as where no such effect exists. For instance, the kinetics associated with the acid/base hydrolysis of ciclosidomine were found to be strongly affected by the concentration of buffer used to set the solution pH for each study. [26] However, because a linear rela- tionship was found between buffer concentration and observed first-order rate constant, the effect of pH on the degradation was assessed by extrapolating to zero buffer concentration. This information was used to deduce the buffer-independent pH–rate profile. In another study on solutions of spironolactone, the concentration of buffer was found to exert a strong influence on the degradation rate constants. [27] At the same time, the ionic strength of the medium did not appear to affect the rate constants. The decomposition pathway for aqueous solutions of batanopride hydro- chloride was found to depend on the pH of the med- ium used for the study, although the concentration of buffer was found to exert catalytic effects. [28] To those beginning work in this field, the study reported by Zhou and Notari on the kinetics of ceftazidime degradation in aqueous solutions may be used as a study design template. [29] First-order rate constants were determined for the hydrolysis of this compound at several pH values and at several tem- peratures. The kinetics were separated into buffer- independent and buffer-dependent contributions, and the temperature dependence in these was used to calculate the activation energy of the degradation via the Arrhenius equation. Ceftazidime hydrolysis rate constants were calculated as a function of pH, tempera- ture, and buffer by combining the pH–rate expression with the buffer contributions calculated from the buffer catalytic constants and the temperatur e dependencies. These equations and their parame ter values were able to calculate over 90% of the 104 experi mentally deter- mined rate constants with errors less than 10%. Use of Buffers to Study the pH Dependence of Drug Substance Solubility An evaluation of the effect of pH on the aqueous solu- bility of a drug substance is an essential component of preformulation research, and such work is usually conducted along with determinations of ionization constants, solubilization mechanisms, and dissolution rates. [30] Methods for the d etermination of the solubility 390 Buffers, Buffering Agents, and Ionic Equilibria Bio-V–Buffer of pharmaceutical solids have been discussed at length, [31] and a large number of pH–solubility profiles have been published in the 30 volumes of the Analytical Profiles series. [32–34] A general treatment of the characteristics of the p H–solubility p rofiles of weak ac ids a nd bases is avai lable. [35] When the pH conditions used for a given solubility determination are set through the use of buffers, the possible solubilization of the buffering systems must be established. For instance, no buffer effect was reported during the determination of the solubilities of trimethoprim and sulfamethoxazole at various pH values. [36] On the other hand, correction for buffer effects was made during studies of some isoxazolyl- naphthoquinone derivatives. [37] With the continuing development of compounds exhibiting low degrees of intrinsic aqueous solubility, the combination of pH control and complexing agents in formulations has become important, and buffers play an important role in many of these formulations. A theoretical analysis of the synergistic effect observed in the combined systems has been developed and used to explain the solubilization noted for flavopiridol. [38] In a subsequent work, the solubilization of this sub- stance by pH control combined with cosolvents, surfactants, or complexing agents was investigated. [39] The combined effect of pH and surfactants on the dissolution of piroxicam has been reported. [40] In this system, the dissolution rate and solubility of the drug substance could be well estimated by a simple additive model for the effect of pH and surfactant, where the total dissolved concentration equaled the summation of the amount of dissolved non-ionized substance, the amount of dissolved io nized substance, and the amount of substance solubilized in the surfactant micelles. It was suggested that the model developed in this work could be useful in establishing an in vitro–in vivo correlation for piroxicam. An equilibrium-based model was proposed to char- acterize the drug–surfactant interactions observed in the system consisting of furbiprofen and polysorbate 80 in solutions of different pH. [41] The model reflected both interactions and interdependence among all drug- containing species, namely, non-ionized drug in water, ionized drug in water, non-ionized drug in micelles, and ionized drug in micelles. The mathematical treat- ment also enabled modeling of the drug solubilization in the pH–surfactant solutions without requiring the use of inappropriate approximations. It was found that the solubility data estimated by the proposed model were more reliable when the surfactant concentration was high in the system. This finding confirmed that that consideration of interrelations and interdependence of all drug species in the various solutions was appro- priate for this model. CONCLUSIONS Buffers and buffering agents have been widely used for the stabilization of pharmaceutical formulations, and this aspect has proven to be especially important for parenteral products. Buffers and buffering agents have also been found to play a vitally important role during drug characterization studies, being vitally important to the conduct of solubility and drug stability studies. The range of pharmaceutically acceptable buffer sys- tems spans all useful pH values, and it can be said that there is a buffer available for every intended purpose. REFERENCES 1. Dean, J.A. Lange’s Handbook of Chemistry, 12th Ed.; McGraw-Hill: New York, 1979; 5–7. 2. Boylan, J.C. Liquids. In The Theory and Practice of Indus- trial Pharmacy; Lachman, L., Lieberman, H.A., Kanig, J., Eds.; Lea & Febiger: Philadelphia, 1986; 459–460, Chapter 15. 3. Martell, A.E.; Smith, R.M. Critical Stability Constants; Amino Acids; Plenum Press: New York, 1974; Vol. 1. 4. Smith, R.M.; Martell, A.E. Critical Stability Constants; Amines; Plenum Press: New York, 1975; Vol. 2. 5. Martell, A.E.; Smith, R.M. Critical Stability Constants; Other Organic Ligands; Plenum Press: New York, 1977; Vol. 3. 6. Smith, R.M.; Martell, A.E. Critical Stability Constants; Inorganic Complexes; Plenum Press: New York, 1976; Vol. 4. 7. Wang, Y C.J.; Kowal, R.R. 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Pharm. Sci. 2000, 89, 268– 274. 41. Li, P.; Zhao, L. Solubilization of flurbiprofen in pH–surfac- tant solutions. J. Pharm. Sci. 2003 , 92, 951–956. 392 Buffers, Buffering Agents, and Ionic Equilibria . autoionization con- stant of water. (From Ref. [1] .) 386 Buffers, Buffering Agents, and Ionic Equilibria Bio-V–Buffer Eq. (19) contains the right-hand side expression of Eq. (10), so one deduces that K B ¼. etermination of the solubility 390 Buffers, Buffering Agents, and Ionic Equilibria Bio-V–Buffer of pharmaceutical solids have been discussed at length, [31] and a large number of pH–solubility. titration of 1.0 M acetic acid, plotted as a function of the acetate ion concentration. Buffers, Buffering Agents, and Ionic Equilibria 387 Bio-V–Buffer observed pH reveals the buffer region of the system. For