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EPT-Buffers, Buffering Agents, And Ionic Equilibria

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          B        i      o     -        V    –        B      u         f        f      e       r 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 whenexposed to certain acidic or basic conditions, and suchinformation is routinely gathered during the preformu-lation stage of development. When such instabilitiesare identified, one tool of the formulation sciences isto include a buffering agent (or agents) in the dosageform 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 isderived from their qualities as weak acids or bases, andhave 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 arisefrom the transfer of a proton from a water moleculeto another:H 2 O  þ  H 2 O  $  H 3 O þ þ  OH  ð 1 Þ In Eq. (1), H 3 O þ is known as the  hydronium  ion,and OH  is known as the  hydroxide  ion. This reactionisreversible,andthereactantsareknowntoproceedonlyslightlyontotheproducts.Approximatingtheactivityof the various species by their concentrations, one can writethe equilibrium constant for this reaction as K  C  ¼ ½ H 3 O þ ½ OH  ½ H 2 O  2  ð 2 Þ In aqueous solutions, the concentration of water iseffectively a constant (55.55M), and so Eq. (2) simpli-fies to: K  W  ¼ ½ H 3 O þ ½ OH   ð 3 Þ 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, beingequal to 1.007    10  14 at a temperature of 25  C. [1] For the sake of convenience, Sørensen proposed the‘‘p’’ scale, where numbers such as  K  W  would beexpressed as the negative of their base10 logarithms.The value of p K  W  would then be calculated asp K  W  ¼  log ð K  W Þ ð 4 Þ and would have a value equal to 13.997 at 25  C.Defining pH aspH  ¼  log ½ H 3 O þ  ð 5 Þ andpOH  ¼  log ½ OH   ð 6 Þ then Eq. (3) can then be expressed asp K  W  ¼  pH  þ  pOH  ð 7 Þ The autoionization of water is an endothermic reac-tion, so  K  W  increases as the temperature is increased. [1] This temperature dependence is plotted in Fig. 1. IONIC EQUILIBRIA OF ACIDICAND BASIC SUBSTANCES Of the numerous definitions of acids and bases thathave been employed over the years, the 1923 defini-tions of J. N. Brønsted and T. M. Lowry have provento be the most useful for discussions of ionic equilibriain aqueous systems. According to the Brønsted–Lowrymodel, an  acid  is a substance capable of donating aproton to another substance, such as water:HA  þ  H 2 O  $  H 3 O þ þ  A  ð 8 Þ The acidic substance (HA) that srcinally donatedthe proton becomes the  conjugate base  (A  ) of thatsubstance, because the conjugate base could conceiva-bly accept a proton from an even stronger acid thanthe srcinal substance. One can write the equilibriumconstant expression corresponding to Eq. (8) as K  C  ¼ ½ H 3 O þ ½ A  ½ HA ½ H 2 O  ð 9 Þ Encyclopedia of Pharmaceutical Technology  DOI: 10.1081/E-EPT-120011975Copyright # 2007 by Informa Healthcare USA, Inc. All rights reserved.  385  B  i      o - V  –B   u f     f      e r    But because [H 2 O] is a constant, one can collect theconstants on the left-hand side of the equation toderive the  acid ionization constant  expression: K  A  ¼ ½ H 3 O þ ½ A  ½ HA  ð 10 Þ And, of course, one can define p K  A  asp K  A  ¼  log ð K  A Þ ð 11 Þ A  strong acid  is a substance that reacts completelywith water, so that the acid ionization constant definedin Eq. (10) or (11) is effectively infinite. This situationcan only be achieved if the conjugate base of the strongacid is very weak. A  weak acid  will be characterized byan acid ionization constant that is considerably lessthan unity, so that the position of equilibrium in thereaction represented in Eq. (8) favors the existence of unreacted free acid.A discussion of the ionic equilibria associated withbasic substances parallels that just made for acidic sub-stances. A  base  is a substance capable of accepting aproton donated by another substance, such as water:B  þ  H 2 O  $  BH þ þ  OH  ð 12 Þ The basic substance (B) that srcinally accepted theproton becomes the  conjugate acid  (BH þ ) of thatsubstance, because the conjugate acid could conceivablydonate a proton to an even stronger base than thesrcinal substance. The equilibrium constant expressioncorresponding to Eq. (12) is: K  C  ¼ ½ BH þ ½ OH  ½ B ½ H 2 O  ð 13 Þ Because [H 2 O] is a constant, the constants are col-lected on the left-hand side of the equation to derivethe  base ionization constant  expression: K  B  ¼ ½ BH þ ½ OH  ½ B  ð 14 Þ p K  B  is defined asp K  B  ¼  log ð K  B Þ ð 15 Þ A  strong base  is a substance that reacts completelywith water, so that the base ionization constant definedin Eq. (14) or (15) is effectively infinite. This situationcan only be realized if the conjugate acid of the strongbase is very weak. A  weak base  will be characterized bya base ionization constant that is considerably lessthan unity, so that the position of equilibrium in thereaction represented in Eq. (12) favors the existenceof unreacted free base. IONIC EQUILIBRIA OF CONJUGATEACIDS AND BASES Once formed, the conjugate base of an acidic substance(i.e., the anion of that acid) is also capable of reactingwith water:A  þ  H 2 O  $  HA  þ  OH  ð 16 Þ Because aqueous solutions of anions are commonlyprepared by the dissolution of a salt containing thatanion, reactions of the type described by Eq. (16) areoften termed  hydrolysis  reactions. Eq. (16) is necessa-rily characterized by its base ionization constantexpression: K  B  ¼ ½ HA ½ OH  ½ A   ð 17 Þ and a corresponding p K  B  defined in the usual manner,but because ½ OH   ¼  K  W = ½ H 3 O þ  ð 18 Þ it follows that K  B  ¼ ½ HA  K  W ½ A  ½ H 3 O þ  ð 19 Þ Temperature (°C)     p      K    w Fig. 1  Temperature dependence of the autoionization con-stant of water. (From Ref. [1] .) 386 Buffers, Buffering Agents, and Ionic Equilibria          B        i      o     -        V    –        B      u         f        f      e       r Eq. (19) contains the right-hand side expression of Eq. (10), so one deduces that K  B  ¼  K  W = K  A  ð 20 Þ or K  W  ¼  K  A K  B  ð 21 Þ The same relation between ionization constants of aconjugate acid–base pair can be developed if one wereto 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 anapproximately equal pH value even if small amounts of acidic or basic substances are added. To function inthis manner, a buffer solution will necessarily containeither an acid and its conjugate base, or a base andits conjugate acid.The action of a buffer system can be understoodthrough the use of a practical example. Consider aceticacid, for which  K  A  ¼  1.82    10  5 (p K   ¼  4.74). Thefollowing pH values can be calculated (for solutionshaving a total acetate content of 1.0M) using its acidionization constant expression: Acetic acid, [HA] Acetate ion, [A  ] Calculated pH  0.4 0.6 4.920.5 0.5 4.740.6 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 acidiccomponent. One therefore concludes from the tablethat the addition of either 0.1M acid or 0.1M baseto a buffer system consisting of 0.5M acetic acid and0.5M acetate ion would cause the pH to change byonly 0.18pH units. This is to be contrasted with thepH 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 6.0pH units), or from the addition of 0.1M base towater (i.e., 13.0 to 1.0, also for a change of 6.0pHunits).A very useful expression for describing the proper-ties of buffer system can be derived from considerationof ionization constant expressions. For an acidicsubstance, Eq. (10) can be rearranged as ½ H 3 O þ  ¼  K  A ½ A  ½ HA  ð 22 Þ Taking the negative of the base 10 logarithms of thevarious quantities yields the relation known as theHenderson–Hasselbach equation:pH  ¼  p K  A  þ  log f½ A   = ½ HA g ð 23 Þ Eq. (23) indicates that when the concentration of acidand its conjugate base are equal (i.e., [HA]  ¼  [A  ]),then the pH of the solution will equal the p K  A  value.Therefore, a buffer system is chosen so that the targetpH is approximately equal to the p K  A  value.Viewed in this light, a buffer system can be envi-sioned as a partially completed neutralization reactionHA  þ  OH  $  A  þ  H 2 O  ð 24 Þ where comparable amounts of HA and A  are presentin the solution. The buffer region within a neutraliza-tion reaction is shown in Fig. 2, where the horizontalregion in the graph of anion concentration and [acetate]      p        H Fig. 2  Neutralization curve obtained during the titrationof 1.0M acetic acid, plotted as a function of the acetate ionconcentration. Buffers, Buffering Agents, and Ionic Equilibria 387  B  i      o - V  –B   u f     f      e r    observed pH reveals the buffer region of the system.For practical purposes, the buffer region would extendover [HA]/[A  ] ratios of approximately 0.2 to 0.8. SELECTION OF AN APPROPRIATEBUFFER SYSTEM The selection of a buffer system for use in a pharma-ceutical dosage form is relatively straightforward. Itis evident from the preceding discussion that the mostimportant prerequisite for a buffer is the approximateequality of the p K  A  value of the buffer with theintended 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 whichformulation is desirable, and the basis for the mostappropriate buffer system would be the weak acid orbase whose p K  A  or p K  B  value was numerically equalto the midpoint of the pH range of stability.There are, of course, other considerations that needto be monitored, such as compatibility with the drugsubstance. Boylan [2] has provided a summary of theselection criteria for buffering agents:1. The buffer must have adequate capacity in thedesired pH range.2. The buffer must be biologically safe for theintended use.3. The buffer should have little or no deleteriouseffect on the stability of the final product.4. The buffer should permit acceptable flavoringand coloring of the product.A practical consequence of Eq. (23) is that as long asthe concentration of a buffer is not overcome by reac-tion demands, a buffer system will exhibit adequatecapacity within   1pH unit with respect to its p K  A  orp K  B  value.The second criterion from the preceding list restrictsbuffering agents to those deemed to be pharmaceuti-cally acceptable. A list of appropriate buffer systemsis provided in Table 1, along with values for theirp K  A  or p K  B  values sourced from the compilations of Martell and Smith. [3–6] The use of buffering agents ismost critical for parenteral formulations, and it hasbeen noted over the years that phosphate, citrate,and acetate are most commonly used for such pur-poses. [7,8] Ethanolamine and diethanolamine are alsoused 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 reviewedthe scope of drug–excipient interactions in parenteralformulations and has provided an overview of theeffect of buffers on drug substance stability. Table 1  Acids and bases suitable for use as buffer systems in pharmaceutical products Basis for buffering system p K  1  p K  2  p K  3 Martell andSmith reference Acetic acid 4.56 — — [5], p. 3Adipic acid 5.03 4.26 — [5], p. 118Arginine 9.01 2.05 — [3], p. 43Benzoic acid 4.00 — — [5], p. 16Boric acid 8.97 — — [6], p. 25Carbonic acid 10.00 6.16 — [6], p. 37Citric acid 5.69 4.35 2.87 [5], p. 161Diethanolamine 8.90 — — [4], p. 80Ethanolamine 9.52 — — [4], p. 15Ethylenediamine 9.89 7.08 — [4], p. 36Glutamic acid 9.59 4.20 — [3], p. 27Glycine 9.57 2.36 — [3], p. 1Lactic acid 3.66 — — [5], p. 28Lysine 10.69 9.08 2.04 [3], p. 58Maleic acid 5.83 1.75 — [5], p. 112Phosphoric acid 11.74 6.72 2.00 [6], p. 56Tartaric acid 3.95 2.82 — [5], p. 127Triethanolamine 7.80 — — [4], p. 118Tromethamine 8.09 — — [4], p. 20 388 Buffers, Buffering Agents, and Ionic Equilibria

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