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Through consideration of the ionic equilibria of acids and bases, one may readily calculate the formation constant of a salt species solely on the basis of knowledge of the pKA value of the acid and the pKB value of the base.
Any drug substance can be classified as either an acid or base because the drug substance possesses the ability to react with other, stronger acids or bases. As such, the drug substance also would possess the ability to exist as an ionic species when dissolved in suitable fluid media. Often, the state of ionization of a substance will profoundly affect its degree of aqueous solubility, as shown by the high solubility of sodium benzoate compared with the low solubility of benzoic acid. The utility of salt forms as active pharmaceutical ingredients is well known and represents one of the ways to increase the degree of solubility of an otherwise intractable substance (1–3) and bioavailability (4).
Historically, the process of selecting the most appropriate salt form of a drug substance has been approached in an empirical manner, where one prepares a large number of salts of the substance and then evaluates their qualities. Those products that exhibit acceptable degrees of aqueous solubility and dissolution rate, appropriate crystal form of low hygroscopicity, high melting point, good mechanical properties, and acceptable chemical stability become the chosen candidates for further development. This approach reached its epitome with the use of high-throughput screening methods, where substances are dispensed in 96-well plates and automated methods are used to set up the formation of multiple series of salts (5). Practically, the only restriction placed in these studies is that the salt-forming counterion must be one of the pharmaceutically acceptable species identified in compilations (1–3, 6).
Numerous attempts have been made to instill an intelligent design into the salt-selection process. Gould used a decision analysis process to develop a rational process of salt selection for basic drugs, where the course of the work was guided by the pivotal issues of melting point, solubility, and hydrophobicity (7). Morris et al. described a general method that was used to guide the salt selection of a drug candidate through consideration of hygroscopicity, physical stability, aqueous solubility, and chemical stability (8). The theoretical basis and application of in situ salt screening has been applied to monobasic and monoacidic substances (9) and extended to cover multibasic drugs in multiprotic acids (10). Procedures for salt selection and optimization have been reviewed, as have strategies for salt selection and optimization of salt forms (11–13). More recently, the use of a grid-based molecular modeling method for salt screening has been described (14).
Over time, it has become very clear that the ability to prepare and isolate a salt form of a drug substance in its solid state, and the stability of that salt form with respect to disproportionation when dissolved in an aqueous solution, is fundamentally determined by the relative acidity or basicity of the drug substance and its salt-forming counterion. Valuable insight into the salt-formation process can be gleaned from an evaluation of the chemical equilibria associated with weak acids, bases, and their salts. Manipulation of equilibrium expressions yields useful relations that can be used to predict the ability of a salt form to exist, and such predictions can be used to focus a salt-selection process.
Ionic equilibria of acidic and basic substances
There are many definitions for acids and bases, but the 1923 definitions of J.N. Brønsted and T.M. Lowry are 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 substance, such as water:
The acidic substance (HA) that originally donated the proton becomes the conjugate base (A– ) of that substance because the conjugate base could conceivably accept a proton from an even stronger acid than the original substance. The thermodynamic equilibrium constant expression for Equation 1 would be:
In Equation 2, the quantities in square brackets represent the molar concentrations of the various species, and the γ quantities are the activity coefficients of those species. For an acid capable of ionizing into a univalent anion, γH+ and γA– will be approximately equal, and γHA can be approximated as unity, so that the concentration-based equilibrium constant expression can be simply written as:
For weak acids, the magnitude of KA is very small, and therefore, the resulting H3O+ and A– ions will be produced in small amounts. Under those conditions, both γH+ and γA– will be approximately equal to one, facilitating the approximation that the thermodynamic equilibrium constant, K, equals the concentration-based ionization constant, KA. Making use of the Sørensen scale, one can define the pKA of a weak acid as:
A strong acid is defined as a substance that reacts completely with water so that the acid ionization constant defined in Equation 2 or 3 is very large. This situation 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 Equation 1 favors the existence of nonionized free acid. The implication of these properties is that the conjugate base of the weak acid must be moderately strong.
A discussion of the ionic equilibria associated with basic substances exactly parallels that just developed for acidic substances. A base is a substance capable of accepting a proton donated by another substance, such as water:
The basic substance (B) that originally accepted the proton becomes the conjugate acid (BH+ ) of that substance, since the conjugate acid could conceivably donate a proton to an even stronger base than the original substance. The concentration-based ionization constant expression corresponding to Equation 5 is:
and pKB is defined as:
A strong base is a substance that reacts completely with water, so the base ionization constant defined in Equation 6 is effectively infinite. This situation can only be realized if the conjugate acid of the strong base is very weak. Since the conjugate acid of a weak base will be moderately strong, the base ionization constant will be considerably less than one, and the position of equilibrium in the reaction represented in Equation 5 will favor the existence of a nonionized free base.
Once formed, the conjugate base of an acidic substance (i.e., the anion of that acid) would also be capable of reacting with water:
Because aqueous solutions of anions are commonly prepared by the dissolution of a salt containing that anion, reactions of the type described by Equation 8 are often termed hydrolysis reactions. Equation 8 is necessarily characterized by a base ionization constant expression:
and a corresponding pKB defined in the usual manner.
However, because these ionic equilibria are taking place in aqueous media, the autoionization of water:
must also be considered. The equilibrium constant for this reaction would be:
In aqueous solutions, the concentration of water is effectively a constant (55.55 M), and so Equation 11 simplifies to:
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 X 10–14 at a temperature of 25 °C (15). Substitution of Equation 12 into Equation 9 yields the relation:
However, the concentration terms in Equation 13 constitute the ionization constant expression for the conjugate acid of the conjugate base, providing the very useful relation regarding the relative strengths of conjugate acids and bases:
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 Equation 14 is recognized as a general property of conjugate acid–base pairs.
Ionic equilibria of salts
Salts are chemical compounds formed by the transfer of a proton from an acid (HA) to a base (B) capable of accepting that proton:
When dissolved in aqueous media at low to moderate concentrations, the (HB+)(A–) salt will ordinarily exist in the form of dissociated HB+)(A– and A– ions:
As previously discussed, the free acid and free base are subject to their individual ionic equilibrium expressions. So Equation 16 can be expanded as:
Equation 17 is simply another way to express the neutralization reaction of Equation 16, and the complete equilibrium constant expression for this reaction would be:
Recognizing again that the concentration of water is a constant factor, one can define the neutralization constant (KN) expression as:
Comparison of Equation 19 with the weak-acid ionization constant expression of Equation 3 and the weak base ionization constant expression of Equation 6 leads to a simple relation that defines KN:
As previously defined in Equation 12, the product of the concentration terms for the hydronium and hydroxide ions equals the autoionization constant of water, so:
Equating Equations 20 and 21, and collecting the various constants on the left-hand side yields the relation:
Equation 22 is nothing more than the equilibrium constant expression associated with the chemical reaction of Equation 16. If one defines the salt formation constant as:
then Equation 22 becomes:
When converted to the Sørensen scale, Equation 23 becomes:
Equation 25 can be used to make rapid deductions regarding the strength of a particular salt species. Suppose one were contemplating forming a salt between an acid having a pKA value of 4.79 and a base having a pKA value of 9.45. For the base, it would follow that the pKB would equal 4.55, and because pKW = 14.0 at 25 °C, the pKS of the salt would equal -4.66, and that KS would equal approximately 45,710 . A reaction characterized by an equilibrium constant of this magnitude would clearly go to completion, and one would predict that the salt in question would be formed without difficulty.
The ability to calculate KS enables one to estimate the relative position of the equilibrium described by Equation 16. Consider the solution prepared by mixing an acid at an initial concentration of CHA with a base at an initial concentration of CB. For a salt form having a 1:1 stoichiometry, the concentrations of conjugate acid and conjugate base formed in the reaction would necessarily be equal. If the resulting ionic concentrations are represented by X, then the concentration of residual acid would equal (CHA–X) and the concentration of residual base would equal (CB–X). Equation 24 would then have the form:
Because obtaining the solution of Equation 26 by means of the quadratic equation is trivial, the degree of formation of a salt through the mixing of equimolar amounts of acid and base (i.e., CHA = CB) can be easily calculated. For example, if log(KS) = 2, it follows that X = 0.9091, indicating that equation 16 would proceed 90.91% to completion. Similarly, if log(KS) = 3, then X = 0.9693 and the efficiency of salt formation would be 96.93%. If log(KS) = 4, the salt would be 99.01% formed, and if log(KS) = 5, then the salt would be 99.68% formed. It is often stated in the literature that if the ionization constants of the acid and base involved in salt formation differ by 2 or 3 pK units, then the salt would be formed. Use of the log(KS) quantity serves to place the old empirical rule on a more fundamental basis and facilitates calculation of the actual percentage of salt formation.
Knowledge of the log(KS) quantity also permits one to deduce the degree of disproportionation that would be anticipated if one were to dissolve a salt in pure water. If the X factor of Equation 26 represents the fraction of salt being formed by the reaction of the acid and base, then it follows that the fraction of salt that would disproportionate would necessarily be given by (1–X), and its percentage as 100 times that quantity.
Utility of salt-form ionic equilibria in the design of salt-selection studies
The ability to calculate log(KS) values can be very helpful when designing the scope of a salt-selection study because it can be used to determine the acidity or basicity range of potential salt-forming species. For example, consider a drug substance containing a basic functionality characterized by a pKA value of 10.60 so that pKB would equal 3.40. One can then calculate the log(KS) values for a series of acids of varying pKA values, obtaining the results shown in Table I. If an acceptable salt is defined as one whose degree of formation would exceed 99%, then it would follow that any acid characterized by a pKA value that was less than 6.0 would form a product that would be worth isolating. The value of this rather strict definition is that any salt whose degree of formation exceeded 99% would also be predicted to undergo less than 1% disproportionation when dissolved in water.
Table I: Predicted degree of salt formation for a strong base* with acids of differing pK A values.
Continuing the analysis, now consider a drug substance containing a basic functionality characterized by a pKA value of 8.55, so that pKB would equal 5.45. Again calculating the log(KS) values for a series of acids of varying pKA values yields the results shown in Table II.
Table II: Predicted degree of salt formation for a moderate base* with acids of differing pK A values.
Using the definition of an acceptable salt as one whose degree of formation would exceed 99%, then it follows that only acids characterized by pKA values less than 4.0 would form acceptable salts that would not be susceptible to disproportionation.
Finally, consider a weakly basic drug substance containing a functionality characterized by a pKA value of 7.25. Since its pKB would equal 6.75, the log(KS) values shown in Table III were calculated for the series of acids of varying pKA values.
Table III: Predicted degree of salt formation for a weak base* with acids of differing pK A values.
To form an acceptable salt whose degree of formation exceeded 99%, then only acids characterized by pKA values less than 3.0 would form acceptable salts that would not be susceptible to disproportionation.
In the illustrated case of a basic drug substance, once the range of acceptable acidic salt-formers has been determined, one only needs to consult the various compilations of pharmaceutically acceptable acids (1–3, 6) to specify the list of salts that would be actually prepared in the laboratory.
To further illustrate the strategy that would be used to select the range of salt-forming species for a particular drug substance, consider a hypothetical selection process for ibuprofen. The pKA of this acidic compound is 4.41 (16), and equations 25 and 26 can be used to calculate the degree of salt formation as a function of the pKA value of potential basic salt-formers. These results are plotted in Figure 1, and if one accepts the definition of an appropriate salt as one whose degree of formation equals 99% or higher, then one would only form ibuprofen salts with bases whose pKA values exceed 8.41. The formation of sodium or potassium salts (for which pKA is approximately 14) is obvious, as would be the formation of salts with arginine (pKA = 9.59), lysine (pKA = 9.48), ethanolamine (pKA = 9.16), diethanolamine (pKA = 8.71), and erbumine (pKA = 10.68).
Figure 1: Degree of salt formation calculated for the reaction of ibuprofen with basic substances of varying pK values, where it may be noted that the 99% formation criterion interacts with the curve at a pK A value of 8.41.
The preparation of these salts could be affected by the simple mixing of equimolar amounts of ibuprofen and the pharmaceutically acceptable bases deduced to have appropriate pKA values. These salts would be evaluated on the basis of the degree of acceptability associated with their solubility, hygroscopicity, or other physical properties. For example, the tiered acceptability criteria outlined in Morris et al. could be used to design the program of salt form evaluation (8).
The identification of a salt form of an active pharmaceutical ingredient becomes essential if the characteristics of the free acid or free base are not found to be acceptable. Selection of an appropriate salt form of a chemical entity provides one with the possibility to selectively modify the aqueous solubility, dissolution rate, solution pH, crystal form, hygroscopicity, chemical stability, melting point, or mechanical properties of a drug substance. The identification of suitable counterions to be used in the formation of acceptable salt forms does not have to be conducted following trial-and-error methodologies, but instead appropriate salt-forming candidates can be readily identified through knowledge of the magnitude of the ionization constants of the acids and bases involved.
An equation has been developed based on the ionic equilibria of acids and bases that permits one to calculate the formation constant of a salt species solely on the basis of knowledge of the pKA value of the acid and the pKB value of the base. The initial stages of a salt-selection process for a particular drug substance would begin with knowledge of its ionization constants and culminate with the calculation of the range of ionization constants of salt-forming agents that would ensure the formation of salts in high degrees of efficiency. The salt forms identified in this manner would be predicted to be stable with respect to disproportionation.
Harry G. Brittain, PhD, is the director of the Center for Pharmaceutical Physics and a member of Pharmaceutical Technology's editorial advisory board, 10 Charles Rd., Milford, NJ 08848, tel. 908.996.3509, fax 908.996.3560, firstname.lastname@example.org
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