Acids, Bases, and Salts in Mixed-Aqueous Solvents - American

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Acids, Bases, and Salts in Mixed-Aqueous Solvents Brian G. Cox* AstraZeneca - Research and Development, S41/15 PR&D Building, Charter Way, Silk Road Business Park, Macclesfield SK10 2NA, U.K. ABSTRACT: The dependence of the dissociation constants of acids and bases and their tendency to form salts upon solvent composition in mixed-aqueous solvents are reviewed, along with the activities of the solvent components. The acid−base equilibria are dominated by preferential solvation of the ions by water molecules in the mixtures, compounded by the very high water activities across most of the solvent composition range; the neutral components are normally preferentially solvated by the organic component of the solvent mixture. Neutral acids, such as carboxylic acids and phenols, show only modest increases in pKa (1−2 pK units) in solvent mixtures containing up to 60−70 wt % organic component; thereafter is a much steeper, solventdependent increase to the value in the pure organic solvent. Cationic acids, such as protonated amines, anilines, and pyridines, display a universal decrease in pKa (∼1 pK unit) up until around 80 wt % organic solvent, almost independent of the nature of the base or the solvent; beyond this, there is a relatively strong increase in pKa to the value in the pure solvent. The protonation of amines by carboxylic acids becomes progressively more difficult as the organic content of the solvent mixtures increases, with equilibrium constants for protonation in 60 wt % solvent being typically reduced by 3 orders of magnitude relative to those in water. The solubilities of salts formed between simple carboxylic acids and amines with a strong difference in aqueous pKa values will show a monotonic decrease with added organic component of the solvent; where one of the acid or base species has a high “organic” (hydrophobic) component, the solubility will typically pass through a maximum as the organic content of the solvent mixture increases. In cases where salt formation is strongly limited in aqueous solution (acids and bases with similar pKa values), the solubilities of the salts will increase continuously with added organic component of the solvent.

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INTRODUCTION

K a(HA)

RCO2 H XoooooooY H+ + RCO2−

The use of mixed-aqueous solvents in analytical, synthetic, and crystallization processes is widespread. In liquid chromatography, for example, mixed-aqueous mobile phases, commonly comprising acetonitrile (MeCN)−water or methanol (MeOH)− water mixtures, are regularly used in the separation of acid- or base-sensitive substances.1−3 Similarly, the isolation, purification, and formulation of many pharmaceutical actives are frequently achieved by salt formation between the (basic) actives and appropriate acids in mixed solvents, such as alcohol−water or tetrahydrofuran (THF)− water. Typically the active is a base that has limited aqueous solubility and the counterion is from a relatively soluble acid. Such salts may offer advantages over the free base (or acid) through improved physical properties such as thermal stability, crystallinity, hygroscopicity, dissolution rate, and solubility (bioavailability).4 In all of these systems, crucial to the optimization, quantification, and modeling of the processes is a knowledge of the dissociation constants of the participating acids and bases in the various solvent mixtures and their tendencies to form salts. This review provides a general background to the physicalorganic behaviour of acids and bases in mixed-aqueous solvent systems. The most commonly used acids include carboxylic acids, sulfonic acids, and phenols, and the bases are typically nitrogen bases such as amines, anilines, and pyridines (eqs 1 and 2), and the response of the dissociation of such acids and bases to solvent variation is normally dominated by the interactions between the solvent and the ionic species.5 © XXXX American Chemical Society

(1)

K a(R3NH+)

R3NH+ XoooooooooooY H+ + R3N

(2)

The neutral components of the equilibria, RCO2H and R3N, are almost universally more soluble in non-aqueous solvents than in water, i.e., they have lower activities in the non-aqueous solvents. Amongst non-aqueous solvents, however, there is little variation in their activities. In contrast, the solvation of the ions is very sensitive to the nature of the solvent; it may be stronger or weaker than solvation by water. The energy changes associated with transfer of ions among solvents are also typically much larger than those of nonelectrolytes. Neutral acids, such as carboxylic acids and phenols, are typically much weaker in non-aqueous solvents than in water, and they show considerably larger variations in acidity with solvent than protonated nitrogen bases. A brief inspection of eqs 1 and 2 suggests an obvious underlying reason: the dissociation of RCO2H generates two charged species, whereas there is no change in charge upon dissociation of R3NH+. The more polar non-aqueous solvents that are normally miscible with water may be conveniently classified into three groups, the members of each of which have closely related effects on acid−base dissociation constants: protic (typically alcohols), strongly basic aprotic (e.g., dimethyl sulfoxide (DMSO) and Nmethylpyrrolidin-2-one (NMP)), and weakly basic aprotic (e.g., Special Issue: Polymorphism & Crystallisation 2015 Received: November 12, 2014

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DOI: 10.1021/op5003566 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

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Organic Process Research & Development

that of pure water; in MeOH−water, the corresponding figure is 31%. In the remainder of this review, we use for convenience the weight-fraction scale rather than the volume-fraction scale to represent solvent composition, largely for three reasons: the majority of literature data are reported in terms of weight fraction (or wt %); it is simpler in practical terms on a large scale to prepare mixtures on the basis of weight rather than volume; and ambiguities in compositions based on volume fractions can often arise because of nonzero volumes of mixing of liquids. The weight-fraction and volume-fraction scales are of course numerically very similar because the densities, ρS, of most common solvents lie in the range 0.75 ≤ ρS ≤ 1.1 (i.e., they are similar to that of water). It follows from eq 4 that the changes in the activities of the solvent components are directly related to the changes in partial molar vapour pressures of the components (γi = pi/(p°i wi)), and hence, it is instructive to look at the measured vapour pressures in commonly used aqueous−solvent mixtures, particularly with respect to the water activity. Relative vapour pressures, p/p° (25 °C), for the components are presented in Figures 1−8, grouped as follows: protic solvents, typically alcohols (Figures 1−3); nonbasic aprotic solvents, such as MeCN and THF (Figures 4 and 5); and basic aprotic solvents, such as NMP, DMF, and DMSO (Figures 6−8). The dotted lines in all cases refer to an ideal mixture (eq 4, γ = 1). (i). Alcohol−Water Mixtures. It is noticeable that the water activities are in all cases higher than those expected for the ideal mixtures and that the deviations increase in the order MeOH < EtOH < i-PrOH (Figures 1−3). In i-PrOH−water mixtures, for

MeCN and THF). The protic solvents are distinguished by their ability to form hydrogen bonds with suitable anions, whereas the aprotic solvents are invariably poor at solvating anions. The aprotic solvents show wide variations in their ability to interact with cations, depending upon their basicity.5 In mixed solvents, an additional factor needs to be considered, namely, selective or preferential solvation by one or the other of the solvent components. For example, the dissociation of acetic acid in THF−water mixtures is dominated by interactions of the ions with water molecules across most of the composition range from pure water. The magnitude of the solute−solvent interactions is in turn strongly influenced by the activities of the solvent molecules. The dependence of the activities of the individual solvent components upon composition is therefore also an important consideration in any discussion of the behaviour of typical acids and bases in mixed (aqueous) solvents. In this review, we look primarily at the properties of simple acids and bases in aqueous solvent mixtures and their tendency to form salts in solution. As a background to these discussions, however, we begin by considering briefly the properties of the solvent components themselves in the mixtures. In particular, the individual vapour pressures of the components directly reflect their activities in the mixtures compared with the pure solvent.

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SOLVENT ACTIVITIES IN MIXED-AQUEOUS SOLVENTS The activity of a particular component i in a given mixture relative to that in the pure liquid, ai, is simply the ratio of its partial vapour pressure in the mixture, pi, to its vapour pressure in the pure liquid at the same temperature, pi° (eq 3). It is independent of how we choose to define the composition scale for the mixtures (i.e., mole fraction xi, weight fraction wi, or volume fraction vi). ai = pi /pi°

(3)

Depending upon the concentration scale we choose to represent the mixtures, we can further relate the activity of a given solvent component to the solvent composition by, for example, eq 4, which relates to the weight-fraction scale: ai = wiγi

or

pi = pi° wiγi

(4)

in which wi is the weight fraction and γi represents the activity coefficient of the component in the mixture (γi = 1 in the pure liquid). An ideal mixture is then defined as one in which the activity or the partial vapour pressure is directly proportional to the weight faction in the mixture (i.e., γi = 1 across the whole range of solvent compositions).a In choosing a concentration scale to represent changes in solvent composition, it is important to note that the magnitude of the interactions in the mixtures, either between the solvent components themselves or between the solutes and solvent components, is dependent upon the average distance between the solute and water molecules (i.e., volume concentration) rather than simply the relative number of moles of the two solvent components (i.e., mole f raction). Thus, it is sensible to choose a scale that closely reflects changes in volume concentrations, i.e., either the volume-fraction scale or the closely similar weightfraction scale. Both of these differ considerably from the molefraction scale in aqueous mixtures in particular because of the low molecular weight of water compared with other common solvent components. Thus, for example, in an NMP−water mixture with a mole fraction 0.5, the molar concentration of water is only 17% of

Figure 1. Relative vapour pressures of water and methanol in MeOH− water mixtures.6

example, even in mixtures containing only 20 wt % water, the water activity is 80% of its value in pure water. The alcohols show considerably smaller deviations from ideality. (ii). Weakly Basic Aprotic Solvent−Water Mixtures. The pronounced positive deviations from ideality of water in THF− and MeCN−water mixtures are such that across the majority of the composition range, the water activity remains at around 90% or greater of its value in pure water (Figures 4 and 5). Furthermore, it is apparent that small amounts of water in the pure solvents, MeCN and THF, generate very high water activities.b The activities of MeCN and THF are also high across the majority of the solvent composition range, but both are slightly stabilised by the addition of small amounts of water. (iii). Basic Aprotic Solvent−Water Mixtures. Perhaps surprisingly, despite the known strong interactions between the B


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Figure 2. Relative vapour pressures of water and ethanol in EtOH− water mixtures.7

Figure 5. Relative vapour pressures of water and tetrahydrofuran in THF−water mixtures.13

Figure 3. Relative vapour pressures of water and isopropanol in iPrOH−water mixtures.8

Figure 6. Relative vapour pressures of water and N-methylpyrrolidin-2one in NMP−water mixtures.9

Figure 4. Relative vapour pressures of water and acetonitrile in MeCN− water mixtures.12

Figure 7. Relative vapour pressures of water and dimethylformamide in DMF−water mixtures.10

solvents and water molecules (especially DMSO−water), the water activities in all cases show positive deviations from ideality (Figure 6−8). The deviations are, however, typically much smaller than those exhibited by mixtures with the weakly basic aprotic solvents. It seems that the interactions between the aprotic solvents and water molecules are not sufficient to compensate for the reduced water−water interactions in the mixtures. The organic components, though, are very strongly stabilised by the water molecules across the whole range of solvent composition. The most notable feature of all of these examples (Figures 1−8) is the fact that in every case the water activity in the mixtures is higher than that based upon its weight fraction alone and is frequently very much higher. The deviations are most striking in

mixtures with the weakly basic aprotic solvents, MeCN and THF, but even in mixtures involving basic solvents, such as NMP, DMF and DMSO, the water activity shows strongly positive deviations from ideality (Figures 6−8). The water activities in alcohol− water mixtures are also high and, for a given solvent composition, increase in the order MeOH < EtOH < i-PrOH (Figures 1−3). We can expect that the high water activities in all of the solvent mixtures will strongly influence the variations in dissociation constants of acids and bases in the mixtures. The non-aqueous solvent components are all stabilised by the addition of small amounts of water. In the case of basic solvents, such as DMSO, this stabilisation extends across the whole range of solvent compositions, but the very weakly basic solvents, such C


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behaviour reflects primarily the selective solvation of the ions by water in the mixtures. The behaviour exhibited in Figure 9 is typical of that for carboxylic acids in aqueous solvent mixtures, and very similar trends are also seen for phenols, as shown in Figure 10.17

Figure 8. Relative vapour pressures of water and dimethyl sulfoxide in DMSO−water mixtures.11

as MeCN and THF, show strongly positive deviations across the majority of the composition range. Finally, we note that all of the mixtures in Figures 1−8 are homogeneous across the whole range of solvent compositions, but both MeCN− and THF−water mixtures show properties close to those of immiscible mixtures.c Indeed, it has been shown that MeCN−water and even i-PrOH−water readily form biphasic systems upon addition of salts to the aqueous phase.14,15

Figure 10. Changes in pKa values of acetic acid, benzoic acid, and phenol in MeOH−water mixtures at 25 °C. pKa(H2O) values: acetic acid, 4.76; benzoic acid, 4.20; phenol, 9.96.

Dicarboxylic acids, in particular oxalic, maleic, fumaric, malonic, and tartaric acids, are useful for the formation of molecular salts because of their low pKa1 values, as is the tricarboxylic acid citric acid. In the majority of cases, the first pKa values typically mirror those of monocarboxylic acids such as benzoic acid and acetic acid.24 The second dissociation constants behave in a qualitatively similar way but are normally slightly more sensitive to solvent variation, as are the second and third pKa values of citric acid. Figure 11, for example, shows a comparison the solvent dependences of oxalic acid and acetic acid in EtOH−water mixtures.25

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DISSOCIATION CONSTANTS IN AQUEOUS/SOLVENT MIXTURES (i). Neutral Acids: Carboxylic Acids and Phenols. Carboxylic acids are almost universally weaker in non-aqueous solvents than in water, and there is strong discrimination amongst the solvents. For example, the pKa of acetic acid increases from 4.76 in water to 9.7 in methanol, 12.6 in dimethyl sulfoxide, 13.8 in dimethylformamide, and 23.5 in acetonitrile.5 In aqueous−solvent mixtures, however, this discrimination is strongly manifested only in the latter part of the composition scale, i.e., in mixtures containing low amounts of water. This is illustrated in Figure 9, which shows pKa values for acetic acid in

Figure 11. Changes in pKa values of oxalic acid and acetic acid in EtOH−water mixtures at 25 °C. pKa(H2O) values: acetic acid, 4.76; oxalic acid, pKa1 = 1.27 and pKa2 = 4.27. Figure 9. pKa values of acetic acid in aqueous−solvent mixtures at 25 °C. pKa(H2O) = 4.76.

An exception to this general behaviour is exhibited by maleic acid, which shows a greater contrast between the first and second pKa values. This is illustrated in Figure 12, which shows a comparison of the behaviours of maleic acid, fumaric acid, and acetic acid in MeOH−water mixtures.24 Intramolecular Hbonding in the monoanion of maleic acid leads to a high acidity relative to other carboxylic acids and also renders its first pKa less sensitive to the influence of solvent.d (ii). Cationic Acids (Nitrogen Bases). The response of typical nitrogen bases to changes in solvent composition is

mixtures of water with MeOH,16,17 EtOH,18 i-PrOH,19 DMSO,20 MeCN,21 and THF.22 Values in DMF23 are closely similar to those in DMSO. It is apparent that up to around 60 wt % solvent, the increases in pKa are small (∼1.5 pK units) and similar for all of the solvent mixtures. It is only beyond 80 wt % that the rate of increases becomes rapid and strongly dependent upon the nonaqueous solvent component. We will see below that this D


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Figure 12. Changes in pKa values of acetic acid, fumaric acid, and maleic acid in MeOH−water mixtures at 25 °C. pKa(H2O) values: acetic acid, 4.76; fumaric acid, pK1 = 3.02 and pK2 = 4.38; maleic acid, pK1 = 2.00 and pK2 = 6.20.

mixtures: MeOH−water,24 EtOH−water,27 THF−water,28 and MeCN−water.21 In contrast to the neutral acids, the addition of the non-aqueous solvent to water invariably leads to a decrease in the pKa of the protonated amine (decrease in amine basicity), which persists until about 80−90 wt %. Beyond this point, there is a relatively sharp increase in pKa to the value in the pure organic solvent. Once again, strong discrimination among the solvents occurs only in the region of high organic content of the mixtures; the changes are almost solvent-independent up to around 80 wt % organic component. The behaviour is also largely independent of the nature of the base, as, for example, in the cases of aniline,21 triethylamine,21 and pyridine29 in MeCN−water (Figure 15).

largely independent of the base or the solvent mixture across a large part of the composition range, but it is very different from that of carboxylic acids. This is illustrated in Figure 13 for several

Figure 13. Changes in pKa values of protonated amines and anilines from water to EtOH−water mixtures at 25 °C. pKa(H2O) values: ptoluidinium, 5.10; anilinium, 4.64; methylaminium, 10.70; trimethylaminium, 9.97.

protonated amines and anilines in EtOH−water mixtures26 and in Figure 14 for the anilinium ion in several solvent−water Figure 15. Changes in pKa values of protonated nitrogen bases in MeCN−water mixtures at 25 °C (the data for aniline and pyridine are essentially coincident up to 60 wt % MeCN). pKa(H2O) values: anilinium, 4.64; triethylaminium, 10.66; pyridinium, 5.17.

In general, the protonated acids are modestly weaker in the pure non-aqueous solvents; the overall changes in pKa values are, however, small compared with the corresponding changes for carboxylic acids and phenols.5

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DISSOCIATION CONSTANTS AND SOLVATION The changes in dissociation constants illustrated above are a reflection of changes in the free energies of the species involved in the equilibria as the solvent composition changes from water to mixed solvent, S. We can express these in terms of activity

Figure 14. Changes in pKa values of protonated aniline in solvent mixtures at 25 °C. pKa(H2O) = 4.64. E


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Organic Process Research & Development coefficients (solvent-transfer activity coefficients), γ, according to eq 5 for the dissociation of the acid HA (and similarly for the acid BH+):5 K a(H 2O) = K a(S)γHγA /γHA

decrease in pKa, and the strongest effects occur at high DMSO content in the mixture. This is consistent with the low activity of DMSO across much of the range (Figure 8), which hinders its interaction with the free base aniline, and its higher basicity, which leads to favorable solvation of both the proton and the protonated base.

(5)

Hence,

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ΔpK a = pK a(S) − pK a(H 2O) = log γH + log γA − log γHA

SALT FORMATION AND ISOLATION The discussion and data considered to date refer to the distribution of species in solution, which is particularly relevant to chromatographic applications such as HPLC1−3 and the optimisation of salt screening protocols.4 The precipitation and isolation of salts is, however, additionally controlled by the stabilities (lattice energies) of the salts. With regard to the distribution of species in solution, the protonation of amines by carboxylic acids becomes progressively more difficult as the organic content of the solvent mixture increases. For example, the equilibrium constant for the protonation of aniline by benzoic acid (eq 8) in EtOH−water mixtures decreases by almost 5 orders of magnitude in going from water to ethanol as the solvent (Figure 17). It is noticeable that even in 60% EtOH the equilibrium constant has decreased almost 1000-fold compared with its value in water.

(6)

The activity coefficient for species i, γi, is simply related to the free energy change for transfer of i from water to S, ΔGtr(i), by eq 7: ΔGtr(i) = RT ln γi

(7)

As an example, taking data for benzoic acid in MeCN−water (Figure 9)21 together with measured activity coefficients for benzoic acid in the mixtures,30 we obtain Figure 16, which shows

Ke

ArCO2 H + ArNH 2 ⇄ ArNH3+ + ArCO2−

(8)

Figure 16. Changes in pKa values for benzoic acid in MeCN−water mixtures together with the corresponding changes in the activity coefficients (log γ) of the ions (H+ + BzO−) and undissociated benzoic acid at 25 °C.

the change in pKa analysed in terms of the contributions from the changes in the free energies (expressed as log γi) of the neutral acid and the generated ions. It is apparent that up to around 60 wt % MeCN there is little change in the activity coefficients (free energies) of the ions, consistent with the high activities of water in these mixtures (Figure 4). The observed modest increase in pKa is primarily due to the increased stability of the undissociated benzoic acid molecules; beyond 60 wt % MeCN, the rapid increase in pKa to its value in pure MeCN is, however, almost entirely due to the sharply decreased solvation of the ions. A similar analysis holds for neutral acids in all of the solvent mixtures, i.e., modest increases in the free energies of the ions up to 60−70 wt % organic component followed by a more rapid increase as the solvent composition approaches that of the pure solvent. The same principles apply to the dissociation of protonated nitrogen bases (eq 2). In this case, however, the neutral species, R3N, is a product of the dissociation, so a reduction in its free energy with increasing organic component in the solvent mixture leads to an initial increase in the dissociation constant (decrease in the pKa value) (Figures 13−15). As the water level decreases significantly, however, the influence of the decreased solvation of the proton increasingly dominates, leading in the majority of cases to a net increase in pKa at high levels of the organic component of the mixture. An exception is the pKa of anilinium ion in DMSO−water mixtures:31 there is a small overall net

Figure 17. pKa and equilibrium constant (log Ke) values for benzoic acid/aniline equilibria in EtOH−water mixtures at 25 °C.

The explanation for this is apparent from an inspection of eq 8, which shows that the reaction corresponds to a conversion of neutral reactants into ionic products. Thus, addition of ethanol stabilises both reactants, tending to decrease Ke, but has relatively little effect on the product ions because of their preferential solvation by water. At higher EtOH levels, decreased solvation of the ions becomes important, leading to further decreases in Ke. An example of such behaviour is provided by the formation of the acetate salt of the model pharmaceutical base (1R,2S)-2methylamino-1-phenylpropan-1-ol ((1R,2S)-ephedrine, I) in methanol and water.4 In water the pKa values of acetic acid and ephedrine (4.76 and 9.74, respectively) are such that essentially quantitative protonation of ephedrine occurs, but in methanol there is no pH value at which signif icant quantities of the ions coexist because of the reversal in the pKa values (9.71 and 8.74, respectively). Acids such as maleic acid, oxalic acid, and methanesulfonic acid, however, remain strong enough even in pure solvents, such as the alcohols, to protonate all but the weakest bases. F


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solubility is given by S = [HA] + [A−] = [BH+] + [B]. The response of this system to solvent changes (assuming that the solubility product of the salt is sufficiently low to allow salt formation) depends upon the value of Ke in water (i.e., K°e ). When K°e is sufficiently high that essentially quantitative salt formation occurs in aqueous solution (e.g., amines plus carboxylic acids and especially dicarboxylic acids, such as oxalic acid, maleic, and fumaric acids), the dominant equilibrium governing crystallization is that between the ions (BH+ and A−) and the solid, i.e., the solubility product Ksp (eq 9). In such cases, for salts comprising essentially hydrophilic ions (simple cations, halide and carboxylate anions), decreased solvation of the ion as the organic component of the solvent increases will lead to decreased solubility, slowly at first but increasingly rapidly as the water level is strongly reduced, in accordance with the discussion above on preferential solvation of the ions in the mixtures. For an organic salt, e.g., [R3NH+R′CO2−], in which (typically) one of the ions has a large hydrophobic part, the solubility will initially increase as the organic component of the solvent mixture is added but then will pass through a maximum and decrease again as decreased solvation of the carboxylate ion becomes important. This behaviour is illustrated in Figure 18, which shows the

The decrease in Ke of around 3 orders of magnitude in 60 wt % solvent (Figure 17) is typical of combinations of acid and base in solvent mixtures, but the magnitude of the decrease in Ke in the pure solvent is more strongly solvent-dependent. For example, in MeCN−water mixtures, the behaviour up to 60 wt % is very similar to that in Figure 16, but the decrease in pure MeCN is 11 orders of magnitude because of the very poor solvation of both ions in MeCN.5,21 Exactly analogous considerations apply to intramolecular proton transfers, such as the formation of zwitterions in amino acids, as in the case of 4-aminobenzoic acid:

As expected, in ethanol−water mixtures the equilibrium proportion of the zwitterion decreases strongly as the ethanol content of the mixture increases, falling from 10% in water to 0.27% in 50 wt % EtOH and 0.015% in 75 wt % EtOH, the latter corresponding to a decrease in log Ke of 4.8 units.32 The change in the equilibrium proportion of the neutral and zwitterionic forms can also have implications for the crystallization of amino acids, as in the case of anthranilic acid: Figure 18. Changes in the solubility products of NaCl and Bu4NCl in MeCN−water mixtures at 25 °C.

contrasting changes in solubilities of NaCl and Bu4NCl in MeCN−water mixtures, computed from the changes in free energies of the component ions in the mixtures.34 The sharp difference between the two types of salt is apparent. When Ke° is low (and crystallization is therefore driven by a low Ksp), the dominant equilibrium is between the neutral species (HA and B) and the solid. The solubility will then increase with increasing organic content of the mixture because of stabilisation of the neutral species. We can analyse the system quantitatively by including the appropriate activity coefficients to allow for the influence of the solvent on the equilibria (eqs 10−12):

The crystal structures of two polymorphs of anthranilic acid are known. Form I contains both un-ionised and zwitterionic molecules in a 1:1 ratio, whereas form II contains only uncharged molecules. Changing the solvent does not change the relative thermodynamic stability of these two polymorphs, with form 1 being the stable phase at room temperature, but the solvent is expected to affect the crystallization kinetics. The unionised anthranilic acid species is at relatively much higher concentrations in organic solvents, so they should favor initial isolation as form II. This is exactly what was found: form II crystallised initially from ethanol and methanol, and an unstirred ethanol slurry of form II showed complete transformation to form I after 12 h.33 The precipitation and crystallization of the salts are, however, driven by a combination of the solubility product of the salt and the extent of ionisation in solution (eq 9): Ke

Ke° =

[HA][B]γ 2

(10)

° = [BH+][A−]γ±2 K sp

(11)

S = [HA] + [A−]

(12)

where K°e and K°sp refer to the equilibrium constants and solubility products in water, respectively, γ± = (γ+γ−)1/2 is the mean ionic activity coefficient, and γ is the activity coefficient of the neutral species. For simplicity, we consider the case where the initial

K sp

HA + B ⇄ BH+ + A− XooY (BH+Ar −)c

[BH+][A−]γ±2

(9)

in which Ksp = [BH+][A−] is the solubility product of the salt in the solvent mixture. For a 1:1 mixture of HA and B, the total G


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Organic Process Research & Development concentrations of HA and B are equal. Under these conditions, Ksp ° = [A−]2γ±2, and substitution into eq 11 yields Ke° = Ksp °/ [HA]2γ2. Thus, by substitution into eq 12, the solubility in the mixtures, S, is given by eq 13: 1/2

S=

°) (K sp

1/2

(Ke°)

•

1/2

°) (K sp 1 + γ γ±

(13)

•

This equation indicates the following: • When Ke° is very large, S ≈ (Ksp ° )1/2/γ±, and for simple ions it will decrease with increasing organic content of the solvent, as γ± increases due to weaker solvation of the ions; for organic ions with a significant hydrophobic component, the solubility will typically pass through a maximum (Figure 18). • When K°e is very small, S ≈ {(K°sp)/(K°e }1/2/γ, and the solubility will increase with increasing organic content of the solvent, as γ decreases due to stronger solvation of the neutral species (e.g., see the activity coefficient for benzoic acid in MeCN−water in Figure 16). • In the intermediate case, both terms in eq 13 will contribute to the observed behaviour, with the neutral and hydrophobic species dominating at low organic component of the solvent mixtures and the decreased solvation of the hydrophilic species dominating at lower water content. The result will normally be a maximum in the solubility with solvent composition. In the case of dibasic acids, the stoichiometry of the isolated salt may depend upon the solvent from which it is isolated because of the rapid changes in ionic composition of the solution accompanying solvent change. Such an example arises in the isolation of the anilinoquinazoline kinase inhibitor II35 as a fumarate salt:

•

•

•

•

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DMSO, DMF, and NMP, are higher than those based upon its weight fraction across the whole composition range and are frequently very much higher. The variation in pKa values across the solvent range is strongly influenced by preferential solvation of the ions by water and the neutral acid or base form by the organic component of the solvent. Neutral acids, such as carboxylic acids and phenols, typically show only modest increases in pKa (1−2 pK units) in solvent mixtures containing up to 60−70 wt % organic component; thereafter is a much steeper, solvent-dependent increase to the value in the pure organic solvent. Cationic acids, such as protonated amines, anilines, and pyridines, display a universal decrease in pKa (∼1 pK unit) up until around 80 wt % organic solvent, almost independent of the nature of the base or the solvent. Beyond this, decreased solvation of the proton leads to a relatively sharp increase in pKa to the value in the pure solvent. The protonation of amines by carboxylic acids becomes progressively more difficult as the organic content of the solvent mixture increases, with equilibrium constants for protonation in 60 wt % solvent being typically reduced by 3 orders of magnitude relative to those in water. This results from a combination of stabilisation of the neutral acid and amine forms by the organic component of the mixture and destabilisation of the product ions as the water content of the mixture decreases. The solubility of salts formed between simple carboxylic acids and amines with a strong difference in aqueous pKa values will show a monotonic decrease with added organic component of the solvent; where one of the acid of base species has a high “organic” (hydrophobic) component, the solubility will typically pass through a maximum as the organic content of the solvent mixture increases. In cases where salt formation is strongly limited in aqueous solution (acids and bases with similar pKa values), the solubility of the salts will increase continuously with added organic component of the solvent.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Crystallization from alcohol−water mixtures gives a 2:1 salt involving the diprotonated substrate (IIH22+) and the monoanion of fumaric acid (HA−): [(IIH22+)(HA−)2]. In water, however, the recovered product is a 1.5:1 salt, which includes the both the fumarate mono- and dianions: [(HA−)(IIH22+)(A2−)(IIH22+)(HA−)], isolated as the hydrate. The ionic product of the two species decreases as the alcohol content of the solvent increases, in line with the discussion above, but the dominant differentiating effect is the severe reduction in the equilibrium level of the fumarate dianion, which drastically decreases the ionic product of the latter salt.

ACKNOWLEDGMENTS I wish to thank Dr. Simon Black and Dr. Lai Chan for helpful discussions and suggestions. ADDITIONAL NOTES Analogous equations for the volume-fraction and mole-fraction scales are pi = pi°viγi and pi = pi°xiγi, respectively. The numerical value of γi of course depends upon the concentration scale chosen. b A consequence is that the activity of the proton in these solvents (and hence the measured pKa value) is very strongly affected by traces of water. In some cases, e.g., acetonitrile, it is possible to measure equilibrium constants for hydration of the proton, Kh(H2O)n, which are very high:36 the Kh(H2O)n values for n = 1 to 4 are successively 1.6 × 102 M−1, 8 × 103 M−2, 6 × 104 M−3, and 2 × 105 M−4. a

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SUMMARY This review has highlighted the following points: • The water activities in a wide range of aqueous−solvent mixtures, including alcohols, weakly basic aprotic solvents such as MeCN and THF, and basic aprotic solvents such as H


Review


Olivier, A.; Otterbein, L.; Plé, P. A.; Warin, N.; Costello, G. J. Med. Chem. 2006, 49, 6465. (36) Chantooni, M. K.; Kolthoff, I. M. J. Am. Chem. Soc. 1970, 92, 2236. (37) Hong, G.-B.; Lee, M.-J.; Lin, H. Fluid Phase Equilib. 2002, 203, 227. (38) Ashworth, I. W.; Bush, E.; Chan, L. C.; Cherryman, J.; Cox, B. G.; Muir, J.; Korupoju, S. R.; Keshwan, J. Org. Process Res. Dev. 2012, 16, 1646.

Kh(H 2O)n

H+ + nH 2O XoooooooooY H(H 2O)n+ c

Immiscible systems are characterised by constant total and partial vapour pressures across the region where immiscibility occurs, e.g., ethyl acetate (EtOAc)−water mixtures, which are immiscible between 6.87 and 96.34 wt % EtOAc at 35 °C.37 d It may also be noted that the relatively high acidity of maleic acid leads to a strong tendency to form the methyl ester when this acid is dissolved in pure methanol.38

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REFERENCES

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Acids, Bases, and Salts in Mixed-Aqueous Solvents - American

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