In general it is possible to classify solutes as either electrolytes or non-electrolytes, and then to sub-classify the electrolytes into strong and weak categories. An electrolyte is essentially a solute which dissociates into ions producing a solution capable of conducting electricity. Strong electrolytes dissociate completely in dilute solution, while weak electrolytes partially dissociate.

Consider the following comprehensive scheme for an undefined hypothetical chemical AB:

Eq. (1)

where, AB_(solid) refers to the chemical in the solid form, AB_(soln) to the chemical in solution in an undissociated form, A⁺ and B^- to ions of the dissociated solute in solution, and [A⁺..B^-] to a neutral ion-pair in solution. Each solubility analysis will involve one or more of the species identified in this scheme.

For example, the equilibrium solubility relationship for a non-electrolyte only involves one dissolved species:

          Eq. (2)

where the equilibrium constant, K_o, is also known as S_o, the intrinsic solubility.

            Eq. (3)

Note that in the ideal case, activities and concentrations are equivalent, and the activity (or concentration) of the pure solid is assigned a value of unity. The term intrinsic is chosen to refer to the fact that the species in solution is the same as that of the solid form. As will be seen later, the total solubility observed represents the sum of the equilibrium concentrations of all species present. For a non-electrolyte, the total solubility is the intrinsic solubility.

When the dissolved species are in equilibrium with solid at a specified temperature in a specified solvent system, the concentration of those species are at a maximum. In this discussion, concentration terms such as (AB) are maximum, equilibrium molar concentrations under specified conditions.

A strong electrolyte is characterized by complete dissociation. That is to say that there is no species AB in solution.

    Eq. (4)

In dilute solution,

              Eq. (5)

where K_o^* is the equilibrium constant. If the solubility of the strong electrolyte is indeed low, and the ratio of A:B is 1, then the equilibrium constant is equivalent to the well known solubility product (K_sp).

Since the solubility of this 1:1 electrolyte is equal to the concentration of either ionic species:

      Eq. (6)

where S_o^* is the intrinsic solubility of the strong electrolyte.

In general, ionized species have greater solubility in water than uncharged species due to dipolar interactions with water. As a result of increased concentration of ions in solution, electrostatic interactions between oppositely charged ions lead to ion pair formation,

   Eq. (7) 

and a complex equilibrium results.

Weak electrolytes are characterized by partial dissociation. As a result, there is an undissociated species in solution identical in chemical structure to that of the solid:

     Eq. (8)

With weak electrolytes, there are both uncharged and charged species of the drug in solution at the same time. If we regard A as the drug in this case, the the total solubility, S_t , is the sum of all species that contain A:

       Eq. (9)

The main objective of this report is to examine the effect of pH on the solubility of drugs. Non-electrolytes, and strong electrolytes where neither A nor B is acidic or basic, generally do not display solubility characteristics that are directly dependent upon pH.

B. Strong Electrolytes

There may be an indirect, yet significant effect if a spectator ion of a strong acid or base forms a slightly soluble strong electrolyte with the drug. For example, the addition of HCl to a silver nitrate solution will decrease pH and result in the formation of a precipitate. However, the precipitate is silver chloride, a slightly soluble strong electrolyte, and the solubilty decrease is due to the presence of chloride ion and not a consequence of the increased hydronium ion concentration.

A mathematical analysis of slightly soluble strong electrolytes can be conducted if the equilbrium characteristics and solubility product are known:

    Eq. (10)

Regarding silver as the "drug", and noting that there are other sources of chloride, then the total solubility is:

        Eq. (11)

Increasing chloride concentrations result in decreasing solubility.

Several drugs of interest are weak electrolytes which also form slightly soluble strong electrolytes with chloride ion (e.g., terfenadine), and therefore a portion of a solubility profile may reflect the effect of pH while another portion reflects the influence of a common ion as described in equation 11.

One manifestation of the common ion effect can be dramatically different solubility values for a drug at the same pH, but using different buffer systems. In this example, if pH is lowered with sulfuric acid instead of hydrochloric acid, the observed solubility at a particular pH will be much higher.

The other aspect of strong electrolytes that is relevant here is the fact that salts of weak electrolytes (e.g., Sodium Naproxen) are actually strong electrolytes. In most cases, the salt may be considered to be completely dissociated in aqueous solution and the companion ion (sodium in this case) plays no role in the ideal solubility analysis. However, these so-called spectator ions do contribute to the ionic strength of the solution and can contribute to significant deviations from that ideal behavior.

C. Weak Electrolytes

1.Weak Acids

Equation 8 can be written in the following form if the weak electrolyte is a weak acid:

     Eq. (12)

where HA is the proton-donating drug and K_a is the dissociation constant for the weak acid in solution. Once again, since the solid form of drug is present, the concentration of all species containing A is at a maximum for a specified system: solvent, temperature, and hydrogen ion concentration. Thus,

           Eq. (13)

and,

     Eq. (15)

Equation 15 is the fundamental equation for modeling the effect of pH on the solubility of a weak acid.

2. Weak Bases

Equation 8 may be rewritten as follows when the drug of interest is a weak base:

     Eq. (16)

where B is the proton-accepting drug, and K_b is the association constant for the weak base. The appearance of the hydroxide ion accounts for the basic character of an aqueous solution of the weak base. Total solubility includes all species of B:

       Eq. (17)

Since we choose to use pH instead of pOH to characterize these solubility relationships, the conjugate equilibrium is used as the basis for development of a descriptive equation:

     Eq. (19)

Equation 19 is the fundamental equation for modeling weakly basic drugs.

3. Salts of weak acids

In solutions of high pH, a solid salt form of a weak acid may be obtained. In our example, we could designate the sodium salt as NaA. This salt is a strong electrolyte with its own intrinsic solubility:

          Eq. (20)

It completely dissociates and the intrinsic solubility of the salt is designated S_o^*,

               Eq. (21)

where the concentration of the ionic form of A is at its maximum, since there is excess salt present in the solid form.

Since the ionized form of a weak acid is a base (i.e., it can now accept a proton), equation 19 can be modified to describe the effect of pH on the solubility of the "salt":

              Eq. (23)

and there is a specific pH (e.g., the pH of maximum solubility) which occurs at the intersection of the profiles predicted by equations 15 and 22.

4. Salts of weak bases

In solutions of low pH, a solid salt form of a weak base may be obtained. In our example, we could designate the hydrochloride salt as BHCl. This salt is a strong electrolyte with its own intrinsic solubility:

        Eq. (24)

where the concentration of the ionic form of B is at its maximum, since there is excess salt present in the solid form.

Since the ionized form of a weak base is an acid (i.e., it can now donate a proton), equation 15 can be modified to describe the effect of pH on the solubility of the "salt":

       Eq. (27)

and again there is a specific pH (e.g., the pH of maximum solubility) which occurs at the intersection of the profiles predicted by equations 19 and 27.

D. Polyfunctional Weak Electrolytes

Consider first the case of the drug with two weakly acidic groups:

          Eq. (28)

If there is a substantial difference in the dissociation constants, as evidenced by pK_a's that are separated by at least 2 units, this chemical may be treated as separate cases of a monoprotic weak acid. That is, there would be three distinct forms of the drug that could be available: diprotic weak acid, and monobasic and dibasic salts.

While the total solubility would be:

         Eq. (29)

this equation would simplify to one of the following:

         Eq. (30)

or

because of the difference in the pK values. As a result, the appropriate intrinsic solubility would need to be employed in equation 15. A pH solubility profile would include three regions as evidenced in the figure below .

The solubility value near A would be the intrinsic solubility of the diprotic weak acid and region AB corresponds to the profile expected for a weak acid as pH increases. Point B is the maximum solubility observed for the equilibrium that involves the acid and monobasic salt, where the concentrations in equation 30 are at a maximum. Region BC represents the decrease in apparent solubility as the concentration of uncharged species decreases. Point C represents the intrinsic solubility of the monobasic, singly charged ionic form. The solid form present in region BCD is the monobasic salt (e.g., NaHA).

The region CD of the profile in the figure corresponds to the expected behavior for the weak acid during its second ionization. Point D is the maximum solubility for the monobasic and dibasic forms, where the concentrations in equation 31 are at a maximum. Finally, point E is the intrinsic solubility of the dibasic salt, and region DE represents the decrease in apparent solubility observed as the concentration of monobasic form diminishes to essentially zero at pH values significantly above pK₂ . The solid form present in region DE would be the dibasic salt (e.g., Na₂A).

The same analysis would apply in reverse for a weak base with two basic functional groups of significantly differing strength.

If the pK values are essentially equal, the coexistence of the three species (uncharged, monobasic and dibasic) in solution would generally manifest itself as a typical pH solubiity profile for a monoprotic weak electrolyte, possibly with a higher that expected maximum solubility due to the contribution of the additional, doubly charged anionic form. The region above pK₁ would be associated with high solubility and unlikely to be associated with compromised bioavailability.

Drugs with both weakly acidic and basic character present extremely interesting possibilites in terms of their solubility characteristics. Since zwitterions are possible, molecular flexibility is an important issue that has not been addressed up to this point. If a single molecule has both a positively and negatively charged region, solubility may be enhanced (ion-dipole interactions with water) or diminished (intramolecular electrostatic neutralization).

E.  Effect of Temperature on Solubility

         Eq. (32)

This differential expression indicates that the sign and magnitude of the heat of solution determine the direction and magnitude of a temperature change. If the heat of solution is positive (endothermic), then increasing temperature results in an increase in solubility. If the heat of solution is negative (exothermic), then increasing temperature will be accompanied by a decrease in solubility.

If the assumption is made that the heat of solution is constant over the temperature range of interest, then Eq. 32 may be integrated:

         Eq. (33)

or,

        Eq. (35)

where S_t.2 is the solubility at temperature T₂, and S_t.1 is the solubility at temperature T₁.

From a physiologic point of view, the solubility of a drug at 37 ^oC is the most relevant information. However, the experimental determination of solubility at room temperature is much easier than conducting measurements at higher temperatures.

There is, of course, the issue of temperature control as well as the problems associated with solvent evaporation and/or solute crystalization prior to completion of the analytical procedures. Therefore, it would be expeditious to be able to conduct solubility determinations at room temperature, and reliably predict the degree to which solubility will be altered at body temperature.