pH and Solubility, Stability, and Absorption, Part I

Principles of pH
In pharmacy practice, pH is a critical variable and a basic understanding of its principles and measurement is important. It is vitally important to understand pH and its influence on drug solubility, stability, and absorption. We will look at each of these separately over three issues of this newsletter.

Let's begin with a definition of the term pH. The "p" comes from the word "power." The "H," of course, is the symbol for "hydrogen." Together, the term pH means the hydrogen ion exponent. In terms of the hydrogen ion activity, pH is defined as:

pH = - log₁₀ a_H+ or 10^-pH = a_H+

pH equals the negative logarithm of the hydrogen ion activity, or the activity of the hydrogen ion is 10 raised to the exponent -pH. The latter expression renders the use of the p exponent more obvious. The activity is the effective concentration of the hydrogen ion in solution. The difference between effective and actual concentration decreases as one moves toward more dilute solutions, in which ionic interaction becomes progressively less important.

Drug Solubility
The effect of pH on solubility is critical in IV admixtures, TPN solutions, and in the formulation of aqueous liquid dosage forms, including oral and topical solutions. The solubility of a weak acid or base is often pH dependent. The total quantity of a monoprotic weak acid (HA) in solution at a specific pH is the sum of the concentrations of both the free acid and salt (A^-) forms. If excess drug is present, the quantity of free acid in solution is maximized and constant because of its saturation solubility. As the pH of the solution increases, the quantity of drug in solution increases because the water-soluble ionizable salt is formed. The expression is:

        K_a
 HA ↔ H⁺ + A^-

where K_a is the dissociation constant.

There may be a certain pH level reached where the total solubility (S_T) of the drug solution is saturated with respect to both the salt and acid forms of the drug, that is, the pH_max. The solution can be saturated with respect to the salt at pH values higher than this, but not with respect to the acid. Also, at pH values less than this, the solution can be saturated with respect to the acid but not to the salt. This is illustrated in the accompanying figure constructed by adding excess free acid form of a drug to water; we are in the "pH<pHmax" portion of the graph. Base (i.e., sodium hydroxide) is added dropwise, and, as the free base is converted into a salt, the salt goes into solution. At this point, we have both free acid and the formed salt in solution. Additional base is added until all the free acid is converted into the salt form and we are at the "pH>pHmax" portion of the graph.

To calculate the total quantity of drug that will remain dissolved in solution at a selected pH, either of two equations can be used, depending on whether the product is to be in a pH region above or below the pH_max. The following equation is used in the pH range below the pH_max:

S_T = S_a (1 + K_a/[H⁺])  (Equation 1)

The next equation is used in the pH range above the pH_max:

where

S_a is the saturation solubility of the free acid and
S'_a is the saturation solubility of the salt form.

Example
A pharmacist prepares a 3.0% solution of an antibiotic as an ophthalmic solution and dispenses it to a patient. A few days later the patient returns the eye drops to the pharmacist because the preparation contains a precipitate. The pharmacist, checking the pH of the solution and finding it to be 6.0, reasons that the problem may be pH related. The physicochemical information of interest on the antibiotic includes the following:

Using Equation 1, the pharmacist calculates the quantity of the antibiotic in solution at a pH of 6.0 (Note: pH of 6.0 = [H⁺] of 1 × 10^-6)

From this, the pharmacist knows that at a pH of 6.0 a 0.0809-molar solution can be prepared. However, the concentration that was prepared was a 0.1053 molar solution. Consequently, the drug will not all be in solution at that pH. The pH may have been all right initially but shifted to a lower pH over time, resulting in precipitation of the drug. The question is at what pH will the drug remain in solution? This can be calculated using the same equation and information. The S_T value is 0.1053 molar.

[H+] = 7.333 × 10^-7, or a pH of 6.135

The pharmacist prepares a solution of the antibiotic, adjusting the pH to above about 6.2, using a suitable buffer system, and dispenses the solution to the patient—with positive results.

An interesting phenomenon concerns the close relationship of pH to solubility. At a pH of 6.0, only a 0.0809 molar solution could be prepared, but at a pH of 6.13 a 0.1053 molar solution could be prepared. In other words, a difference of 0.13 pH units resulted in

(0.1053 - 0.0809)/0.0809 = 30.1%

more drug going into solution at the higher pH than at the lower pH.

In other words, a very small change in pH resulted in about 30% more drug going into solution. According to the figure, the slope of the curve would be very steep for this example drug, and a small change in pH (x-axis) results in a large change in solubility (y-axis). From this, it can be reasoned that if one observes the pH-solubility profile of a drug, it is possible to predict the magnitude of the pH change on its solubility.


Loyd V. Allen, Jr., Ph.D., R.Ph.

(Adapted from Allen LV Jr., Popovich NG, Ansel HC. Ansel's Pharmaceutical Dosage Forms and Drug Delivery Systems. Philadelphia, PA: Lippincott Williams & Wilkins; 2011: 102–104.)

Next month, we will look at the effect of pH on drug stability.