To ensure a clear homogeneous solution and maximum therapeutic effectiveness, the preparations should be adjusted to an optimum pH. The pH below which the salt of a weak acid,. sodium phenobarbital, for example, begins to precipitate from aqueous solution is readily calculated in the following manner
Representing the free acid form of phenobarbital as HP and the soluble ionized form as P–, we write the equilibria in a saturated solution of this slightly soluble weak electrolyte as:
Because the concentration of the un-ionized form in solution, HPsol is essentially constant, the equilibrium constant for the equation is:
Where is molar or intrinsic solubility. The constant for the acid-base equilibrium is:
The total solubility, S of phenobarbital consists of the concentration of the undissociated acid, [HP], and that of the conjugate base or ionized form, [P–]:
Substituting for [HP] from equation (9-3) and the expression from equation (9-5) for [P–] yields:
Where pHp is the pH below which the drug separates from solution as the undissociated acid.
As seen from equation (9-9), pHp depends on the initial molar concentration, S, of salt added, the molar solubility of the undissociated acid, (also known as the intrinsic solubility) and the pKa.
An analogous derivation can be carried out to obtain the equation for the solubility of a weak base as a function of the pH of a solution.
Where S is the concentration of the drug initially added as the salt and is the molar solubility of the free base in water. Here pHp is the pH above which the drug begins to precipitate from solution as the free base.
Example:
Below what pH will free phenobarbital begin to separate from a solution having an initial concentration of 1 g of sodium phenobarbital per 100 mL at 25°C ? The molar solubility, of phenobarbital is 0.005 and the pKa is 7.41 at 25°C. The secondary dissociation of Phenobarbital can be disregarded. The molecular weight of sodium phenobarbital is 254.
The molar concentration of salt initially added is: