Concept:
According to the pH-partition hypothesis, weak acids are less ionized in acidic environments, which increases their lipid solubility and enhances absorption across biological membranes via passive diffusion.
Mathematical Justification using the Henderson-Hasselbalch Equation:
• A drug with a $\text{pK}_a$ of 4.7 is a weakly acidic drug (such as ibuprofen or aspirin).
• For a weak acid, the ratio of ionized to unionized forms is calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log\left( \frac{[\text{Ionized}]}{[\text{Unionized}]} \right) \]
• In the Stomach ($\text{pH} \approx 1 \text{ to } 2.5$):
Since $\text{pH} < \text{pK}_a$, we substitute these values into the equation:
\[ 1.5 = 4.7 + \log\left( \frac{[\text{Ionized}]}{[\text{Unionized}]} \right) \quad \implies \quad \log\left( \frac{[\text{Ionized}]}{[\text{Unionized}]} \right) = -3.2 \]
\[ \frac{[\text{Ionized}]}{[\text{Unionized}]} = 10^{-3.2} \approx 0.00063 \]
This indicates that the drug remains almost entirely in its non-ionized, lipophilic form within the stomach.
• In the Intestine ($\text{pH} \approx 6 \text{ to } 7.5$):
Since $\text{pH} > \text{pK}_a$, the equation shows that the ionized hydrophilic form will predominate, reducing membrane permeability.
Therefore, the drug is less ionized and more readily absorbed through the lipophilic membranes of the stomach.