Henderson-Hasselbalch equation

**Equation** - General form: pH = pKa + log([A⁻]/[HA]), where A⁻ is the conjugate base and HA is the weak acid. - When pH = pKa, [A⁻] = [HA] (50% ionized). This is also the point of maximal buffering capacity. A buffer works best within about ±1 pH unit of its pKa.

**Bicarbonate buffer (acid-base physiology)** - pH = 6.1 + log([HCO₃⁻] / (0.03 × PaCO₂)) - 0.03 is the solubility coefficient of CO₂ (mmol/L/mmHg), so 0.03 × PaCO₂ equals the dissolved CO₂ (H₂CO₃). - Normal values: HCO₃⁻ 24 mEq/L and PaCO₂ 40 mmHg give a ratio of 24/1.2 = 20. log 20 ≈ 1.3, so pH ≈ 7.4. - Rearranged: pH rises with ↑HCO₃⁻ (metabolic alkalosis) or ↓PaCO₂ (respiratory alkalosis). pH falls with ↓HCO₃⁻ (metabolic acidosis) or ↑PaCO₂ (respiratory acidosis). - The bicarbonate system is clinically important because the lungs (CO₂) and kidneys (HCO₃⁻) regulate it. It is an open system. - Compensation: the body moves the other variable in the same direction to restore the HCO₃⁻/CO₂ ratio. Examples are hyperventilation in metabolic acidosis and renal HCO₃⁻ retention in chronic respiratory acidosis. - Other buffers: phosphate (pKa ~6.8, important in urine), proteins/hemoglobin, and ammonia (NH₃/NH₄⁺, pKa ~9.2).

**Pharmacology (ionization and ion trapping)** - Weak acid: pH = pKa + log([A⁻]/[HA]). It is ionized (A⁻) when pH > pKa. - Weak base: pH = pKa + log([B]/[BH⁺]). It is ionized (BH⁺) when pH < pKa. - Only the uncharged form crosses membranes easily. Ionized drugs are trapped in the compartment where they are ionized. - Weak acids are ionized in basic environments, so they are trapped there. Weak bases are ionized in acidic environments, so they are trapped there. - Clinical applications: - Aspirin or phenobarbital overdose (weak acids): alkalinize the urine with NaHCO₃. The drug becomes ionized in the tubular lumen, so it is trapped and renal excretion rises. - Amphetamine or other weak base overdose: acidify the urine (for example with NH₄Cl or vitamin C). The drug becomes ionized and trapped in the urine. - Local anesthetics (weak bases, for example lidocaine) work poorly in infected, acidic tissue. More of the drug is ionized, so less crosses the membrane to reach the intracellular binding site on the sodium channel. - Stomach (pH ~1-2) favors absorption of weak acids such as aspirin because they are non-ionized there. Fetal pH is slightly lower than maternal pH, so weak bases can become trapped in the fetus.

**Amino acids and titration curves** - The equation also describes titration curves. At pH = pKa the group is half-protonated. - The isoelectric point (pI) is the pH at which the net charge is zero. It is the average of the pKa values flanking the neutral species.

**High-yield pearls** - Normal arterial pH is 7.35-7.45. - Winter's formula for expected PaCO₂ in metabolic acidosis: 1.5 × [HCO₃⁻] + 8 ± 2. - Rule of thumb: ionized drugs are not reabsorbed, and non-ionized (lipid-soluble) drugs are reabsorbed passively. - A 10-fold change in the base/acid ratio changes pH by 1 unit, because the relationship is logarithmic.