The Henderson–Hasselbalch equation is a fundamental relationship in acid–base chemistry and biochemistry that provides a quantitative link between the pH of a solution, the acid dissociation constant, and the ratio of concentrations of a weak acid and its conjugate base. It is especially important in understanding buffer systems, which play a central role in maintaining physiological pH in biological systems.
Concept and Definition
A buffer solution consists of a weak acid (HA) and its conjugate base (A⁻), or a weak base and its conjugate acid. Such systems resist changes in pH upon addition of small amounts of acid or base. The Henderson–Hasselbalch equation expresses the pH of such systems as:
Where:
• pH = negative logarithm of hydrogen ion concentration
• pKa = negative logarithm of the acid dissociation constant Ka
• [] = concentration of conjugate base
• [HA] = concentration of weak acid
This equation shows that pH depends not only on the intrinsic strength of the acid (through pKa) but also on the relative proportions of acid and base present.
Derivation of the Equation
The Henderson–Hasselbalch equation is derived from the equilibrium expression for a weak acid dissociation:
HA ⇌ H+ + A−
The equilibrium constant is given by:
Rearranging for hydrogen ion concentration:
Taking negative logarithm on both sides:
Since:
• −log[H+] = pH
• −logKa = pKa
The equation becomes:
Thus, the Henderson–Hasselbalch equation is essentially a logarithmic transformation of the acid dissociation equilibrium expression.
Assumptions and Approximations
The equation is based on several simplifying assumptions:
1. The acid is weak and only partially dissociates.
2. The concentrations of acid and conjugate base are much higher than the concentration of hydrogen ions.
3. Activity coefficients are approximated as unity (i.e., activities ≈ concentrations).
4. Contribution of water auto-ionization is negligible.
These assumptions allow the use of analytical concentrations instead of equilibrium concentrations, simplifying calculations significantly.
Biological and Physiological Significance
The Henderson–Hasselbalch equation has profound importance in life sciences, particularly in physiological buffering systems:
(a) Bicarbonate Buffer System
One of the most important applications is in blood pH regulation:
H2CO3 ⇌ H+ + HCO3−
The equation is expressed as:
This system maintains blood pH around 7.35–7.45 and is crucial in conditions such as acidosis and alkalosis.
(b) Intracellular Buffering
Proteins, phosphate buffers, and amino acid side chains rely on this equation to maintain intracellular pH and enzyme activity.
Applications
The Henderson–Hasselbalch equation is widely used in:
| Application Area | Description |
| Buffer preparation | Determines required ratio of acid to base for desired pH |
| Biochemistry | Understanding enzyme activity and protein ionization |
| Medicine | Blood gas analysis and acid–base disorders |
| Pharmacology | Drug ionization and absorption |
| Environmental science | Ocean buffering and carbon dioxide equilibrium |
It is particularly useful in predicting pH changes when small amounts of acid or base are added to a buffer system.
Buffer Range and Interpretation
A key implication of the equation is that effective buffering occurs when:
pH ≈ pKa ± 1
This corresponds to a ratio of [A−]/[HA] between 0.1 and 10, indicating that both acid and conjugate base must be present in appreciable amounts.
Limitations
Despite its utility, the Henderson–Hasselbalch equation has limitations:
• It is less accurate for strong acids or bases.
• It assumes ideal behavior (ignores ionic strength effects).
• Not suitable for highly dilute solutions.
• Deviations occur when the acid is not weak or when concentrations are very unequal.
Summary
The Henderson–Hasselbalch equation provides a simple yet powerful tool to understand and calculate the pH of buffer systems. By linking pH with the ratio of conjugate base to weak acid, it enables prediction and control of acid–base behavior in chemical and biological systems. Its importance spans across physiology, medicine, biochemistry, and environmental science, making it a cornerstone concept in life sciences at the postgraduate level.