Henderson-Hasselbalch Equation
Calculate buffer pH using the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA])
The Formula
The Henderson-Hasselbalch equation is one of the most important equations in biochemistry and biology. It describes the relationship between the pH of a solution and the ratio of the concentrations of a conjugate acid-base pair. This equation is essential for understanding how biological buffer systems maintain stable pH levels in living organisms.
In biological systems, maintaining a precise pH is critical for survival. Human blood, for example, must remain between pH 7.35 and 7.45. Even small deviations outside this range can be life-threatening. The Henderson-Hasselbalch equation helps scientists and medical professionals understand how buffer systems resist changes in pH when acids or bases are added.
The equation was first derived by Lawrence Joseph Henderson in 1908, who wrote it in the form of a hydrogen ion concentration equation. Karl Albert Hasselbalch later rewrote it in logarithmic form in 1917, giving us the modern version we use today. The equation assumes that the concentrations of the acid and its conjugate base at equilibrium are close to the formal (analytical) concentrations, which holds true for weak acids and bases.
Buffer capacity is strongest when the ratio of conjugate base to acid is close to 1, meaning the pH is near the pKa. In practice, buffers are considered effective within approximately one pH unit above or below the pKa value.
Variables
| Symbol | Meaning |
|---|---|
| pH | The negative logarithm of the hydrogen ion concentration; measures acidity or basicity |
| pKa | The negative logarithm of the acid dissociation constant Ka; a characteristic of each acid |
| [A−] | The molar concentration of the conjugate base (deprotonated form) |
| [HA] | The molar concentration of the weak acid (protonated form) |
Example 1
Problem: Calculate the pH of a buffer made from 0.20 M acetic acid (pKa = 4.76) and 0.35 M sodium acetate.
pH = pKa + log([A−] / [HA])
pH = 4.76 + log(0.35 / 0.20)
pH = 4.76 + log(1.75)
pH = 4.76 + 0.243
pH = 5.00
Example 2
Problem: A bicarbonate buffer in blood has pKa = 6.1. If [HCO3−] = 24 mM and [H2CO3] = 1.2 mM, what is the blood pH?
pH = 6.1 + log(24 / 1.2)
pH = 6.1 + log(20)
pH = 6.1 + 1.301
pH = 7.40 (normal blood pH)
When to Use It
The Henderson-Hasselbalch equation is used across many fields in science and medicine.
- Preparing laboratory buffers at a specific target pH for experiments
- Understanding the bicarbonate buffer system that regulates human blood pH
- Predicting how drugs behave in different body compartments based on pH (pharmacology)
- Analyzing acid-base disorders in clinical medicine
- Designing fermentation and cell culture media in biotechnology
- Understanding ocean acidification and its effects on marine chemistry