Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation calculates pH of buffer solutions from pKa and concentration ratios.
Essential for chemistry.
The Formula
The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of the acid and the ratio of the conjugate base to the weak acid concentrations.
Variables
| Symbol | Meaning |
|---|---|
| pH | The acidity of the solution (dimensionless, logarithmic scale) |
| pKa | The acid dissociation constant of the weak acid (dimensionless, equals −log Ka) |
| [A⁻] | Concentration of the conjugate base (measured in mol/L, M) |
| [HA] | Concentration of the weak acid (measured in mol/L, M) |
Key Insights
When [A⁻] = [HA], the log term equals zero, so pH = pKa. This is the point of maximum buffering capacity — the buffer is most effective at resisting pH changes.
When [A⁻] > [HA], pH > pKa (more basic).
When [A⁻] < [HA], pH < pKa (more acidic).
A buffer works effectively within ±1 pH unit of its pKa. Outside this range, the buffer capacity is too weak to resist pH changes.
Common Buffer Systems
| Buffer | pKa | Useful pH Range |
|---|---|---|
| Acetic acid / Acetate | 4.76 | 3.8 - 5.8 |
| Carbonic acid / Bicarbonate | 6.35 | 5.4 - 7.4 |
| Dihydrogen phosphate / Hydrogen phosphate | 7.20 | 6.2 - 8.2 |
| Ammonium / Ammonia | 9.25 | 8.3 - 10.3 |
Example 1
An acetic acid buffer contains 0.20 M acetate (A⁻) and 0.10 M acetic acid (HA). What is the pH? (pKa = 4.76)
Apply the formula: pH = 4.76 + log(0.20 / 0.10)
pH = 4.76 + log(2) = 4.76 + 0.301
pH = 5.06
Example 2
What ratio of A⁻ to HA is needed to make a phosphate buffer at pH 7.40? (pKa = 7.20)
Rearrange: log([A⁻]/[HA]) = pH − pKa = 7.40 − 7.20 = 0.20
[A⁻]/[HA] = 10^0.20
[A⁻]/[HA] = 1.58 (about 1.6 parts base to 1 part acid)
When to Use It
Use the Henderson-Hasselbalch equation for buffer calculations and acid-base equilibrium.
- Calculating the pH of buffer solutions
- Determining the ratio of acid to base needed for a target pH
- Choosing the right buffer system for a desired pH range
- Blood chemistry — the bicarbonate buffer maintains blood pH at 7.35-7.45
- Preparing laboratory buffers for biochemistry and molecular biology experiments