Buffer Capacity Formula
Calculate buffer capacity using β = ΔB/ΔpH.
Learn how to measure a buffer solution's resistance to pH change with worked examples.
The Formula
Buffer capacity (β) measures how well a buffer solution resists changes in pH when an acid or base is added. A higher buffer capacity means the solution can absorb more acid or base before the pH shifts significantly.
This is critical in biochemistry, medicine, and industrial chemistry. Blood, for example, has a tightly controlled buffer capacity that keeps pH between 7.35 and 7.45.
Buffer capacity is highest when the pH equals the pKa of the buffering acid. It also increases with higher total buffer concentration.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| β | Buffer capacity | mol/(L·pH unit) |
| ΔC_b | Amount of strong base (or acid) added per liter | mol/L |
| ΔpH | Resulting change in pH | pH units |
Van Slyke Equation
For a more precise calculation, the Van Slyke equation gives buffer capacity as a function of concentration and pH:
Where C is the total buffer concentration, Ka is the acid dissociation constant, and [H⁺] is the hydrogen ion concentration.
Example 1
Adding 0.02 mol/L of NaOH to a buffer changes the pH from 7.00 to 7.10. What is the buffer capacity?
Identify values: ΔC_b = 0.02 mol/L, ΔpH = 7.10 − 7.00 = 0.10
Apply the formula: β = ΔC_b / ΔpH = 0.02 / 0.10
β = 0.2 mol/(L·pH unit)
Example 2
A phosphate buffer at pH 7.2 has a total concentration of 0.1 M. The pKa of H₂PO₄⁻ is 7.2. What is its buffer capacity?
Since pH = pKa, [H⁺] = Ka. The Van Slyke equation simplifies.
β = 2.303 × C × (Ka × Ka) / (Ka + Ka)² = 2.303 × C × Ka² / (4Ka²)
β = 2.303 × 0.1 / 4 = 2.303 × 0.025
β ≈ 0.0576 mol/(L·pH unit) — this is the maximum buffer capacity for this concentration
When to Use It
- Designing buffer solutions for laboratory experiments
- Understanding blood buffering in medical physiology
- Quality control in pharmaceutical manufacturing
- Water treatment and environmental chemistry
- Food science — maintaining consistent pH during processing