Understanding the Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation is the fundamental tool for understanding buffer chemistry and predicting the pH of buffer solutions. Derived from the acid dissociation equilibrium, this equation relates pH to the ratio of conjugate base and acid concentrations, providing the theoretical foundation for buffer preparation in laboratories worldwide.
The calculator above handles all common buffer calculations: finding pH from known concentrations, determining the required acid/base ratio for a target pH, and calculating the amounts needed to prepare buffers. Built-in presets for common buffer systems eliminate the need to look up pKa values.
The Henderson-Hasselbalch Equation
pH = pKa + log([A⁻]/[HA])
Where:
- pH = pH of the buffer solution
- pKa = Acid dissociation constant (-log Ka)
- [A⁻] = Concentration of conjugate base
- [HA] = Concentration of weak acid
Derivation from Equilibrium
The equation derives from the weak acid equilibrium:
HA ⇌ H⁺ + A⁻
Ka = [H⁺][A⁻] / [HA]
Rearranging for [H⁺]:
[H⁺] = Ka × [HA] / [A⁻]
Taking -log of both sides:
-log[H⁺] = -log(Ka) + log([A⁻]/[HA])
pH = pKa + log([A⁻]/[HA])
Key Insights from the Equation
When pH = pKa
At the pKa, the ratio [A⁻]/[HA] = 1, meaning equal concentrations of acid and conjugate base. This is the point of maximum buffer capacity where the buffer most effectively resists pH changes.
The pKa ± 1 Rule
Buffers work effectively when pH is within one unit of the pKa (from pKa - 1 to pKa + 1). Outside this range, one component dominates so much that the buffer loses its resistance to pH change.
| pH - pKa | [A⁻]/[HA] | % as A⁻ | % as HA |
|---|---|---|---|
| -2 | 0.01 | 1% | 99% |
| -1 | 0.1 | 9.1% | 90.9% |
| 0 | 1 | 50% | 50% |
| +1 | 10 | 90.9% | 9.1% |
| +2 | 100 | 99% | 1% |
Common Buffer Systems and Their pKa Values
| Buffer System | pKa (25°C) | Useful pH Range |
|---|---|---|
| Phosphoric acid (pKa₁) | 2.15 | 1.1 - 3.1 |
| Citric acid (pKa₁) | 3.13 | 2.1 - 4.1 |
| Acetic acid | 4.76 | 3.8 - 5.8 |
| Citric acid (pKa₃) | 6.40 | 5.4 - 7.4 |
| Carbonic acid (pKa₁) | 6.35 | 5.4 - 7.4 |
| MOPS | 7.20 | 6.2 - 8.2 |
| Phosphate (pKa₂) | 7.20 | 6.2 - 8.2 |
| HEPES | 7.55 | 6.6 - 8.6 |
| Tris | 8.06 | 7.1 - 9.1 |
| Ammonia | 9.25 | 8.3 - 10.3 |
| Carbonate (pKa₂) | 10.33 | 9.3 - 11.3 |
Buffer Preparation Examples
Example 1: Acetate Buffer at pH 5.0
Goal: Prepare 500 mL of 0.1 M acetate buffer at pH 5.0 (pKa = 4.76)
Step 1: Find the required ratio
[A⁻]/[HA] = 10^(pH - pKa) = 10^(5.0 - 4.76) = 10^0.24 = 1.74
Step 2: Calculate individual concentrations
Let [HA] + [A⁻] = 0.1 M and [A⁻]/[HA] = 1.74
[HA] = 0.1 / (1 + 1.74) = 0.0365 M
[A⁻] = 0.1 - 0.0365 = 0.0635 M
Step 3: Calculate amounts for 500 mL
Acetic acid: 0.0365 mol/L × 0.5 L × 60.05 g/mol = 1.10 g
Sodium acetate: 0.0635 mol/L × 0.5 L × 82.03 g/mol = 2.60 g
Example 2: Phosphate Buffer at Physiological pH
Goal: Prepare 1 L of 50 mM phosphate buffer at pH 7.4 (pKa₂ = 7.20)
Step 1: Find the required ratio
[HPO₄²⁻]/[H₂PO₄⁻] = 10^(7.4 - 7.2) = 10^0.2 = 1.58
Step 2: Calculate concentrations
[H₂PO₄⁻] = 0.05 / (1 + 1.58) = 0.0194 M = 19.4 mM
[HPO₄²⁻] = 0.05 - 0.0194 = 0.0306 M = 30.6 mM
Step 3: Use monobasic and dibasic phosphate salts
NaH₂PO₄·H₂O: 19.4 mmol × 138.0 g/mol = 2.68 g
Na₂HPO₄ (anhydrous): 30.6 mmol × 142.0 g/mol = 4.35 g
Buffer Capacity
Buffer capacity (β) measures how well a buffer resists pH change. It depends on the total buffer concentration and the ratio of components:
Buffer Capacity Formula
β = 2.303 × C × ([A⁻]/[HA]) / (1 + [A⁻]/[HA])²
Maximum buffer capacity occurs at pH = pKa (when [A⁻] = [HA])
To increase buffer capacity:
- Increase total buffer concentration
- Choose a buffer with pKa close to desired pH
- Keep pH within ±1 unit of pKa
Temperature Effects on Buffer pH
The pKa of buffer systems changes with temperature, which affects pH. This is particularly important for biological buffers:
| Buffer | ΔpKa/°C | Temperature Effect |
|---|---|---|
| Tris | -0.028 | Large decrease with temperature |
| HEPES | -0.014 | Moderate decrease |
| Phosphate | -0.003 | Minimal change |
| Acetate | 0.0002 | Nearly constant |
For Tris buffer, a solution prepared at pH 7.5 at 25°C will have pH approximately 7.22 at 37°C—a significant difference for biological experiments.
Biological Buffer Systems
Blood Buffer System
The carbonic acid/bicarbonate system is the primary blood buffer:
CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻
Normal blood: [HCO₃⁻] ≈ 24 mM, pCO₂ ≈ 40 mmHg
Using the Henderson-Hasselbalch equation with apparent pKa = 6.1:
pH = 6.1 + log(24/1.2) = 6.1 + log(20) = 6.1 + 1.3 = 7.4
Intracellular Buffers
Inside cells, phosphate and protein buffers maintain pH. Proteins contain histidine residues (pKa ≈ 6) that buffer effectively at physiological pH.
Good's Buffers for Biological Research
Norman Good developed a series of buffers specifically for biological research with desirable properties:
- pKa in physiological range (6-8)
- High water solubility
- Minimal membrane permeability
- Minimal metal binding
- Minimal effects on biochemical reactions
Common Good's buffers: MES, PIPES, MOPS, HEPES, HEPPS, TAPS, CHES, CAPS
Frequently Asked Questions
Why doesn't my buffer have the expected pH?
Common reasons include: using the wrong pKa value (different temperatures have different pKa), impure reagents, calculation errors in weighing, or ionic strength effects. The Henderson-Hasselbalch equation works best at low ionic strength; concentrated solutions may deviate from predicted pH.
Can I use any buffer for any application?
No. Some buffers interfere with specific reactions. Phosphate buffers can precipitate with calcium and inhibit some enzymes. Tris can interfere with protein assays. HEPES generates radicals under UV light. Choose buffers compatible with your specific application.
How do I adjust an existing buffer's pH?
Add small amounts of the acid form (to lower pH) or base form (to raise pH) of your buffer. Alternatively, use dilute HCl or NaOH, but this dilutes the buffer and may add unwanted ions.
What is the minimum buffer concentration I should use?
Buffer concentration should be at least 10-fold higher than the expected proton flux. For most biochemical applications, 10-50 mM is sufficient. For reactions producing significant acid or base, use higher concentrations (50-100 mM).
Why use log([A⁻]/[HA]) and not log([HA]/[A⁻])?
The equation is derived to give positive pH above pKa when base predominates. Using the inverse ratio would give the Henderson-Hasselbalch equation for bases: pOH = pKb + log([BH⁺]/[B]).