Buffer pH Calculator
Calculate the pH of a buffer solution using the Henderson-Hasselbalch equation. Enter the pKa of the weak acid, the concentration of the acid [HA], and the concentration of the conjugate base [A⁻] to determine the buffer pH, ratio, and buffer capacity. Essential for biochemistry, analytical chemistry, and laboratory preparation. See also our pH Calculator and Titration Calculator.
Acetic acid = 4.76
How to Calculate Buffer pH
A buffer solution resists changes in pH when small amounts of acid or base are added. Buffers consist of a weak acid and its conjugate base (or a weak base and its conjugate acid) in equilibrium. The Henderson-Hasselbalch equation provides a direct way to calculate the pH of a buffer solution without solving the full equilibrium expression.
The Henderson-Hasselbalch equation is derived from the acid dissociation equilibrium expression Ka = [H⁺][A⁻]/[HA]. Taking the negative logarithm of both sides and rearranging gives pH = pKa + log([A⁻]/[HA]). This equation assumes that the concentrations of HA and A⁻ at equilibrium are approximately equal to their initial (analytical) concentrations, which is valid when the buffer components are present in much higher concentrations than the H⁺ or OH⁻ produced by the equilibrium.
- Identify the weak acid and its conjugate base in the buffer
- Look up or calculate the pKa of the weak acid
- Determine the molar concentrations of [HA] and [A⁻]
- Apply the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA])
- When [A⁻] = [HA], the pH equals the pKa (maximum buffer capacity)
Formula
Henderson-Hasselbalch Equation:
pH = pKa + log([A⁻] / [HA])
Where:
pH = hydrogen ion concentration (log scale)
pKa = -log(Ka) = acid dissociation constant
[A⁻] = concentration of conjugate base (mol/L)
[HA] = concentration of weak acid (mol/L)
Buffer Capacity (Van Slyke equation):
β = 2.303 × C × Ka × [H⁺] / (Ka + [H⁺])²
Where C = total buffer concentration ([HA] + [A⁻])
For base buffers:
pOH = pKb + log([BH⁺] / [B])
pH = 14 - pOH
Example Calculation
Problem: Calculate the pH of a buffer made from 0.1 M acetic acid and 0.1 M sodium acetate (pKa = 4.76).
Given: pKa = 4.76, [HA] = 0.1 M, [A⁻] = 0.1 M
Solution:
pH = pKa + log([A⁻]/[HA])
pH = 4.76 + log(0.1/0.1)
pH = 4.76 + log(1)
pH = 4.76 + 0 = 4.76
Problem 2: What if [A⁻] = 0.2 M and [HA] = 0.1 M?
pH = 4.76 + log(0.2/0.1) = 4.76 + log(2) = 4.76 + 0.301 = 5.06
Common Buffer Systems Reference Table
| Buffer System | pKa | Effective pH Range | Common Use |
|---|---|---|---|
| Phosphoric acid / H₂PO₄⁻ | 2.15 | 1.15 – 3.15 | Cola beverages |
| Citric acid / Citrate | 3.13 | 2.13 – 4.13 | Food preservation |
| Acetic acid / Acetate | 4.76 | 3.76 – 5.76 | Vinegar, lab buffers |
| MES | 6.15 | 5.15 – 7.15 | Biological research |
| H₂CO₃ / HCO₃⁻ | 6.35 | 5.35 – 7.35 | Blood buffer |
| MOPS | 7.20 | 6.20 – 8.20 | Cell culture |
| Tris | 8.07 | 7.07 – 9.07 | Molecular biology |
| Boric acid / Borate | 9.24 | 8.24 – 10.24 | Electrophoresis |
| Bicarbonate / Carbonate | 10.33 | 9.33 – 11.33 | Water treatment |
| HPO₄²⁻ / PO₄³⁻ | 12.35 | 11.35 – 13.35 | Alkaline buffers |
Buffer Capacity and Effective Range
Buffer capacity (β) measures how well a buffer resists pH changes. It is defined as the number of moles of strong acid or base required to change the pH of one liter of buffer by one unit. Buffer capacity is maximum when pH = pKa (i.e., when [A⁻] = [HA]), and decreases as the ratio deviates from 1:1. A buffer is generally considered effective within ±1 pH unit of its pKa.
Increasing the total concentration of buffer components increases buffer capacity proportionally. A 1 M acetate buffer has 10 times the buffer capacity of a 0.1 M acetate buffer at the same pH. However, very high concentrations can introduce ionic strength effects that shift the effective pKa, so practical buffers are typically in the 0.01–0.5 M range.
The effective buffering range is typically defined as pKa ± 1, corresponding to [A⁻]/[HA] ratios between 0.1 and 10. Outside this range, the buffer has insufficient capacity to resist pH changes effectively. When selecting a buffer for a specific application, choose one whose pKa is as close as possible to the desired pH.
Biological Buffer Systems
The most important biological buffer is the bicarbonate buffer system in blood: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻. Despite having a pKa of 6.1 (seemingly far from blood pH 7.4), this system is effective because the lungs can rapidly adjust CO₂ levels and the kidneys regulate HCO₃⁻ concentration. The normal blood ratio of [HCO₃⁻]/[H₂CO₃] is approximately 20:1.
In biochemistry laboratories, Good's buffers (HEPES, MOPS, MES, PIPES, Tris) are widely used because they have minimal interaction with biological molecules, are chemically stable, and have pKa values near physiological pH. Tris buffer (pKa = 8.07 at 25°C) is particularly common in molecular biology for DNA and protein work, though its pKa is temperature-sensitive (decreasing about 0.03 units per °C increase).
Frequently Asked Questions
What is the Henderson-Hasselbalch equation?
The Henderson-Hasselbalch equation (pH = pKa + log([A⁻]/[HA])) relates the pH of a buffer solution to the pKa of the weak acid and the ratio of conjugate base to acid concentrations. It is derived from the Ka expression and provides a quick way to calculate buffer pH without solving quadratic equations.
When does pH equal pKa?
pH equals pKa when the concentrations of the weak acid [HA] and conjugate base [A⁻] are equal. At this point, log([A⁻]/[HA]) = log(1) = 0, so pH = pKa + 0 = pKa. This is also the point of maximum buffer capacity.
What is buffer capacity?
Buffer capacity (β) is the amount of strong acid or base (in moles) needed to change the pH of 1 liter of buffer by 1 unit. Higher buffer concentrations give greater capacity. Maximum capacity occurs at pH = pKa, and the effective range is typically pKa ± 1.
How do I prepare a buffer at a specific pH?
Choose a buffer system with pKa close to your target pH. Use the Henderson-Hasselbalch equation to calculate the required [A⁻]/[HA] ratio: ratio = 10^(pH - pKa). Then prepare the solution with the appropriate amounts of weak acid and conjugate base salt to achieve this ratio at your desired total concentration.
Why does blood pH stay at 7.4?
Blood pH is maintained at 7.35–7.45 by the bicarbonate buffer system (H₂CO₃/HCO₃⁻), phosphate buffers, and protein buffers (especially hemoglobin). The lungs regulate CO₂ (volatile acid) and kidneys regulate HCO₃⁻, providing dynamic control that keeps the [HCO₃⁻]/[H₂CO₃] ratio near 20:1.
Can I use Henderson-Hasselbalch for strong acids?
No. The Henderson-Hasselbalch equation only applies to weak acid/conjugate base buffer systems. Strong acids (like HCl) dissociate completely and do not form buffer solutions. The equation assumes equilibrium between HA and A⁻, which does not exist for strong acids.