Henderson-Hasselbalch Calculator
Calculate the pH of a buffer solution using the Henderson-Hasselbalch equation. Enter pKa (or Ka), conjugate base and acid concentrations to find the pH.
🧪 Henderson-Hasselbalch Equation
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What Is the Henderson-Hasselbalch Equation?
The Henderson-Hasselbalch equation is a fundamental equation in acid-base chemistry that relates the pH of a buffer solution to the pKa of the acid and the ratio of conjugate base to conjugate acid concentrations. Named after Lawrence Joseph Henderson and Karl Albert Hasselbalch, it provides a simple way to calculate buffer pH without solving the full equilibrium expression.
Where:
- pH — The pH of the buffer solution
- pKa — The negative log of the acid dissociation constant: pKa = −log10(Ka)
- [A−] — Molar concentration of the conjugate base
- [HA] — Molar concentration of the weak acid
How to Use the Henderson-Hasselbalch Equation
- Find the pKa of the weak acid. If given Ka, calculate pKa = −log10(Ka).
- Determine the concentrations of the conjugate base [A−] and the weak acid [HA].
- Calculate the ratio [A−]/[HA] and take the log10.
- Add to pKa to get pH.
Given: Ka = 1.4 × 10−5, [A−] = 0.7 M, [HA] = 0.5 M
Step 1: pKa = −log10(1.4 × 10−5) = 4.854
Step 2: log10(0.7 / 0.5) = log10(1.4) = 0.146
Step 3: pH = 4.854 + 0.146 = 5.00
Rearranged Forms
| Solve For | Formula |
|---|---|
| pH | pH = pKa + log([A−]/[HA]) |
| pKa | pKa = pH − log([A−]/[HA]) |
| [A−] | [A−] = [HA] × 10(pH − pKa) |
| [HA] | [HA] = [A−] / 10(pH − pKa) |
What Is a Buffer Solution?
A buffer solution resists changes in pH when small amounts of acid or base are added. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). Buffers are most effective when the pH is within ±1 unit of the pKa, i.e., when the ratio [A−]/[HA] is between 0.1 and 10.
Common Buffer Systems
| Buffer System | pKa | Useful pH Range | Application |
|---|---|---|---|
| Citric acid/Citrate | 3.13 | 2.1–4.1 | Food preservation |
| Acetic acid/Acetate | 4.76 | 3.8–5.8 | Laboratory, food industry |
| Carbonic acid/Bicarbonate | 6.35 | 5.4–7.4 | Blood pH regulation |
| Phosphate (H2PO4−/HPO42−) | 7.20 | 6.2–8.2 | Biological buffers, PBS |
| Tris | 8.06 | 7.1–9.1 | Biochemistry research |
| Ammonia/Ammonium | 9.25 | 8.3–10.3 | Industrial processes |
| Bicarbonate/Carbonate | 10.33 | 9.3–11.3 | Water treatment |
Henderson-Hasselbalch in Blood Chemistry
The human body maintains blood pH at approximately 7.35–7.45 using the carbonic acid/bicarbonate buffer system:
Normal blood has [HCO3−] ≈ 24 mM and [H2CO3] ≈ 1.2 mM, giving a ratio of 20:1 and pH = 6.1 + log(20) = 6.1 + 1.30 = 7.40.
- Acidosis (pH < 7.35): The ratio drops below 20:1, often due to metabolic or respiratory disorders.
- Alkalosis (pH > 7.45): The ratio exceeds 20:1.
Limitations of the Henderson-Hasselbalch Equation
- Assumes dilute solutions: Activity coefficients are assumed to be 1.
- Only works for weak acids/bases: Strong acids fully dissociate and don't form buffers.
- Near pKa only: Accuracy decreases far from the pKa (ratio < 0.1 or > 10).
- Temperature dependent: pKa values change with temperature; always use values for your conditions.
Frequently Asked Questions
What happens when [A−] equals [HA]?
When the concentrations are equal, log(1) = 0, so pH = pKa. This is the center of the buffer range and where the buffer has maximum capacity.
How do I convert between Ka and pKa?
pKa = −log10(Ka) and Ka = 10−pKa. For example, Ka = 1.8 × 10−5 gives pKa = 4.74.
Can I use this equation for bases?
Yes, for bases use: pOH = pKb + log([BH+]/[B]), then pH = 14 − pOH. Alternatively, use the conjugate acid's pKa (pKa = 14 − pKb) directly in the standard Henderson-Hasselbalch equation.