Engineering
Henderson-Hasselbalch equation: Buffer pH & Conjugate Base/Acid ratio
Estimate buffer pH from a weak-acid/conjugate-base concentration ratio, and invert the approximation for a target pH.
Formulate Acetate, Phosphate, and Tris buffers with pH = pKa + LOG10([A-]/[HA])
For a weak acid and its conjugate base, the concentration form pH ≈ pKa + log10([base]/[acid]) is a useful approximation when activities can be approximated by concentrations. Using preparation concentrations additionally assumes their equilibrium changes are small. Temperature, ionic strength and dilution affect the result.
With illustrative pKa=4.76 and concentrations 0.15 M and 0.05 M, the estimate rounds to 5.24. Equal concentrations give pH≈pKa under these assumptions. Inverting the equation gives a ratio of 10 for target pH=5.76; it does not specify the total buffer concentration or capacity.
| Acetate Buffer Case (pKa = 4.76) | [Base A-] / [Acid HA] | Computed Buffer pH |
|---|---|---|
| 0.15 M Base / 0.05 M Acid | 3.00 : 1 | 4.76 + LOG10(3) = 5.24 |
| 0.10 M Base / 0.10 M Acid (Equimolar) | 1.00 : 1 | 4.76 (under the approximation) |
| Target pH = 5.76 (+1.0 above pKa) | 10^(5.76 - 4.76) = 10.0 : 1 | 5.76 |
Henderson-Hasselbalch Buffer pH and Required [Base]/[Acid] Ratio formulas
The range around pKa ±1 is a useful rule of thumb, not a guarantee of adequate buffer capacity. This exercise calculates a ratio and estimate, not a validated buffer preparation protocol.
=IF(OR(COUNT(A2:C2)<>3,B2<=0,C2<=0),"Invalid inputs",ROUND(A2+LOG10(B2/C2),2))Solve required Conjugate Base-to-Acid molar ratio [A-] / [HA] for Target pH D2
Inverts LOG10 via base-10 exponentiation 10 ^ (Target_pH - pKa).
=IF(OR(NOT(ISNUMBER(A2)),NOT(ISNUMBER(D2))),"Invalid inputs",ROUND(10^(D2-A2),4))Try the example
Use the original values or change them to test your understanding.