Calculator
Example data
| Scenario | pKa | [HA] (mol/L) | [A−] (mol/L) | Expected pH |
|---|---|---|---|---|
| Equal acid and base | 4.76 | 0.10 | 0.10 | 4.76 |
| Base ten times acid | 6.10 | 0.02 | 0.20 | 7.10 |
| Acid dominates | 9.25 | 0.50 | 0.05 | 8.25 |
Formula used
The Henderson–Hasselbalch relation connects pH to an acid–base pair:
When activities are approximated by concentrations, the equation becomes:
If you enable activity correction, activities use a = γ·c with γ from the Davies equation for a chosen ionic strength.
How to use this calculator
- Select what you want to solve for.
- Enter pKa directly, or enable Ka input.
- Provide the required values for the selected mode.
- Optional: enable activity correction and set ionic strength.
- Press Calculate to view results above the form.
- Use the export buttons to download CSV or PDF.
Article
1) Why this relation matters in physical chemistry
The Henderson-Hasselbalch relation turns an equilibrium constant into a practical pH estimate. In solution physics, pH sets molecular charge and can change diffusion, electrophoretic mobility, adsorption, and interfacial forces. Buffers help keep chemical conditions stable while you measure transport, spectra, or electrochemical signals.
2) Core equation and its meaning
The calculator uses pH = pKa + log10(a(A-)/a(HA)), where a denotes activity. Activities represent the effective thermodynamic concentrations that drive equilibrium. When solutions are dilute and non-ideal effects are small, activities are often approximated by concentrations, giving pH = pKa + log10([A-]/[HA]).
3) Ratio sensitivity and logarithmic scaling
Because the relation is logarithmic, changing the base-to-acid ratio by a factor of 10 shifts pH by exactly 1 unit at fixed pKa. At pH = pKa the activity ratio is 1, meaning equal effective amounts of A- and HA. At pH = pKa + 1 the ratio is 10; at pH = pKa - 1 the ratio is 0.1.
4) Buffer window and useful operating range
Buffers work best near their pKa. A common design rule is that effective buffering occurs roughly within pKa plus or minus 1 pH unit, corresponding to ratios between 0.1 and 10. Maximum buffering capacity typically occurs near pH close to pKa, and it increases with total buffer concentration C_T = [HA] + [A-].
5) Inverse problems used in experiments
Many workflows are inverse. If you need a target pH, the tool can compute the required [A-]/[HA] ratio. If you have measured pH and independently know the ratio, the tool can estimate pKa (and Ka) for fitting titration data. These modes support instrument calibration, sensor modeling, and cross-checks against literature constants.
6) Activity corrections and ionic strength
In saline or electrolyte-rich media, concentrations and activities differ. The optional activity mode estimates activity coefficients using the Davies equation, which depends on ionic strength I and ionic charge z. When gamma(A-) and gamma(HA) are not equal, the effective ratio becomes ([A-]/[HA])*(gamma(A-)/gamma(HA)), shifting pH by log10 of that correction factor. Treat this as an approximation.
7) Practical workflow and reporting
Start by choosing what to solve for, then enter pKa (or Ka) and the required inputs for that mode. Keep concentration units consistent (mol/L) so ratios are meaningful. If you enable activity correction, set a reasonable ionic strength and charges for your species. After calculation, export the result table to CSV or PDF for lab notes and reproducible reporting.
FAQs
1) When is Henderson-Hasselbalch most accurate?
It is most accurate for buffer mixtures where both HA and A- are present in appreciable amounts and the solution behaves nearly ideally. Extremely high ionic strength, strong interactions, or very low concentrations can reduce accuracy.
2) What does pKa represent here?
pKa is the negative base-10 logarithm of Ka. It marks the pH where the effective activities of A- and HA are equal, so the ratio a(A-)/a(HA) equals 1.
3) Why can activity correction change the pH?
Non-ideal solutions have activity coefficients gamma that scale effective concentration. If gamma(A-) differs from gamma(HA), the activity ratio changes, which adds a log10(gamma(A-)/gamma(HA)) shift to the pH prediction.
4) What ratio gives maximum buffer effectiveness?
Buffer capacity is typically highest near pH close to pKa, where the ratio is about 1. Ratios between 0.1 and 10 still buffer well, but capacity declines toward the extremes.
5) Can I use this for polyprotic acids?
Use it one dissociation step at a time. Choose the relevant pKa for the conjugate pair you are modeling. For full speciation across many pH values, a multi-equilibrium solver is more appropriate.
6) What units should I enter for concentrations?
Any consistent units work because the equation uses a ratio, but mol/L is standard. If you compute unknown [HA] or [A-], the output assumes the same units you used for inputs.
7) How should I pick ionic strength I?
Ionic strength summarizes electrolyte content. If you know major ion concentrations, estimate I = 0.5*sum(c_i*z_i^2). Otherwise, use a typical experimental value and interpret activity-corrected results as approximate.