What this calculator does
Buffer capacity measures how much strong acid or base a solution can absorb per unit of pH change. It peaks when the pH equals the pKa and falls away sharply on either side.
The fall is steep. A 0.1 mol/L acetate buffer at its pKa of 4.76 has a capacity of 0.0576 mol/(L·pH); one pH unit away it is about a third of that, and two units away it is a tenth. This is the quantitative basis for the rule that a buffer works only within roughly one unit of its pKa.
The formula
The Van Slyke equation sums three contributions: free hydrogen ions, the buffer pair itself, and hydroxide from water. The buffer term dominates in the useful range and is largest when the pH equals the pKa, where the acid and conjugate base are present in equal amounts and either can be consumed. Capacity scales directly with total buffer concentration.
| Term | Meaning |
|---|---|
| Buffer capacity (β) | Moles of strong acid or base absorbed per litre per unit pH change. |
| Van Slyke equation | The 1922 expression used here, which includes water self-ionisation. |
| Buffer range | pKa plus or minus 1, where capacity remains a useful fraction of its peak. |
| Total buffer concentration | Acid plus conjugate base, which sets the scale of the capacity. |
The inputs explained
| Field | What to enter |
|---|---|
| Buffer pH | The pH at which capacity is being evaluated. |
| pKa of the weak acid | pKa of the weak acid. Capacity is greatest where the pH equals this. |
| Total buffer concentration (THA) (mol/L) | Total buffer concentration, acid plus conjugate base combined. |
When to use it
Choosing a buffer
Select an acid whose pKa is close to the target pH, since capacity falls quickly with distance from it.
Sizing a buffer concentration
Capacity scales with concentration, so the required strength follows from how much acid or base must be absorbed.
Diagnosing a drifting pH
A buffer running out of capacity is the usual reason a supposedly buffered system moves.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How fast does capacity fall away from the pKa?
The same buffer evaluated at a range of pH values.
| Buffer pH | Buffer capacity β | [H+] used | Ka used |
|---|---|---|---|
| pH 2.76 | 0.0063 mol/(L·pH) | 0.0017378 mol/L | 0.00001738 mol/L |
| pH 3.76 | 0.0194 mol/(L·pH) | 0.00017378 mol/L | 0.00001738 mol/L |
| pH 4.76 | 0.0576 mol/(L·pH) | 0.00001738 mol/L | 0.00001738 mol/L |
| pH 5.76 | 0.0190 mol/(L·pH) | 0.00000174 mol/L | 0.00001738 mol/L |
| pH 6.76 | 0.0023 mol/(L·pH) | 1.7378e-7 mol/L | 0.00001738 mol/L |
Questions
What is a good buffer capacity?
It depends on how much acid or base the system will encounter. A capacity of 0.05 mol/(L·pH) means adding 0.05 mol of strong acid per litre moves the pH by one unit. Work out the expected load first, then choose a concentration that absorbs it with margin.
Why is capacity greatest at the pKa?
Because that is where the weak acid and its conjugate base are present in equal amounts, so the buffer can absorb addition in either direction equally well. Away from the pKa one component is depleted, and the buffer becomes lopsided.
How do I increase buffer capacity?
Increase the total concentration, since capacity scales directly with it. Going from 0.1 to 0.5 mol/L takes the capacity from 0.0576 to 0.2879, five times as much. The alternative, choosing an acid with a pKa nearer the target pH, helps only if you are currently off-peak.
Why does the equation include a water term?
Because at extreme pH values water self-ionisation itself provides buffering. Below about pH 2 or above about pH 12 the free hydrogen or hydroxide concentration dominates and the buffer pair becomes irrelevant. In the normal working range the water term is negligible.
For the buffer pH itself, see the Henderson-Hasselbalch calculator. For pKa from Ka, see the pKa calculator.