Buffer Capacity and Buffer Range

Two buffers can have exactly the same pH and behave completely differently. Add a few drops of acid to one and its pH barely moves. Add the same drops to the other and its pH drops by a whole unit. The difference is buffer capacity: how much acid or base a buffer can absorb before its pH changes significantly.

Along with buffer range, the pH window in which a buffer works well, capacity is what you need to think about when you actually design a buffer for a real job.

Two separate questions

• What pH does the buffer hold? Set by the pKa of the weak acid and the ratio [A⁻] ÷ [HA]. See the Henderson–Hasselbalch equation.
• How strongly does it hold that pH? Set by the buffer capacity, which depends mainly on the amounts of HA and A⁻ present.

A good analogy: pH is the temperature a thermostat is set to; capacity is how powerful the heating system is. Two houses can both be set to 20 °C, but on a freezing day only one with a powerful boiler will actually stay there.

Defining buffer capacity

Buffer capacity, often written β (beta), is the amount of strong acid or strong base needed to change the pH of 1 dm³ of buffer by one unit. In practice, chemists often just compare how much the pH changes when a fixed amount of acid or base is added.

A larger β means a more robust buffer.

Factor 1: total concentration

The more weak acid and conjugate base there are, the more added H⁺ or OH⁻ they can neutralise.

Example. Compare two ethanoic acid/ethanoate buffers, both pH 4.76 (equal amounts, pKa 4.76), each 1.00 dm³. Add 0.010 mol HCl to each.

Buffer A: 0.100 mol CH₃COOH + 0.100 mol CH₃COO⁻

After adding acid: CH₃COO⁻ = 0.090 mol, CH₃COOH = 0.110 mol

pH = 4.76 + log(0.090 ÷ 0.110) = 4.67 (change −0.09)

Buffer B: 0.020 mol CH₃COOH + 0.020 mol CH₃COO⁻

After adding acid: CH₃COO⁻ = 0.010 mol, CH₃COOH = 0.030 mol

pH = 4.76 + log(0.010 ÷ 0.030) = 4.28 (change −0.48)

Same starting pH, but buffer B is five times more dilute and its pH moves more than five times as far. Doubling the concentrations of both components roughly doubles the capacity.

Factor 2: the ratio of acid to base

Capacity is greatest when [HA] = [A⁻], which is when pH = pKa. At that point the buffer has equal reserves to fight added acid and added base.

Example. Two buffers, each containing a total of 0.200 mol of ethanoic acid + ethanoate in 1.00 dm³. Add 0.010 mol HCl.

Starting mix (HA : A⁻)	Starting pH	pH after 0.010 mol HCl	Change
0.100 : 0.100	4.76	4.67	−0.09
0.180 : 0.020	3.81	3.48	−0.33

The lopsided buffer has very little A⁻ to react with added acid, so it’s much weaker against acid, even with the same total amount of material. It’s much stronger against added base, but that’s rarely what you want.

Buffer range: pKa ± 1

Because capacity falls away as the ratio moves away from 1 : 1, buffers only work well over a limited pH window. The usual rule of thumb is:

Effective buffer range ≈ pKa ± 1

That corresponds to ratios of [A⁻] : [HA] from 1 : 10 to 10 : 1. Outside this range, one component is so scarce that small additions exhaust it.

Buffer system	pKa (25 °C)	Useful range
Citric acid / citrate (1st step)	3.13	2.1–4.1
Methanoic acid / methanoate	3.75	2.8–4.8
Ethanoic acid / ethanoate	4.76	3.8–5.8
Carbonic acid / hydrogencarbonate	6.35	5.4–7.4
Dihydrogenphosphate / hydrogenphosphate	7.20	6.2–8.2
Tris / Tris-H⁺	8.07	7.1–9.1
Ammonium / ammonia	9.25	8.3–10.3
Hydrogencarbonate / carbonate	10.33	9.3–11.3

To choose a buffer, pick a weak acid whose pKa is within about one unit of the pH you need, ideally as close as possible. Then adjust the ratio to hit the exact pH, and choose the concentration to give enough capacity.

Quantifying capacity (for advanced readers)

For a buffer containing a total concentration C of weak acid plus conjugate base, the buffer capacity is approximately:

β ≈ 2.303 × C × [Ka[H⁺] ÷ (Ka + [H⁺])²]

(ignoring the contributions of water’s own H⁺ and OH⁻, which matter only at extreme pH).

This expression has its maximum when [H⁺] = Ka, that is, when pH = pKa, where it simplifies to:

β(max) ≈ 0.576 × C

So a 0.20 mol/dm³ buffer at pH = pKa has β ≈ 0.115 mol/dm³ per pH unit: you’d need about 0.1 mol of strong acid per dm³ to shift its pH by roughly one unit (in practice the change isn’t perfectly linear, but it’s a good estimate). At pH = pKa ± 1, β falls to about a third of its maximum.

Capacity is used up as you add acid or base

Every addition of acid consumes some A⁻, and every addition of base consumes some HA. A buffer’s capacity isn’t a fixed shield; it wears down. Once one component is almost gone, the next small addition causes a big pH jump.

Example. A buffer with 0.050 mol HA and 0.050 mol A⁻ in 1.00 dm³ (pKa 4.76):

Total HCl added (mol)	A⁻ left	HA	pH
0	0.050	0.050	4.76
0.020	0.030	0.070	4.39
0.040	0.010	0.090	3.81
0.049	0.001	0.099	2.76
0.060	0 (exhausted)	0.100	about 2.0 (excess strong acid)

The first 0.020 mol barely changes the pH; the last 0.009 mol drops it by a full unit. This is exactly the shape of the flat buffer region and the steep section on a titration curve.

Designing a buffer: a checklist

1. Target pH. What pH do you need?
2. Choose the acid. Pick a weak acid with pKa within ±1 of the target (closer is better).
3. Check compatibility. The buffer must not react with or interfere with your system. Phosphate, for instance, precipitates with calcium ions; borate interferes with some sugars; many biological buffers were designed specifically to avoid these problems.
4. Set the ratio with Henderson–Hasselbalch.
5. Set the concentration to give enough capacity for the acid or base you expect. Biological buffers are typically 10–100 mmol/dm³.
6. Consider temperature. pKa values change with temperature. Tris is notorious: its pH drops by about 0.03 units per °C rise.
7. Measure and adjust with a pH meter. Calculations get you close; the meter gets you exact.

The practical steps are in how to prepare a buffer.

Real-world examples of capacity mattering

• Blood. Its main buffer isn’t at its pKa (7.4 vs 6.1), so its chemical capacity against acid is actually quite good (lots of HCO₃⁻) but weak against base. The lungs and kidneys compensate. See the blood buffer system.
• Swimming pools. “Total alkalinity” measures the pool’s hydrogencarbonate buffer capacity. Low alkalinity means pH swings wildly with every addition of chlorine or every rainstorm.
• Oceans. Seawater’s carbonate system gives it buffer capacity against CO₂, but as more CO₂ dissolves, that capacity is gradually used up.
• Shampoos and cosmetics. Many are buffered with citrate to stay mildly acidic, close to the pH of skin and hair, even when diluted or mixed with tap water.

Common misconceptions

• “A buffer keeps pH completely constant.” It resists change; it doesn’t prevent it.
• “More concentrated means a different pH.” Concentration changes capacity, not pH (as long as the ratio is the same).
• “Any weak acid can buffer at any pH.” Only within about one unit of its pKa.
• “Dilution doesn’t affect a buffer.” It doesn’t change the pH, but it reduces capacity.

Key takeaways

• Buffer capacity is how much acid or base a buffer can absorb with little pH change.
• It increases with total concentration and is highest when [HA] = [A⁻], i.e. pH = pKa.
• The useful buffer range is roughly pKa ± 1.
• Choose the weak acid by pKa, set the pH with the ratio, and set the robustness with the concentration.
• For calculations of pH after additions, see buffer calculations.