Buffer Capacity Calculator

Calculate buffer capacity beta using the Van Slyke equation from pKa, concentration, and pH.

Total buffer concentration C (mol/L) (M)

pKa of weak acid

HEPES=7.55, Phosphate=7.21, Acetate=4.76

Solution pH

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What Buffer Capacity Measures

A buffer resists pH change, but not equally at every pH. Buffer capacity β quantifies that resistance: how many moles of strong acid or base must be added per litre to shift the pH by one unit. Higher β means a more resilient buffer.

β = 2.303 × C × (K_a[H⁺]) / (K_a + [H⁺])²

The expression peaks sharply when [H⁺] equals K_a — that is, when pH = pK_a. At that point the weak acid and its conjugate base are present in equal amounts, so the system can absorb added acid or base with equal facility. The maximum simplifies neatly:

β_max = 2.303 × C / 4 = 0.576 × C

That gives a useful rule of thumb: a 0.1 M buffer at its pK_a has a capacity of about 0.058 mol/L per pH unit, regardless of which acid it is. Capacity scales linearly with concentration, so doubling the buffer concentration doubles β.

The Useful Range

pH relative to pK_a	Ratio base:acid	β as % of β_max
pK_a	1:1	100%
pK_a ± 0.5	~3:1	~80%
pK_a ± 1	10:1	~33%
pK_a ± 2	100:1	~4%

This is the basis of the familiar “pK_a ± 1” rule. Beyond one unit either side, capacity has fallen to about a third of maximum and continues dropping steeply — at two units away the buffer is doing almost nothing. Choosing a buffer whose pK_a is close to the target pH matters far more than choosing a high concentration.

Worked Examples

Example 1: Phosphate: 0.1M, pKa=7.21, pH=7.4

beta=2.303x0.1xKaxH/(Ka+H)^2

Result: beta=0.0549 mol/L/pH

Near-maximal capacity; pH is close to pKa

Example 2: Same buffer at pH=pKa=7.21

Max beta=2.303xC/4

Result: beta_max=0.0576 mol/L/pH

Maximum capacity at half-neutralization

Example 3: One pH unit from pK_a

0.1 M acetate, pK_a = 4.76, working at pH 5.76

Result: β ≈ 0.019 mol/L/pH

About a third of the 0.058 maximum. Still usable, but the buffer is working near the edge of its effective range.

Example 4: Doubling concentration

0.2 M phosphate at pH = pK_a = 7.21

Result: β_max = 0.576 × 0.2 = 0.115 mol/L/pH

Capacity is exactly double the 0.1 M case. Concentration scales β linearly, which is the straightforward lever once pK_a is right.

Example 5: Wrong buffer for the job

0.1 M acetate (pK_a 4.76) used at pH 7.0

Result: β ≈ 0.0013 mol/L/pH

More than two units from pK_a, capacity has collapsed to about 2% of maximum. The solution contains acetate but is not meaningfully buffered.

Common Mistakes

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Selecting a buffer by name rather than pK_a

The only question that matters is how close the pK_a is to your working pH. A phosphate buffer is excellent at pH 7.2 and nearly useless at pH 5.0, where acetate would be far better.

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Assuming more concentration compensates for wrong pK_a

Capacity scales linearly with concentration but falls steeply with distance from pK_a. Two pH units away you would need roughly 25 times the concentration to match a well-chosen buffer.

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Ignoring ionic strength and temperature effects

pK_a values shift with ionic strength and temperature. Tris is notorious — its pK_a changes by about −0.03 per °C, so a buffer set at room temperature drifts noticeably at 37°C.

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Forgetting that dilution changes capacity but not pH much

Diluting a buffer leaves pH nearly unchanged, since the acid-to-base ratio is preserved. But capacity falls proportionally, so the diluted buffer is far more easily overwhelmed.

Frequently Asked Questions

What does beta tell you?

Beta = moles of strong acid/base to change 1L by 1 pH unit. Higher beta = more resistant to pH change. Maximum at pH=pKa where HA=A- (50/50 ratio).

Buffer range rule?

Use buffer within +-1 pH unit of pKa for effective buffering. Beyond this range, one species is depleted and beta drops sharply.

What does buffer capacity tell you?

How many moles of strong acid or base per litre are needed to change the pH by one unit. It quantifies how much disturbance a buffer can absorb before pH moves appreciably.

When is buffer capacity greatest?

When pH equals pK_a, where the weak acid and conjugate base are in equal concentration. Maximum capacity is 0.576 times the total buffer concentration.

Why the pK_a ± 1 rule?

Beyond one pH unit from pK_a, capacity has fallen to roughly a third of maximum and drops steeply thereafter. At two units away only about 4% remains.

Does diluting a buffer change its pH?

Barely — the acid to base ratio is preserved, so pH stays close. But capacity falls in proportion to concentration, making the buffer much easier to overwhelm.

Why does Tris buffer drift with temperature?

Its pK_a has an unusually large temperature coefficient of roughly −0.03 per °C. A Tris buffer adjusted to pH 8.0 at 25°C sits near pH 7.7 at 37°C.

Formula Explorer connections

Interpretation: This relationship connects hydrogen-ion activity, dissociation, conjugate ratios or titration stoichiometry to acid–base behavior. Assumption: Concentration approximates activity mainly in dilute solutions. Temperature, ionic strength, acid strength and equilibrium approximations affect accuracy.

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