Buffer Capacity Calculator

Estimate How Strongly a Buffer Resists pH Change

Buffer Capacity

Formula

\[ \beta = 2.303 \left( [\mathrm{H^+}] + [\mathrm{OH^-}] + \frac{C_{\text{tot}} \, K_a \, [\mathrm{H^+}]}{\left( K_a + [\mathrm{H^+}] \right)^2} \right) \]

Where:

\(\beta\) — buffer capacity (mol/L per pH unit)
\([\mathrm{H^+}]\) — hydrogen ion concentration, \(10^{-\mathrm{pH}}\) mol/L
\([\mathrm{OH^-}]\) — hydroxide ion concentration, \(K_w/[\mathrm{H^+}]\) mol/L
\(C_{\text{tot}}\) — total concentration of the buffer pair, \([\mathrm{HA}] + [\mathrm{A^-}]\) (mol/L)
\(K_a\) — acid dissociation constant, \(10^{-\mathrm{p}K_a}\)

This is the Van Slyke equation: it gives the amount of strong acid or base (in moles per litre) needed to shift the pH of the solution by one unit at 25 °C. The water term \([\mathrm{H^+}] + [\mathrm{OH^-}]\) matters only at extreme pH; near the pKa the buffer pair term dominates.

Buffer Capacity – Calculation Example

Example: an acetate buffer contains 0.1 M acetic acid (HA) and 0.1 M sodium acetate (A⁻). Acetic acid has pKa = 4.76, and the buffer pH is 4.76. What is the buffer capacity?

\[ C_{\text{tot}} = 0.1 + 0.1 = 0.2\ \text{mol/L}, \quad K_a = [\mathrm{H^+}] = 10^{-4.76} \approx 1.74 \times 10^{-5} \]
\[ \beta = 2.303 \left( 1.74\times 10^{-5} + 5.8\times 10^{-10} + \frac{0.2 \times (1.74\times 10^{-5})^2}{(2 \times 1.74\times 10^{-5})^2} \right) = 2.303 \left( 1.74\times 10^{-5} + 0.05 \right) \approx 0.115 \]

Result: \(\beta \approx 0.115\) mol/L per pH unit. About 0.115 mol of strong acid or base per litre (11.5 mmol per 100 mL) would shift the pH by roughly one unit. The effective buffering range is pH 3.76 – 5.76, and because the pH equals the pKa exactly, the buffer is at its strongest.

How to Use the Buffer Capacity Calculator

Enter the Weak Acid Concentration [HA] and choose the unit (mol/L or mmol/L).
Enter the Conjugate Base Concentration [A⁻] (for example, from the sodium salt of the acid) and its unit.
Enter the Acid Dissociation Constant as the pKa of the weak acid (the default 4.76 corresponds to acetic acid).
Enter the Buffer pH at which you want the capacity evaluated — ideally the working pH of your solution.
Read the results: the buffer capacity β in mol/L per pH unit, the effective buffering range (pKa ± 1), a strength assessment, and a detailed breakdown of the calculation.

What Is Buffer Capacity?

Buffer capacity β measures how strongly a solution resists changes in pH when acid or base is added. It is defined as the amount of strong acid or base required to change the pH of one litre of solution by one unit:

\[ \beta = \frac{\mathrm{d}n}{\mathrm{d(pH)}} \]

A larger β means the buffer can absorb more added acid or base before its pH drifts noticeably. For example, β = 0.05 mol/L per pH unit means 0.05 moles of strong base per litre would raise the pH by about one unit.

Capacity depends on two things: the total concentration of the buffer components and the position of the pH relative to the pKa. Maximum capacity occurs when pH = pKa, because then the acid HA and base A⁻ forms are present in equal amounts and either added acid or added base can be neutralised efficiently. As the pH moves away from the pKa, one form is depleted and capacity falls — roughly by a factor of 3 at 1 pH unit away and by more than an order of magnitude beyond 2 units.

For this reason a practical rule of thumb is that a buffer works within pKa ± 1 and is considered adequate for laboratory use when β is about 0.1 mol/L per pH unit or higher, while values below about 0.01 are usually too weak to be useful. Typical biological buffers fall in the range 0.01 – 0.1 mol/L total concentration.

Assumptions, Limitations and Practical Tips

The calculation uses the Van Slyke equation for a monoprotic weak acid/conjugate-base pair at 25 °C. Polyprotic systems (e.g. phosphate at high pH, citrate) need the capacity summed over each dissociation step.
Activity coefficients are assumed to be 1. In concentrated or high-ionic-strength solutions the true capacity can differ noticeably; see the Ionic Strength Calculator to check how far your solution deviates from ideal behaviour.
The entered pH should be consistent with the composition via the Henderson–Hasselbalch relationship \( \mathrm{pH} = \mathrm{p}K_a + \log([\mathrm{A^-}]/[\mathrm{HA}]) \). If they disagree, the calculator still evaluates β at the stated pH, but your mixture may not actually sit there — check with the Henderson–Hasselbalch Calculator or the pH Calculator.
Dilution lowers capacity in direct proportion: halving both concentrations halves β. To buffer a larger volume, scale the amounts of acid and salt up, not the ratio.
When preparing the buffer, remember that capacity is consumed as acid/base is added. If you expect to add a significant amount of acid or base, design for a starting pH on the opposite side of the pKa and verify the endpoint with a Titration Calculator.
Choose an acid whose pKa is within 1 unit of your target pH. Common pairs: acetate (pKa 4.76), phosphate (pKa2 7.21), borate (pKa 9.24), ammonia/ammonium (pKa 9.25).

Frequently Asked Questions

How do I calculate buffer capacity by hand?

Use the Van Slyke equation. First convert pKa to \(K_a = 10^{-\mathrm{p}K_a}\) and pH to \([\mathrm{H^+}] = 10^{-\mathrm{pH}}\). Then compute \(\beta = 2.303\left([\mathrm{H^+}] + [\mathrm{OH^-}] + \frac{C_{\text{tot}} K_a [\mathrm{H^+}]}{(K_a + [\mathrm{H^+}])^2}\right)\), where \(C_{\text{tot}} = [\mathrm{HA}] + [\mathrm{A^-}]\) and \([\mathrm{OH^-}] = 10^{-14}/[\mathrm{H^+}]\). A shortcut when pH = pKa: the buffer term simplifies to \(2.303 \times C_{\text{tot}}/4 \approx 0.576\,C_{\text{tot}}\).

What is a good or normal buffer capacity value?

For most laboratory work, a buffer capacity of about 0.1 mol/L per pH unit or higher is considered practical. Values between 0.01 and 0.1 are usable for gentle conditions, while below roughly 0.01 mol/L per pH unit the buffer is usually too dilute to be reliable. Typical biological buffers are prepared at 0.01–0.1 mol/L total concentration, which corresponds to maximum capacities of roughly 0.006–0.06 at pH = pKa.

Does buffer capacity have units, and how do I convert them?

Buffer capacity is expressed in moles of strong acid or base per litre per pH unit (mol·L⁻¹·pH⁻¹). Some textbooks use equivalents (eq/L per pH unit) for the same thing. To convert to mmol/L per pH unit, multiply by 1000; a β of 0.115 mol/L equals 115 mmol/L. If you work per 100 mL of solution, divide by 10: β = 0.115 means about 11.5 mmol shifts the pH of 100 mL by one unit.

Why is buffer capacity highest when pH equals the pKa?

At pH = pKa the acid HA and conjugate base A⁻ are present in exactly equal amounts, so the buffer can neutralize added strong acid and added strong base equally well. Mathematically, the term \(K_a[\mathrm{H^+}]/(K_a + [\mathrm{H^+}])^2\) reaches its maximum of 1/4 when \([\mathrm{H^+}] = K_a\). Once the pH moves more than one unit from the pKa, one form is nearly depleted and capacity falls steeply — that is why pKa ± 1 is the practical working range.

Can this calculator be used for polyprotic buffers like phosphate or citrate?

Not directly. The Van Slyke equation used here applies to a single monoprotic acid/base pair. For polyprotic systems such as phosphate or citrate, you must evaluate the buffer term for each dissociation step (using each pKa) at the same pH and add the contributions together. Near pH 7.2 only phosphate's second dissociation (pKa2 = 7.21) matters significantly, so treating it as monoprotic is a good approximation there.

What happens to buffer capacity when I dilute the buffer?

Capacity falls in direct proportion to dilution: diluting the buffer tenfold with distilled water reduces β tenfold, even though the pH itself barely changes because the [A⁻]/[HA] ratio is preserved. This is a common mistake when preparing buffers — always check the final volume when calculating how much acid or base the buffer can absorb. To buffer a larger volume, scale up the absolute amounts of both components rather than changing their ratio.

My pH and Henderson–Hasselbalch ratio don't match — which pH should I enter?

Enter the pH the solution actually has, not the one you intend. The Henderson–Hasselbalch equation \(\mathrm{pH} = \mathrm{p}K_a + \log([\mathrm{A^-}]/[\mathrm{HA}])\) links composition to pH; if your inputs disagree, the mixture will equilibrate to the Henderson–Hasselbalch value (minus small corrections). The calculator will still evaluate β at whatever pH you type, so an inconsistent entry gives a capacity for a state the buffer never reaches. Measure the real pH with a meter if accuracy matters.