Which concentration is C?

C is the total buffer pair concentration at the working pH: C = [HA] + [A−].

Buffer Capacity Calculator

Q: When should I include the water term?

At very low or very high pH, the water contribution β_water = 2.303([H+]+[OH−]) can be significant. Near pH ≈ pKa it is often small.

Q: Does this handle polyprotic buffers?

This calculator uses a monoprotic model. For polyprotic systems, sum the Van Slyke terms for each dissociation step.

Compute a monoprotic buffer’s buffer capacity β at a specified pH using the Van Slyke equation. Enter pKa/Ka, total buffer concentration C, and pH. Optionally include the water term.

Background

Buffer capacity, β = d(nacid/base)/d(pH) per liter, measures a buffer’s resistance to pH change. For a simple HA/A⁻ system at 25 °C:

β_buffer = 2.303 · C · (K_a[H⁺]) / (K_a + [H⁺])²

Many texts add the water contribution: β_water = 2.303 · ([H⁺] + [OH⁻]), so β_total = β_buffer + β_water. Capacity peaks near pH ≈ pK_a.

Enter buffer data

Provide:

pK_a

K_a

pK_a:

Total buffer concentration C (mol·L⁻¹):

C = [HA] + [A⁻] at the working pH (Henderson–Hasselbalch defines the split).

Target pH:

Options:

Include water contribution (β_water)

Round to sensible significant figures

Quick picks:

Result:

No results yet. Enter inputs and click Calculate.

How to use this calculator

Choose whether to enter pK_a or K_a, then provide its value.
Enter total buffer concentration C (mol·L⁻¹) and the target pH.
Optionally include the water term (recommended near very acidic/basic pH).
Click Calculate to see β_buffer, β_water, and β_total with the HA/A⁻ split.

Assumes 25 °C (K_w = 1.0×10⁻¹⁴). Monoprotic buffer pair only.

Formula & Equation Used

Henderson–Hasselbalch: pH = pK_a + log₁₀([A⁻]/[HA])

Split at pH: R = 10^(pH − pK_a), [A⁻] = C·R/(1+R), [HA] = C/(1+R)

Van Slyke (buffer pair): β_buffer = 2.303·C·(K_a[H⁺])/(K_a + [H⁺])²

Water term (optional): β_water = 2.303·([H⁺] + [OH⁻])

Total: β_total = β_buffer + β_water

Example Problems & Step-by-Step Solutions

Example 1 — Acetate at pH = pK_a

pK_a=4.76, C=0.100 M, pH=4.76 → [H⁺]=1.74×10⁻⁵, R=1 ⇒ [HA]=[A⁻]=0.0500 M.
β_buffer=2.303·0.100·(K_a[H⁺])/(K_a+[H⁺])² ≈ 0.0576 mol·L⁻¹·pH⁻¹.
β_water≈2.303·([H⁺]+[OH⁻]) is negligible near neutrality → β_total≈β_buffer.

Example 2 — Phosphate (2nd step) near neutral pH

pK_a2=7.21, C=0.050 M, pH=7.20 → R≈0.98 ⇒ [A⁻]≈0.025 M, [HA]≈0.0255 M.
Compute β_buffer as above; add β_water if desired for total capacity.

Frequently Asked Questions

Q: When should I include the water term?

At very low/high pH, β_water=2.303([H⁺]+[OH⁻]) can be significant. Near pH≈pK_a it’s usually small.

Q: Which concentration do I enter for C?

Use the total buffer pair concentration C = [HA]+[A⁻] at the working pH.

Q: Does this handle polyprotic buffers?

This tool uses a monoprotic model. For polyprotic systems, sum Van Slyke terms for each relevant step.

Acids Introduction