Henderson-Hasselbalch Calculator

Calculate buffer pH, ratio of acid/base forms, and buffer preparation using Henderson-Hasselbalch equation.

Calculate

pKa of weak acid

Acetic: 4.76, Phosphate: 7.21, HEPES: 7.55, Tris: 8.06

Concentration of conjugate base [A-] (M) (M)

Concentration of weak acid [HA] (M) (M)

Target pH for preparation

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Where the Equation Comes From

Henderson–Hasselbalch is simply the acid dissociation expression rearranged into logarithmic form. Starting from K_a = [H⁺][A⁻]/[HA], taking negative logarithms of both sides gives the familiar result.

pH = pK_a + log([A⁻]/[HA])

Because only the ratio appears, two consequences follow immediately. At equal concentrations the log term vanishes and pH equals pK_a. And dilution leaves pH almost unchanged, since both concentrations fall together.

Ratio [A⁻]/[HA]	pH relative to pK_a	Buffer capacity
1:10	−1.00	~33% of maximum
1:2	−0.30	~89%
1:1	0	100% — maximum
2:1	+0.30	~89%
10:1	+1.00	~33%

The Assumptions That Limit It

The equation is an approximation that assumes the dissociation of HA and the hydrolysis of A⁻ are both negligible compared with the amounts already present. That holds well in the pK_a ± 1 window with reasonably concentrated buffers, and fails outside it.

Situation	Problem
More than 1 unit from pK_a	One component is nearly exhausted; approximation degrades
Very dilute buffer	Water autoionisation becomes significant
High ionic strength	Activities differ from concentrations; use activity coefficients
Polyprotic acid	Use the relevant pK_a; adjacent equilibria may overlap

Physiologically the equation explains why blood pH is so tightly held. The bicarbonate system has a pK_a of 6.1, well below blood pH of 7.4 — a poor buffer in isolation. It works because it is open: the lungs adjust CO₂ and the kidneys adjust bicarbonate, so both components are actively regulated rather than fixed.

Worked Examples

Example 1: Acetate buffer: pKa=4.76, [OAc-]=0.1, [HOAc]=0.1

pH=4.76+log(1)

Result: pH=4.76=pKa — maximum buffer capacity

Equal amounts of acid and conjugate base

Example 2: Phosphate buffer target pH=7.4: pKa=7.21

[HPO4²-]/[H2PO4-]=10^(7.4-7.21)=1.55

Result: 60.8% HPO4²-, 39.2% H2PO4-

Standard physiological phosphate buffer recipe

Example 3: Preparing a buffer at a target pH

Target pH 7.4 with phosphate, pK_a = 7.21

Result: Ratio = 10^0.19 = 1.55

That means 60.8% HPO₄²⁻ and 39.2% H₂PO₄⁻. Multiply by total buffer concentration to get each component.

Example 4: Why blood pH is stable

Bicarbonate pK_a = 6.1, blood pH = 7.4

Result: Ratio is about 20:1

Far from pK_a, this would be a weak buffer if closed. It works because lungs and kidneys actively regulate both components independently.

Common Mistakes

⚠️

Using it far from pK_a

Beyond one pH unit either side, one component is nearly consumed and the underlying approximations break down. Choose a buffer with a closer pK_a.

⚠️

Assuming dilution changes pH

It barely does, since only the ratio matters. What falls is buffer capacity, which drops in proportion to concentration.

⚠️

Using the wrong pK_a for polyprotic acids

Phosphate has three. For pH 7.4 work the relevant value is 7.21, not 2.15 or 12.35.

⚠️

Ignoring ionic strength in precise work

The equation uses concentrations while the true relationship involves activities. At physiological ionic strength the apparent pK_a shifts measurably.

Frequently Asked Questions

Why buffer works best at pH=pKa?

At pH=pKa: [A-]=[HA]=50/50 ratio. Adding acid converts A- to HA (both present to absorb). Adding base converts HA to A- (both present). When ratio shifts to 10:1 or 1:10, buffering fails. Effective range: pKa±1 pH unit.

Common biological buffers?

PBS (phosphate, pH 7.4), HEPES (7.55), MOPS (7.2), TRIS (8.06), sodium citrate (3.1), MES (6.15), PIPES (6.76). Biological buffers chosen to not interfere with biochemistry. 'Good's buffers' designed for biological work.

Why is buffer capacity greatest at pH = pK_a?

Because acid and conjugate base are present in equal amounts, so the system can absorb added acid or base equally well. The log term is zero there.

Does diluting a buffer change its pH?

Almost not at all, since only the concentration ratio appears in the equation. Capacity falls proportionally, however.

Which pK_a do I use for phosphate?

The one nearest your target pH. For physiological work at 7.4 that is 7.21, the second dissociation.

Why is bicarbonate an effective blood buffer despite its pK_a?

Because it is an open system. The lungs control CO₂ and the kidneys control bicarbonate, so both components are actively adjusted rather than fixed.

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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