The Henderson-Hasselbalch Equation: Buffer pH from pKa and the Conjugate Base Ratio

A buffer is a mixture of a weak acid and its conjugate base that holds pH steady when you add a little acid or base. The whole behavior collapses into one line of algebra, the Henderson-Hasselbalch equation:

pH = pKa + log([A⁻]/[HA])

Here pKa belongs to the weak acid, [HA] is the weak acid concentration, and [A⁻] is the conjugate base concentration. That single expression is enough to design most buffers you will ever mix, and it is the relationship the Henderson-Hasselbalch calculator runs in both directions.

What each term actually means

Read the equation as two pieces added together. The first piece, pKa, is fixed by chemistry: it is the negative log of the acid dissociation constant, and it does not change when you dilute or concentrate the buffer. The second piece, the log of the ratio, is the part you control by choosing how much base and how much acid to mix.

Because only the ratio sits inside the log, absolute concentrations cancel out of the pH calculation. A buffer that is 0.2 M base over 0.1 M acid gives exactly the same pH as 0.02 M over 0.01 M, since both reduce to a 2:1 ratio. What the absolute concentration controls is buffer capacity, the amount of added acid or base the buffer can absorb before the pH starts to slide. So the workflow is two separate decisions: set the ratio to hit your pH, then scale both components up together for the capacity you need.

The case everyone should memorize: pH = pKa

The most useful single fact in buffer chemistry falls straight out of the equation. When you mix the conjugate base and the weak acid in equal amounts, [A⁻] equals [HA], so the ratio is 1. The log of 1 is 0. The whole second term vanishes:

pH = pKa + log(1) = pKa + 0 = pKa

Take an acetate buffer, pKa 4.76. Dissolve equal moles of sodium acetate and acetic acid and the pH lands on 4.76, no calculator required. That point is not just convenient arithmetic, it is the center of the buffer's working range and the spot where buffer capacity peaks. At a 1:1 ratio, adding a small slug of acid or base moves the pH less than it would anywhere else, because both reaction partners are present in abundance. If you ever need to remember one thing about buffers, remember that a half-and-half mix parks the pH right at the pKa.

Move off that center and the math is still tidy. Make the base ten times the acid, a 10:1 ratio, and log(10) = 1, so pH rises one full unit to 5.76. Flip it to 1:10 and pH drops to 3.76. Each factor of ten in the ratio is worth exactly one pH unit, which is why the buffer range is usually quoted as pKa ± 1: beyond a 10:1 imbalance the buffer is mostly one species and stops resisting change.

A worked example, forward and reverse

Suppose a problem set hands you a phosphate buffer: pKa2 = 7.21, with 0.2 M dibasic phosphate (the base, [A⁻]) and 0.1 M monobasic phosphate (the acid, [HA]). Plug in:

pH = 7.21 + log(0.2 / 0.1) = 7.21 + log(2) = 7.21 + 0.30 = 7.51

The 2:1 base-to-acid ratio lifts the pH about half a log unit above the pKa, exactly as you would expect.

Now run it the other way, which is what you actually do at the bench. You want an acetate buffer at pH 5.0 for an enzyme assay, and acetate's pKa is 4.76. Rearrange the equation to solve for the ratio:

[A⁻]/[HA] = 10^(pH − pKa) = 10^(5.0 − 4.76) = 10^0.24 ≈ 1.74

So you need roughly 1.74 parts acetate for every 1 part acetic acid. Multiply that ratio against your chosen total buffer concentration to get the moles of sodium acetate and acetic acid to weigh out. I always check the reverse calculation by flipping back to forward mode and confirming the pH reads 5.0 again before I trust a single number going into the pH meter; a transposed base and acid is the easiest mistake to make, and it is invisible until your buffer comes out a full unit off.

When I first learned this in a biochemistry lab, I wasted an afternoon making a Tris buffer that read 8.9 instead of 8.0. The culprit was nothing exotic: I had divided acid by base instead of base by acid, so my log term had the wrong sign. Watching the ratio and the pH update together on screen, one input at a time, is the fastest way I know to build the intuition for which direction the log pushes.

Choosing the buffer pair by its pKa

Because a buffer is strongest at its pKa and useful only within about ± 1 unit, the first decision is never the ratio, it is the pair. Match the pKa to your target pH and the rest is gentle:

• Acetate, pKa 4.76 — mildly acidic work, around pH 4 to 6.
• Bicarbonate/carbonic acid, effective pKa ≈ 6.1 — the dominant buffer in blood.
• Phosphate, pKa2 = 7.21 — sits right at physiological pH, which is why it is everywhere in biology.
• Tris, pKa 8.06 — slightly basic conditions, common in molecular biology.

If you target pH 8 with phosphate (pKa 7.21), the equation demands a ratio near 8:1, which is lopsided and weakly buffering; Tris gives you nearly 1:1 at the same target and far better capacity. That comparison is two presets and a glance, instead of three log calculations on scratch paper. Once the ratio is set, a pH calculator is handy for sanity-checking the strong-acid or strong-base titration steps that sit outside the buffer region entirely.

Where the equation stops being exact

Henderson-Hasselbalch is an approximation, and it is worth knowing its edges. It assumes the equilibrium concentrations equal the amounts you mixed in, which holds well when both species are present in real quantities but breaks down for very dilute buffers or when the target pH strays far from the pKa. It also uses concentrations rather than activities, so at high ionic strength the predicted pH drifts a little from the meter reading. For teaching, homework, and routine bench buffers it is plenty accurate; for a buffer at the extreme edge of its range or a published procedure, calibrate against an actual pH meter after mixing.

None of that changes the core picture. Pick a pair whose pKa is close to your target, set the conjugate base to acid ratio with the equation, scale up for capacity, and verify. The Henderson-Hasselbalch equation turns buffer design from a guessing game into one clean line: pH = pKa + log([A⁻]/[HA]).

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Made by Toolora · Updated 2026-06-13