Why does pH equal pKa at the half-equivalence point?

At half the equivalence volume, exactly half of a weak acid has been converted to its conjugate base, so their concentrations are equal. The Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]), then reduces to pH = pKa + log(1) = pKa. This makes the half-equivalence point the standard way to read a weak acid's pKa directly off a titration curve.

Why isn't the equivalence point always at pH 7?

Only a strong acid titrated with a strong base gives pH 7 at equivalence, because the salt formed is neutral. When a weak acid is titrated with a strong base, the solution at equivalence contains the conjugate base, which is itself a weak base and raises the pH above 7. When a weak base is titrated with a strong acid, the conjugate acid lowers the pH below 7. The weaker the analyte, the further the equivalence pH sits from 7.

How do I calculate the equivalence point volume?

Set moles of titrant equal to moles of analyte. For a one-to-one reaction, the equivalence volume equals the analyte concentration times the analyte volume, divided by the titrant concentration. For example, 25 mL of 0.10 M acid titrated with 0.10 M base reaches equivalence at 25 mL, while titrating the same acid with 0.20 M base reaches it at 12.5 mL.

What is the buffer region on a titration curve?

The buffer region is the gently sloped stretch on either side of the half-equivalence point, roughly pKa plus or minus 1, where a weak acid and its conjugate base are both present in meaningful amounts. Adding titrant here shifts their ratio only slightly, so the pH resists change. Strong acid or strong base titrations have no buffer region, which is why their curves are flat then jump sharply.

Why is the curve nearly vertical near the equivalence point?

Near equivalence, almost all of the analyte has reacted, so each additional drop of titrant has very little left to neutralize and instead swings the pH sharply. A small volume of titrant produces a large pH change, which is why an indicator changes color abruptly there and why the steep jump is used to locate the endpoint.

Acid-Base Titration Curve Calculator, Free

What are you titrating? (titrant is the opposite strong reagent)

Analyte concentration (M)

Analyte volume (mL)

Titrant concentration (M)

pKa of the weak acid

Titrant added: 0.0 mL

pH at this volume

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Starting pH

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Equivalence

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Half-eq (pKa)

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How to read the curve

A titration adds a strong reagent (the titrant) a bit at a time and tracks the pH. Four landmarks tell you almost everything: the starting pH, the gently sloped buffer region, the flat half-equivalence point where a weak acid's pH equals its pKa, and the steep equivalence point where moles of titrant finally match moles of analyte. Every pH here comes from solving the full charge-balance equation, so weak, strong, dilute, and concentrated cases are all handled the same honest way rather than with shortcut approximations.

The four regions, at a glance

Region	What is happening	pH behavior
Start (0 titrant)	Only the analyte is present	Set by the analyte's strength
Buffer region	Weak acid and conjugate base coexist	Slow change; pKa ± 1
Half-equivalence	Analyte exactly half neutralized	pH = pKa (weak acid)
Equivalence	Moles titrant = moles analyte	Steep vertical jump

Strong-with-strong titrations skip the buffer region entirely: the pH barely moves, then jumps through pH 7 at equivalence, then levels off.

FAQ

Why does pH = pKa at half-equivalence?
Half the weak acid has become conjugate base, so [A-] = [HA] and Henderson-Hasselbalch gives pH = pKa + log(1) = pKa.

Why isn't equivalence always pH 7?
Only strong-with-strong lands at 7. A weak acid finishes basic (its conjugate base hydrolyzes); a weak base finishes acidic. The weaker the analyte, the further from 7.

How do I find the equivalence volume?
moles titrant = moles analyte, so V(eq) = (C_analyte × V_analyte) / C_titrant. Same acid with a titrant twice as concentrated reaches equivalence at half the volume.

What is the buffer region?
The gently sloped stretch around half-equivalence (pKa ± 1) where weak acid and conjugate base both exist and resist pH change. Strong-strong curves have none.

Why is the jump so steep?
Near equivalence almost no analyte is left, so each drop of titrant swings the pH sharply. That is why an indicator flips color abruptly there.