Titration Curve pH Calculator

Calculate pH at any point during strong or weak acid-base titrations.

Titration type

Analyte concentration Ca (M) (M)

Analyte volume Va (mL) (mL)

Titrant concentration Cb (M) (M)

Volume titrant added Vb (mL) (mL)

pKa of weak acid (if applicable)

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Reading a Titration Curve

A titration curve has four distinct regions, and each requires different chemistry to calculate. Recognising which region you are in is the whole skill — applying the wrong equation is the most common source of error.

Region	Volume added	What controls pH	Calculation
Initial	V = 0	The analyte alone	Strong acid: pH = −log C. Weak: ICE table
Buffer region	0 < V < V_eq	Mixture of acid and conjugate base	Henderson–Hasselbalch
Equivalence	V = V_eq	The conjugate species only	Hydrolysis of the conjugate
Excess titrant	V > V_eq	Leftover strong titrant	Dilute the excess into total volume

The Half-Equivalence Point

At exactly half the equivalence volume, half the weak acid has been converted to its conjugate base, so [HA] = [A⁻]. The log term in Henderson–Hasselbalch becomes log(1) = 0, giving the elegant result pH = pK_a.

This is the standard experimental method for measuring pK_a: titrate the acid, find the volume at the equivalence point, halve it, and read the pH there. It is also the point of maximum buffer capacity, since the acid and base forms are equally abundant.

Why Equivalence Is Not Always pH 7

Titration	Species at equivalence	pH at equivalence
Strong acid + strong base	Neutral spectator ions only	7.0
Weak acid + strong base	Conjugate base (e.g. acetate)	Above 7
Weak base + strong acid	Conjugate acid (e.g. ammonium)	Below 7

Only the strong-strong case gives exactly 7. Titrating acetic acid with NaOH leaves acetate in solution, which hydrolyses and produces hydroxide — equivalence lands near pH 8.7. This is why indicator choice matters: phenolphthalein, changing around pH 8.2–10, suits weak acid titrations, while methyl orange would change far too early.

The vertical jump at equivalence is also smaller for weak acids. A strong-strong titration jumps several pH units within a fraction of a millilitre; a weak acid titration gives a gentler rise, which is why very weak acids (pK_a above about 8) cannot be titrated accurately in water at all.

Worked Examples

Example 1: Weak acid+SB: 0.1M HOAc, 25mL, 0.1M NaOH, Vb=12.5mL (half-eq)

pH=pKa+log(1)

Result: pH=4.76 = pKa (half-equivalence)

Buffer region maximum capacity

Example 2: SA+SB: 0.1M HCl 25mL, 0.1M NaOH, Vb=30mL (past eq)

5mL excess NaOH in 55mL

Result: pH=12.96

Excess base controls pH

Example 3: Weak acid equivalence point

0.1 M acetic acid, 25 mL, titrated with 0.1 M NaOH

Result: pH ≈ 8.72 at equivalence

At equivalence, 0.05 M acetate remains in 50 mL. K_b = K_w/K_a = 5.6 × 10⁻¹⁰, giving [OH⁻] = 5.3 × 10⁻⁶ and pH 8.72 — clearly basic, not neutral.

Example 4: Buffer region

Same titration at V_b = 20 mL of 25 mL required

Result: pH = 4.76 + log(20/5) = 5.36

Four fifths converted to acetate. Henderson–Hasselbalch applies directly because both forms are present in appreciable amounts.

Example 5: Choosing an indicator

Weak acid equivalence at pH 8.7

Result: Phenolphthalein, not methyl orange

Phenolphthalein changes at 8.2–10.0, inside the steep region. Methyl orange changes at 3.1–4.4, which here would signal an endpoint well before equivalence.

Common Mistakes

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Using Henderson–Hasselbalch at the equivalence point

At equivalence there is no weak acid left — only the conjugate base. The equation divides by zero conceptually. Use hydrolysis of the conjugate instead.

⚠️

Assuming equivalence is always pH 7

Only for strong acid with strong base. A weak acid titration ends above 7 because the conjugate base hydrolyses; a weak base titration ends below 7.

⚠️

Forgetting dilution when calculating excess titrant

Past equivalence, the excess strong base is diluted into the combined volume of analyte plus titrant, not the titrant volume alone.

⚠️

Choosing an indicator by colour rather than range

The indicator must change within the steep part of the curve. Methyl orange in a weak acid titration changes long before equivalence, giving a badly low endpoint.

Frequently Asked Questions

Why sharp jump at equivalence point?

Buffering capacity is zero at equivalence point. Small addition causes large pH change, creating S-curve. This is why endpoint indicators change color sharply.

Weak acid equivalence pH > 7?

At equivalence, weak acid fully converted to conjugate base. The base hydrolyzes water: A- + H2O = HA + OH-, making solution basic.

Why is pH equal to pK_a at half-equivalence?

Because half the acid has been converted, so [HA] = [A⁻] and the log term in Henderson–Hasselbalch becomes zero. This is the standard way to measure pK_a experimentally.

Why is the equivalence point of a weak acid above pH 7?

The solution contains the conjugate base, which hydrolyses water to produce hydroxide. For acetic acid this puts equivalence near pH 8.7.

What causes the sharp jump at equivalence?

Near equivalence, very little unreacted analyte remains, so each drop of titrant changes the ratio enormously. The jump is largest for strong acid with strong base.

How do I choose an indicator?

Pick one whose colour change range falls inside the steep vertical section of the curve. Phenolphthalein suits weak acid titrations; methyl orange suits weak base titrations.

Can very weak acids be titrated in water?

Not accurately above a pK_a of roughly 8. The equivalence jump becomes too gradual to locate, and a non-aqueous solvent is needed instead.

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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