Titration Calculators

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Titration is a quantitative analytical technique in which a solution of known concentration (titrant) is added to a solution of unknown concentration (analyte) until the reaction between them is complete. The point at which the reaction stoichiometrically completes is the equivalence point; the point detected by an indicator color change is the endpoint. Acid-base titrations are the most common in chemistry and biology labs, used to determine the concentration of acids or bases and to prepare buffered solutions. Potentiometric, redox, and complexometric titrations extend the technique to a wide range of analytes.

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Acid-Base Titration Procedure

A burette filled with titrant (e.g., NaOH) is added drop by drop to a flask containing the analyte (e.g., HCl) with an indicator. As titrant is added, pH changes gradually at first, then sharply near the equivalence point. The sharp pH jump (inflection point in the titration curve) marks the equivalence point. The volume of titrant used is recorded to calculate the analyte concentration.

Calculating Analyte Concentration

M_analyte = (M_titrant × V_titrant) / V_analyte

For a 1:1 stoichiometry (e.g., HCl + NaOH). Adjust for stoichiometry if the mole ratio differs — e.g., H₂SO₄ + 2 NaOH requires dividing by 2. Always use volumes in the same units (mL or L).

Titration Curve Shapes

  • Strong acid / strong base: Large, steep pH jump at equivalence point (pH 7 at equivalence)
  • Weak acid / strong base: Smaller pH jump; equivalence point above pH 7; buffer region visible
  • Weak base / strong acid: Equivalence point below pH 7
  • Polyprotic acids: Multiple equivalence points visible as distinct inflections

Indicators and pKa

Indicators are weak acids whose conjugate base has a different color. An indicator is effective in a pH range of approximately pKa ± 1. Phenolphthalein (pKa ~9.1) is useful for strong acid/strong base titrations; bromocresol green (pKa ~4.7) works for weak base/strong acid. The indicator should be chosen so its transition range overlaps with the equivalence point pH.

Glossary

Equivalence Point
The point in a titration where moles of titrant added exactly equal moles of analyte present per stoichiometry; estimated from the inflection point of the titration curve.
Indicator
A weak acid or base with different colors in its protonated and deprotonated forms; used to detect the endpoint of a titration by a visible color change.
Half-Equivalence Point
The titration point where half the weak acid has been neutralized; at this point pH = pKa, providing a simple experimental determination of the acid dissociation constant.

Frequently Asked Questions

The equivalence point is the theoretical point in a titration where the moles of titrant added exactly equal the moles of analyte present according to the reaction stoichiometry. It is not directly observable — it is calculated or estimated from the midpoint of the steep portion of the titration curve or from the inflection point identified by the first derivative. The endpoint is the observable color change of an indicator, which is chosen to be as close to the equivalence point as possible.

For a 1:1 strong acid/strong base titration: M_acid = (M_base × V_base) / V_acid. Use volumes in liters or keep both in mL — the unit cancels. Example: 25.0 mL of unknown HCl requires 18.5 mL of 0.100 M NaOH to reach the equivalence point. M_HCl = (0.100 × 18.5) / 25.0 = 0.0740 M. Adjust the numerator by the stoichiometric coefficient if the mole ratio is not 1:1.

The half-equivalence point is reached when exactly half the analyte has been neutralized — half the weak acid is converted to its conjugate base. At this point, [HA] = [A⁻], and by the Henderson-Hasselbalch equation, pH = pKa. Measuring the pH at the half-equivalence point in a weak acid titration directly gives the pKa of the acid. This is a straightforward way to determine Ka experimentally.

In a weak acid/strong base titration, the equivalence point occurs above pH 7 (typically pH 8–10) because the conjugate base of the weak acid hydrolyzes water to produce OH⁻. The curve also shows a buffer region below the equivalence point where added base converts HA to A⁻, resisting pH change. This buffer region is absent in strong acid/strong base titrations because neither product can buffer the solution.