Titration

Definition: Titration is a laboratory technique for determining the concentration of an unknown solution by slowly reacting it with a solution of known concentration until the reaction reaches its equivalence point.

How It Works

A titrant of known concentration is added dropwise from a burette to a measured volume of analyte (the unknown solution) until an indicator changes color or a probe (pH meter, conductivity meter) signals the reaction is essentially complete
Titration data is usually reported as the volume of titrant delivered, read directly from the burette’s graduated markings before and after the addition
The equivalence point is the theoretical point where moles of titrant added exactly match moles of analyte according to the reaction’s stoichiometry; the endpoint is the practically observed point (like an indicator color change) that’s meant to approximate it as closely as possible
Choosing an indicator whose color-change pH range brackets the actual equivalence point pH minimizes the gap between endpoint and equivalence point, called indicator error
A titration curve plots pH (or another measured property) against volume of titrant added, and its exact shape depends on whether the acid and base involved are strong or weak
Strong acid/strong base titrations produce a steep, symmetric jump through pH 7 at the equivalence point, making almost any indicator with a midrange color change adequate
Weak acid/strong base titrations show a buffer region before the equivalence point, and the equivalence point itself lands above pH 7, since the conjugate base produced is itself weakly basic
At the half-equivalence point of a weak acid titration, exactly half the acid has been neutralized, and pH equals the acid’s pKa, a convenient way to determine Ka experimentally
Before use, a titrant’s exact concentration is often determined precisely (standardized) by titrating it against a primary standard, a highly pure, stable, known-mass reference compound
Polyprotic acids and bases produce multiple equivalence points on a single titration curve, one for each acidic or basic proton neutralized in sequence
Redox titrations track electrode potential or use self-indicating reagents (like deep purple potassium permanganate turning colorless once fully reduced) instead of pH-based indicators
A back titration adds a known excess of one reagent to the analyte, lets it react completely, then titrates the unreacted excess, useful when the analyte is a solid, reacts slowly, or lacks a good direct endpoint
Automated titrators use a pH probe and motorized burette to plot the full titration curve electronically, locating the equivalence point mathematically (at the curve’s steepest slope) rather than relying on a visual color change

Under the Hood

For a simple 1:1 acid-base reaction, moles of acid equal moles of base at the equivalence point:

M_acid × V_acid = M_base × V_base       (1:1 stoichiometry)
n_acid × M_acid × V_acid = n_base × M_base × V_base    (general stoichiometry, n = coefficient)

Worked example 1 — finding an unknown concentration. 25.00 mL of unknown HCl is titrated with 0.100 M NaOH, requiring 22.50 mL to reach the endpoint. Find the HCl concentration.

M_acid = (M_base × V_base) / V_acid = (0.100 × 22.50) / 25.00 = 0.0900 M

The unknown HCl solution is 0.0900 M, determined entirely from the known titrant concentration and the two measured volumes.

Worked example 2 — finding Ka from a titration curve. Acetic acid is titrated with NaOH. At the half-equivalence point, the measured pH is 4.74. Find Ka.

At half-equivalence: pH = pKa
pKa = 4.74
Ka = 10^(-pKa) = 10^(-4.74) ≈ 1.8×10⁻⁵

This matches acetic acid’s known literature Ka closely, showing why the half-equivalence point of a weak acid titration is a standard way to measure Ka experimentally.

Worked example 3 — back titration. A 1.000 g antacid tablet is treated with 25.00 mL of 0.500 M HCl (a known excess). The unreacted HCl requires 12.50 mL of 0.200 M NaOH to reach the endpoint. Find the mass and mass percent of CaCO₃ in the tablet. (CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂)

mol HCl added         = 0.02500 L × 0.500 M = 0.01250 mol
mol NaOH used (= mol HCl remaining) = 0.01250 L × 0.200 M = 0.00250 mol
mol HCl reacted with CaCO₃          = 0.01250 - 0.00250 = 0.01000 mol
mol CaCO₃  = 0.01000 mol HCl ÷ 2    = 0.00500 mol
mass CaCO₃ = 0.00500 mol × 100.09 g/mol = 0.500 g
mass % CaCO₃ = (0.500 g / 1.000 g) × 100 = 50.0%

Back titration works here because the tablet dissolves slowly and doesn’t have a clean direct endpoint; adding a measured excess of acid and titrating what’s left avoids that problem entirely.

Choosing an Indicator

Different indicators change color over different, narrow pH ranges, and picking the right one for a given titration is essential:

Indicator	Color change	pH range	Best suited for
Methyl orange	Red → yellow	3.1 - 4.4	Strong acid / weak base
Bromothymol blue	Yellow → blue	6.0 - 7.6	Strong acid / strong base
Phenolphthalein	Colorless → pink	8.2 - 10.0	Weak acid / strong base

Using phenolphthalein for a strong-acid/weak-base titration, for instance, would give a false endpoint far past the true equivalence point, since that titration’s equivalence pH sits below phenolphthalein’s color-change range entirely.

Why It Matters

Pharmaceutical quality control uses titration to verify the exact amount of active ingredient in a batch of tablets, injectables, or raw material before release
Food and beverage industries titrate to measure acidity (like titratable acidity in wine or juice) for quality, flavor, and regulatory labeling purposes
Water hardness testing uses complexometric titration with EDTA to quantify dissolved calcium and magnesium ions
Environmental monitoring titrates water and soil samples to determine dissolved oxygen, chloride content, or acidity relevant to ecosystem and drinking-water safety
Winkler titration, a classic redox-based method, remains a benchmark technique for measuring dissolved oxygen in lakes, rivers, and wastewater treatment plants
Industrial process control relies on titration to verify reagent concentrations before large-scale reactions, since an error in starting concentration can waste an entire production batch
Clinical laboratories use titration-based methods to measure chloride and other electrolytes in blood and urine samples for diagnostic purposes

Common Pitfalls

Confusing the endpoint (observed, indicator-based) with the equivalence point (theoretical, exact stoichiometric match); good technique minimizes the gap, but they’re never mathematically identical
Choosing an indicator whose color-change range doesn’t bracket the actual equivalence point pH, especially in weak acid/strong base or weak base/strong acid titrations where the equivalence point isn’t at pH 7
Assuming every acid-base reaction is 1:1; polyprotic acids like H₂SO₄ or H₃PO₄ require adjusting the stoichiometric ratio in the M₁V₁ = M₂V₂-style calculation
Misreading the burette meniscus due to parallax error, or misjudging the exact drop where the indicator permanently changes color rather than the first faint tint
Forgetting to standardize the titrant against a primary standard first, and instead trusting a stock solution’s labeled concentration, which can drift over time from evaporation or absorption of atmospheric CO₂
Overshooting the endpoint by adding titrant too quickly near the expected equivalence point, which is why technique slows dramatically to dropwise addition as the color change approaches
Neglecting the CO₂ absorbed by a NaOH solution over time, which reacts to form carbonate and slowly changes the solution’s effective concentration and titration behavior if left unstandardized for too long

Comparison

Titration type	What’s measured	Detection method	Example
Acid-base	H⁺/OH⁻ neutralization	pH indicator or pH meter	Vinegar acidity
Redox	Electron transfer	Self-indicating color change or potentiometer	KMnO₄ vs. Fe²⁺
Complexometric	Metal ion concentration	Metal ion indicator (e.g. Eriochrome Black T)	Water hardness (Ca²⁺, Mg²⁺) with EDTA
Precipitation	Ion concentration forming an insoluble salt	Indicator that reacts once ions are consumed	Chloride content with AgNO₃

Example

A chemist titrates vinegar with standardized sodium hydroxide, watching phenolphthalein turn from colorless to persistent light pink at the endpoint, then uses the volume of NaOH consumed and its known concentration to calculate the acetic acid concentration of the vinegar via stoichiometry.

Real-World Application

Before any titrant can be trusted for a real measurement, its exact concentration must be standardized against a primary standard, a compound pure and stable enough that a weighed mass gives a precisely known number of moles. Potassium hydrogen phthalate (KHP) is the standard choice for standardizing NaOH solutions:

KHC₈H₄O₄ (KHP) + NaOH → KNaC₈H₄O₄ + H₂O     (1:1 reaction)

A chemist weighs a precise mass of solid KHP, dissolves it, and titrates it with the NaOH solution of unknown exact concentration; because the moles of KHP are known precisely from its mass and molar mass, the volume of NaOH needed at the endpoint pins down the NaOH’s true molarity, which is then used with confidence in every subsequent titration that day.

FAQ

Why doesn’t a strong acid/strong base titration need a very precise indicator? Its titration curve has an extremely steep pH jump (often 6+ pH units) within a fraction of a milliliter near the equivalence point, so almost any indicator changing color somewhere in that steep region introduces negligible error.

Can titration be used for reactions other than acid-base neutralization? Yes; redox, complexometric, and precipitation titrations all use the same core logic (add a known reagent until a stoichiometric endpoint is reached) applied to different reaction types with different detection methods.

Why is a burette used instead of a graduated cylinder to add titrant? A burette allows very precise, controllable, incremental addition down to a fraction of a drop, which is essential near the endpoint where a single extra drop can overshoot the true equivalence point.

What causes a titration curve to have an S-shape rather than a straight line? pH changes very slowly while there’s still plenty of unreacted acid or base to resist the change (a buffering effect), then swings rapidly once the analyte is nearly consumed, producing the characteristic flat-steep-flat S-shape rather than a straight line.

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