Titration

Titration is a method of analytical chemistry in which measured quantities of a reagent are introduced into a sample until a detectable endpoint is reached. The reagent, called the titrant, usually has a precisely known concentration. The amount of the substance being determined—the analyte—is calculated from the quantity of titrant consumed and the relationship between their reacting amounts. Most titrations measure the volume of a standard solution, but titrant may also be generated electrochemically. Thus, volumetric analysis describes the most familiar form of titration rather than every form of the method. (goldbook.iupac.org)

Principle and calculation

A titration generally relies on a chemical reaction with known stoichiometry. For a reaction written as

where $A$ is the analyte and $B$ the titrant, the reacting amounts satisfy

If the titrant has molar concentration $c_B$, and its volume at equivalence is $V_{\mathrm{eq}}$, then

For an aliquot of sample solution with volume $V_A$,

Volumes must be expressed in units consistent with the concentration. The familiar equation $c_AV_A=c_BV_B$ applies only when the reaction has a 1:1 molar ratio. (chem.libretexts.org)

For example, hydrochloric acid reacts with sodium hydroxide in a 1:1 ratio. In an illustrative determination, a 25.00 mL acid aliquot requiring 20.00 mL of 0.1000 mol L$^{-1}$ sodium hydroxide would have an acid concentration of 0.08000 mol L$^{-1}$, before any correction for previous sample dilution. This is a direct application of the stoichiometric calculation. (chem.libretexts.org)

A suitable titration reaction must be sufficiently complete, rapid on the measurement timescale, and free from significant interfering reactions. Its endpoint must also be detectable with adequate precision. Chemical equilibrium determines how completely the reagents react, while chemical kinetics determines how quickly the measured system responds after an addition. (metrohm.com)

Equivalence point and endpoint

The equivalence point is the theoretical stage at which chemically equivalent quantities of analyte and titrant have been combined. It does not necessarily mean equal numbers of moles: the required ratio depends on the reaction coefficients. The endpoint is the experimentally observed signal used to locate or approximate that stage, such as a persistent colour change or a characteristic change in an instrumental response. (goldbook.iupac.org)

These points are conceptually distinct. An indicator may change colour slightly before or after equivalence, and an instrument may respond with a delay. The difference between endpoint volume and equivalence-point volume produces an endpoint-related titration error. A method therefore specifies not only the reaction but also how the endpoint is recognized. (chem.libretexts.org)

Equivalence is not synonymous with neutral pH. In an aqueous strong-acid–strong-base titration, equivalence is approximately pH 7 at 25 °C under ordinary dilute-solution conditions. A weak acid titrated with a strong base generally has a basic equivalence-point solution because its conjugate base reacts with water; a weak base titrated with a strong acid generally has an acidic equivalence-point solution. (chem.libretexts.org)

Apparatus and standardization

A conventional volumetric titration uses a burette to deliver titrant, a pipette to measure a sample aliquot, and a flask or beaker in which the solutions are mixed. The difference between the initial and final burette readings gives the delivered volume. Automated titrators use motor-driven dosing devices and sensors to control reagent addition and record the response. (edu.rsc.org)

The titrant concentration must be established accurately. A primary standard is a material of known purity and composition that can provide an accurately known amount of substance. Suitable standards remain stable during storage and handling. A solution that cannot be prepared reliably by direct weighing is standardized by reaction with a primary standard or another suitably established standard solution. Potassium hydrogen phthalate, for example, is used to standardize sodium hydroxide solutions. (chem.libretexts.org)

Calibration of measuring equipment and standardization of the titrant are different operations: the former establishes measurement response, whereas the latter establishes reagent concentration. Both contribute to reliable quantitative results. (chem.libretexts.org)

Main reaction types

Acid–base titration

Acid–base titration uses an acid–base reaction to determine acidic or basic substances. Strong acids and bases are common titrants. Endpoints are detected with acid–base indicators or pH measurements. For weak acids or bases, portions of the titration curve exhibit buffer behaviour. Substances capable of donating or accepting several protons may produce multiple equivalence regions, although these are not always sufficiently separated to resolve experimentally. (chem.libretexts.org)

Non-aqueous acid–base titrations use a different solvent to improve solubility or alter acid–base behaviour. They can make determinations possible when an aqueous system gives an inadequate endpoint. (support.metrohmusa.com)

Oxidation–reduction titration

Redox titrations use an oxidation–reduction reaction. Common systems include permanganate with iron(II), and iodine with thiosulfate. Their stoichiometry follows the electron balance of the reaction. Detection may use a redox indicator, the colour of a reagent itself, or an electrode sensitive to changes in potential. Reaction conditions must control competing oxidation or reduction processes. (metrohm.com)

Complexometric titration

Complexometric titration determines substances through formation of a coordination complex. EDTA, a widely used ligand, forms 1:1 complexes with many metal ions. These titrations commonly require controlled pH because ligand protonation and competing reactions affect the effective formation constant. Metal-sensitive colour indicators or instrumental measurements identify the endpoint. A major application is determination of water hardness from calcium and magnesium. (chem.libretexts.org)

Precipitation titration

Precipitation titrations form a sparingly soluble product. A familiar example is chloride determination with silver nitrate:

The titration must provide a sufficiently complete reaction and a detectable change near equivalence. Endpoint techniques include suitable indicators and electrodes responsive to the reacting ions. (metrohm.com)

Direct, back, and coulometric titration

In a direct titration, titrant reacts with the analyte in the sample. In a back titration, a known excess of reagent is first added; the unconsumed excess is then titrated with another reagent. The amount that reacted with the analyte is obtained by subtraction, with the appropriate stoichiometric factors. Back titration is useful when a direct reaction is slow or lacks a satisfactory endpoint. (metrohm.com)

In coulometric titration, the titrant is generated by electrolysis. Its amount is calculated from the electric charge passed. With quantitative current efficiency,

where $Q$ is charge, $z$ is the number of electrons required per generated titrant species, and $F$ is the Faraday constant. This replaces measurement of delivered titrant volume with measurement of charge. (metrohm.com)

Karl Fischer titration determines water using an iodine-based reaction. In its volumetric form, iodine-containing reagent is delivered from a burette; in its coulometric form, iodine is generated electrochemically. The latter is particularly suited to small quantities of water. (metrohm.com)

Titration curves and instrumental detection

A titration curve plots a measured property against the amount of titrant introduced. The property may be pH, electrode potential, electrical conductivity, optical response, or temperature. An endpoint can be identified from a sharp transition, an inflection region, or a change in slope, depending on the chemistry and measurement method. (metrohm.com)

For many acid–base titrations, the steepest part of the pH curve lies close to equivalence. Numerical analysis of the curve can help locate the endpoint, but an inflection point is not universally identical to the stoichiometric equivalence point. Automated evaluation still depends on an appropriate reaction model and adequate sensor response. (chem.libretexts.org)

Applications and limitations

Titration is used to determine acidity and alkalinity, water hardness, chloride, moisture, metal content, and oxidizing or reducing substances. It is valuable in routine quality control because the measured reagent consumption has a direct quantitative relationship to the sample under specified reaction conditions. (metrohm.com)

Its selectivity is limited by the chemistry. Other sample constituents may consume titrant, alter pH, bind metal ions, or obscure endpoint detection. Separation, masking of interfering ions, or adjustment of the reaction medium may therefore be necessary. A titration of total acidity, for example, need not identify the individual acids contributing to the result. (metrohm.com)

Measurement uncertainty arises from titrant concentration, sample preparation, delivered volume, reaction completeness, and endpoint detection. Repeated titrations assess repeatability but cannot by themselves reveal a shared systematic error, such as an incorrectly standardized titrant. Very dilute samples or poorly defined endpoint regions can make titration unsuitable for the required precision. (chem.libretexts.org)

Historical development

Titrimetric methods developed from practical measurements of acid and alkali strength into systematic quantitative analysis. In the nineteenth century, Joseph Louis Gay-Lussac contributed to their development and adoption. Karl Friedrich Mohr improved reagents, indicators, and volumetric apparatus; his treatise, published in two parts in 1855 and 1856, helped disseminate titrimetric analysis throughout Europe. Later developments introduced electrical endpoint measurements, electrochemical titrant generation, and automated dosing and curve evaluation. (diverdi.colostate.edu)

References

1. 1: Overview of Titrimetrychem.libretexts.org
2. 2: Acid–Base Titrationschem.libretexts.org
3. 3: Complexation Titrationschem.libretexts.org
4. 2: Acid–Base Titrationschem.libretexts.org
5. 1: Analytical Signalschem.libretexts.org
6. Analytical Chemistry 2.0 — Chapter 5resources.saylor.org
7. Titration — RSC Educationedu.rsc.org
8. Practical of Titrationmetrohm.com
9. Basic Principles of Titrationmetrohm.com
10. Titratormetrohm.com