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Titration (also called titrimetry and volumetric analysis) is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte (a substance to be analyzed). A reagent, called the titrant or titrator, is prepared as a standard solution of known concentration and volume. The titrant reacts with a solution of analyte (which may also be called the titrand) to determine the analyte's concentration. The volume of titrant that reacted with the analyte is called the titration volume. Titration (also called titrimetry and volumetric analysis) is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte (a substance to be analyzed). A reagent, called the titrant or titrator, is prepared as a standard solution of known concentration and volume. The titrant reacts with a solution of analyte (which may also be called the titrand) to determine the analyte's concentration. The volume of titrant that reacted with the analyte is called the titration volume. The word 'titration' descends from the French word tiltre (1543), meaning the 'proportion of gold or silver in coins or in works of gold or silver'; i.e., a measure of fineness or purity. Tiltre became titre, which thus came to mean the 'fineness of alloyed gold', and then the 'concentration of a substance in a given sample'. In 1828, the French chemist Gay-Lussac first used titre as a verb (titrer), meaning 'to determine the concentration of a substance in a given sample'. Volumetric analysis originated in late 18th-century France. François-Antoine-Henri Descroizilles (fr) developed the first burette (which was similar to a graduated cylinder) in 1791. Joseph Louis Gay-Lussac developed an improved version of the burette that included a side arm, and coined the terms 'pipette' and 'burette' in an 1824 paper on the standardization of indigo solutions. The first true burette was invented in 1845 by the French chemist Étienne Ossian Henry (1798–1873). A major breakthrough in the methodology and popularization of volumetric analysis was due to Karl Friedrich Mohr, who redesigned the burette into a simple and convenient form, and who wrote the first textbook on the topic, Lehrbuch der chemisch-analytischen Titrirmethode (Textbook of analytical chemistry titration methods), published in 1855. A typical titration begins with a beaker or Erlenmeyer flask containing a very precise volume of the analyte and a small amount of indicator (such as phenolphthalein) placed underneath a calibrated burette or chemistry pipetting syringe containing the titrant. Small volumes of the titrant are then added to the analyte and indicator until the indicator changes color in reaction to the titrant saturation threshold, reflecting arrival at the endpoint of the titration. Depending on the endpoint desired, single drops or less than a single drop of the titrant can make the difference between a permanent and temporary change in the indicator. When the endpoint of the reaction is reached, the volume of reactant consumed is measured and used to calculate the concentration of analyte by where Ca is the concentration of the analyte, typically in molarity; Ct is the concentration of the titrant, typically in molarity; Vt is the volume of the titrant used, typically in liters; M is the mole ratio of the analyte and reactant from the balanced chemical equation; and Va is the volume of the analyte used, typically in liters. Typical titrations require titrant and analyte to be in a liquid (solution) form. Though solids are usually dissolved into an aqueous solution, other solvents such as glacial acetic acid or ethanol are used for special purposes (as in petrochemistry). Concentrated analytes are often diluted to improve accuracy. Many non-acid–base titrations require a constant pH throughout the reaction. Therefore, a buffer solution may be added to the titration chamber to maintain the pH. In instances where two reactants in a sample may react with the titrant and only one is the desired analyte, a separate masking solution may be added to the reaction chamber which masks the unwanted ion. Some redox reactions may require heating the sample solution and titrating while the solution is still hot to increase the reaction rate. For instance, the oxidation of some oxalate solutions requires heating to 60 °C (140 °F) to maintain a reasonable rate of reaction.