General concepts. Determining the content (concentration, mass, etc.) of components in the analyzed substance is called quantitative analysis. Using quantitative analysis, the mass ratios of components in the analyzed sample and the concentration of a substance in a solution or gas are determined. In quantitative analysis, certain chemical, physicochemical and physical parameters of the sample being analyzed, which depend on its composition or the content of another component. In most methods, the results obtained from the analysis are compared with the properties known substances. Analysis results are usually expressed in mass fractions, in%.

Quantitative analysis is carried out in a certain sequence, which includes sampling and preparation of samples, analysis, processing and calculation of analysis results. As in qualitative analysis, there are macro methods, semi-micro methods, micro and ultra-micro methods.

Quantitative analysis is widely used to study the composition of ores, metals, inorganic and organic compounds. IN last years Special attention refers to the definition of content toxic substances in the air, water bodies, soils, food products, various goods.

Classification of methods quantitative analysis . All methods of quantitative analysis can be divided into two groups: chemical and instrumental. This division is conditional, since many instrumental methods are based on the use chemical laws and properties of substances. Usually quantitative methods analysis is classified according to the measured physical or chemical properties.

Table 18.3 - Basic methods of quantitative analysis

Measured quantity (property)	Method name	Measurable mass of matter	Theoretical foundations of the method (see paragraph or chapter)
Mass Volume Density Absorption or emission of infrared rays Vibrations of molecules Absorption or emission of visible, ultraviolet and x-rays. Vibrations of atoms. Light scattering Diffusion current at the electrode Electrode potential Amount of electricity Electrical conductivity Radioactivity Reaction rate Thermal effect of reaction Viscosity Surface tension Decreased freezing point Increased boiling point	Gravimetric Mass spectrometric Titrometric Gas volumetric Densimetric Infrared spectroscopy Raman scattering Spectral and X-ray spectral Photometric (colorimetry, spectrophotometry and others) Atomic adsorption spectroscopy Luminescent Polarography and voltammetry Potentiometric Coulometric Con ductomeric Radioactive indicators Kinetic Catalytic Thermometry and calorimetry Viscometer Tensometric Cryoscopic Ebulioscopic	From macro- to ultra-micro quantities Micro quantities From macro to ultra-micro quantities The same Macro and micro quantities The same The same Semi-micro and micro quantities The same Micro quantities The same Semi-micro and micro quantities Macro and micro quantities Micro and ultra-micro quantities Macro and micro quantities From macro- to ultra-micro quantities Macro and micro quantities Macro quantities The same » » »	Section 8.6 - Ch. 8 Ch. 8 - Paragraph 1. 1, 7.4 - Paragraph 1.1-1.3,7.4 Paragraph 2.4, 2.5, 3.4 - - Paragraph 9.5 Paragraph 9.3, 9.4 Paragraph 9.2 Paragraph 8.4 Chapter 17 Paragraph 7.1-7.3 Paragraph 7.5 Paragraph 5.1 - Paragraph 4.3, 6.2 Paragraph 8.1 Paragraph 8.1

The textbook will discuss only some methods based on the theoretical principles studied in previous chapters.

Gravimetric method. The essence of the method is to obtain a sparingly soluble compound that contains the component being determined. To do this, a sample of the substance is dissolved in one solvent or another, usually water, and precipitated using a reagent that forms a poorly soluble compound with a low PR value with the analyzed compound (see paragraph 8.3). Then, after filtering, the precipitate is dried, calcined and weighed. Based on the mass of the substance, the mass of the component being determined is determined and its mass fraction in the analyzed sample is calculated. Some reagents (group and individual) were discussed in paragraph 16.1.

There are variations of the gravimetric method. In the distillation method, the analyzed component is isolated in the form of a gas that reacts with the reagent. The change in the mass of the reagent is used to judge the content of the component being determined in the sample. For example, the carbonate content of a rock can be determined by exposing the analyzed sample to acid, which releases CO2:

CO+2НН2СО3Н2О+СО2

The amount of CO2 released can be determined by the change in the mass of the substance, for example CaO, with which CO2 reacts.

One of the main disadvantages of the gravimetric method is its labor intensity and relatively long duration. Less labor-intensive is the electrogravimetric method, in which the metal to be determined, such as copper, is deposited on a cathode (platinum mesh)

Based on the difference in the mass of the cathode before and after electrolysis, the mass of the metal in the analyzed solution is determined. However, this method is only suitable for the analysis of metals that do not produce hydrogen (copper, silver, mercury).

Titrimetric analysis. The essence of the method is to measure the volume of a solution of a particular reagent consumed in the reaction with the analyzed component. For these purposes, so-called titrated solutions are used, the concentration of which (usually the titer of the solution) is known. Title is the mass of a substance contained in 1 ml (1 cm) of a titrated solution (in g/ml and g/cm). Determination is carried out using the method titration, those. gradual addition of a titrated solution to a solution of the analyte, the volume of which is accurately measured. Titration stops when it reaches equivalence points, those. achieving equivalence of the reagent of the titrated solution and the analyzed component.

There are several types of titrimetric analysis: acid-base titration, precipitation titration, complexometric titration, and redox titration.

At the core acid-base titration lies the neutralization reaction

The method allows you to determine the concentration of acid or cations that are hydrolyzed to form hydrogen ions by titration with an alkali solution or to determine the concentration of bases, including anions that are hydrolyzed to form hydroxide ions by titration with acid solutions. The equivalence point is established using acid-base indicators that change color in a certain pH range. For example, using the acid-base titration method, you can determine the carbonate hardness of water, i.e. concentration of HCO in water by titrating its solution with HCl in the presence of methyl orange indicator

HCO+ H= H2O+ CO2

At the equivalence point, the yellow color of the indicator turns into pale pink. The calculation is made using the equation of the law of equivalents

, (18.2)

where are the volumes of the analyzed and titrated solutions;

Normal concentration of HCl equivalents in a titrated solution

Determined molar concentration of equivalents of HCO ions in the analyzed solution.

At precipitation titration the analyzed solution is titrated with a reagent that forms a poorly soluble compound with a component of the titrated solution. The equivalence point is determined using an indicator that forms a colored compound with the reagent, for example, a red precipitate of Ag2CrO4 when the K2CrO4 indicator reacts with an excess of Ag ions when titrating a chloride solution with a silver nitrate solution.

Complexometric titration. In complexometric titration, the component to be determined in a solution is titrated with a solution of a complexone, most often ethylenediaminetetraacetic acid (EDTA, complexone II) or its disodium salt (complexone III or Trilon B). Complexons are ligands and form complexes with many cations. Indicators of equivalence are usually ligands that form a colored complex compound with the analyzed ion. For example, the indicator chromogen black with calcium and magnesium forms complexes and is red. As a result of titration of a wine-red solution containing calcium, magnesium and indicator ions with a solution of complexone III, calcium is bound into a more stable complex with the complexone; at the equivalence point, the indicator anions are released and impart to the solution blue color. This complexometric titration method is used, for example, to determine the total hardness of water.

Redox titration. This method consists of titrating a reducing agent solution with a titrated solution of an oxidizing agent or titrating an oxidizing solution with a titrated solution of a reducing agent. Solutions of potassium permanganate KMnO4 (permanganatometry), potassium dichromate K2Cr2O7 (dichromatometry), and iodine I2 (iodometry) have been used as titrated solutions of oxidizing agents. Among titrated solutions of reducing agents, solutions of hydrazine N2H4 (hydrazinometry) should be noted.

During permanganatometric titration in an acidic medium, Mn (VII) (raspberry color) turns into Mn (II) (colorless solution). For example, permanganometric titration can determine the nitrite content in a solution

2KMnO4 + 5KNO2 + 3H2SO4 = 2MnSO4 + K2SO4 + 5KNO3 + 3H2O

In dichromatometric titration, the indicator is diphenylamine, which colors the solution in Blue colour with an excess of dichromate ions. In iodometric titration, starch serves as an indicator. Iodometric titration is used to analyze solutions of oxidizing agents, in which case the titrated solution contains iodide ion. For example, copper can be determined by titrating its solutions with an iodide solution

2Cu

Then the resulting solution is titrated with a titrated solution of sodium thiosulfate Na2S2O3 with a starch indicator added at the end of the titration

2Na2S2O3 + I2 = 2NaI + Na2S4O6

So there is big number types of quantitative chemical analysis that allow the determination of various substances over a wide range of concentrations. Among chemical methods analysis, the most common are titrimetric and gravimetric methods.

The task of quantitative analysis is to determine the quantitative content of individual components in the test substance or mixture. results quantification usually expressed as a percentage. Quantitative analysis is used in biology, physiology, medicine, biochemistry, chemistry food products etc.

All methods of quantitative analysis can be divided into three main groups.

1. Gravimetric (weight) analysis. Gravimetric analysis is the determination of the amount of a component (element or ion) based on the mass of the substance obtained as a result of the analysis. In the methods of this group, the determined part of the analyte is isolated in pure form or in the form of a compound of known composition, the mass of which is determined.

For example, to determine the amount of barium in its compounds, the Ba 2+ ion is precipitated using dilute sulfuric acid:

BaС1 2 + H 2 S0 4 = BaS0 4 | + 2HC1.

The BaS0 4 precipitate is filtered, washed, calcined and accurately weighed. Knowing the mass of the BaS0 4 sediment and its formula, calculate how much barium it contains. The gravimetric method gives results high precision, but it is very labor intensive.

2. Titrimetric (volumetric) analysis. Titrimetric analysis is based on precise measurement the amount of reagent spent on the reaction with the determined
component. The reagent is taken in the form of a solution of a certain concentration - titrated solution. Moment,
when the reagent is added in an amount equivalent to the content of the component being determined, i.e., the moment of completion of the reaction is determined different ways. When titrating, add an amount of reagent equivalent to the amount of the substance being determined. Knowing the volume and exact concentration of the solution that reacted with the analyte, the amount of the analyte is calculated.

Titrimetric analysis gives less accurate results than gravimetric analysis, but its important advantage is the greater speed of analysis. Depending on the type of reactions occurring during the titration process, titrimetric analysis is divided into three groups: acid-base titration methods, redoximetry methods, and precipitation and complexation methods.

3. Photometric methods. In this method, the amount of a substance is determined by the color intensity of the solution. For this purpose, so-called color reactions are used, i.e. reactions accompanied by a change in the color of the solution. For example, when determining the amount of iron, the reaction is used

FeCl3 + 3KSCN 7-Fe(SCN)3 + 3KCI,

leading to the formation of a red solution. The color intensity of the solution is assessed visually or using appropriate instruments.

Sometimes the component being determined is converted into a slightly soluble compound and the content of the substance being determined is judged by the intensity of the solution turbidity. A method based on this principle is called nephelometry. The methods of photometry and nephelometry are used to determine the components that make up the analyte in very small quantities. The accuracy of this method is lower than that of gravimetric or titrimetric methods.

In addition to these methods, there are others: gas analysis, spectral analysis, electrochemical and chromatographic methods. IN this textbook these methods are not considered.

All methods of quantitative analysis are divided into chemical and physicochemical. Chemical methods include gravimetric, titrimetric and gas analysis, physicochemical methods include photometry and nephelometry, electrochemical, spectral, chromatographic methods of analysis.

In quantitative analysis, there are macro-, micro- and semi-micro methods. This textbook covers only the macro method. When performing macro determinations, relatively large (0.01-0.1 g) amounts of the substance are determined. The exception is photometric and nephelometric methods, in which the amount of the substance being determined is a fraction of a milligram.

OBJECTIVES AND METHODS OF QUANTITATIVE ANALYSIS

The task of quantitative analysis is to determine quantitative

All methods of quantitative analysis are divided into chemical, physicochemical and physical. Chemical methods include gravimetric, titrimetric and gas analyses, physicochemical methods include photometry, electrochemical and chromatographic analyses, and physical methods include spectral analysis and luminescence.

1. Gravimetric analysis is based on determining the mass of a substance isolated in pure form or in the form of a compound of known composition. For example, to determine the amount of barium in its compounds, the Ba 2+ ion is precipitated using dilute sulfuric acid. The BaSO 4 precipitate is filtered, washed, calcined and accurately weighed. Based on the mass of BaSO 4 sediment and its formula, calculate how much it contains

barium The gravimetric method gives highly accurate results, but it is very labor-intensive.

2. Titrimetric analysis is based on accurate measurement of the volume of the reagent,

spent on a reaction with a certain component. The reagent is taken in the form of a solution of a certain concentration - a titrated (standard) solution. The moment when the reagent is added in an amount equivalent to the content of the substance being determined, i.e. the end of the reaction is determined in various ways. During titration, a reagent is added in an amount equivalent to the amount of the substance being tested. Knowing the volume and exact concentration of the solution that reacted with the substance being determined, its quantity is calculated.

Titrimetric analysis gives less accurate results than gravimetric analysis, but its important advantage is the greater speed of analysis. Depending on the type of reactions occurring during the titration process, titrimetric analysis includes acid-base titration methods, oxidimetric methods, and precipitation and complexation methods.

3. Photometric methods are based on measuring the absorption, transmission and scattering of light by a solution. For most photometric methods, so-called color reactions are used, i.e. chemical reactions, accompanied by a change in the color of the solution. A method based on determining the content of a substance by color intensity is called colorimetry. The color intensity of the solution is assessed visually or using appropriate instruments.

Sometimes the component being determined is converted into a sparingly soluble compound and its content is judged by the intensity of turbidity of the solution. A method based on this principle is called nephelometry. Colorimetry and nephelometry methods are used to determine the components that make up the analyte in very small quantities. The accuracy of this method is lower than that of gravimetric or titrimetric methods.

4. Electrochemical methods. These methods include electrogravimetric analysis, conductometry, potentiometry and polarography. Electrogravimetric method used to determine the concentration of metals. The element to be determined is deposited by electrolysis on an electrode whose mass is known. Conductometry and potentiometry refer to electrotitrimetry. The completion of the reaction during titration is determined either by measuring the electrical conductivity of the solution or by measuring the potential of the electrode immersed in the test solution. The potentiometric method is also used to determine the pH of a solution. Definition based on measurement electromotive force solution (emf), which depends on the concentration of hydrogen ions. In the polarographic method The amount of the ion being determined is judged by the nature of the current-voltage curve (polarogram), obtained by electrolysis of the test solution with a dropping mercury cathode in a special device - a polarograph. This method is different high sensitivity. Using the polarographic method, it is possible to determine qualitatively and quantitatively in the same solution various elements without resorting to chemical reactions.

5. Chromatographic method is based on the use of the phenomenon of selective

adsorption of solutes (or ions) by various solids– adsorbents. Adsorbents may be activated aluminum oxide Al 2 O 3, permutite, synthetic resins, etc. The chromatographic method is used in qualitative and quantitative analysis. This method is especially widely used for the separation of substances or ions.

In quantitative analysis, macro-, micro- and semi-micro methods are distinguished. This textbook discusses the implementation of gravimetric and titrimetric determinations using only the macromethod.

2. GRAVIMETRIAL ANALYSIS

Methods of quantitative analysis. Quantitative analysis is intended to determine the quantitative composition of the analyte. There are chemical, physical and physicochemical methods of quantitative analysis. The basis of all quantitative research is measurement. Chemical methods of quantitative analysis are based on the measurement of mass and volume. Quantitative Research allowed scientists to establish such basic laws of chemistry as the law of conservation of mass of matter, the law of constancy of composition, the law of equivalents, and other laws on which it is based chemical science. The principles of quantitative analysis are fundamental to chemical analytical control production processes various industries industry and constitute the subject of the so-called. technical analysis. There are 2 main methods of quantitative chemical analysis: gravimetric or gravimetric and volumetric or titrimetric.

Weight analysis is a method of quantitative analysis in which only mass is accurately measured. Volumetric analysis is based on the precise measurement of the mass of substances and the volume of a solution of a reagent of known concentration that reacts with a certain amount of the analyte. A special kind count analysis is the analysis of gases and gas mixtures, so-called gas analysis, also performed by measuring the volume or mass of the analyzed mixture or gas. Determination of the same substance can be performed by gravimetric or volumetric methods of analysis. When choosing a determination method, the analyst must take into account the required accuracy of the result, sensitivity of the reaction and speed of analysis, and in the case mass definitions- availability and cost of the reagents used. In connection with this, there are macro-, micro-, semi-micro, ultra-micro methods of quantitative analysis, with the help of which analysis can be carried out minimum quantities analyte. Currently, simple chemical methods are increasingly being replaced by physical and physical and chemical methods, which require expensive instruments and equipment to work with.

Optical, electrochemical, chromatographic, various spectro- and photometric studies (infrared, atomic adsorption, flame, etc.), potentiometry, polarography, mass spectrometry, NMR studies. On the one hand, these methods speed up obtaining results, increase their accuracy and sensitivity of measurements: detection limit (1-10 -9 μg) and limit concentration(up to 10 -15 g/ml), selectivity (it is possible to determine the constituent components of a mixture without their separation and isolation), the possibility of their computerization and automation. But on the other hand, they are increasingly moving away from chemistry, reducing the knowledge of chemical methods of analysis among analysts, which has led to a deterioration in the teaching of chemistry in schools, the lack of good chemist teachers, equipped school chemical laboratories, and a decrease in knowledge of chemistry among schoolchildren.

The disadvantages include a relatively large determination error (from 5 to 20%, while chemical analysis gives an error usually from 0.1 to 0.5%), the complexity of the equipment and its high cost. Requirements for reactions in quantitative analysis. Reactions should proceed quickly, to completion, if possible, with room temperature. The starting substances entering the reaction must react in strictly defined quantitative ratios (stoichiometrically) and without side processes. Impurities should not interfere with quantitative analysis. When carrying out measurements, errors, measurement errors and calculations cannot be excluded. To eliminate errors and minimize them, measurements are carried out in repetitions ( parallel definitions), at least 2, and conduct a metrological assessment of the results (meaning the correctness and reproducibility of the analysis results).

The most important characteristics of analytical methods are their sensitivity and accuracy. The sensitivity of the analysis method is called least amount substances that can be reliably determined by this method. The accuracy of the analysis is called the relative error of determination, which is the ratio of the difference between the found (x 1) and true (x) content of a substance to the true content of a substance and is found using the formula:

Rel. error = (x 1 - x)/ x, to express it as a percentage, multiply by 100. The arithmetic mean content of the substance found when analyzing the sample in 5-7 determinations is taken as the true content.

Method Sensitivity, mol/l Accuracy,%

Titrimetric 10 -4 0.2

Gravimetric 10 -5 0.05

Weight (gravimetric) analysis is a method of quantitative analysis in which quantitative composition the analyte is determined on the basis of mass measurements, by accurately weighing the mass of a stable final substance of known composition into which the given component being determined is completely converted. For example, gravimetric determination of sulfuric acid in an aqueous solution is carried out using aqueous solution barium salts: BaCl 2 + H 2 SO 4 > BaSO 4 v +2 HCl. Precipitation is carried out under conditions in which almost all of the sulfate ion passes into the BaSO 4 precipitate with the greatest completeness - quantitatively, with minimal losses, due to the insignificant but still existing solubility of barium sulfate. Next, the precipitate is separated from the solution, washed to remove soluble impurities, dried, calcined to remove volatile sorbed impurities, and weighed on an analytical balance in the form of pure anhydrous barium sulfate. And then the mass of sulfuric acid is calculated. Classification of gravimetric analysis methods. Methods of precipitation, distillation, isolation, thermogravimetric methods (thermogravimetry).

Deposition methods - determined component quantitatively linked into such chemical compound, in the form of which it can be isolated and weighed. The composition of this compound must be strictly defined, i.e. express yourself accurately chemical formula, and it should not contain any foreign impurities. The compound in which the component being determined is weighed is called the gravimetric form. Example, determination of H 2 SO 4 (above), determination of the mass fraction of iron in its soluble salts, based on the precipitation of iron (111) in the form of hydroxide Fe(OH) 3 xH 2 O, followed by its separation and calcination to Fe 2 O 3 oxide (weight form). Distillation methods. The component to be determined is isolated from the analyzed sample in the form gaseous substance and measure either the mass of the distilled substance (direct method) or the mass of the residue (indirect method).

The direct method is widely used to determine the water content of analytes by distilling it from a suspended sample and condensing it, and then measuring the volume of condensed water in a receiver. Based on density, the volume of water is recalculated per mass and, knowing the mass of the sample and water, the water content in the analyzed sample is calculated. The indirect distillation method is widely used to determine the content of volatile substances (including weakly bound water) by changing the mass of the sample before and after drying to a constant weight in a thermostat (in a drying oven) at a constant temperature. The conditions for conducting such tests (temperature, drying time) are determined by the nature of the sample and are specifically indicated in the methodological manuals.

Isolation methods are based on the isolation of the analyte component from a solution by electrolysis on one of the electrodes (electrogravimetric method). Then the electrode with the released substance is washed, dried and weighed. By increasing the mass of the electrode with the substance, the mass of the substance released on the electrode is determined (alloys of gold and copper are transferred into solution).

Thermogravimetric methods are not accompanied by the separation of the test substance, but the sample itself is examined; therefore, these methods are conventionally classified as gravimetric methods of analysis. The methods are based on measuring the mass of the analyzed substance during its continuous heating in a given temperature range at special devices- derivatographs. From the obtained thermogravigrams, when interpreted, it is possible to determine the moisture content and other components of the analyzed substance.

The main stages of gravimetric determination: calculation of the mass of the sample being analyzed and the volume (or mass) of the precipitant; weighing (taking) a sample sample; dissolving a portion of the analyzed sample; precipitation, i.e. obtaining a deposited form of the component being determined; filtration (separation of sediment from the mother liquor); washing the sediment; drying and (if necessary) calcination of the sediment until constant mass, i.e. obtaining a gravimetric form; gravimetric form weighing; calculation of analysis results, their statistical processing and presentation. Each of these operations has its own characteristics.

When calculating the optimal mass of a sample of the analyzed substance, the possible mass fraction of the analyzed component in the analyzed sample and in gravimetric form, the mass of the gravimetric form, the systematic error of weighing on an analytical balance (usually 0.0002), and the nature of the resulting sediment - amorphous, fine-crystalline, coarse-crystalline. The initial sample is calculated based on the fact that the mass of the gravimetric sample must be at least 0.1 g. general case the lower limit of the optimal mass m of the initial sample of the analyzed substance (in grams) is calculated by the formula: m = 100m (GF) F/ W(X), where m(GF) is the mass of the gravimetric form in grams; F - gravimetric factor, conversion factor, analytical factor); W(X) - mass fraction(in%) of the determined component in the analyzed substance. Gravimetric factor F numerically equal to mass of the determined component in grams, corresponding to one gram of gravimetric form.

The gravimetric factor is calculated using the formula as the ratio of the molar mass M(X) of the determined component X to molar mass gravimetric form M(GF), multiplied by the number n moles of the component being determined, from which one mole of gravimetric form is obtained: F = n M(X) / M (GF). So, if from 2 moles of Fe C1 3 6H 2 O one mole of the gravimetric form Fe 2 O 3 is obtained, then n = 2. If from one mole of Ba(NO 3) 2 one mole of the gravimetric form BaCrO 4 is obtained, then n = 1.

These are gravimetric and titrimetric methods. Although they are gradually giving way to instrumental methods, they remain unsurpassed in accuracy: their relative error less than 0.2%, while instrumental ones are 2-5%. They remain standard for assessing the validity of the results of other methods. Main application: precision determination of large and medium quantities of substances.

Gravimetric method consists of isolating the substance in its pure form and weighing it. Most often, isolation is carried out by precipitation. The precipitate should be practically insoluble. The component being determined should precipitate almost completely, so that the concentration of the component in the solution does not exceed 10 -6 M. This precipitate should be as coarse-crystalline as possible so that it can be easily washed. The precipitate must be a stoichiometric compound of a certain composition. During precipitation, impurities are captured (co-precipitation), so it must be washed. The sediment must then be dried and weighed.

Application of gravimetric methods:

Most inorganic cations, anions, and neutral compounds can be determined. Inorganic and organic reagents are used for precipitation; the latter are more selective. Examples:

AgNO 3 +HCl=AgCl+HNO 3

(determination of silver or chloride ions),

BaCl 2 +H 2 SO 4 =BaSO 4 +2HCl

(determination of barium or sulfate ions).

Nickel cations are precipitated by dimethylglyoxime.

Titrimetric methods use reactions in solutions. They are also called volumetric, as they are based on measuring the volume of a solution. They involve the gradual addition to a solution of a substance being determined with an unknown concentration of a solution of a substance that reacts with it (with a known concentration), which is called a titrant. Substances react with each other in equivalent quantities: n 1 = n 2.

Since n=CV, where C is the molar concentration of the equivalent, V is the volume in which the substance is dissolved, then for stoichiometrically reacting substances the following is true:

C 1 V 1 =C 2 V 2

Therefore, it is possible to find the unknown concentration of one of the substances (for example, C 2) if the volume of its solution and the volume and concentration of the substance that reacted with it are known. Knowing the molecular weight of the equivalent M, you can calculate the mass of the substance: m 2 = C 2 M.

In order to determine the end of a reaction (called the equivalence point), a change in the color of the solution is used or some physicochemical property of the solution is measured. Reactions of all types are used: neutralization of acids and bases, oxidation and reduction, complex formation, precipitation. The classification of titrimetric methods is given in the table:

Titration method, reaction type	Subgroups of methods	Titrant substances
Acid-base	Acidimetry
	Alkalimetry	NaOH, Na 2 CO 3
Redox	Permanganatometry
	Iodometry
	Dichromatometry
	Bromatometry
	Iodatometry
Complexometric	Complexometry
Precipitative	Argentometry

Titration can be direct or reverse. If the reaction rate is low, a known excess of titrant is added to bring the reaction to completion, and then the amount of unreacted titrant is determined by titration with another reagent.

Acid-base titration is based on a neutralization reaction; during the reaction, the pH of the solution changes. The graph of pH versus titrant volume is called a titration curve and usually looks like:

To determine the equivalence point, either pH measurements or indicators that change color when a certain value pH. The sensitivity and accuracy of titration are characterized by the steepness of the titration curve.

Complexometry is based on the reaction of complex formation. The most commonly used is ethylenediaminetetraacetic acid (EDTA).

(HOOC)(OOC-H2C)NH-CH2CH2-NH(CH2COO)(CH2COOH)

or its) disodium salt. These substances are often called complexones. They form strong complexes with cations of many metals, so their use for titration requires separation.

Redox titration is accompanied by a change in the potential of the system. The progress of the titration is usually controlled by the potentiometric method, see later.

Precipitation titration - Argentometry is most often used as a method for determining halide ions. The latter form a practically insoluble precipitate with silver cations.

Methods of titrimetric analysis are highly accurate (relative error of determination - 0.1 - 0.3%), low labor intensity, and simple instrumentation. Titrimetry is used for the rapid determination of high and medium concentrations of substances in solutions, including non-aqueous ones.