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Titrimetric or volumetric analysis- a method of quantitative analysis based on measuring the volume (or mass) of the reagent T spent on the reaction with the analyte X. In other words, titrimetric analysis is an analysis based on titration.

The purpose of laboratory classes on titrimetric methods of analysis is to develop practical skills in the technique of performing titrimetric analysis and master the methods of statistical processing of analysis results using the example of specific quantitative determinations, as well as to consolidate theoretical knowledge by solving typical calculation problems for each topic.

Knowledge of the theory and practice of titrimetric analysis methods is necessary for the subsequent study of instrumental methods of analysis, other chemical and special pharmaceutical disciplines (pharmaceutical, toxicological chemistry, pharmacognosy, pharmaceutical technology). The studied methods of titrimetric analysis are pharmacopoeial and are widely used in the practice of a pharmacist to control the quality of drugs.

Conventions

A, X, T - any substance, analyte and titrant, respectively;

m(A), m(X), t(T)- mass of any substance, analyte and titrant, respectively, g;

M(A), M(X), M(T)- molar mass of any substance, analyte and titrant, respectively, g/mol;

n(A), n(X), n(T) - the amount of any substance, analyte and titrant, respectively, mol;

The amount of the substance of the equivalent of any substance, the substance to be determined and the titrant, respectively, mol;

- the volume of a solution of any substance, analyte and titrant, respectively, l;

- the volume of an aliquot of the analyte, equal to the capacity of the pipette, l;

- the volume of the analyzed solution of the analyte, equal to the capacity of the flask, l.

1. Basic concepts of titrimetric

analysis

1.1. Titration- the process of determining substance X by the gradual addition of small amounts of substance T, in which, in some way, the detection of the point (moment) when all substance X has reacted is provided. Titration allows you to find the amount of substance X from a known amount of substance T added up to this point (moment), taking into account the fact that the ratio in which X and T react is known from stoichiometry or otherwise.

1.2. titrant- a solution containing active reagent T, with which the titration is carried out. Titration is usually carried out by adding titrant from a calibrated burette to the titration flask containing the solution to be analyzed. Into this flask before titration add aliquot analyzed solution.

1.3. Aliquot share (aliquot)- precisely known part of the analyzed solution, taken for analysis. It is often taken with a calibrated pipette and its volume is usually indicated by the symbol V ss .

1.4. Equivalence point (TE)- such a point (moment) of titration at which the amount of added titrant T is equivalent to the amount of titrated substance X. Synonyms for TE: stoichiometric point, theoretical end point.

1.5. End point titration (KTT) - the point (moment) of the titration, at which some property of the solution (for example, its color) shows a noticeable (sharp) change. LTT corresponds more or less to TE, but most often does not coincide with it.

1.6. Indicator- a substance that exhibits a visible change in the TE or near it. Ideally, the indicator is present at a concentration low enough to transition interval not cost-

a significant amount of titrant T was used. A sharp visible change in the indicator (for example, its color) corresponds to CTT.

1.7. Indicator transition interval- the area of ​​concentration of hydrogen, metal or other ions within which the eye is able to detect a change in hue, color intensity, fluorescence or other property of a visual indicator caused by a change in the ratio of two corresponding forms of the indicator. This area is usually expressed as the negative logarithm of the concentration, for example: For a redox indicator, the transition interval is the corresponding region of the redox potential.

1.8. Degree of titration - volume ratio V (T) of the added titrant to the volume V (TE) of the titrant corresponding to the TE. In other words, the degree of titration of a solution is the ratio of the amount of the titrated substance to its initial amount in the analyzed solution:

1.9. Titration level- order the concentration of the titrant solution used, for example, 10 -1 , 10 -2 , 10 -3 , etc.

1.10. Titration curve - graphic representation of the dependence of the change in concentration c (X) of the analyte X or some related property of the system (solution) on the volume V (T) added titrant T. The value of c (X) during the titration changes by several orders of magnitude, so the titration curve is often plotted in the coordinates: The abscissa shows the volume of added titrant V (T) or degree of titration / . If the equilibrium concentration c (X) or the intensity of a property proportional to it is plotted along the y-axis, then we get linear titration curve. If on the y-axis we set aside or the logarithm of the intensity of a property proportional to c(X), then one gets logarithmic (or monologarithmic) titration curve. To more clearly identify the features of the titration process and for applied purposes, sometimes they build differential titration curves, plotting along the abscissa axis the volume of the added titrant V (T), and along the y-axis - the first derivative of the logarithm of the concentration (or the intensity of a property proportional to it) with respect to the volume of the added titrant: Such titration curves are usually used in physicochemical methods of analysis, for example, in potentiometric titrations.

1.11. Standard solution- a solution having a known concentration of the active substance.

1.12. Standardization- the process of finding the concentration of an active reagent in a solution (most often by titrating it with a standard solution of the corresponding substance).

1.13. Titration jump- the interval of a sharp change in any physical or physico-chemical property of the solution near the equivalence point, usually observed when 99.9-100.1% of the titrant is added compared to its stoichiometric amount.

1.14. Blank titration- titration of a solution that is identical to the analyzed solution in terms of volume, acidity, amount of indicator, etc., but does not contain the analyte.

2. Basic operations of titrimetric analysis

2.1. Cleaning, washing, storage of measuring utensils.

2.2. Checking the capacity of measuring utensils.

2.3. Taking a sample with a precisely known mass by the difference between the results of two weighings (usually on an analytical balance).

2.4. Quantitative transfer of a sample of a substance into a volumetric flask and dissolution of the substance.

2.5. Filling volumetric utensils (flasks, burettes, pipettes) with a solution.

2.6. Emptying pipettes, burettes.

2.7. Selection of an aliquot of the analyzed solution.

2.8. Titration and calculations based on titration results.

3. Calibration of measuring instruments

In titrimetric analysis, the exact volumes of the solution are measured using measuring utensils, which are volumetric flasks with a capacity of 1000, 500, 250, 100, 50 and 25 ml, pipettes and graduated pipettes with a capacity of 10, 5, 3, 2 and 1 ml. The capacity of the flask and pipette at 20 °C is engraved on the neck of the flask or on the side of the pipette (nominal volume). In the mass production of volumetric utensils, the actual (true) capacity of volumetric flasks, burettes, pipettes may differ from the nominal values ​​indicated on the utensil. To achieve the required accuracy of the obtained results of titrimetric analysis

Calibration of volumetric glassware is based on determining the exact mass of distilled water poured in or poured out, which is determined by the results of weighing the glassware before and after pouring in or pouring out water. The volume of water in the calibrated vessel (its capacity) and the mass of water are related by the ratio:

where - density of water at the temperature of the experiment, g/ml.

The density of water depends on temperature, so when making calculations, you should use the data in Table. 2-1.

Table 2-1. Density values ​​of water at the corresponding temperature

Volumetric flasks are calibrated for infusion, and burettes and pipettes are calibrated for pouring, since small amounts of liquid always remain on the walls of the dish during pouring.

3.1. Volumetric flask capacity check

The flask is thoroughly washed, dried and weighed on an analytical balance with an accuracy of ± 0.002 g. Then it is filled with water (hereinafter - distilled) along the lower meniscus, the drops of water in the upper part of the neck of the flask are removed with filter paper and weighed again. Each weighing of an empty flask and a flask with water is carried out at least twice, while the difference between two weighings should not exceed ± 0.005 g. The difference between the mass of a flask with water and the mass of an empty flask is equal to the mass of water contained by the flask at a given temperature. The true capacity of the flask is calculated by dividing the average mass of water by its density at the test temperature (see Table 2-1).

For example, if a volumetric flask with a nominal volume of 100 ml is calibrated, the average mass of water at 18 °C is 99.0350 g. Then the true capacity of the volumetric flask is:

3.2. Burette capacity check

The burette is a glass cylinder, the inner diameter of which can vary slightly along the length of the burette. Equal divisions on the burette in its various parts correspond to unequal volumes of the solution. That is why burette calibration calculates the true volumes for each selected buret site.

A clean and dried burette is filled with water to the zero mark along the lower meniscus and water drops are removed from the inner surface of the upper part of the burette with filter paper. Then, under the burette substitute a bottle, previously weighed with a lid on an analytical balance. A certain volume of water (for example, 5 ml) is slowly poured into the bottle from the burette. After that, the bottle is closed with a lid and weighed again. The difference between the mass of the weighing bottle with water and the empty weighing bottle is equal to the mass of water contained in the burette between divisions of 0 and 5 ml at the temperature of the experiment. Then the burette is again filled with water to the zero mark along the lower meniscus, 10 ml of water is slowly poured into an empty bottle and the mass of water contained in the burette between divisions 0 and 10 ml is determined in a similar way. When calibrating the burette, for example, for 25 ml, this operation is carried out 5 times and the mass of water corresponding to the nominal volumes indicated on the burette of 5, 10, 15, 20 and 25 ml is calculated. Each weighing of an empty bottle and a bottle of water is repeated at least twice, while the difference between two weighings should not exceed ± 0.005 g.

Then according to the table. 2-1 determine the density of water at the temperature of the experiment and calculate the true capacity of the burette for each value of the nominal volume indicated on it.

Based on the data obtained, the correction value is calculated equal to the difference between the calculated value of the true capacity and the corresponding value of the nominal volume of the burette:

and then draw a curve of burette capacity errors in coordinates (Figure 2-1).

For example, let the following experimental data be obtained when calibrating a burette with a capacity of 25 ml at a temperature of 20 °C, which, together with the results of the corresponding calculations, are presented in Table. 2-2.

Based on the obtained tabular data, a capacity correction curve for a given buret is plotted, using which it is possible to refine the results of reading by buret.

Table 2-2. Calibration results for a 25 ml burette

Rice. 2-1. Burette capacity correction curve

For example, let 7.50 ml of titrant be used for titration of an aliquot of the analyte according to the results of counting on a buret. According to the graph (see Fig. 2-1), the correction value corresponding to this nominal volume is 0.025 ml, the true volume of titrant used is: 7.50 - 0.025 = 7.475 ml.

3.3. Checking pipette capacity

A pipette, clean and weighed on an analytical balance, is filled with water to the zero mark along the lower meniscus and then the water is slowly filled.

poured along the wall into a pre-weighed bottle. The bottle is covered with a lid and weighed with water. Each weighing of an empty bottle and a bottle with water is repeated at least two times, while the difference between two weighings should not exceed ± 0.005 g. The difference between the mass of a bottle with water and an empty bottle is equal to the mass of water contained by a pipette. The true capacity of the pipette is calculated by dividing the average mass of water by the density of the water at the test temperature (see Table 2-1).

4. Typical calculations in titrimetric analysis

4.1. Ways of expressing concentrations used for calculations in titrimetric analysis

4.1.1. Molar concentration of substance c (A), mol / l - the amount of substance A in mol contained in 1 liter of solution:

(2.1)

where - the amount of substance A in mol, dissolved in V (A) l

solution.

4.1.2. Molar concentration equivalent of a substance , mol / l - the amount of substance A equivalent in mol contained in 1 liter of solution (the former name is the “normality” of the solution):

(2.2)

where
- the amount of substance equivalent to A in mol,

dissolved in V (A) l of solution; - molar mass of the equivalent of ve-

substances A, g / mol; - the equivalence factor of the substance.

4.1.3. Substance titer T(A), g / ml - the mass of solute A in grams, contained in 1 ml of solution:

4.1.4. Titrimetric conversion factor I, g / ml - mass of the analyte in grams, interacting with 1 ml of titrant:

(2.4)

4.1.5. Correction factor F- a value showing how many times the practical concentrations of the titrant differ from the corresponding theoretical values ​​specified in the method:

(2.5)

4.2. Calculation of the molar mass equivalent of substances in reactions used in titrimetric analysis

An equivalent is a real or conditional particle that can add or donate one hydrogen ion H + (or be otherwise equivalent to it in acid-base reactions) or add or donate one electron in redox reactions.

Equivalence factor - a number indicating which

the equivalent fraction is from a real particle of substance A. The equivalence factor is calculated based on the stoichiometry of this reaction:

where Z- the number of protons donated or added by one reacting particle (molecule or ion) in an acid-base reaction, or the number of electrons donated or accepted by one reacting particle (molecule or ion) in an oxidation or reduction half-reaction.

The molar mass of the equivalent of a substance is the mass of one mole of the equivalent of a substance, equal to the product of the equivalence factor by the molar mass of the substance, g / mol. It can be calculated using the formula:

(2.6)

4.3. Preparation of a solution by diluting a more concentrated solution with a known concentration

When carrying out titrimetric analysis, in some cases it is required to prepare a solution of substance A with a volume approximately known concentration by diluting a more concentrated solution.

When the solution is diluted with water, the amount of substance A or the amount of substance A does not change, therefore, in accordance with expressions (2.1) and (2.2), we can write:

(2.7)
(2.8)

where indices 1 and 2 refer to solutions before and after dilution, respectively.

From the ratios obtained, the volume of a more concentrated solution is calculated , which must be measured to prepare a given solution.

4.4. Preparation of a predetermined volume of solution by weighing a precisely known mass

4.4.1. Sample Weight Calculation

The theoretical mass of a sample of a standard substance A, necessary to prepare a given volume of a solution with a known concentration, is calculated from expressions (2.1) and (2.2). It is equal to:

(2.9)

if the molar concentration of a substance in solution is used, and:

(2.10)

if the molar concentration of the equivalent of the substance in solution is used.

4.4.2. Calculation of the exact concentration of the prepared solution

The concentration of a solution of substance A, prepared by an accurate sample of mass m (A), is calculated from the relationships (2.1-2.3), where t(A)- the practical mass of substance A, taken from the difference between two weighings on an analytical balance.

4.5. Calculation of titrant concentration during its standardization

Known volume of standard solution with concentration titrated with a titrant solution of volume V (T)(or vice versa). In this case, for the reaction taking place in the solution during the titration process , the law of equivalents has the form:

and

From here, an expression is obtained for calculating the molar concentration of the titrant equivalent from the results of titration:

(2.12)

4.6. Calculation of the mass of the analyte in the analyzed solution4.6.1. direct titration

The substance to be determined in the analyzed solution is titrated directly with a titrant.

4.6.1.1. Calculation using titrant equivalent molar concentration

An aliquot of the analyte solution titrated

titrant solution with volume V(T). In this case, for the reaction occurring in the solution during the titration process:

the law of equivalents has the form: and

(2.13)

Hence, the molar concentration of the equivalent of the analyte, calculated from the results of titration, is equal to:

(2.14)

The resulting expression is substituted into equation (2.2) and a formula is obtained for calculating the mass of the analyte in a flask with a volume according to the results of direct titration:

(2.15)

If, during titration, part of the titrant is consumed by the reaction with the indicator, a "blank experiment" is carried out and the volume of titrant V "(T) is determined,

used for indicator titration. In calculations, this volume is subtracted from the volume of the titrant, which was used to titrate the solution of the analyte. Such an amendment is made during the "blank experiment" in all calculation formulas used in titrimetric analysis. For example, formula (2.15) for calculating the mass of the analyte, taking into account the “blank experiment”, will look like:

(2.16)

4.6.1.2. Calculation using titrimetric conversion factor

We have an analyzed solution with a volume For titration of alik-

mil's share solution of analyte used volume of titrant V (T) with theoretical titrimetric conversion factor and correction factor F. Then the mass of the analyte in an aliquot is equal to:

(2.17)

and throughout the analyzed volume

(2.18)

4.6.2. substitution titration

a known excess of reagent A is added and substituent B is isolated in an amount equivalent to the analyte:

Substituent B is titrated with a suitable titrant:

The law of equivalents for substitution titration:

using relation (2.8) can be written in the form:

From here, a formula is obtained for calculating the molar concentration of the equivalent of the analyte in solution according to the results of substitution titration:

which has the same form as in direct titration (2.14). That is why all calculations of the mass of the analyte in the analyzed problem during substitution titration are carried out according to formulas (2.15-2.18) for direct titration. 4.6.3. Back titration

To an aliquot of the analyte add famous excess of the first titrant :

Then the excess of the unreacted first titrant is titrated with the second titrant, which consumes the volume :

The law of equivalents in this case can be written as:

From here, the molar concentration of the equivalent of substance X in solution is calculated:

(2.19)

Substitute the resulting expression into equation (2.2) and obtain a formula for calculating the mass of the analyte in the analyzed solution, equal to the volume of the flask, based on the results of back titration:

5. Implementation and provision of practical work on titrimetric analysis

5.1. General provisions

When studying the section "Titrimetric analysis", it is planned to carry out work on the following topics.

Theme I Methods of acid-base titration.

Theme II. Methods of redox titration.

Topic III. Methods of precipitation titration.

Topic IV. Methods of complexometric titration.

Lesson 1. Preparation of hydrochloric acid solution and its standardization.

Lesson 2. Determination of the mass of alkali in solution. Determination of the mass of carbonates in solution. Determination of the mass of alkali and carbonate in solution in the joint presence.

Lesson 3. Determination of the mass of ammonia in solutions of ammonium salts.

a) Test control 1.

b) Determination of the mass of ammonia in solutions of ammonium salts. Lesson 4. Permanganometric titration.

a) Written test 1.

b) Determination of the mass of hydrogen peroxide in solution.

c) Determination of the mass of iron(II) in a salt solution. Determination of the mass fraction of iron(II) in a salt sample.

Lesson 5. Iodometric titration.

a) Determination of the mass of hydrogen peroxide in solution.

b) Determination of the mass of copper(II) in solution. Lesson 6. iodimetric titration.

Lesson 7. Bromatometric titration. Determination of the mass of arsenic (III) in solution.

Lesson 8. bromometric titration. Determination of the mass fraction of sodium salicylate in the preparation.

Lesson 9. Nitritometric titration.

a) Test control 2.

b) Determination of the mass fraction of novocaine in the preparation. Lesson 10. Argentometric titration and hexacyanoferratom-

tric titration.

a) Written test 2.

b) Determination of the mass of potassium bromide and potassium iodide in solution by argentometric titration.

c) Determination of the mass of zinc in solution by hexacyanoferratometric titration.

Lesson 11. Complexometric determination of the mass of zinc and lead in solution.

a) Test control 3.

b) Determination of the mass of zinc and lead in solution.

Lesson 12. Complexometric determination of iron(III) and calcium in solution.

a) Written test 3.

b) Determination of the mass of iron(III) and calcium in solution.

Depending on the specific situation, it is allowed to carry out some work during not one, but two lessons. It is also possible to shift the timing of test controls and written tests.

At the end of each topic, examples of test items for intermediate control of students' knowledge, the content of the final written test, an example of a ticket for a written test are given.

At the end of each lesson, the student draws up a protocol that includes the date and name of the work performed, the essence of the methodology, the order of work, the experimental data obtained, calculations, tables, conclusions. All calculations of the results of the analysis (concentration of the solution, mass of the analyte) are performed by students with an accuracy of the fourth significant figure, except for cases specifically specified in the text.

Intermediate control of practical skills and theoretical knowledge is carried out with the help of test control and written tests.

5.2. Material support for classes in titrimetric analysis

Glassware: 5 ml burettes, 2 and 5 ml volumetric pipettes, 25, 50, 100 and 250 ml volumetric flasks, 10-25 ml conical flasks, glass bottles, 20-30 mm glass funnels, plain or dark glass flasks with a capacity of 100, 200 and 500 ml, measuring cylinders with a capacity of 10, 100 ml.

Reagents: Reagents of "chemically pure" qualification are used in the work and "ch.d.a.", indicator paper.

Devices: analytical balances with weights, technical balances with weights, oven, laboratory thermometer with a scale of 20-100 °C, stands with burette clamps and rings for asbestos nets, gas burners, water baths.

Auxiliary materials and accessories: detergents (soda, washing powders, chromium mixture), dishwashing brushes, rubber bulbs, asbestos nets, stationery glue, glass pencils, filter paper.

Bibliography

1. Lectures for students on the section "Titrimetric analysis".

2.Kharitonov Yu.Ya. Analytical chemistry (analytics): In 2 volumes - ed. 5th - M .: Higher School, 2010 (hereinafter referred to as the "Textbook").

3.Lurie Yu.Yu. Handbook of Analytical Chemistry.- M.: Chemistry, 1989 (hereinafter referred to as the "Handbook").

4.Dzhabarov D.N. Collection of exercises and tasks in analytical chemistry.- Moscow: Russian doctor, 2007.

Classification of titrimetric analysis methods

Analytical chemistry

Methods of titrimetric analysis can be classified according to the nature of the chemical reaction underlying the determination of substances, and according to the method of titration.

By their nature, the reactions used in titrimetric analysis are of various types - ion combination reactions and oxidation-reduction reactions. In accordance with this, titrimetric determinations can be divided into the following main methods: acid-base titration (neutralization), precipitation and complexation methods, oxidation-reduction method.

Method of acid-base titration (neutralization). This includes definitions based on the interaction of acids and bases, i.e. on the neutralization reaction:

The method of acid-base titration (neutralization) determines the amount of acids (alkalimetry) or bases (acidimetry) in a given solution, the amount of salts of weak acids and weak bases, as well as substances that react with these salts. The use of non-aqueous solvents (alcohols, acetone, etc.) made it possible to expand the range of substances that can be determined by this method.

Methods of precipitation and complex formation. This includes titrimetric determinations based on the precipitation of an ion in the form of a poorly soluble compound or its binding into a poorly dissociated complex.

Methods of oxidation - recovery (redoximetry). These methods are based on oxidation and reduction reactions. They are usually named according to the titrated reagent solution used, for example:

permanganatometry, which uses oxidation reactions with potassium permanganate KMnO4;

iodometry, which uses oxidation reactions with iodine or reduction with I-ions;

bichromatometry, which uses oxidation reactions with potassium dichromate K2Cr2O7;

bromatometry, which uses the oxidation reactions with potassium bromate KBrO3.

The oxidation-reduction methods also include cerimetry (oxidation with Ce4+ ions), vanadatometry (oxidation with VO3 ions), titanometry (reduction with T13+ ions). According to the method of titration, the following methods are distinguished.

Direct titration method. In this case, the ion to be determined is titrated with a reagent solution (or vice versa).

replacement method. This method is used when, for one reason or another, it is difficult to determine the equivalence point, for example, when working with unstable substances, etc.

Back titration method (titration by residue). This method is used when no suitable indicator is available or when the main reaction is not proceeding very rapidly. For example, to determine CaCO3, a sample of a substance is treated with an excess of titrated hydrochloric acid solution:

Whichever method is used to determine, it is always assumed:

1) accurate measurement of the volumes of one or both reacting solutions;

2) the presence of a titrated solution, with which titration is carried out;

3) calculation of the results of the analysis.

In accordance with this, before proceeding to the consideration of individual methods of titrimetric analysis, let us dwell on the measurement of volumes, calculation of concentrations and preparation of titrated solutions, as well as calculations for titrimetric determinations.

Equivalence point

Equivalence point (in titrimetric analysis) - the moment of titration when the number of equivalents of the added titrant is equivalent or equal to the number of equivalents of the analyte in the sample. In some cases, several equivalence points are observed, following one after another, for example, when titrating polybasic acids or when titrating a solution in which several analyte ions are present.

The titration curve plot has one or more inflection points corresponding to equivalence points.

The end point of a titration (similar to the equivalence point, but not the same) is the point at which the indicator changes color in a colorimetric titration.

Methods for determining the equivalence point

Using indicators

These are substances that change their color due to chemical processes. Acid-base indicators, such as phenolphthalein, change color depending on the pH of the solution they are in. Redox indicators change their color following a change in the potential of the system, and are thus used in redox titrations. Before the start of titration, a few drops of the indicator are added to the test solution and the titrant is added dropwise. As soon as the solution after the indicator changes its color, the titration is stopped, this moment is approximately the equivalence point.

Indicator selection rule - when titrating, an indicator is used that changes its color near the equivalence point, i.e. the transition interval of the color of the indicator should, if possible, coincide with the jump in the titration.

Potentiometry

In this case, a device is used to measure the electrode potential of the solution. When the equivalence point is reached, the potential of the working electrode changes dramatically.

With pH meters

A pH meter is essentially also a potentiometer, which uses an electrode whose potential depends on the content of H+ ions in the solution, this is an example of using an ion selective electrode. In this way, the change in pH can be monitored during the entire titration process. When the equivalence point is reached, the pH changes dramatically. This method is more accurate than titration using acid-base indicators, and can be easily automated.

Conductivity

The conductivity of an electrolyte solution depends on the ions present in it. During a titration, the conductivity often changes significantly (For example, in an acid-base titration, the H+ and OH− ions interact to form a neutral H2O molecule, which causes a change in the conductivity of the solution). The overall conductivity of the solution also depends on other ions present (for example, counterins), which make different contributions to it. It, in turn, depends on the mobility of each ion and on the total concentration of ions (ionic strength). In this regard, it is much more difficult to predict the change in conductivity than to measure it.

Color change

During some reactions, a color change occurs even without the addition of an indicator. This is most often observed in redox titrations, when the starting materials and reaction products have different colors in different oxidation states.

precipitation

If an insoluble solid is formed during the reaction, a precipitate is formed at the end of the titration. A classic example of such a reaction is the formation of highly insoluble silver chloride AgCl from Ag+ and Cl− ions. Surprisingly, this does not accurately determine the end of the titration, so the precipitation titration is most often used as a back titration.

Isothermal calorimetric titration

An isothermal titration calorimeter is used, which determines the equivalence point by the amount of heat released or absorbed by the reacting system. This method is important in biochemical titrations, for example, to determine how an enzyme substrate binds to an enzyme.

Thermometric titrimetry

Thermometric titrimetry is an extremely flexible technique. It differs from calorimetric titrimetry in that the heat of reaction, indicated by a fall or rise in temperature, is not used to determine the amount of a substance contained in the test sample. On the contrary, the equivalence point is determined based on the area in which the temperature change occurs. Depending on whether the reaction between the titrant and the analyte is exothermic or endothermic, the temperature during the titration process will rise or fall accordingly. When all of the test substance has reacted with the titrant, changing the area in which the temperature rises or falls makes it possible to determine the equivalence point and the bend in the temperature curve. The exact equivalence point can be determined by taking the second derivative of the temperature curve: a clear peak will indicate the equivalence point.

Spectroscopy

The equivalence point can be determined by measuring the light absorption of the solution during the titration if the spectrum of the product, titrant, or analyte is known. The relative content of the reaction product and the test substance allows you to determine the equivalence point. However, the presence of free titrant (indicating the completion of the reaction) can be detected at very low values.

Amperometry

A method that allows you to determine the equivalence point by the magnitude of the current at a given potential. The magnitude of the current due to the oxidation/reduction reaction of the test substance or product at the working electrode depends on their concentration in the solution. The equivalence point corresponds to a change in the magnitude of the current. This method is most useful when it is necessary to reduce the consumption of titrant, for example, when titrating halides with Ag+ ion.

Direct and back titration.

In the simplest variant of titration, the analyte interacts directly with the titrant. The amount of analyte is calculated from the molar concentration of the titrant, its volume required to reach the equivalence point, and the stoichiometry of the reaction between the analyte and the titrant.

In a back titration, the analyte does not interact with the titrant, but with another reagent present in excess. The excess is then determined by titration. If the initial amount of the reagent is known and its excess is determined, then the difference between them is the amount of the reagent that went into the reaction with the analyte.

Back titration is used, for example, when the equilibrium constant of the direct titration reaction is too small. Other reasons for using back titration include the lack of a suitable indication method or the insufficient reaction rate in direct titration.

substitution titration.

Magnesium complex MgY2- is added to the analyzed solution containing metal ions to be determined. Because it is less stable than the complex of the metal ion to be determined with the complexone, then a substitution reaction takes place and the Mg2+ ion is released.

Then the Mg2+ ion is titrated with complexone III in the presence of eriochrome black T.

Based on the volume of EDTA used for titration, the mass of the metal ion to be determined is calculated. This method of titration is possible only if the complex compounds of the analyzed metals are more stable than the magnesium complex.

___________________________________________________________________________________________________________________________________________________________________________________________

Lecture 7. Titrimetric method of analysis.

1. The essence of the titrimetric method of analysis

2. Classification of titrimetric methods of analysis

3. Calculations in titrimetry. Standard and working solutions

4. Errors of the titrimetric method

5. Construction of titration curves.

The titrimetric method of analysis is based on the fact that substances react with each other in equivalent quantities:

wheren1 andn2 amounts of substance 1 and 2, [ n ]= mole

whereCmolar equivalent concentration;Vsolution volume [V]= l

Then, for two stoichiometrically reacting substances, the relation is true:

Titrimetric analysis is a method for determining the amount of a substance by accurately measuring the volume of solutions of substances that react with each other.

Titer- the amount of g of the substance contained in 1 ml of solution or equivalent to the substance to be determined. For example, if the H2SO4 titer is 0.0049 g/ml, this means that each ml of the solution contains 0.0049 g of sulfuric acid.

A solution whose titer is known is called a titrated solution. Titration- the process of adding to the test solution or an aliquot of an equivalent amount of a titrated solution. In this case, standard solutions are used - solutions with an exact concentration of a substance (Na2CO3, HCl).

The titration reaction must meet the following requirements:

1) The reaction must proceed quantitatively, be strictly stoichiometric

2) The reaction must proceed at a high rate;

3) The reaction must proceed to the end, there must be no competing processes;

4) For a given reaction, there must be a convenient way to fix the end of the reaction (the equivalence point).

For example, acid-base titration:

HCl + NaOH → NaCl + H2O (methyl orange indicator)

Classification of methods of titrimetric analysis.

Titrimetric methods of analysis can be classified according to several criteria. For example, according to the type of the main reaction that occurs during titration:

1) acid-base titration (neutralization): H3O + + OH - ↔ 2H2O

this method determines the amount of acid or alkali in the analyzed solution;

a) acidimetry

b) alkalimetry

2) redox titration (redoximetry):

Ox1 + Red2 ↔ Ox2 + Red1

a) permanganatometry (KMnO4);

b) iodometry (I2);

c) bromatometry (KBrO3);

d) dichromatometry (K2Cr2O7);

e) cerimetry (Ce(SO4)2);

f) vanadometry (NH4VO3);

g) titanometry (TiCl3), etc.

3) precipitation titration: Me + X ↔ MeX↓

a) argentometry Ag+ + Cl - "AgCl $

b) mercurometry

4) complexometric titration Mem+ + nL ↔ m+

a) mercury

b) complexometry (EDTA)

The main task of titrimetric analysis is not only to use a solution of exactly known concentration, but also to correctly determine the equivalence point. There are several ways to fix an equivalence point:

1. According to the color of the ions of the element being determined, for example, permanganate ions MNO4 - have a crimson color

2. With the help of indicators, for example, acid-base indicators are used in the neutralization reaction: litmus, phenolphthalein, methyl orange - organic compounds that change color when moving from an acidic to an alkaline medium.

Indicators- organic dyes that change their color when the acidity of the medium changes. Schematically (omitting intermediate forms), the indicator equilibrium can be represented as an acid-base reaction

HIn + H2O In - + H3O +

The area of ​​color transition of the indicator (position and interval) is affected by all the factors that determine the equilibrium constant (ionic strength, temperature, foreign substances, solvent), as well as the indicator.

3. By substance-witness

Example: Ag+ + Cl - " AgCl $

Ag+ + CrO4" Ag2CrO4$ (bright orange color)

A small amount of salt K2CrO4 is added to the flask where it is required to determine the chlorine ion (witness). Then, the test substance is gradually added from the burette, while chloride ions are the first to react and a white precipitate (AgCl) is formed, i.e. PR AgCl<< ПР Ag2Cr O4.

Thus, an extra drop of silver nitrate will give a bright orange color, since all the chlorine has already reacted.

Titration methods.

1. direct titration, at direct titration the titrant is directly added to the substance to be titrated. This method is applicable only if all the requirements listed above are met.

2. back titration(with excess), used in a slow reaction. If the reaction rate is low, or it is not possible to select an indicator, or side effects are observed, for example, losses of the analyte due to volatility, you can use the technique back titration: add a known excess of titrant T1 to the substance to be determined, bring the reaction to completion, and then find the amount of unreacted titrant by titrating it with another reagent T2 with a concentration of C2. it is obvious that the amount of titrant T1, equal to the difference CT1VT1 = CT2VT2, is spent on the analyte.

3. indirect titration (by substitution), used in the analysis of organic compounds. If the reaction is non-stoichiometric or proceeds slowly, then substituent titration is used, for which a chemical reaction of the analyte with an auxiliary reagent is carried out, and the product obtained in an equivalent amount is titrated with a suitable titrant.

Methods for expressing the concentration of a solution.

Molar concentration - mol / l

1M - 1 liter contains 1 g / mol of a substance

Molar concentration of equivalents (normal solutions) (the solution must contain a given number of equivalent masses in 1 liter).

The chemical equivalent is the amount of a substance equivalent to one g of a hydrogen atom.

Solution titer T

Titer for the working substance: https://pandia.ru/text/79/035/images/image004_113.gif" width="133" height="48 src="> [g/ml]

The titer for the working substance must be converted to the titer for the analyte using the conversion factor: Tonp = Trab F

Example: https://pandia.ru/text/79/035/images/image006_73.gif" width="72" height="46 src=">

a - sample of the analyzed substance

Standard and working solutions

A titrant with a known concentration is called a standard solution. According to the method of preparation, primary and secondary standard solutions are distinguished. A primary standard solution is prepared by dissolving a precise amount of a chemically pure substance of known stoichiometric composition in a specified volume of solvent. A secondary standard solution is prepared as follows: prepare a solution with an approximate concentration and determine its concentration (standardize) against an appropriate primary standard.

Primary reference substances must meet a number of requirements:

1. The composition of the substance must strictly correspond to the chemical formula. Impurity content less than 0.05%

2. The substance must be stable at room temperature, not hygroscopic, not oxidized by atmospheric oxygen, not absorb carbon dioxide, not volatile.

3. The substance must have a sufficiently high molecular weight to reduce weighing errors.

For the preparation of primary standard solutions, you can use fixanal - an ampoule in which a known amount of a standard substance or solution is sealed.

KYRGYZ NATIONAL UNIVERSITY them. J. BALASAGYNA

FACULTY OF CHEMISTRY AND CHEMICAL TECHNOLOGY

UNESCO Chair in Environmental Education and Natural Sciences

ESSAY

by discipline: Analytical chemistry

on the topic:

METHOD OF NEUTRALIZATION IN THE TITRIMMETRIC METHOD OF ANALYSIS

Second year students gr. xr-1-08

Name: Baytanaeva A.

Lecturer: Associate Professor Lee S.P.

Bishkek-2010

Introduction

Analytical chemistry. Methods of determination

Titrimetric method of analysis

Preparation of the titrated solution

Titration. Indicators

Methods for establishing equivalence points. Classification of titrimetric analysis methods

Vessels used for titration

Calculations in Volumetric Analysis

Acid-base titration methods, or neutralization methods

Conclusion

References

Introduction

Analytical chemistry is a fundamental chemical science that occupies a prominent place among other chemical disciplines. At the same time, analytical chemistry is closely related to everyday practice, since without analysis data on the content of the main components and impurities in the raw material or final product, it is impossible to competently conduct the technological process in the metallurgical, chemical, pharmaceutical and many other industries.

Chemical analysis data are required when solving economic and other important issues.

The modern development of analytical chemistry, due to a large extent to the progress of various industries.

Analytical chemistry. Methods of determination

analytical chemistry titrimetric neutralization

Analytical chemistry- it is the science of determining the chemical composition of substances and partly their chemical structure. The methods created by analytical chemistry allow answering questions about what a substance consists of, what components are included in its composition. Analytical methods often make it possible to find out in what form a given component is present in a substance, for example, what is the oxidation state of an element.

Methods of determination can be classified based on the property of the substance, which is the basis of the definition. If the sediment mass is measured, the method is called gravimetric, if the color intensity of the solution is determined, it is photometric, and if the EMF value is called potentiometric.

Methods of determination are often divided into chemical(classic), physical and chemical(instrumental) and physical.

Chemical in analytical chemistry, it is commonly referred to as gravimetric and titrimetric methods. These methods are the oldest, but widely used to date, playing an important role in the practice of chemical analysis.

Gravimetric (weight) analysis is the measurement of the mass of the analyte or its constituents isolated in a chemically pure state or in the form of the corresponding compounds.

Titrimetric (volume) analysis is the measurement of the volume of a reagent of precisely known concentration consumed in a reaction.

Physico-chemical and physical analysis methods are usually divided into the following groups:

1) electrochemical

2) spectral (optical)

) chromatographic

) radiometric

) mass spectrometry

Titrimetric method of analysis

A titrimetric method of analysis is a method of quantitative analysis based on measuring the amount of a reagent required to complete a reaction with a given amount of analyte.

The method consists in the fact that a reagent solution of a known concentration is gradually added to the solution of the analyte. The addition of the reagent is continued until its amount becomes equivalent to the amount of the analyte reacting with it.

Quantitative determinations using the volumetric method are very fast. The time required to complete the determination by the titrimetric method is measured in minutes. This makes it possible to carry out several serial and parallel determinations without much effort.

The founder of titrimetric analysis is the French scientist JL Gay-Lussac.

A chemical element, a simple or complex substance, the content of which is determined in a given sample of the analyzed product, is called defined substance.

The substances to be determined also include atoms, ions, bound free radicals and functional groups.

A solid, liquid or gaseous substance that reacts with a certain substance is called reagent.

Titration - this is the addition of one solution to another with continuous mixing. The concentration of one solution is known exactly.

titrant(standard or titrated solution) is a solution with a precisely known concentration.

Normality solution N - the amount of gram-equivalent of the substance contained in 1 liter of solution.

N 1 V 1 \u003d N 2 V 2

Titer(T) - the exact concentration of the standard solution (titrant).

Expressed as the number of grams of solute contained in 1 ml of solution, g / ml.

In analytical chemistry, titer is one way of expressing the concentration of a solution.

N - normality of the solution, g-eq / l

E is the equivalent of the solute

T- titer, g/cm 3 (ml).

Chemical elements or their compounds enter into chemical reactions with each other in strictly defined weight quantities corresponding to their chemical equivalents (gram equivalents).

In other words, The gram equivalent of one substance reacts with one gram equivalent of another substance.

Preparation of a titrated solution according to the exact weight of the starting substance

The first way to prepare a solution of exactly known concentration, i.e. characterized by a certain titer, is the dissolution of an exact sample of the initial chemically pure substance in water or other solvent and the dilution of the resulting solution to the required volume. Knowing the mass of a chemically pure compound dissolved in water and the volume of the resulting solution, it is easy to calculate the titer (T) of the prepared reagent, in g / ml :

This method prepares titrated solutions of substances that can be easily obtained in pure form and whose composition corresponds to a precisely defined formula and does not change during storage. Weighing of the substance is carried out in a bottle. In this way, it is impossible to prepare titrated solutions of substances that are highly hygroscopic, easily lose water of crystallization, are exposed to carbon dioxide in the air, etc.

Preparation of titrated solutions according to "Fixanal"

Very often, in practice, for the preparation of titrated solutions, precisely weighed quantities of solid chemically pure compounds or accurately measured volumes of their solutions of a certain normality prepared at chemical plants or in special laboratories are used.

To prepare the required titrated solution, the ampoule is broken over a special funnel equipped with a punching device, its contents are quantitatively transferred into a volumetric flask and the volume is adjusted to the mark with water.

Usually ampoules contain 0.1 g-eq of the substance, i.e. as much as is required to prepare 1 liter of 0.1 n. solution.

Titration

Titration is carried out as follows. The burette is filled with working solution to zero division so that there are no air bubbles at its lower end. The test solution is measured with a pipette and transferred to a conical flask. A few drops of the indicator solution are also poured here, except in cases where one of the solutions taken is an indicator. To the solution in the flask, gradually pour the solution from the buret until the color of the solution in the flask changes. First, the solution is poured from the buret in a thin stream, continuously stirring the solution to be titrated by rotating the flask. As the titration progresses, the working solution is added more and more slowly and by the end of the titration it is added drop by drop.

During the titration, it is necessary to control the clamp of the burette with the left hand, and simultaneously rotate the flask with the titrated liquid with the right hand, thus mixing the titrated solution.

The results of the titration will be correct if, at the end of the titration, the color of the titrated solution changes sharply from one drop of the working solution. To make the color transition of the solution more visible, the flask with the solution to be titrated is placed on a white stand during titration.

After each titration, the volume of the spent working solution is counted on the burette scale and the result of the reading is recorded in the laboratory journal. Each solution is titrated at least three times, the results of the titration should not differ from each other by more than 0.1 ml. The concentration of the solution is calculated from the average value.

Indicators

Indicators are called substances, with the help of which the moment of equivalence between titrated solutions is established. As indicators, substances are most often used that are capable of giving an easily noticeable color reaction with one of the reacting substances. For example, starch, interacting with a solution of iodine, turns intense blue. Therefore, starch is an indicator for free iodine. The same indicator under different conditions often acquires a different color. For example, phenolphthalein is colorless in an acidic and neutral environment, and takes on a red-violet color in an alkaline environment.

Sometimes the indicator is directly one of the reacting substances. For example, a solution of the oxidizing agent KMnO 4 in an acidic medium becomes colorless when a reducing agent is gradually added to it. As soon as an excess drop of KMnO 4 appears in the solution, the solution will turn a pale pink color.

Methods for establishing equivalence points

Establishing the end point of the titration or equivalence point is the most important operation of the titrimetric method of analysis, since the accuracy of the analysis results depends on the accuracy of determining the equivalence point. Usually, the end of the titration is determined by the change in color of the titrated solution or by the indicator introduced at the beginning or during the titration. Non-indicator methods will also be used, based on the use of special instruments that make it possible to judge the changes that occur in the titrated solution during the titration process. Such methods are called physicochemical or instrumental methods for determining equivalence points. They are based on the measurement of electrical conductivity, potential values, optical density and other physicochemical parameters of titrated solutions, which change dramatically at the equivalence point.

The equivalence point can be determined by the following methods:

) visually - by changing the color of the solution, if the substance or reagent being determined is colored; since at the equivalence point the concentration of the analyte decreases to a minimum, and the concentration of the reagent begins to increase.

) visually - by the appearance of turbidity or by a change in the color of the solution caused by the formation of reaction products, or an indicator if they are colorless.

) by physicochemical methods with subsequent analysis of titration curves that reflect the changes in the physicochemical parameters of the titrated solutions occurring during the titration process, regardless of color. The equivalence point is set at the intersection of the curves or at the jump of the titration curve.

Titration classification

)Neutralization Method based on the use of neutralization reactions of acids, bases, salts of weak acids or weak bases that are strongly hydrolyzed in aqueous solutions, various inorganic and organic compounds that exhibit acidic or basic properties in non-aqueous solutions, etc.

)Redox method is based on the use of oxidation-reduction reactions of elements that are capable of moving from lower to higher oxidation states, and vice versa, as well as ions and molecules that react with oxidizing or reducing agents without being directly oxidized or reduced.

)Deposition method based on the use of precipitation reactions.

)Complex formation method is based on the use of complex formation reactions, of which the reactions of metal ions with the so-called complexones are most widely used.

Vessels used for titration

Volumetric flasks are used to measure the volume of solutions, preparation of solutions of a certain concentration. The volume of liquid contained in the flask is expressed in milliliters. On the flask indicate its capacity and temperature (20 0 C) at which this capacity is measured.

Volumetric flasks come in various capacities: from 25 to 2000 ml.

Pipettes are used to measure small volumes of solutions and transfer a certain volume of solution from one vessel to another. The volume of liquid held by a pipette is expressed in milliliters. On the expanded part of the pipette indicate its capacity and the temperature (usually 20 0 C) at which this capacity is measured.

Pipettes come in different capacities: from 1 to 100 ml.

Measuring pipettes of small capacity have no extension and are graduated from 0.1-1 ml.

Burettes are narrow, graduated in length cylindrical glass tubes. One end of the burette is narrowed and equipped with a glass stopcock or a rubber tube connected to a capillary through which the solution is poured out of the burette. The rubber tube is clamped on the outside with a metal clamp. When pressing on the clamp with the forefinger and thumb, liquid pours out of the burette.

A well-washed burette is rinsed 2-3 times with distilled water, and then with the solution with which it will be filled. No air bubbles should remain in the faucet capillary. When counting divisions, the observer's eye should be at the level of the meniscus. The volume of light liquids is counted along the lower meniscus, dark ones, for example, KMnO 4, I 2, - along the upper one.

conical flask

Measuring cylinders

Calculation in volumetric analysis

Gram equivalent

A gram equivalent is the number of grams of a substance that is equivalent (chemically equivalent) to a gram atom or a gram ion of hydrogen in a given reaction. From this definition it follows that the gram equivalent of the same substance in different reactions can be different. For example, Na 2 CO 3 with acid can react in two ways:

Na 2 CO 3 + HCI \u003d NaHCO 3 + NaCI (1) 2 CO 3 + 2HCI \u003d NaCI + H 2 CO 3 (2)

In reaction (1), one gram-molecule of Na 2 CO 3 reacts with one gram-molecule of HCI, which corresponds to one gram-atom of hydrogen. In this reaction, the gram equivalent of Na 2 CO 3 is equal to the mole M (Na 2 CO 3), which is expressed by the equality E (Na 2 CO 3) \u003d M (Na 2 CO 3). In reaction (2), one gram-molecule of Na 2 CO 3 reacts with two moles of HCI. Consequently,

E (Na 2 CO 3) \u003d \u003d 53 g.

Normal and molar solutions

Normality solution N - the amount of gram-equivalent of the substance contained in 1 liter of solution.

Molarity solution indicates how many moles of a solute are contained in 1 liter of solution.

Knowing the concentration of the solution, expressed in grams per certain volume, it is possible to calculate its normality and molarity:

Example: 250 ml of calcium hydroxide solution contains 3.705 g of Ca(OH) 2 . Calculate the normality and molarity of the solution.

Solution: First, we calculate how many grams of Ca (OH) 2 are contained in 1 liter of solution:

3.705 g Ca (OH) 2 - 250 ml X \u003d 14.82 g / l

X g Ca (OH) 2 - 1000 ml

Find the gram molecule and the gram equivalent:

M ( Ca (OH) 2) \u003d 74.10 g. Oe ( Ca (OH) 2) \u003d 37.05 g.

Normality of the solution:

05g/l - 1n. X=0.4n.

14.82g/l - X n.

Molarity of solution:

10g/l - 1mol X=0.2M

82g/l - X mol

Knowing the normality or molarity of the solution, you can calculate its titer.

Example: Calculate the titer of 0.1n. H 2 SO 4 solution over NaOH.

Solution:

TH 2 SO 4 / NaOH = g/ml

In volumetric analysis, several calculation methods are used.

) Calculation of the normality of the analyzed solution from the normality of the working solution. When two NaOH substances interact, the gram equivalent of one substance reacts with the gram equivalent of the other. Solutions of different substances of the same normality contain in equal volumes the same number of gram equivalents of the solute. Therefore, equal volumes of such solutions contain equivalent amounts of the substance. Therefore, for example, to neutralize 10 ml of 1N. HCI is required to spend exactly 10 ml of 1N. NaOH solution.

Solutions of the same normality react in equal volumes.

Knowing the normality of one of the two reacting solutions and their volumes spent on titrating each other, it is easy to determine the unknown normality of the second solution. Let us denote the normality of the first solution by N 2 and its volume by V 2 . Then, on the basis of what has been said, we can make an equality:

V 1 N 1 \u003d V 2 N 2

Example. Determine the normality of a hydrochloric acid solution if it is known that 28.00 ml of 0.1100 N was required to neutralize 30.00 ml of it. NaOH solution.

Solution .

HCI V HCI = N NaOH V NaOH

N HCI == .

) Calculation of the amount of the analyte by the titer of the working solution, expressed in grams of the analyte. The titer of the working solution in grams of the analyte is equal to the number of grams of the analyte, which is equivalent to the amount of the substance contained in 1 ml of the working solution. Knowing the titer of the working solution for the analyte T= and the volume of the working solution used for titration, it is possible to calculate the number of grams (mass) of the analyte.

Example. Calculate the percentage of Na 2 CO 3 in the sample, if for titration of a sample of 0, 100 gr. spent 15.00 ml of 0.1N. HCI.

Solution.

M (Na 2 CO 3) \u003d 106.00 gr. E (Na 2 CO 3) \u003d 53.00 gr.

T (HCI / Na 2 CO 3) \u003d =g / ml (Na 2 CO 3) \u003d T (HCI / Na 2 CO 3) V HCI \u003d 0.0053 * 15.00 \u003d 0.0795 g.

The percentage of Na 2 CO 3 is

3) Calculation of the number of milligram equivalents of the test substance. Multiplying the normality of the working solution by its volume used for titration of the test substance, we obtain the number of milligram equivalents of the dissolved substance in the titrated part of the test substance. The mass of the substance to be determined is equal to:

(gr.)

Statistical processing of analysis results

When analyzing substances (samples), several parallel determinations are usually carried out. In this case, the individual results of the determinations should be close in magnitude and correspond to the true content of the components (elements) in the test substance (sample).

There are two factors by which the analyst judges the results of the analysis

1) Reproducibility of the obtained results.

2) Compliance with their composition of the substance (sample)

The reproducibility of the results of the analysis depends on the random errors of the analysis. The larger the random error, the greater the spread of values ​​when the analysis is repeated. Random error can have the dimension of the measured values ​​(mg, mg/l) or can be expressed as a percentage. Therefore, reproducibility determines the probability that the results of subsequent measurements will be in some given interval, in the center of which is the average value of all determinations made by this method.

Unlike random errors, systematic errors always affect all measurements to the same extent.

The goal of all analytical determinations and studies is to find results that are closest to the true composition or to the true content of the components of the sample.

To assess the accuracy or reliability of the results of analytical determinations, statistical processing of the results is used and the following quantities are calculated:

1) Arithmetic mean

) Dispersion

mean square error

S=

3) The mean square error of the arithmetic mean

a=0.95; R=2

4)
Confidence interval

Acid-base titration methods, or neutralization methods

Neutralization methods are based on the use of neutralization reactions. The basic equation of the neutralization process in aqueous solutions is the interaction of hydronium (or hydrogen) ions with hydroxyl ions, accompanied by the formation of weakly dissociated water molecules:

H 3 O + +OH - → 2H 2 O or

H + +OH - →H 2 O

Neutralization methods make it possible to quantify acids (using titrated alkali solutions), bases (using titrated acid solutions) and other substances that react in stoichiometric ratios with acids and bases in aqueous solutions.

The determination technique consists in the fact that a titrated acid (or base) solution is gradually poured from a burette to a certain amount of a base (or acid) solution until the equivalence point is reached. The amount of base (or acid) contained in the test solution is calculated by the volume of the titrated acid (or base) solution used to neutralize a certain volume of the solution of the analyzed sample or a sample of the test product.

The acidity or alkalinity of a solution is determined using indicators. To develop the color, it is enough to add only 1-2 drops of a 0.1% indicator solution to the test solution. The colors of various indicators in solutions of acids and alkalis are given in the table.

Table 1. Coloring of indicators in solutions of alkalis and acids.

Let's consider a specific example. Let there be a NaOH solution of unknown concentration. 10.0 ml of this solution was placed in a flask and 1 drop of a weak solution of phenolphthalein was added. The solution turned crimson (Fig. 1a).

Titration of a strong acid with a strong base

A) Preparation of 0.1 n. HCI solution

To prepare 0.1n. HCI solution take an acid of lower concentration, about 20%. Its density is determined with a hydrometer (it is equal to 1.140), for this acid is poured into a high glass cylinder, the diameter of which exceeds the diameter of the hydrometer ball. Carefully lower the hydrometer into the liquid and make sure that it floats freely without touching the walls of the cylinder. Counting is carried out on a hydrometer scale. The division of the scale, coinciding with the level of the liquid, shows the density of the solution. Then they find out the percentage concentration (according to the reference book) and calculate how much of this acid should be taken to get 500 ml of 0.1N. HCI solution.

C(HCI)=28.18%

Calculation of a sample for the volume of a volumetric flask (250 ml.)

m= = 36.5*0.1*0.25=0.92 HCI.

gr. initial acid contains --- 28.18 gr. h.h. HCI.

X gr. --- 0.92 gr. HCI.

X= 3.2 gr. h.h. HCI.

In order not to weigh hydrochloric acid, but to measure it with a beaker, we calculate the volume of 28.18% acid required to prepare the solution. To do this, we divide the mass of 28.18% acid by the density:

V= = =2.8 ml. HCI

Then 2.8 ml of acid is measured, transferred to a 500 ml volumetric flask and the volume of the solution is adjusted to the mark, and, having closed the flask with a stopper, mix. Having received approximately 0.1 n. HCI solution, set the titer and its normal concentration according to sodium tetraborate solution.

B) Preparation of 0.1n. sodium tetraborate solution (borax)

To determine the titer of the HCI solution, sodium tetraborate crystal hydrate is taken. This salt satisfies almost all the requirements for starting materials, but is relatively slightly soluble in cold water. The recrystallized product is used to set the HCI or sulfuric acid titer.

When sodium tetraborate is dissolved in water, the hydrolysis reaction proceeds:

B 4 O 7 2- + 5H 2 O D 2H 2 BO 3 - + 2H 3 BO 3

H 2 BO 3 ions, in turn, undergo hydrolysis:

H 2 BO 3 - + H 2 OD OH - + H 3 BO 3

The ions are titrated with acid, and the hydrolysis proceeds to completion. In total, the titration reaction can be expressed by the equation:

B 4 O 7 2- + 2H + + 5 H 2 OD 4H 3 BO 3

E (Na 2 B 4 O 7 10H 2 O) \u003d 190.6

1000ml (H 2 O) --- 190.6 gr. (Na 2 B 4 O 7 10H 2 O) X \u003d 95, 3g. (Na 2 B 4 O 7 10H 2 O)

500 ml (H 2 O) --- X gr. (Na 2 B 4 O 7 10H 2 O)

95, 3 gr. --- 1n. X \u003d 9, 5g. (Na 2 B 4 O 7 10 H 2 O)

X gr. --- 0.1n.

To dissolve sodium tetraborate, pour about ½ of the volume of the flask of distilled water into the flask, heat it in a water bath, stirring the contents of the flask with a rotational movement until the salt is completely dissolved. After dissolution, the flask with sodium tetraborate is cooled to room temperature and brought to the mark with distilled water, first a little, and then drop by drop using a capillary pipette. Close the flask with a stopper and mix thoroughly.

When calculating the titer and normal concentration of a sodium tetraborate solution, the following formulas are used:

T (Na 2 B 4 O 7 10H 2 O) \u003d (g/ml)

N (Na 2 B 4 O 7 10H 2 O) \u003d (g-eq/l)

C) Determination of the titer of the HCI solution by sodium tetraborate by pipetting.

Take a clean 10 ml pipette, rinse with a solution of sodium tetraborate (from a volumetric flask). Fill the pipette with the solution up to the mark and transfer it to another flask for titration, add 2-3 drops of methyl orange indicator. Before titration, the burette is washed twice with a small amount of HCl and then filled to bring the meniscus to zero. After checking that there are no air bubbles in the capillary tube (“nose”), begin to titrate until a pale red color appears. The titration is repeated 3 times and the average value is calculated.

titration 15.0 ml HCI

2 titration 14.8 ml HCI V CP = 14.76 ml

3 titration 14.5 ml HCI

After titration, the normal concentration of the HCI solution is calculated. Acid normality is calculated from the average of three determinations. The calculation is carried out according to the formula:

N SALT V SALT= N CISL V CISL

N HCI=

N HCI == 0.06775 (g-eq/l)

D) Preparation of a titrated solution of sodium hydroxide

Sodium hydroxide reagents often contain impurities of sodium carbonate, and therefore, for accurate work, the alkali solution must be chemically pure.

When determining the titer of a solution of sodium hydroxide by hydrochloric acid, a 100 ml volumetric flask is taken. An unknown amount of NaOH is added with distilled water up to the mark, stoppered and mixed. Then, with a 10 ml pipette, an alkali solution is taken from a volumetric flask and transferred to a titration flask, 2-3 drops of Phenolphthalein are added and titrated with hydrochloric acid until discoloration. The titration is repeated 3 times and the average value is calculated.

E titration - 1.8 ml

2nd titration - 1.7 ml V CP = 1.7 ml

3rd titration - 1.6 ml

T HCI / NaOH = = = 0.00271 g/ml

m NaOH =

1) m NaOH = \u003d 0.04878 gr.

) m NaOH \u003d 0.00271 * 1.7 * 10 \u003d 0.04606 gr.

) m NaOH \u003d 0.00271 * 1.6 * 10 \u003d 0.04336 gr.

Statistical processing of analysis results

		(Xi -) 10 - 3 (Xi -) 10 - 6 Terms
			0,000001

) S 2 \u003d \u003d \u003d 4 * 10 -6

3) S = ==2*10 -3

) = ==1, 1*10 -3

6) åa=ta, R S= 4.303*1, 1*10 -3 =4*10 -3

7) a= ±åa=(0.04606±4*10 - 3)

Determination of sodium hydroxide and sodium carbonate in their joint presence

Sodium and potassium hydroxides from the air absorb CO 2 and turn into carbonates:

NaOH + CO 2 Na 2 CO 3 + H 2 O

Therefore, both the solid and the solutions of these reagents often contain an admixture of carbonates. In laboratory practice, it is often necessary to determine sodium carbonate in the presence of sodium hydroxide. For this, 2 methods can be used: the first is by fixing (on the Na 2 CO 3 titration curve) two equivalence points (Warder's method); the second is by titrating the NaOH solution, first precipitating the carbonate ion CO 3 2- with the barium ion Ba 2+ (Winkler method).

According to the first method, titration of a mixture of sodium carbonate and sodium hydroxide with hydrochloric acid is expressed by the following equations:

NaOH + Na 2 CO 3 + 2HCI g 2NaCI + NaHCO 3 + H 2 O 3 + HCIg NaCI + H 2 O + CO 2 h

The first phase ends at pH8.3 in the region of the color transition of the phenolphthalein indicator, and the second at pH3.85 in the range of the methyl orange color change. Therefore, at the first equivalence point, all NaOH and half of Na 2 CO 3 are titrated with phenolphthalein, and at the second, the remaining half of sodium carbonate is titrated with methyl orange.

Taking a sample of NaOH

Calculation of a sample for the volume of a volumetric flask (250 ml):

Mr(NaOH)=40 m= ==1 gr.NaOH

E (NaOH) \u003d 40 g.

Take hinges Na2CO3

Mr (Na 2 CO 3) \u003d 106 m \u003d =53*0, 1*0, 25= 1,3 gr . Na 2 CO 3

E (Na 2 CO 3) \u003d 53 g

Progress

A portion of NaOH and Na 2 CO 3 is placed in a 250 ml volumetric flask, dissolved with distilled water and the volume is adjusted to the mark.

Then take 10 ml of this solution with a pipette, transfer to another flask and add 4-5 drops of 0.1% phenolphthalein solution, and titrate with HCl solution until colorless.

The amount of HCI consumed is measured by burette and recorded. Then, 2-3 drops of methyl orange are added to the same flask with a solution, a yellow color of the analyzed solution is obtained and titrated from the same HCI burette until an orange color appears. Again make a count on the buret. The titration is repeated 3 times and, as always, the average value is taken.

a) titration with phenolphthalein:

1) 12.2 ml HCI

) 12.1 ml HCI Vav = 12.06 ml HCI

2. N NaOH = NaOH = =0.048 (g-eq/l)

We calculate the number of grams of sodium hydroxide in 250 ml of solution:

m = =0.6775(g)

T the concentration of the solution and the amount of sodium carbonate are also calculated:

N (Na 2 CO 3) \u003d \u003d 0.06715 (g-eq / l) \u003d =0.8976 (g)

D To improve the accuracy of the analysis, it is recommended: a) titration with phenolphthalein should be carried out carefully, especially towards the end, in order to reduce the possibility of formation of carbonic acid; b) reduce the absorption of CO 2 from the air by the analyzed solution, for which you should not allow the solution to stand in an open flask before titration, carefully mix it during the titration.

Test

Titration with phenolphthalein:

1) 4.4 ml HCI

2) 4.4 ml HCI

3) 4.6 ml HCI

Titration with methyl orange:

1) 6.3 ml HCI

2) 6.4 ml HCI

3) 6.3 ml HCI

1) Therefore, 4.6 ml HCI was used for titration of NaOH and half of Na 2 CO 3 , and 6.6 ml of HCI was used for all NaOH and Na 2 CO 3 ;

half Na 2 CO 3 - (6.3-4.4) \u003d 1.9 ml

for the entire amount of Na 2 CO 3 - (1.9 * 2) \u003d 3.8 ml

2) 4.8 ml of HCI was used for titration of NaOH and half of Na 2 CO 3 , and 6.7 ml of HCI was used for all NaOH and Na 2 CO 3 .

half Na 2 CO 3 - (6.4-4.4) \u003d 2 ml

for the entire amount of Na 2 CO 3 - (2 * 2) \u003d 4 ml

for titration of NaOH - (6.4-4) = 2.4 ml

) 5 ml HCI was used for titration of NaOH and half of Na 2 CO 3 , and 6.8 ml of HCI for all NaOH and Na 2 CO 3 .

half Na 2 CO 3 - (6.3-4.6) = 1.7 ml

for the entire amount of Na 2 CO 3 - (2 * 1.7) \u003d 3.4 ml

for titration of NaOH - (6.3-3.4) = 2.9 ml

T HCl / NaOH = = g/ml

m NaOH =

) m NaOH \u003d 0.0027 * 2. 5 * 10 \u003d 0.0675 g.

) m NaOH \u003d 0.0027 * 2.4 * 10 \u003d 0.0648g.

) m NaOH \u003d 0.0027 * 2.9 * 10 \u003d 0.0783 g.
=3

References

1) Vasiliev V.P. Analytical Chemistry, Part I Moscow 1989

2) Zolotov Yu.A. Analytical Chemistry: Problems and Achievements Moscow 1992

) Kreshkov A.P. Fundamentals of Analytical Chemistry, Part II

) Loginov, Shapiro S.A. Analytical Chemistry Moscow1971

In titrimetric analysis, the quantitative determination of a substance is carried out on the basis of the volume of a solution of a known concentration spent on the reaction with a certain substance.

The process of determining the content of a substance or the exact concentration of a solution by volumetric analysis is called titration. This most important operation of titrimetric analysis consists in the fact that another solution of precisely known concentration is slowly added to the test solution in an amount equivalent to the amount of the compound being determined.

The volumes of solutions that quantitatively react with each other are inversely proportional to the normal concentrations of these solutions:

V 1 = N 2 or V 1 x N 1 = N 2 x V 2 V 1 x N 1 = V 2 x N 2

Where V is the volume of the reacting solution, l; N – concentration, n.

This provision underlies titrimetric analysis. In order to determine the concentration of one of the solutions, one must know exactly the volumes of the reacting solutions, the exact concentration of the other solution, and the moment when the two substances react in equivalent quantities. The conditions for titrimetric determination are:

a) accurate measurement of volumes of reactants;

b) preparation of solutions of precisely known concentration, with the help of which titration is carried out, the so-called working solutions (titranes)(often such solutions of known concentration are called standard (titrated);

c) determination of the end of the reaction.

Titrimetric determination takes much less time than gravimetric determination. Instead of many lengthy operations of gravimetric analysis (precipitation, filtration, weighing, etc.), only one operation is carried out in titrimetric determination - titration.

The accuracy of titrimetric determinations is somewhat less than the accuracy of gravimetric analysis, but the difference is small, therefore, where possible, they try to carry out the determination by a faster method.

In order for a particular reaction to serve as a basis for titration, it must satisfy a number of requirements.

1. The reaction must pass quantitatively according to a certain equation without side reactions. You need to be sure. That the added reagent is consumed exclusively for the reaction with the substance being determined.

2. The end of the reaction should be accurately recorded so that the amount of reagent is

equivalent to the amount of the analyte. The equivalence of the reactants is the basis for the calculation of the results of the analysis.

3. The reaction must proceed at a sufficient rate and be practically irreversible. It is almost impossible to accurately fix the equivalence point for slow reactions.

TITRATION METHODS

According to the method of performing titration, direct, reverse or indirect titration (substitution method) is distinguished.

In direct titration, the titrant is added directly to the analyte solution. For analysis by this method, one working solution is sufficient. For example, to determine an acid, a working solution of an alkali is needed, to determine an oxidizing agent, a solution of a reducing agent is required.

In a back titration, a known volume of the working solution, taken in excess, is added to the solution of the analyte. After that, the residue of the first working solution is titrated with another working solution and the amount of the reagent that has reacted with the analyte is calculated. For example, to determine chloride ions, a known volume of AqNO 3 solution, taken in excess, is added to the analyzed chloride solution. There is a reaction

Aq + +Cl = AqCl↓.

The excess of AqNO 3 solution is determined using another working solution - ammonium thiocyanate NH 4 SCN:

Aq + + SCN - = AqSCN↓.

In indirect titration, an excess of a reagent is added to the analyzed solution, which reacts with the substance to be determined. Then one of the reaction products is determined by titration. For example, to determine hydrocyanic acid, a solution of AqNO 3 is added in excess. There is a reaction

HCN + AqNO 3 = AqCN↓ + HNO 3

Then nitric acid is easily determined using a working alkali solution of NaOH:

HNO 3 + NaOH = NaNO 3 + H 2 O

In this case, the weak hydrocyanic acid is replaced in equivalent quantities by the strong one.

3. CLASSIFICATION OF TITRIMETRIC METHODS

ANALYSIS

Titrimetric analysis uses reactions of various types (acid-base interaction, complex formation, etc.) that meet the requirements that apply to titrimetric reactions. Separate titrimetric methods are named after the type of the main reaction that occurs during titration or by the name of the titrant (for example, in argentometric methods, the titrant is an AqNO 3 solution, in permanganometric methods, a KMnO 4 solution, etc.). According to the method of fixing the equivalence point, titration methods with color indicators, methods of potentiometric titration, conductometric, photometric, etc. When classifying according to the type of the main reaction occurring during titration, the following methods of titrimetric analysis are usually distinguished:

1. acid-base titration methods based on the reactions associated with the proton transfer process:

H + + OH - \u003d H 2 O, CH 3 COOH + OH - \u003d CH 3 COO - + H 2 O,

CO 3 2- + H + \u003d HCO - 3;

2. methods of complexation using the reactions of formation of coordination compounds (for example, complexometry):

Mg 2+ + H 2 V 2- \u003d MgV 2_ + 2H +

Where V 2 \u003d CH 2 - N /

׀ / CH 2 – COO-

3. Precipitation methods based on the formation of sparingly soluble

connections:

Aq + + Cl - + AqCl↓ (argentometry),

Hg 2 2+ + 2Cl - \u003d Hg 2 Cl 2 ↓ (mercury);

4.methods of redox titration. based

on redox reactions (oxydimetry):

MnO 4 - + 5Fe 2+ + 8H + = Mn 2+ + 5Fe 3+ + 4H 2 O (permanganatometry);

2S 2 O 3 2- + l 2 \u003d S 4 O 6 2- + 2l - (iodine);

5NO - 2 + 2MnO 4 - + 6H + + 5NO - 3 + 2Mn 2+ + 3H 2 O (nitritometry);

3SbCl 4 - + Br - 3 + 6H + + 6Cl - = 3SbCl 6 - + Br _ + 3H 2 O (bromatometry).

In titrimetry, a wide variety of reactions are used. Depending on which reaction underlies the titration, the following methods of titrimetric analysis are distinguished.

Acid-base methods, based on the neutralization reaction:

H + + OH - → H 2 O

This method determines the amount of acids, bases, and some salts.

Oxidation - reduction methods(oxydimetry). These methods are based on oxidation-reduction reactions. Using a solution of an oxidizing agent, the amount of a substance that is a reducing agent is determined and vice versa.

Precipitation and complex formation methods are based on the precipitation of ions in the form of sparingly soluble compounds and on the binding of ions into a poorly dissociated complex.

There are the following titration methods:

straight, when during titration a reaction occurs between the analyte and the titrant;

the opposite, to when a deliberately excessive, but accurately measured volume of a solution of a known concentration is added to the solution to be determined, and the excess of the reagent is titrated with a titrant;

substituent titration when the product of the reaction of the analyte with any reagent is titrated with a titrant.

TITRANTS

titrant a solution is called, with the help of which a titrimetric determination is made, i.e. solution to be titrated. To carry out the determination using a titrant, you need to know its exact concentration. There are two methods for preparing titrated solutions, i.e. solutions of known concentration.

1. An accurate sample taken on an analytical balance is dissolved in a volumetric flask, i.e. a solution is prepared in which the amount of the solute and the volume of the solution are known. In this case, the solutions are called solutions with prepared titers.

2. The solution is prepared to approximately the desired concentration, and the exact concentration is determined by titration, having another solution with a prepared titer. Titrated solutions, the exact concentration of which is found as a result of titration, are called fixed titer solutions.

Titrants are usually prepared at approximately the desired concentration, and their exact concentration is determined. It must be remembered that the titer of solutions changes over time and must be checked at regular intervals (from 1 to 3 weeks, depending on the substance from which the solution is prepared). Therefore, if the titrant is prepared according to a precisely taken sample, then its titer corresponds to that prepared only for a limited time.

One of the rules of titrimetric analysis is the following: the titres of the titrants should be set under the same conditions under which the analysis will be performed.

To determine the exact concentration of the titrant (“titer setting” or standardization) use the so-called starting or setting substance.

The accuracy of determining the titer titer, and, consequently, the accuracy of all subsequent analyzes, depends on the properties of the adjusting substance. The installation substance must meet the following requirements.

Correspondence of the composition of a substance with its chemical formula.

Chemical purity - the total amount of impurities should not exceed 0.1% - Stability in air, i.e. carbon dioxide.

Stable in solution (does not oxidize or decompose).

Perhaps a large equivalent mass - this reduces the relative error in the determination.

Good solubility in water.

The ability to react with a solution whose titer is set according to a strictly defined equation and at high speed.

To set the titer of the titrant from the adjusting agent prepare an exact solution according to a precisely taken sample. The solution is prepared in a volumetric flask. The volumetric flask should be washed with chromium mixture until it "runs down", rinsed many times with tap water and then 3-4 times with distilled water. The funnel must be clean, dry and free to enter the neck of the flask.

A portion of the adjusting substance is weighed on an analytical balance in a bottle. You can weigh out exactly the calculated amount, or you can take the amount close to the calculated, but accurately weighed. In the first case, the solution will be exactly the specified concentration, and in the second, the exact concentration is calculated.

The sample taken is carefully transferred through the funnel into a volumetric flask. The remains of the weighing bottle are thoroughly washed into the funnel with distilled water from the wash bottle. Then they wash the inner walls of the funnel and, slightly raising it, the outer part of the tube. It is necessary to ensure that the total amount of water used to wash the weighing bottle and funnel does not take more than half of the flask. Stir the contents of the flask with a gentle twisting motion until the sample is completely dissolved. Then, the contents of the flask are brought to the mark with distilled water from the wash bottle. To do this, pour water about 1 cm below the mark. Place the flask so that the mark is at eye level and carefully, drop by drop, add water until the lower part of the meniscus touches the mark on the neck of the flask (Fig. 1). Close the flask carefully with a stopper and, inverting the flask, mix the solution 12-15 times. Solutions for setting the titer should be freshly prepared.

Often used to prepare titrated solutions. fixed channels, which are sealed glass ampoules with accurate weighed reagents. Each ampoule has an inscription showing what substance and in what quantity is in the ampoule.

A funnel is inserted into the volumetric flask, also thoroughly washed and rinsed with distilled water. If the ampoule contains not a solution, but a dry substance, then the funnel must be dry. Then a special glass head is inserted into the funnel (usually attached to the box with fixes), also rinsed with distilled water. The ampoule is wiped with ethyl alcohol to remove the inscription and washed with distilled water. Then it is inserted into the funnel so that it touches the striker with its thin, inwardly curved bottom, lifts it up and lightly hits the end of the striker. In this case, the contents of the ampoule enter the flask through the funnel (Fig. 2). On the side or top of the ampoule there is a recess in which a hole is punched with a glass rod with a pointed end. Through this hole, the inner walls of the ampoule are washed with distilled water from the washer. You need to rinse many times in small portions. After that, the outer walls of the ampoule are rinsed and the ampoule is discarded. Rinse the funnel and the head, then raise the funnel and wash the outer

Part of the funnel tube. Wash the top of the neck of the volumetric flask. When performing all these washing operations, make sure that the amount of water in the volumetric flask by the end of all operations does not exceed 2∕3 of the volume of the flask. Gently swirl the contents of the flask. If fixanal contained a dry substance, stir it until complete dissolution. Then dilute the contents of the flask to the mark with distilled water. Close the flask carefully and stir the solution 12-15 times.

To set the titer of the titrant, separate portions of the solution are taken with a pipette and titrated. You can also take separate weighed portions of the starting material and, dissolving each of them in an arbitrary amount of water, titrate the entire resulting solution. This method gives more accurate results than the first, but is too laborious. Therefore, in the laboratory, practically when performing analyzes, they use the first method.

5. DETERMINATION OF THE EQUIVALENCE POINT AND END

REACTIONS

During titration, not an excess of the reagent is used, but an amount equivalent to the amount of the analyte. A necessary condition for determining the content of a substance titrimetrically is the exact establishment of the moment when the reaction between the titratable substance and the titrant ends, that is, fixing the point equivalence. The more precisely the end of the reaction is determined, the more accurate the result of the analysis will be.

To determine the end of the reaction, special reagents, the so-called indicators, are used. The action of indicators is usually reduced to the fact that after the completion of the reaction between the titrated substance and the titrant, in the presence of a small excess of the latter, they undergo changes and change the color of the solution or precipitate. When so much titrant is added from the burette that a noticeable change in the color of the titrated solution is observed, it is said that end point of the titration.

In most cases, indicators are added to a solution of the analyte and the titration takes place in the presence of the indicator. These are the so-called internal indicators. In some cases, they act differently: as the titration proceeds, a drop of the solution is taken from the titrated solution with a capillary, to which a drop of indicator is added over a porcelain plate. Thus, the reaction with the indicator takes place outside the titrated solution. The indicators used in this case are called external.

There are separate indicators for each titrimetric method. In acid-base titrations, indicators change color when the pH of the solution changes. In precipitation methods, the equivalence point is found by the cessation of precipitation. The indicators used in these methods form a brightly colored precipitate or solution with an excess of titrant. Sometimes, if one titrates with a brightly colored solution, for example, with a KMnO 4 solution, the end of the titration can be seen without an indicator, since the first drop of titrant, which does not react with a certain substance, changes the color of the titrated solution.

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