Course work

Methods of qualitative and quantitative analysis. Method for determination of Cu2+ cation

Uralsk-2013

Introduction

Qualitative Analysis

1 "Dry" method of analysis

2 "Wet" method of analysis

Quantitative Analysis

3 Redox titration. Iodometry

Separation of the proposed mixture

Methods and technique for determining the Cu2+ cation

1 General characteristics of cations of the V analytical group

Conclusion

mixture cation purification separation

Introduction

Target term paper- study of methods for separating mixtures, consideration of methods of qualitative and quantitative analysis.

In accordance with the goal, the following tasks are solved: to define the methods of qualitative and quantitative analysis, to consider the methods and methodology for determining the Cu2+ cation, to analyze the properties of substances in the proposed mixture, to identify the method of purification and detection of the proposed cation

Subject of research - methods of analysis of mixtures of cations

The object of study in this work is the Cu2+ cation.

The relevance of the work. The main practical task of analytical chemistry is to determine the composition of substances and their mixtures. Knowledge of the theory and methods of performing chemical analysis, knowledge of chemical methods of analysis is necessary to control raw materials, semi-finished products and finished products in the chemical and pharmaceutical industries.

The task of qualitative analysis is to establish the composition of a substance, that is, to find out from which atoms, molecules, ions, etc. substance consists. Qualitative analysis can be carried out by chemical, physicochemical and physical methods.

Chemical methods are based on the use of analytical reactions carried out with the analyte using reagents. The analytical reaction must be accompanied by such changes in the system that can be fixed visually or with the help of one or another device. If a change, on the basis of which it is possible to draw a conclusion about the presence of certain components in the analyte, is noted visually, then the corresponding method belongs to the classical chemical method.

Qualitative analysis can be carried out without the help of an analytical reaction, but by carrying out certain physical operations. The corresponding methods are physical. Since special instruments are used in the analysis by physicochemical and physical methods, these methods are often called instrumental.

Quantitative analysis allows you to establish the elemental and molecular composition of the object under study or the content of its individual components.

Depending on the object of study, inorganic and organic analysis. In turn, they are divided into elemental analysis, the task of which is to establish how many elements (ions) are contained in the analyzed object, into molecular and functional analyzes, which give an answer about the quantitative content of radicals, compounds, and functional groups of atoms in the analyzed object.

1. Qualitative analysis

The analyzed sample in most cases contains several components in various ratios. To separate and concentrate the components of the analyzed mixture, the methods of precipitation, coprecipitation, extraction, chromatography, electrolysis, electrophoresis, distillation, sublimation, zone melting, flotation, etc. are used. Most separation methods are based on the principle of selective distribution of sample components between two separating phases. The sample component to be opened is transferred as completely as possible into one of the phases.

For the analysis of complex multicomponent mixtures, the method of successive separation of small groups of ions using group reagents is used. Further analysis of these groups is carried out by the fractional method, and if necessary, use additional separation in each group. A strict sequence of separation of groups using group reagents is called a systematic course of analysis. Groups of ions that are successively separated in the systematic course of analysis are called analytical groups. They underlie the analytical classification of ions. For different schemes of systematic analysis, the composition of the analytical groups is different; it depends on the used group reagents and precipitation conditions. Thus, in practice, for the analysis of mixtures of elements, a combination of fractional and systematic analysis is used.

There are several schemes for the systematic analysis of ion mixtures. They most widely use precipitation for separation purposes, followed by extraction and partition (paper) and ion exchange chromatography. Preliminary fractional tests are usually carried out before systematic analysis. Their results, together with other data on the properties and expected composition of the sample, help to choose one or another scheme for the systematic course of analysis.

Qualitative analysis allows you to determine which elements, molecules are part of the analyzed sample or which are absent. When analyzing inorganic substances usually they deal with aqueous solutions of salts, acids and bases, in the solutions of which they are dissociated into ions. Therefore, reactions occur between free ions and it is not the elements that are directly opened, but the ions formed by them (cations and anions). For example, to open chlorine in HCI or chloride solutions, they are treated with AgNO3 solution. In this case, a characteristic curdled precipitate of white color AgCI falls out:

The essence of the reaction under consideration lies in the interaction of the Ag+ and Cl- ions in the solution. But if chlorine were present in the form of ClO3 - - the chlorate ion - or in the form of undissociated molecules of chloroform CHCl3, then this reaction would not take place. From this it is clear that by applying this reaction, we are not discovering the element chlorine, but the ion Cl-. If an element forms ions of different valency, then each of them has its own reactions.

Therefore, the qualitative analysis of inorganic substances is divided into the analysis of cations and the analysis of anions of a complex substance.

In chemical qualitative analysis, two types of reactions are used:

· detection reactions (ion discovery);

· ion separation reactions.

Detection reactions - an analytical signal - must be accompanied by a visual effect:

· precipitation of a certain color and structure;

· change in the color of the solution;

release of gas

· the disappearance of color;

· sediment dissolution.

Thus, according to these signs, the presence or absence of an ion is judged.

Separation reactions are used in systematic analysis when the presence of some ions interferes with the detection of other ions, and reagents are used that can separate one or more ions: in the form of a precipitate; by dissolving the precipitate.

Separation requirements:

· reactions must proceed quickly;

· products must have low solubility for complete precipitation;

· the resulting precipitates should have a crystalline structure.

Methods for Performing Analytical Reactions

In some cases, substances are analyzed in a dry way, i.e. without transferring them into solution, and in other cases - by wet.

1 "Dry" method of analysis

When performing the analysis of the "dry" method, the test substances and reagents are in a solid state. Most of these determinations are related to heating and form a group of pyrochemical methods of analysis. These include the method of coloring the flame, the method of coloring the "pearls" of borax, soda and other compounds, the method of heating in an incandescent tube, etc. The "dry" methods of analysis also include the method of grinding powders.

When performing reactions in a dry way, the substances are taken in solid form and are usually heated to a high temperature. The analytical signal is:

· Flame coloring with volatile salts of certain metals is based on the ability of certain elements and their compounds (alkaline, alkaline earth metals, copper, boron, etc.) to color the flame in a certain color. For example: sodium - yellow, potassium - purple, calcium - brick red, strontium - carmine red, barium - yellowish green, copper - bright green. A test for the presence of an ion is carried out using a carefully cleaned platinum or nichrome wire, one end of which is fused into a glass tube of small diameter, and the other is bent into a small loop (eyelet). An incandescent wire eye is introduced into the analyte and then brought into the hottest part of the gas burner.

· the formation of colored pearls (glasses). Some substances, when fused with sodium tetraborate Na2B4O7?10H2O, "phosphate salt" NaNH4HPO4?4H2O and other compounds, give colored glass - "pearls". To obtain a "pearl" of borax, the ear of a hot platinum wire is introduced into a solid borax, heated in the flame of the burner until swelling stops, cooled and, having touched the resulting "pearl" of the analyzed substance, the eye of the wire is reintroduced into the flame of the burner, and then cooled. By coloring "pearl" judge the presence of a particular element. If the substance does not sublimate at all, there are no volatile components in its composition. The presence of certain compounds can be judged by the color of the sublime. Thus, ammonium salts, mercury chloride and bromide, arsenic and antimony oxides give white sublime, sulfur compounds of mercury and arsenic, mercury iodide, sulfur - yellow sublimation; other compounds of mercury, arsenic, iodides - gray or black sublime. Along with sublimation, when heated, various gases and vapors can be released, which will provide information about the qualitative composition of the substance. For example, oxygen is released if permanganates, nitrates, peroxides, etc. are present in the analyzed sample; carbon monoxide (IV) CO2 is released during the decomposition of carbonates; nitrogen oxides - during the decomposition of nitrates and nitrites; water vapor - during the decomposition of crystalline hydrates, hydroxides, organic compounds etc. The incandescent tube is a test tube made of refractory glass or quartz, 5-6 cm long, 0.5 cm in diameter. a large number of the analyte is poured into the tube, heated slowly and carefully in the flame of the burner, and the phenomenon observed is observed.

· Powder grinding method. The presence of ions of one or another element is detected by the formation of compounds with a characteristic color or odor. So, when grinding a mixture of ammonium thiocyanate NH4NCS or potassium thiocyanate KNCS with Fe3+ salts, a red-brown color appears, and with Co2+ salts - blue. Grinding is carried out in a porcelain mortar or on a special porcelain plate.

All "dry" methods of analysis are used only for auxiliary or verification determinations.

2 "Wet" method of analysis

In the wet route analysis, the test substance is brought into solution using distilled water, mineral acids, water solution ammonia, strong alkali, some organic solvents, etc., and analyze the solution. Therefore, the mechanism of ongoing reactions can only be represented by an ionic equation. For example, for the reaction Pb(NO3)2 + 2KI ? PbI2? + 2KNO3 the equation in ionic form is:

Рb2+ +2I- ? PbI2?.

It can be seen from the ionic equation that the PbI2 precipitate is formed during the interaction of Pb2+ cations and I- anions. The same element can exist in solutions in the form of different ions:

Fe3+ - Fe2+; Zn2+ - ZnO22-;+ - MnO4- - MnO42-;+ - SnO22- - SnO32- etc.

Each of these ions has its own characteristic reactions. Reactions are carried out by the "wet" method in chemical or centrifuge test tubes and on filter paper.

Classification of methods by the amount of substance

Depending on the mass of the analyte and the volume of solutions, analysis methods are divided into macro-, semi-micro-, micro-, ultramicro-, submicro- and subultramicromethods. Accordingly, the technique of performing individual operations is also distinguished.

The most widely used as an analysis was the semi-micromethod with elements of microanalysis. This method has a number of advantages: a small amount of analyte and reagents is consumed to perform the reaction; the time spent on analysis is reduced by replacing the filtering of sediments with centrifugation; the emission of harmful gaseous substances is sharply reduced, thereby improving sanitary and hygienic working conditions.

3 Microcrystalloscopic method of analysis

Crystals of a characteristic shape are obtained by introducing a drop of a solution or a crystal of a reagent into a drop of the test substance placed on a glass slide. As the water evaporates along the perimeter of the drop, crystals of the reaction product of a characteristic shape appear, which are examined under a microscope.

When carrying out an analytical reaction, it is necessary to create certain conditions that depend on the properties of the resulting products, since otherwise the result of the reaction will be unreliable. These conditions include:

) The pH of the solution - the proper environment - is one of the most important conditions for the reaction, which, if necessary, is created by adding acid or alkali to the solution. Acid or alkali is added dropwise to the analyzed solution to the desired pH value, constantly checking on the color scale of the universal indicator;

) temperature - to obtain an analytical signal, some reactions must be carried out when heated in a water bath or an alcohol lamp flame, since they do not pass in the cold or at room temperature;

) concentration - it must be large enough, otherwise, at low concentrations, the reactions cease to succeed. The reason for observing the condition of sufficient concentration: any substance can precipitate only when it is formed in solution in a concentration exceeding its solubility under given conditions. If the substance is very difficult to dissolve, it precipitates already at a very low concentration of the ion to be discovered: the corresponding reaction is called sensitive. And with a significant solubility of the resulting compound, the reaction is not very sensitive and succeeds only at a high concentration of the ion to be discovered. The same applies to reactions accompanied by a change in color.

Quantitatively, the sensitivity of reactions is characterized by mutually related indicators: the opening minimum and the limiting dilution. The minimum discoverable is the smallest amount of a substance or ion that can be discovered by a given reaction, expressed in micrograms (m) (10-6 g). The revealed minimum does not fully characterize the sensitivity of the reaction, since not only the absolute amount matters, but also the concentration of the corresponding substance or ion in the solution. Therefore, the limiting dilution is also indicated, which characterizes the lowest concentration of a substance (ion) at which it can be detected. The limiting dilution is expressed as the ratio of the weight of the substance to the weight of the solution (G).

Between the opening minimum m (expressed in micrograms) and the limiting dilution (G) there is a relationship

where V is the volume of the solution, ml.

The sensitivity of the reactions that serve to open the same ion is different.

For example, for the Cu2+ ion:

Reagent Formed compoundReaction effect Minimum opening, mg Limit dilution 1: G1. HCI H Green color solution 11:500002. NH3СI2 Blue color solution 0.2 0.21:2500003.Cu2K4 Brown color solution/precipitate 0.021:2500000

Thus, the most sensitive reaction is No. 3 with K4, which makes it possible to detect 50 times less copper in solution than under the action of HCI, and 10 times less than under the action of NH3.

4 Fractional and systematic analysis

There are two methods for performing a qualitative analysis of a mixture of cations and anions.

Fractional analysis (method) consists in the fact that the analyzed solution is divided into a large number of portions and individual ions are detected in each of them by specific reactions. A specific reaction to a given ion is the reaction that allows you to open it in a mixture with other ions by specific reagents. The advantage of the method is the speed of the analysis. However, only a few ions can be discovered in this way, since the number of specific reactions is small. Often there are ions in the solution that interfere with the determination. If the action of these ions is difficult to eliminate, then a systematic or sequential analysis is used.

In the course of a systematic analysis, a certain sequence of detection of the desired ions is observed. In this case, along with the reactions of discovery of individual ions, one has to resort to reactions of separating them from each other by group reagents. The order of separation of ions by group reagents must be carried out in a certain sequence, which must not be violated. In the systematic course of analysis, ions are isolated from a complex mixture not one at a time, but in whole groups, using the same ratio of them to the action of group reagents.

Methodology for performing the basic operations of semi-microanalysis

Precipitation is the basis of many analytical reactions. The corresponding reagent is added dropwise to the analyzed solution in a conical test tube. During precipitation, it is necessary to stir the solution. After precipitation, it is necessary to check the completeness of precipitation. To do this, after the liquid above the precipitate becomes transparent, add another drop of precipitant. If turbidity does not appear in the solution, the completeness of precipitation has been achieved. Otherwise, add a few more drops of precipitant. If it is necessary to heat the solution for precipitation, the test tubes are placed in a water bath. Centrifugation is used to separate precipitates from solutions in a qualitative analysis. Therefore, the analysis is carried out in conical centrifuge tubes. After centrifugation is completed, a dense precipitate remains at the bottom of the tube, while the centrifugate (supernatant) is clarified and can be easily separated from the precipitate with a pipette or by draining. If the precipitate is analyzed, then before dissolving it is washed 2-3 times with a small amount of distilled water, each time separating the filtrate by centrifugation. To reduce the solubility of precipitates, a few drops of a precipitant are added to the wash water. Dissolution of precipitates is carried out by slow (dropwise) addition of the solvent to the precipitate with simultaneous stirring with a glass rod. If necessary, the mixture is heated in a water bath.

5 Methods for separating mixtures of cations

The use of various group reagents made it possible to develop various analytical classifications of cations (and anions). The most widespread are sulfide, acid-base and ammonia-phosphate classifications.

Sulfide classification, proposed back in 1871 by N.A. Menshutkin and since then has been repeatedly subjected to various changes and improved through the use of new reagents and experimental methods. The hydrogen sulfide method of analysis based on sulfide classification has two main disadvantages: the toxicity of hydrogen sulfide requires specially equipped chemical laboratories; analysis is time consuming.

Schemes for qualitative chemical analysis using H2S

Classical hydrogen sulfide (sulfide) scheme for separating cations into groups

Group number Cations Group reagent Formed compounds Note ILi+, Na+, , K+, Rb+, Cs+, Mg2+NoCations in ammonium buffer solution preliminarily open IICa2+, Sr2+, Ba2+, Ra2+(NH4)2CO3 in ammonium buffer p-reOc. carbonates at loading IIIBe2+, ​​Zn2+, Al3+, Y3+, Sc3+, lanthanides, actinides, Ga3+, In3+, Tl3+, Ti(IV), Zr(IV), Hf(IV), Th4+, V(V), Nb(V), Ta(V), Cr3+, U(VI), U(IV), Mn2+, Fe(II), Fe(III), Co2+, Ni2+(NH4)2S in ammonium buffer p-peOc. sulfides and hydroxides solution neutral NH4OH (without ) saturate the gas. H2S (or add H2S solution in acetone). In the presence (, F?, ) precipitated and group II, so they are pre-separated. can be removed with Fe3+ ion in acetate buffer, with Zr(IV), Ti(IV) ions - in hydrochloric acid, Sn(IV) - in nitric acid p-reIVAu3+, Ag+, Bi3+, Cd2+, Cu2+, Cu+, Hg2+, Os(VII), Pb2+, Pd(II), Pd(IV), Rh(III), Ru(III)H2S at pH? 0.5Os. sulfides of groups IV and V, after the action of (NH4) 2S2 - a precipitate of sulfides of group IV. In3 +, Zn2 + are partially precipitated. Pb2+ ions (not completely), Ag+, separated before the siege. H2S in the form of chlorides in insoluble wasps. when adding HCl to the original sample VAs(III, V), Ge(IV), Mo(VI), Re(VII), Sb(III, V), Se(IV), Sn(II, IV), Te(IV)(NH4 )2S2 act on the precipitate of sulfides of groups IV and V. Solution of thiosalts V gr. partially fall W(V), V(III), Au(III), Ir(III, IV), Pt(IV)

The classical hydrogen sulfide method is based on the division of the most common metal compounds into 5 analytical groups depending on the precipitation of cations by one or another common reagent. At the same time, for group I cations (K+, Na+, NH+), there is no common reagent. Most salts of these metals are soluble. Group II cations (Mg2+, Ca2+, Ba2+, Sr2+) precipitate in contrast to compounds I analytical group in the form of carbonates and phosphates and do not precipitate, in contrast to the cations of III, IV and V groups in the form of sulfides.

A common reagent for cations of III analytical group (Mn2+, Cr3+, Zn2+, Al3+, Fe3+, Ni2+, Co2+, T13+) is ammonium sulfide or hydrogen sulfide in an alkaline (NH4OH) medium, and for group IV (Cu2+, Cd2+, Ag+, Bi3+, Hg2+ , Pb2+) and group V (As3+, Sb3+, Sn2+) - hydrogen sulfide in an acidic environment. In this case, the sulfides of the V analytical group, in contrast to the sulfides of the IV analytical group, are dissolved in ammonium polysulfide.

After the division of the cations into groups, further separation of the cations and their qualitative detection are carried out already within a certain analytical group.

The main disadvantages of the hydrogen sulfide method from the standpoint of toxicological chemistry are: 1) imperfection of precipitation and separation of cations; 2) the duration of the analysis; 3) the toxicity of gaseous hydrogen sulfide and 4) the inability to combine qualitative analysis with quantitative analysis in the study of one sample of the object. As a rule, after a qualitative analysis, it is necessary to subject a new portion of the object to the study to quantify the detected element.

The imperfection of precipitation and separation by hydrogen sulfide is primarily due to the different degree of solubility of metal sulfides. The solubility products of sulfides vary over a very wide range.

The solubility products of sulfide cations fluctuate not only when passing from one cation to another, they are not always stable even for the same cation. For example, the solubility product of flesh-colored MnB is 1-10 15, and MpB of green color is 6.2-10 22. The first modification is obtained by saturating the Mn2+ salt solution in the cold, the second - when heated.

The solubility products of sulfides also fluctuate depending on the conditions of their formation: the pH of the medium, the temperature of the solution, the rate and duration of saturation of the solution with gaseous hydrogen sulfide, and other factors.

When analyzing according to the hydrogen sulfide scheme, elements in the form of volatile compounds are often preliminarily isolated from the analyte using the reagents indicated in brackets: Si (HF); Se, As, Ge (HBr + Br2); Os (HNO3); Ru(HClO4); Re (H2SO4), as well as a group of noble metals: Au, Ag, Pt, Pd (Ir, Rh, Hg are not completely isolated).

Precipitation is carried out from a hot solution, saturating it with gaseous H2S, kept at 70-90 ° C 10-15 min, cool and re-saturate with H2S, close the vessel and leave for 15 min. In the presence of molybdenum, after bubbling with H2S, add some H2O2 and saturate again with H2S.

Group V is isolated from a mixture of sulfides by the action of an excess of (NH4)2S2 with slight heating.

To precipitate group III, the acidic solution is neutralized with NH4OH (without ), add an excess of it, saturate with H2S, and add NH4OH again. In the presence of interfering anions, group II precipitates together with III, so these anions must first be removed. IN modern conditions this is easiest to do with an anion exchanger. In addition, the most common ion can be precipitated with Fe3+ ions in an acetate buffer when heated, as well as with Zr(IV) or Ti(IV) ions in hydrochloric acid and Sn(IV) ions in a nitric acid solution.

Precipitation of group II is carried out with (NH4)2CO3 by heating in an ammonium buffer solution.

As can be seen from the above classification scheme, under the action of hydrogen sulfide on a solution of a complex mixture of cations of all groups, cations of groups I and II do not precipitate in the form of sulfides, and the precipitated sulfides can be isolated in a certain sequence. This sequence is determined by the concentration of the sulfide ion, which, in turn, directly depends on the concentration of hydrogen ions in the analyzed solution. The concentration of sulfur ions in the solution is controlled by weak hydrosulfide acid, which dissociates in two steps with dissociation constants K1 and K2, respectively:

H2S Û HS- + H+ TO 1 = 8,9 ? 10-8Û S2- + H + K2 \u003d 1.3? 10-13

For the H2S reaction? Û 2H+ + S2?? dissociation constant

The concentration of a saturated H2S solution at normal pressure and 25 ° C is equal to or less than 0.1 mol?l-1 Then 2 ? = 1.2? 10-21 mol?l-1, i.e. the concentration of the sulfide ion is inversely proportional to the square of the concentration of hydrogen ions. Thus, by changing the concentration of hydrogen ions, it is possible to control the concentration of sulfur ions.

Comparison of the solubility products of sulfides makes it possible to divide them into two groups. One of them has values ​​of solubility products of the order of 10-15-10-23, the other - of the order of 10-27-10-50. The boundary lies between zinc and cadmium sulfides: PRZnS = 2.5? × 10-22; PRCdS = 7.9?× 10-27.

By creating a concentration of sulfur ions to completely precipitate cadmium sulfide and leave the zinc ion in solution, it is possible to separate cadmium sulfide and less soluble sulfides from zinc sulfide and more soluble sulfides.

The conditional boundary of the complete precipitation of cadmium can be considered its concentration equal to 10-6 mol l-1. For sulfur ions

Mol?l-1.

This concentration of sulfide ion is formed in an H2S solution at an H+ concentration equal to

The concentration of the cation in the analyzed solution is usually close to 0.01 mol l-1. If the zinc concentration is taken equal to this value, then the product of the ion concentrations ? = 0.01? 7.9? 10-21 = 7.9? 10-23, which is less than the value of the solubility product of zinc sulfide PRZnS = 2.5? 10-22.

Consequently, the Zn2+ ion and all ions for which the sulfide solubility products are larger than for ZnS will not precipitate.

Equilibrium in the sediment-solution system is not established immediately. It is known that the solubility of compounds changes over time (the highest solubility is in freshly precipitated compounds). In the case of sulfides, this is primarily due to the fact that they precipitate in metastable and more soluble modifications, which, upon storage of sulfides, transform into more stable and less soluble forms. These forms differ in structure crystal lattice, sometimes in color (a-MnS -pink ,b-MnS - green) and values ​​of solubility products. Therefore, when calculating the conditions for the separation of sulfides by adjusting the acidity of the solution, one should use the tabular values ​​of the SP of only freshly precipitated forms (as a rule, more soluble).

In the processes of separation of ions in the form of sulfides, a significant role is played by the processes of sorption and after precipitation (leading to incomplete separation, in particular, of cadmium and zinc), as well as the formation of stable colloids.

Acid-base classification is based on the different solubility of hydroxides, chlorides, sulfates. The group reagents of this method are solutions of acids and bases.

According to the acid-base classification, cations are divided into six analytical groups

K+, Na+, Mg2+NoCations in solutionChlorides, sulfates and hydroxides are soluble in water IIBa2+, Sr2+, Ca2+H2SO4Oc.: BaSO4, SrSO4, (CaSO4) Sulfates are insoluble in water and acids. Ca2+ partially remains in solution IIIAg+, Hg22+, Pb2+HClOc.: AgCl, Hg2Cl2, (PbCl2) Chlorides are insoluble in water and dilute acids. Pb2+ partially remains in solution IVZn2+, Al3+, Sn(II,IV), Cr3+NaOH + H2O2 Hydroxides of higher oxidation states p-we in the hut. NaOHVSb(III,V), Bi3+, Mn2+, Fe(II,III)NH4OH + H2O2Oc.: HSbO3, Bi2O3 ? xH2O, MnO(OH)2, Fe2O3 ? xH2O Hydroxides are insoluble in excess. NH4OHVICo2+, Ni2+, Cu2+, Cd2+, Hg2+, (Mg2+)NH4OH + H2O2 Hydroxides are soluble in excess. NH4OH; magnesium hydroxide is soluble in solutions of ammonium salts

Preliminary tests help to optimize procedures for separating or opening ions and to interpret the observed signals. During preliminary tests:

Determine the pH using a universal indicator.

Check the ratio to 6 M HCl. The presence of an insoluble precipitate indicates the possible presence of group III chlorides, group II sulfates, SbOCl, BiOCl, PbSO4.

Check the ratio to excess 2 M NaOH. The dissolution of the precipitate indicates the presence of amphoteric hydroxides.

The sample is dissolved in 2 M HCl and cations are detected in separate samples by a fractional method. , K+, Na+, Ca2+, Fe3+, Co2+, Mn2+, Ni2+, Cr3+, Mg2+, using specific and selective reactions and masking interfering ions.

Performing an acid-base analysis has certain advantages:

· the acid-base properties of elements, the ability to complex formation, the amphotericity of hydroxides are used, which is due to their position in the periodic system of elements D.I. Mendeleev;

· the toxic effect of hydrogen sulfide is excluded;

· time spent on analysis is reduced.

· The method is simple, does not require expensive reagents, and is easy to master.

· The principle of a systematic course of analysis is being implemented.

Disadvantages of the method:

· 1. Fuzzy separation of cations into groups due to the relatively high solubility of PbCl2 and CaSO4 in water, different ratios of Sb(III) and Sb(V) to excess NaOH, partial dissolution of Cu(OH)2 in excess NaOH.

· 2. The need to perform a laborious and lengthy operation of converting group II sulfates into carbonates.

· 3. The method is not applicable in the presence of a number of anions, including the phosphate ion. In this case, either complex operations are carried out to remove interfering anions, or an analysis is performed using the ammonia-phosphate method.

The acid-base method (as well as hydrogen sulfide) is significantly complicated by the presence of PO43- ion, therefore, in the presence of this ion, the ammonia-phosphate method acquires certain advantages.

The method is based on the use of different solubility of phosphates in water, strong and weak acids, alkalis and ammonia solution. analysis scheme. In addition, in this case, it is necessary to establish by a fractional method the presence or absence of Na+, K+, NH4+ ions, which will be introduced in the further course of the analysis, as well as cations that facilitate or hinder the analysis. These include Fe2+, Fe3+, As(III), As(V), Sn(II), Sn(IV), Cr3+.

Classification of cations according to the ammonia-phosphate scheme

Group number Cations Group reagent Formed compounds Notes I Na+, K+ No Phosphate solutions in water III subgroup: Li+, Mg2+, Ca2+, Ba2+, Sr2+, Mn2+, Fe2+ II subgroup: Al3+, Cr3+, Fe3+, Bi3+(NH4)2HPO4 + NH4OHLi3PO4, MgNH4PO4, CaHPO4, MnNH4PO4, FeHPO4 , SrHPO4, BaHPO4, AlPO4, CrPO4, FePO4, BiPO4 Phosphates are insoluble in water and NH4OH. Phosphates of the I subgroup p-we in CH3COOH. Phosphates of the II subgroup are insoluble in CH3COOH, solutions in HClIIICo2+, Ni2+, Cu2+, Zn2+, Cd2+, Hg2+NH4OH Phosphate solutions in NH4OHIVAs (III, V), Sb (III, V), Sn (II, IV) HNO3HSbO3, H2SnO3, H3AsO4 Metatinic and metaantimony acids are insoluble and adsorb H3AsO4VAg +, Pb2+HClAgCl, Hg2Cl2, PbCl2 Chlorides are insoluble in water and dilute acids

After the preliminary tests are completed, the systematic course of the analysis is started.

Advantages of the method:

· Hydrogen sulfide is not used.

· Does not interfere with the presence of an ion

· Retaining all the advantages of systematic analysis, it is characterized by rapidity and relatively high clarity of separation.

Disadvantages of the method

· The need to discover a large number of ions by fractional methods at the stage of preliminary tests.

· The analysis requires the addition of SnCl4, Na2HPO4, FeCl3.

· The need to convert hydrochloric acid solutions to nitric acid and vice versa.

2. Quantitative analysis

Quantitative analysis - a section of analytical chemistry, the task of which is to determine the amount (content) of elements, ions, functional groups, compounds or phases in the analyzed object. Along with qualitative analysis, quantitative analysis is one of the main branches of analytical chemistry. Depending on the objects of study, inorganic and organic analysis are distinguished, which, in turn, are divided into elemental, functional, and molecular analysis. In addition to specificity and sensitivity, an important characteristic of quantitative analysis methods is accuracy, that is, the value of the relative error of determination; the accuracy and sensitivity in quantitative analysis is expressed as a percentage. The classical chemical methods of quantitative analysis include gravimetric analysis, based on an accurate measurement of the mass of the analyte, as well as volumetric analysis. The latter includes titrimetric analysis - a method for measuring the volume of a reagent solution consumed in a reaction with an analyte, and gas volume analysis - a method for measuring the volume of analyzed gaseous products. As part of the course of analytical chemistry, gravimetric and titrimetric methods of analysis are studied in detail.

1 Gravimetric method of analysis

Gravimetry (from Latin gravis-heavy and Greek metreo-measure) is a set of methods of quantitative analysis based on measuring the mass of the analyte isolated from the analyzed sample either in a free state or in the form of a compound of known composition. Mass is the analytical signal in gravimetry. Gravimetry can be used to determine almost any component of the analyzed object, if their content in the sample exceeds 0.1%. Gravimetry is a standardless method. The main advantage of gravimetry is the high reliability of the results. The error of determination does not exceed 0.1-0.2%. Disadvantages are associated with high complexity and duration of analytical operations, difficulties in determining very small amounts of substances, and low selectivity. Therefore, in mass laboratory analyzes, it is replaced, if possible, by other methods. In gravimetric analysis, two groups of methods are usually distinguished: precipitation and distillation. Deposition methods are of the greatest practical importance. From a part of the test substance of a known mass (a sample), the component to be determined is isolated in one way or another in the form of a compound.

Direct isolation is possible only in a few cases, for example, the removal of hygroscopic or crystallization water by heating. Usually a hanger solid transferred to a solution, from which, using a suitable reagent, the component to be determined is isolated in the form of a practically insoluble substance (precipitable form). The precipitate is separated by filtration, decantation, or other methods, washed from traces of sorbed components, and often re-precipitated. Then it is dried or calcined to form a stable compound of a strictly defined composition (weight, gravimetric form), the mass of which is measured.

For example, when determining Ca2+, the precipitated form is CaC2O4, the weight form is CaO or CaCO3. Knowing the masses of the sample (a) and the weight form (b), the content x (% by mass) of the determined component is calculated:

= (bF/a). 100(2)

The factor F, called the gravimetric factor, is equal to the content of the determined component in 1 g of its weight form:

MM1/nM2 (3),

where m and n are stoichiometric coefficients in the equation for the chemical transformation of the isolated component into its weight form, M1 is the molar mass of the determined component, M2 is the molar mass of the gravimetric form. For example, when determining iron by mass of Fe2O3, m = 2, n = 1. In cases where the components being determined form volatile compounds, stripping methods can be used. Decomposition of samples with the release of gaseous products is achieved by calcination or the action of reagents (acids, alkalis, etc.) during heating. The volatile component is passed through the absorbent solution, and the amount of the gaseous product released from the sample is calculated from the increase in the mass of the solution (direct methods). The mass of the residue of a substance can be determined after the volatile product has been removed from it. The content of the component in such cases is found by the difference in mass before and after distillation (indirect methods).

2 Titrimetric method of analysis

Titrimetric methods of analysis are called, based on measuring the amount of the reagent consumed for the complete reaction with the analyte. The amount of a reagent is most often determined by accurately measuring the volume of its solution that went into the reaction. Titration is an operation in which small portions of a standard reagent solution are gradually added to a solution of the analyte until the amount of reagent used is equivalent to the amount of the analyte. The reagents used in titrimetric determinations are called titrants. The moment of titration at which the amount of added titrant becomes equivalent to the amount of the analyte is called the equivalence point. Substances react with each other in equivalent quantities. Equivalent - a conditional or real particle that can add, release, replace one hydrogen ion in acid-base reactions or be equivalent to one electron in redox reactions.

where n is the chemical quantity, N is the molar concentration of the equivalent, and V is the volume in which the substance is dissolved, then for two stoichiometrically reacting substances the relation is true:

Therefore, it is possible to find an unknown concentration of one of the substances if the volume of its solution and the volume and concentration of the substance that reacted with it are known. The calculation of the mass of the analyte (A) contained in the volume of the titrated solution taken for titration is carried out according to the following formula:

(A) = Vt Nt E(A) (5)

where: m(A) - mass of the analyte, g; Vt is the volume of titrant used for titration, l; Nt is the molar concentration of the titrant equivalent, mol/l; E(A) - molar mass of the equivalent of the analyte, g/mol-eq.

The titration reaction must meet the following requirements: - be strictly stoichiometric;

flow quickly;

proceed quantitatively;

there must be a reliable way to fix the equivalence point.

Experimentally, the end of the titration process is carried out at the moment of changing the color of the indicator or any physicochemical property of the solution. This point, called the end point of the titration, generally does not coincide with the theoretically calculated equivalence point. Methods of titrimetric analysis classify:

type chemical reaction underlying the analysis of substances. In accordance with this, titrimetric determinations are divided into the following main methods: acid-base, complexometric, redox and precipitation titrations.

according to the method of execution (direct, reverse, substitution, indirect, reverse);

according to the method of performing parallel determinations (the method of separate weights and the method of pipetting).

Measurement of volumes. Volumetric flasks, pipettes and burettes are used to accurately measure volumes in quantitative chemical analysis.

Volumetric flasks. They are used to prepare standard solutions and to dilute test solutions to a certain volume. These are flat-bottomed flasks with a long narrow neck, on which a circular mark is applied. The volume indicated on the wall of the flask corresponds to the volume of liquid (at the calibration temperature), if the flask is filled so that the lower part of the liquid meniscus touches the mark, and bringing the volume of liquid to the mark should be carried out so that the eyes of the observer and the mark are at the same level (mark merges into a straight line). There should be no drops of liquid on the neck of the flask above the mark, the inner walls of the flask should be clean, and the liquid should wet them in an even layer. Close the flasks with special ground stoppers. Do not heat volumetric flasks, otherwise the glass may deform, which will lead to a change in their capacity.

standard solutions. To perform a titrimetric analysis, it is necessary to know the concentration of the titrant. 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 pure chemical known stoichiometric composition in a certain volume of solvent. A secondary standard is prepared as follows: prepare a solution with an approximate concentration close to the desired one and determine its concentration (standardize) against a suitable primary standard.

Primary standards must meet a number of requirements:

) the composition of the compound must strictly correspond to the chemical formula. The amount of impurities should not exceed 0.05%.

) the substance must be stable at room temperature, not hygroscopic, oxidized by atmospheric oxygen, absorb carbon dioxide from the air, change mass upon drying.

) the substance should have as high a molecular weight as possible in order to reduce the effect of weighing error.

Fixanals can be used to prepare many standard solutions. Fixanal is an ampoule in which an exactly known amount of a standard substance or solution is sealed.

2.3 Redox titration. Iodometry

Iodometric titration is a titrimetric method of analysis based on determining the amount of iodine consumed to complete the reaction with a substance with reducing properties, or released as a result of the reaction of KI with a substance with oxidizing properties. Iodometric definitions are based on the following equilibrium:

2?=3I-; E0 = + 0.545 V.

Iodine and sodium thiosulfate are used as titrants in iodometric titration.

Example. Standardization of sodium thiosulfate solution. Potassium bichromate is used to standardize sodium thiosulfate solutions. The reactions of Na2S2O3 with K2Cr2O7 and other strong oxidizing agents proceed nonstoichiometrically, therefore, standardization of sodium thiosulfate solution is carried out by substitutional titration: when K2Cr2O7 reacts with an excess of KI, an amount of iodine equivalent to the first substance is formed, which is then titrated with a standardized Na2S2O3 solution:

O72- + 6I- + 14H+ = 2Cr3+ +3I2 + 7H2O+ S2O32- = 2I- + S4O62- (or - + S2O32- = 3I- + S4O62-)

The end point of the titration in iodometry is found, most often, by the disappearance or appearance of the color of the iodine-starch complex.

Acid-base titration. The acid-base titration method includes titrimetric determinations, which are based on the reaction: + + OH- = H2O

By this method, it is possible to determine various acids, bases, some salts, determine the hardness of water, nitrogen in organic compounds, etc. As titrants, solutions of hydrochloric and sulfuric acids, alkali solutions are usually used.

Redox titration. Redox titration is a group of titrimetric methods of analysis based on the use of redox reactions. The most important methods of redox titration include iodometry, permanganatometry, bichromatometry, cerimetry, etc.

Permanganatometry. Permanganometric titration is called

titrimetric method of analysis based on the use of a KMnO4 solution as a titrant. Since the titrant has an intense color, permanganometric titration is carried out without an indicator. The end point of the titration is determined by the appearance or disappearance of the KMnO4 color. Permanganometric titration is most often carried out in an acidic medium, less often in a neutral one. Used to create an acidic environment sulfuric acid, since nitric acid itself is a strong oxidizing agent, while hydrochloric acid, on the contrary, can be oxidized by a titrant. The method is based on the following balance:

MnO4- + 5? + 8H+ = Mn2+ + 4H2O; E0 = +1.51 V.

Bichromatometry. Bichromatometry is a titrimetric method of analysis based on the use of a solution of K2Cr2O7 as a titrant. The method is based on the following balance:

Cr2O72- + 14H+ + 6 ?? 2Cr3+ + 7H2O; E0 = +1.33 V

Redox indicators are used to detect the end point in bichromatometric titration.

4 Complexometric titration

Complexometric titration is based on the formation of chelate complexes in the interaction of metal cations with aminopolycarboxylic acids (complexons). Of the numerous aminopolycarboxylic acids, ethylenediaminetetraacetic acid (H4Y) is the most commonly used:

Due to the low solubility in water, the acid itself is not suitable for preparing a titrant solution. For this, the dihydrate of its disodium salt Na2H2Y2H2O (EDTA, Trilon B) is usually used. The interaction reactions of various cations with EDTA in solution can be represented by the equations:

Ca2+ +H2Y2- =CaY2-+2H++ +H2Y2-=BiY- +2H+++H2Y2- =ThY+2H +

It can be seen that, regardless of the charge of the cation, complexes with a ratio of components of 1:1 are formed. Therefore, the molar masses of the EDTA equivalent and the metal ion to be determined are equal to their molecular weights. The extent of the reaction depends on the pH and the stability constant of the complexonate. Cations that form stable complexonates, such as Fe(III), can be titrated in acidic solutions. Ions Ca (II), Mg (II) and others, which form relatively less stable complexonates, are titrated at pH? 9 and above. The end point of the titration is determined using metal indicators - organic substances that change their color (or fluorescence) depending on the concentration of metal cations in the solution. Most often, the so-called metallochromic indicators are used in the analysis, which form intra-complex compounds with metal cations, the color of which differs from the color of the free indicator, and the complex of the metal to be determined with the complexone is stronger than the complex of this metal with the indicator. The most common metallochromic indicator is eriochrome black T (chromogen). It is used in solid form: the indicator is mixed in a ratio of 1:200 with some indifferent filler, for example, NaCl or KCl.

3. Separation of the proposed mixture

Initial sample:

AgNO3, CuSO4, NiSO4, ZnCl2, MnCl2, NH4OH

AgNO3 + HCl = AgCl? + HNO3 white precipitate MnCl2 + 2NaOH = Mn(OH)2? + 2NaCl light pink gelatinous precipitate ZnCl2 + 4NaOH = Na2ZnO2 + 2NaCl + 2H2O PrecipitateAgCl + 2NH4OH = Cl + 2H2O Mn(OH)2 + H2SO4 = MnSO4 + 2H2O Na2ZnO2 + 2H2SO4 = ZnSO4 + Na2SO4 + 2H2OCl + KI = AgI? + KCl yellow precipitate Ag(NH3)2+ + I- = AgI + 2NH3 MnSO4 + H2O2 + 2NH4OH = MnO(OH)2? + (NH4)2SO4 + H2O brown precipitate Mn2+ + H2O2 + 2OH- = MnO(OH)2 + H2O Zn SO4 + 2(NH4)2 + CoCl2 = Co?Zn? + NH4Cl + (NH4)2SO4 blue precipitate Zn2+ + 2- + Co2+ = Co?ZnСuSO4+4 NH ?Oh "SO4+4H ?O NiSO4 + 6NH ?Oh "SO4+6H ?OSolution + H2SO4 = CuS04 + 4NH4 + H2SO4 = NiSO4 + 6NH4 NH4OH + H2SO4 = (NH4)2SO4 + H ?OCuS04 + H2S = CuS? +H2SO4 dark precipitate NiSO4 + H2S = NiS? + H2SO4 black precipitate(NH4)2SO4 +2NaOH = Na2SO4 + 2NH3 + 2H2OCuS + HNO3 = Cu(NO3)2 + H2S NiS + HNO3 = Ni(NO3)2 + H2SCu(NO3)2 + Fe = Fe(NO3)3 + Cu Ni(NO3)2 + Fe = Fe(NO3)3 + Ni

Reactions to anions

SO42BaCl ?+ Na ?SO4 "2NaCl + BaSO4 $white precipitate Ba² ?+SO42- "BaSO4Cl ?Ag ?+Cl ?"AgCl $AgCl $+ 2NH ?Oh "Cl+ 2H ?O C l+ H ?"AgCl? +2NH ?NO ??2NO ??+8H ?+3Cu "3Cu² ?+4H ?O+2NO #; 2NO+O ?(air)" 2NO ?

4. Methods and technique for determining the Cu2+ cation

1 General characteristics of cations of the V analytical group

The fifth group includes cations of d-elements - Сu2+, Ni2+, Co2+, Cd2+, Hg2+, which, when interacting with an aqueous solution of ammonia in equivalent amounts, precipitate hydroxides, basic salts or amido complexes (Hg), soluble in an excess of the reagent with the formation of amino complexes. Group reagent - concentrated ammonia solution. The resulting ammine complexes M(NH3)42+ have different stability. The least stable is the hexaamminecobalt (II) ion. It is formed only with a sufficiently large excess of NH3. The Co2+ ion is easily oxidized to the Co3+ ion, therefore, under the action of oxidizing agents, the Co(NH3)62+ ion (K = 2.45 × 105) transforms into the stronger Co(NH3)63+ ion (Kst = 1.62 1035).

Ammino complexes of mercury (II) are formed only with a very large excess of ammonia and ammonium salts. Amino complexes can be destroyed by the action of acids that bind NH3 to the ammonium ion:

In aqueous solutions, group V cations are in a hydrated state in the form of aquacomplexes of the Cu(H2O)62+ type. Aquacomplexes Co2+, Ni2+ and Cu2+ are colored: Co(H2O)62+ - pink, Ni(H2O)62+ - green, Cu(H2O)62+ - blue. Coloring of aquacomplexes is one of characteristic features indicating the presence of these ions in solution. Evaporation of solutions or the action of dehydrating substances, such as alcohol, causes a change in the color of these ions. Thus, the pink color of the Co(H2O)62+ complex changes to blue due to the dehydration of complex ions and the replacement of water molecules by other ligands.

In addition to amino and aqua complexes, group V cations are also capable of forming other complex compounds (for example, HgBr42-, CdI42, Co(SCN)3-, Cu(S2O3)22-, etc.), most of which have a characteristic color.

Copper, cobalt and mercury form compounds with different degrees of ion oxidation, so redox reactions can be used to detect them.

The action of a group reagent on group V cations

A solution of NH4OH added to solutions of salts of group V cations in equivalent amounts precipitates these cations in the form of white or colored basic salts, hydroxides and amido complexes:

CuSO4 + 2NH4OH? (CuOH)2SO4? + (NH4)2SO4, bluish green

CoCl2 + NH4OH? CoOHCl? + NH4Cl, blue

NiSO4 + 2NH4OH ? (NiOH)2SO4? + (NH4)2SO4, light green

CdCl2 + 2NH4OH? Cd(OH)2? + 2NH4CI, White

HgCl2 + 2NH4OH? Cl? + NH4C1 + 2H2O. white

In an excess of NH4OH, these precipitates dissolve with the formation of amino complexes of various colors. The formation of a complex of hexaamminecobalt (II) and tetraamminemercury(II) occurs in the presence of NH4C1 upon heating:

(CuOH)2SO4 + 8NH4OH ? 22+ + SO42- + 2OH- + 8H2O, bright blue + 5NH4OH + NH4+ ? 2+ + Cl- + 6H2O, yellow-brown

(NiOH)2SO4 + 12NH4OH ? 2Ni(NH3)62+ + SO42- + 2OH- + 12H2O, blue(OH)2 + 4NH4OH ? 2+ + 2OH- + 4H2O, colorless

Cl+2NH4OH + NH4+ ? 2+ + Cl- + 2H2O. colorless

Hexaamminecobalt(II) is oxidized by atmospheric oxygen to hexaamminecobalt(III) of a cherry-red color. In the presence of oxidizing agents (H2O2), the formation of hexaamminecobalt (III) occurs instantly:

CoC12 + 10NH4OH + 2NH4C1 + H2O2 ? 2C13 + 12H2O.

Execution of reactions. Place 3 drops of Cu2+, Ni2+, Co2+, Cd2+ and Hg2+ salt solutions into five tubes and add 1-2 drops of 2 M NH4OH solution to each. Add a few drops of a concentrated solution of NH4OH to the precipitates of the basic salts of copper, nickel and cadmium with stirring until the precipitates dissolve. Divide the precipitate of basic cobalt salt into two parts. To one add 3-4 drops of a 3% solution of H2O2, and then dissolve both parts of the precipitate by adding a few drops of a concentrated solution of NH4OH and a saturated solution of NH4C1. Dissolve the precipitate of the amido complex of mercury in a few drops of a concentrated solution of NH4OH and a saturated solution of NH4C1 while heating.

2 Particular analytical reactions of Cu2+ ions

Potassium hexacyanoferrate(II) K4 precipitates the Cu2+ ion in the form of red-brown copper hexacyanoferrate(II):

2Cu2+ + Fe(CN)62- ? Cu2?.

The precipitate does not dissolve in dilute acids, but decomposes with alkalis to form Сu(OH)2.

Execution of the reaction. Add 1-2 drops of reagent to 2-3 drops of CuSO4 solution. Divide the precipitate into two parts, add 2-3 drops of 2 M HCl solution to one, and 2-3 drops of 2 M NaOH solution to the other.

Sodium thiosulfate Na2S2O3, when heated, precipitates monovalent copper sulfide:

2CuSO4 + 2Na2S2O3 + H2O ? Cu2S? + 2S + 2Na2SO4 + H2SO4.

Execution of the reaction. Place 2-3 drops of CuSO4 solution in a test tube, add 4-5 drops of water, 2-3 drops of 1 M H2SO4 solution (to a clearly acidic reaction) and one and a half times the amount of saturated sodium thiosulfate Na2S2O3 solution. Mix, heat up. The formation of a dark brown precipitate of the mixture of Cu2S with sulfur indicates the presence of copper in the solution. Since Cd2+ under the action of sodium thiosulfate in an acid medium does not form a precipitate of sulfide, this reaction can be used to separate Cu2+ from Cd2+.

Ammonia solution, taken without excess, forms a blue-green precipitate Cu(OH)2SO4 with a copper salt solution. The precipitate is soluble in dilute acids and in excess ammonia. When dissolved in an excess of ammonia, complex compound 2- is formed, which is colored bright blue.

SO4 + 10NH4OH? 2(OH)2 + (NH4)2SO4 + 8H2O.

Execution of the reaction. To 5-6 drops of a solution containing copper ions, add 2-3 drops of concentrated ammonia and shake. The intense blue color of the solution indicates the presence of Cu2+ ions.

4. Flame color reaction. Copper salts color a colorless burner flame blue or green color

Determination of copper by substitution titration, which is based on the reaction:

Cu2+ + 4I- = 2CuI? + I2.

Copper(II) in this case acts as an oxidizing agent. As a result of the oxidation of iodide ions, iodine is formed, the amount of which is determined by titrating it with a solution of sodium thiosulfate. The amount of sodium thiosulfate is equivalent to the amount of released iodine, which, in turn, is equivalent to the amount of copper (II) that has entered into the reaction. Thus, the volume of Na2S2O3 solution used for titration of iodine is used to calculate the amount of copper(II) that has entered into the reaction.

Progress

) Prepare the burette for titration as usual and fill it with sodium thiosulfate solution.

) Prepare a volumetric flask with the analyzed copper salt solution and bring the volume of the solution to the mark with distilled water.

) Place 15-20 ml of 10% KI solution into the titration flask. 10 ml of copper salt solution from a volumetric flask and 3 ml of H2SO4 solution (1:4) are added there with a pipette. The titration flask is covered with a watch glass and placed in a dark place for approximately 5 minutes.

) The solution turned brown from the liberated iodine is titrated from a burette with a solution of sodium thiosulfate until the color becomes straw-yellow. After that, a few drops of starch solution are added and titrated until the blue solution becomes colorless.

) Titration is carried out 3 times. According to the obtained average value of the volume of sodium thiosulfate, the copper content (in grams) in the issued sample is calculated, while not forgetting to take into account the volume of an aliquot of the solution taken for titration.

) Calculate the relative error of determining

Conclusion

The significance of analytical chemistry is determined by the need of society for analytical results, in establishing the qualitative and quantitative composition of substances, the level of development of society, the social need for the results of analysis, as well as the level of development of analytical chemistry itself.

Quote from a textbook on analytical chemistry by N.A. Menshutkin, 1897 issue: “Having presented the entire course of classes in analytical chemistry in the form of problems, the solution of which is left to the student, we must point out that analytical chemistry will provide a strictly defined path for such a solution to problems. This certainty (systematic solving problems of analytical chemistry) has great pedagogical importance. At the same time, the student learns to apply the properties of compounds to solve problems, derive reaction conditions, and combine them. This whole series of mental processes can be expressed as follows: analytical chemistry teaches chemical thinking. Achieving the latter seems to be the most important for practical studies in analytical chemistry. "

List of used literature

1.Alekseev V.N. Qualitative chemical semi-microanalysis course. - M.: Chemistry, 1979. - 584 p.

.Hydrogen sulfide-free methods of qualitative semi-microanalysis / under the general. ed. Kreshkova A.P. - M.: Vyssh.shk. 1971. - 222 p.

.Vasiliev V.P. Analytical chemistry: In four parts. - M.: Higher. school, 2004.

.Vasiliev A.M. Collection of problems in analytical chemistry. - M.: Goshimizdat. - 1985, 275 p.

.Zolotov Yu.A. Fundamentals of analytical chemistry. book. 1. - M.: Higher. school, 2004. - 360 p.

.Lurie Yu.Yu. Handbook of analytical chemistry. - M.: Chemistry 1971.- 453 p.

.Murashova V.I., Tananaeva A.N., Khovyakova R.F. Qualitative chemical fractional analysis. - M.: Chemistry, 1976. - 279 p.

.Kharitonov Yu.Ya. Analytical chemistry. Analytics 1. General theoretical basis. Qualitative analysis. - M.: Higher. school, 2001. - 615 p.

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The concepts of quantitative and qualitative methods in psychology

Defining methods as ways of cognition, S.L. Rubinstein noted that the methodology should be conscious and not turn into a form mechanically imposed on specific content Sciences. Consider the question of how cognizant paths in psychology are and how researchers understand and define quantitative and qualitative methods.

As the main psychological methods S.L. Rubinstein in " Fundamentals of General Psychology" names observation, experiment, methods of studying the products of activity. This list does not include quantitative methods.

In the 70s in domestic psychology the second classification of methods has become widespread psychological research, created by B.G. Ananiev.

He distinguishes the following groups of methods:

1. Organizational;
2. empirical;
3. Data processing methods;
4. Interpretation methods.

Quantitative and qualitative methods were classified as data processing methods. He defines quantitative methods as mathematical and statistical methods of processing psychological information, and qualitative methods are a description of those cases that most fully reflect the types and variants of mental phenomena and are an exception to the general rules.

Classification B.G. Ananiev was criticized by the representative of the Yaroslavl school V.N. Druzhinin, offering his own classification.

By analogy with other sciences, he distinguishes three classes of methods in psychology:

1. empirical;
2. Theoretical;
3. Interpretive.

Qualitative and quantitative methods are also not specified separately in the classification, but it is assumed that they are placed in the empirical methods section, which differs from the classification of B.G. Ananiev. Significantly supplemented the classification of B.G. Ananyeva, a representative of the Leningrad school of psychologists V.V. Nikandrov. He classifies quantitative and qualitative methods as non-empirical methods in accordance with the criterion of "staged psychological process". The author understands non-empirical methods as “research methods of psychological work outside the contact of the researcher and the individual.

In addition to the remaining differences in the classifications of S.L. Rubinstein and B.G. Ananiev, there are terminological discrepancies in the understanding of quantitative and qualitative methods.

An exact definition of these methods is not given in the works of V.V. Nikandrov. He defines qualitative methods functionally, from the point of view of the result, and calls them:

1. Classification;
2. Typology;
3. Systematization;
4. periodization;
5. Psychological casuistry.

He replaces the quantitative method with the definition of quantitative processing, which is mainly aimed at a formal, external study of the object. As synonyms for V.V. Nikandrov uses such expressions as quantitative methods, quantitative processing, quantitative research. The author refers to the main quantitative methods methods of primary and secondary processing.

Thus, the problem of terminological inaccuracy is quite relevant and takes on a new meaning when researchers seek to attribute quantitative methods to the new scientific sections "Psychometry" and "Mathematical Psychology".

Reasons for terminological discrepancies

There are a number of reasons why there is no strict definition of quantitative and qualitative methods in psychology:

• Quantitative methods within the framework of the domestic tradition have not received an unambiguously strict definition and classification, and this speaks of methodological pluralism;
• Quantitative and qualitative methods in the tradition of the Leningrad school are considered as a non-empirical stage of research. The Moscow school interprets these methods as empirical and elevates them to the status of a methodological approach;
• In the terminological confusion of the concepts of quantitative, formal, quantative, mathematical and statistical, there is a conventionalism that has developed in psychological society regarding the definition of these quantitative and qualitative methods;
• Borrowing from the American tradition of dividing all methods into quantitative and qualitative methods. Quantitative methods, more precisely research, involve the expression and measurement of results in quantitative terms. Qualitative methods are seen as "humanitarian" research;
• The definition of an unambiguous place and the ratio of quantitative and qualitative methods most likely leads to the fact that quantitative methods are subordinate to qualitative methods;
• The modern theory of method moves away from the classification of methods only on one basis and a strict definition of the procedure of the method. Methodologists distinguish three directions in the theory:
  1. Improvement of the traditional empirical model;
  2. Criticism of the empirical quantitative model;
  3. Analysis and testing of alternative research models.
• Different directions in the development of the theory of method reveal a tendency for researchers to gravitate toward qualitative methods.

Quantitative Methods

Target practical psychology is not about establishing patterns, but about understanding and describing problems, so it uses both qualitative and quantitative methods.

Quantitative methods are techniques for processing digital information, because they are mathematical in nature. Quantitative methods such as categorized observation, testing, document analysis, and even experiment provide information to diagnose a problem. The efficiency of work is determined at the final stage. The main part of the work - conversations, trainings, games, discussions - is carried out using qualitative methods. Of the quantitative methods, testing is the most popular.

Quantitative methods are widely used in scientific research and in the social sciences, for example, in testing statistical hypotheses. Quantitative methods are used to process the results of mass surveys public opinion. To create tests, psychologists use the apparatus of mathematical statistics.

Methods of quantitative analysis are divided into two groups:

1. Methods statistical description. As a rule, they are aimed at obtaining quantitative characteristics;
2. Methods of statistical inference. They make it possible to correctly extend the obtained results to the entire phenomenon, to draw a conclusion of a general nature.

With the help of quantitative methods, stable trends are identified and their explanations are built.

The disadvantages of the quantitative control method are related to its limitations. These methods of assessing knowledge in the field of teaching psychology can only be used for intermediate control, testing knowledge of terminology, textbooks. experimental studies or theoretical concepts.

Qualitative Methods

Increased interest and popularity, qualitative methods acquire only in Lately, which is related to the demands of practice. In applied psychology, the scope of qualitative methods is very wide:

• Social psychology carries out humanitarian expertise of social programs - pension reform, reform of education, health care - using qualitative methods;
• Political psychology. Qualitative methods are necessary here to build an adequate and effective election campaign, to form a positive image of politicians, parties, the entire system government controlled. Important here will be not only quantitative indicators of the trust rating, but also the reasons for this rating, ways to change it, etc.
• With the help of qualitative methods, the psychology of the mass media explores the degree of trust in one or another print publication, specific journalists, and programs.

A decisive role in the development of qualitative methods in psychology was thus played by the need for dialogue psychological science with various fields of practice.

Qualitative methods focus on the analysis of information, which is mainly presented in verbal form, therefore, there is a need to compress this verbal information, i.e. obtain it in a more compact form. In this case, coding acts as the main compression technique.

Coding involves the selection of semantic segments of the text, their categorization and reorganization.

Examples of information compression are schemes, tables, diagrams. Thus, coding and visual representation of information are the main methods of qualitative analysis.

The analysis of a substance can be carried out in order to establish its qualitative or quantitative composition. Accordingly, a distinction is made between qualitative and quantitative analysis.

Qualitative analysis allows you to determine which chemical elements the analyzed substance consists and what ions, groups of atoms or molecules are included in its composition. When studying the composition of an unknown substance, a qualitative analysis always precedes a quantitative one, since the choice of a method for the quantitative determination of the constituent parts of the analyzed substance depends on the data obtained during its qualitative analysis.

Qualitative chemical analysis is mostly based on the transformation of the analyte into some new compound with characteristic properties: a color determined by physical condition, crystalline or amorphous structure, specific odor, etc. The chemical transformation that occurs in this case is called a qualitative analytical reaction, and the substances that cause this transformation are called reagents (reagents).

When analyzing a mixture of several substances with similar chemical properties, they are first separated and only then characteristic reactions are carried out for individual substances (or ions), therefore, qualitative analysis covers not only individual reactions for detecting ions, but also methods for their separation.

Quantitative analysis allows you to establish the quantitative ratio of the parts of a given compound or mixture of substances. Unlike qualitative analysis, quantitative analysis makes it possible to determine the content of individual components of the analyte or the total content of the analyte in the test product.

Methods of qualitative and quantitative analysis, allowing to determine the content in the analyzed substance individual elements, are called elements of analysis; functional groups - functional analysis; individual chemical compounds characterized by a certain molecular weight - molecular analysis.

A set of various chemical, physical and physico-chemical methods for separating and determining individual structural (phase) components of heterogeneous systems that differ in properties and physical structure and are limited from each other by interfaces is called phase analysis.

Qualitative analysis methods

Qualitative analysis uses characteristic chemical or physical properties of the substance to establish the composition of the substance under investigation. There is absolutely no need to isolate the discovered elements in their pure form in order to detect their presence in the analyzed substance. However, the isolation of metals, nonmetals, and their compounds in pure form is sometimes used in qualitative analysis for their identification, although this way of analysis is very difficult. To detect individual elements, simpler and more convenient methods of analysis are used, based on chemical reactions characteristic of the ions of these elements and occurring under strictly defined conditions.

An analytical sign of the presence of the desired element in the analyzed compound is the release of a gas that has a specific odor; in the other - the precipitation, characterized by a certain color.

Reactions between solids and gases. Analytical reactions can take place not only in solutions, but also between solid and gaseous substances.

An example of a reaction between solids is the reaction of the release of metallic mercury when dry salts of it are heated with sodium carbonate. The formation of white smoke from the interaction of gaseous ammonia with hydrogen chloride can serve as an example of an analytical reaction involving gaseous substances.

The reactions used in qualitative analysis can be divided into the following groups.

1. Precipitation reactions, accompanied by the formation of precipitates of various colors. For example:

CaC2O4 - white

Fe43 - blue,

CuS - brown - yellow

HgI2 - red

MnS - flesh - pink

PbI2 - golden

The resulting precipitates may differ in a certain crystal structure, solubility in acids, alkalis, ammonia, etc.

2. Reactions accompanied by the formation of gases with a known odor, solubility, etc.

3. Reactions accompanied by the formation of weak electrolytes. Among such reactions, which result in the formation of: CH3COOH, H2F2, NH4OH, HgCl2, Hg(CN)2, Fe(SCN)3, etc. Reactions of the same type can be considered reactions of acid-base interaction, accompanied by the formation of neutral water molecules, reactions of the formation of gases and precipitates that are poorly soluble in water, and complexation reactions.

4. Reactions of acid-base interaction, accompanied by the transition of protons.

5. Complexation reactions accompanied by the addition of various legends - ions and molecules - to the atoms of the complexing agent.

6. Complexation reactions associated with acid-base interaction

7. Oxidation reactions - reductions, accompanied by the transition of electrons.

8. Oxidation reactions - reductions associated with acid - base interaction.

9. Oxidation-reduction reactions associated with complex formation.

10. Oxidation reactions - reductions, accompanied by the formation of precipitation.

11. Ion exchange reactions occurring on cation exchangers or anion exchangers.

12. Catalytic reactions used in kinetic methods of analysis

Wet and dry analysis

The reactions used in qualitative chemical analysis are most often carried out in solutions. The analyte is first dissolved and then the resulting solution is treated with appropriate reagents.

To dissolve the analyte, distilled water, acetic and mineral acids, aqua regia, aqueous ammonia, organic solvents, etc. are used. The purity of the solvents used is important condition to get correct results.

The substance transferred into solution is subjected to systematic chemical analysis. A systematic analysis consists of a series of preliminary tests and sequentially performed reactions.

The chemical analysis of test substances in solutions is called wet analysis.

In some cases, substances are analyzed dry, without transferring them into solution. Most often, such an analysis is reduced to testing the ability of a substance to color a colorless flame of a burner in a characteristic color or to impart a certain color to a melt (the so-called pearl) obtained by heating a substance with sodium tetraborate (borax) or sodium phosphate ("phosphorus salt") in a platinum wire.

Chemical and physical method of qualitative analysis.

Chemical methods of analysis. Methods for determining the composition of substances based on their use chemical properties are called chemical methods of analysis.

Chemical methods of analysis are widely used in practice. However, they have a number of disadvantages. So, to determine the composition given substance sometimes it is necessary to first separate the determined component from foreign impurities and isolate it in its pure form. The isolation of substances in pure form is often a very difficult and sometimes impossible task. In addition, in order to determine small amounts of impurities (less than 10-4%) contained in the analyte, it is sometimes necessary to take large samples.

Physical methods of analysis. The presence of a particular chemical element in a sample can be detected without resorting to chemical reactions, based directly on the study physical properties of the substance under study, for example, the coloring of a colorless burner flame in characteristic colors by volatile compounds of certain chemical elements.

Methods of analysis, by which it is possible to determine the composition of the substance under study, without resorting to the use of chemical reactions, are called physical methods of analysis. Physical methods of analysis include methods based on the study of optical, electrical, magnetic, thermal and other physical properties of the analyzed substances.

Among the most widely used physical methods of analysis are the following.

Spectral qualitative analysis. Spectral analysis is based on the observation of emission spectra (emission spectra, or radiation) of the elements that make up the analyte.

Luminescent (fluorescent) qualitative analysis. Luminescent analysis is based on the observation of luminescence (light emission) of analytes caused by the action of ultraviolet rays. The method is used to analyze natural organic compounds, minerals, medicines, a number of elements, etc.

To excite the luminescence, the test substance or its solution is irradiated with ultraviolet rays. In this case, the atoms of matter, having absorbed a certain amount of energy, pass into an excited state. This state is characterized by a larger supply of energy than the normal state of matter. During the transition of a substance from an excited to a normal state, luminescence occurs due to excess energy.

Luminescence that decays very quickly after cessation of irradiation is called fluorescence.

Observing the nature of the luminescent glow and measuring the intensity or brightness of the luminescence of a compound or its solutions, one can judge the composition of the substance under study.

In some cases, the definitions are based on the study of fluorescence resulting from the interaction of the analyte with certain reagents. Fluorescent indicators are also known, which are used to determine the reaction of the medium by changing the fluorescence of the solution. Luminescent indicators are used in the study of colored media.

X-ray diffraction analysis. By using x-rays you can set the size of atoms (or ions) and their mutual arrangement in the molecules of the sample under study, i.e., it is possible to determine the structure of the crystal lattice, the composition of the substance, and sometimes the presence of impurities in it. The method does not require chemical treatment of the substance and its large quantities.

Mass spectrometric analysis. The method is based on the determination of individual ionized particles deflected by an electromagnetic field to a greater or lesser extent depending on the ratio of their mass to charge (for more details, see Book 2).

Physical methods of analysis, having a number of advantages over chemical ones, in some cases make it possible to solve problems that cannot be resolved by methods of chemical analysis; using physical methods, it is possible to separate elements that are difficult to separate by chemical methods, as well as to conduct continuous and automatic recording of readings. Very often, physical methods of analysis are used along with chemical ones, which makes it possible to use the advantages of both methods. The combination of methods is of particular importance when determining negligible amounts (traces) of impurities in the analyzed objects.

Macro, semi-micro and micro methods

Analysis of large and small quantities of the test substance. In the old days, chemists used large quantities of the substance to be analyzed. In order to determine the composition of a substance, samples of several tens of grams were taken and dissolved in a large volume of liquid. This also required chemical glassware of the appropriate capacity.

At present, chemists manage in analytical practice with small amounts of substances. Depending on the amount of the analyte, the volume of solutions used for analysis, and mainly on the technique used to perform the experiment, analysis methods are divided into macro-, semi-micro- and micro-methods.

When performing a macro analysis, a few milliliters of a solution containing at least 0.1 g of the substance is taken to carry out the reaction, and at least 1 ml of the reagent solution is added to the test solution. The reactions are carried out in test tubes. During precipitation, voluminous precipitates are obtained, which are separated by filtration through funnels with paper filters.

Drop analysis

Technique for carrying out reactions in drop analysis. The so-called drop analysis, introduced into analytical practice by N. A. Tananaev, has acquired great importance in analytical chemistry.

When working with this method, the phenomena of capillarity and adsorption are of great importance, with the help of which it is possible to open and separate various ions in their joint presence. In drop analysis, individual reactions are carried out on porcelain or glass plates or on filter paper. In this case, a drop of the test solution and a drop of a reagent that causes a characteristic coloration or the formation of crystals are applied to the plate or paper.

When performing the reaction on filter paper, the capillary-adsorption properties of the paper are used. The liquid is absorbed by the paper, and the resulting colored compound is adsorbed on a small area of ​​the paper, thereby increasing the sensitivity of the reaction.

Microcrystalloscopic analysis

The microcrystalloscopic method of analysis is based on the detection of cations and anions by means of a reaction, as a result of which a compound is formed that has a characteristic crystal shape.

Previously, this method was used in qualitative microchemical analysis. Currently, it is also used in drip analysis.

To examine the resulting crystals in microcrystalloscopic analysis, a microscope is used.

Crystals of a characteristic shape are used when working with pure substances by introducing a drop of a solution or a crystal of a reagent into a drop of the test substance placed on a glass slide. After a while, clearly distinguishable crystals of a certain shape and color appear.

Powder grinding method

To detect some elements, the method of grinding a powdered analyte with a solid reagent in a porcelain plate is sometimes used. The element to be discovered is detected by the formation of characteristic compounds that differ in color or odor.

Methods of analysis based on heating and fusion of a substance

pyrochemical analysis. For the analysis of substances, methods based on heating the test solid or its fusion with appropriate reagents are also used. Some substances, when heated, melt at a certain temperature, others sublime, and precipitation characteristic of each substance appears on the cold walls of the device; some compounds, when heated, decompose with the release of gaseous products, etc.

When the analyte is heated in a mixture with the appropriate reagents, reactions occur, accompanied by a change in color, the release of gaseous products, and the formation of metals.

Spectral qualitative analysis

In addition to the method described above for observing the coloring of a colorless flame with the naked eye when a platinum wire with the analyzed substance is introduced into it, other methods for studying light emitted by incandescent vapors or gases are currently widely used. These methods are based on the use of special optical devices, the description of which is given in the physics course. In such spectral devices, the decomposition into a spectrum of light with different wavelengths occurs, emitted by a sample of a substance heated in a flame.

Depending on the method of observing the spectrum, spectral instruments are called spectroscopes, which are used to visually observe the spectrum, or spectrographs, in which spectra are photographed.

Chromatographic analysis method

The method is based on the selective absorption (adsorption) of individual components of the analyzed mixture by various adsorbents. Adsorbents are called solid bodies on the surface of which the adsorbed substance is absorbed.

The essence of the chromatographic method of analysis is briefly as follows. A solution of a mixture of substances to be separated is passed through a glass tube (adsorption column) filled with an adsorbent.

Kinetic methods of analysis

Methods of analysis based on measuring the reaction rate and using its magnitude to determine the concentration are combined under the general name of kinetic methods of analysis (K. B. Yatsimirsky).

Qualitative detection of cations and anions by kinetic methods is carried out quite quickly and relatively simply, without the use of complex instruments.

Qualitative the analysis is intended for the qualitative discovery of individual chemical elements, ions and functional groups. The presence in the analyzed mixture of individual substances, elements, ions and functional groups is usually detected using chemical qualitative reactions or on the basis of some physical properties of substances - spectra in the visible and ultraviolet regions of light, radioactive radiation, capabilities To adsorption.

Quantitative analysis is carried out in various ways. Chemical methods are widespread, in which the amount of a substance is determined by the amount of reagent used for analysis, by the amount of sediment, etc. Often, for the quantitative determination of substances, their physical properties are used - the magnitude of the refractive angle of solutions of substances, the color intensity, the value electric current flowing through the solution.

ANALYSIS METHODS

The analysis can be carried out by chemical, instrumental (physical and physico-chemical) methods.

Chemical methods of analysis involve the chemical interaction of substances. The results of a chemical reaction between a substance and a reagent are important here. Chemical methods of analysis are widely used for qualitative analysis, since the nature of the precipitate, the change in color of the solution, the formation of a certain gas can determine which substance is present in the solution.

In quantitative chemical analysis, the formed precipitate is weighed, the reagent solution is added until the color of the solution or other physical characteristics of the substance change, and the amount of the substance is determined by the amount of the reagent used for analysis.

Instrumental (physical, physico-chemical) methods of analysis use the physical properties of substances. Qualitative analysis when applying physical methods is carried out by changing the color of the flame that occurs when a substance is introduced into it, by the absorption and emission spectra of the substance, by the melting point, boiling point and other properties that are characteristic of substances. Quantitative analysis by physical methods is carried out by observing changes in the physical properties of a substance with a change in its quantity. Usually, the intensity of color, the angle of refraction of the solution, the magnitude of the electric current passing through the solution depend on the amount of the substance, and this dependence can be used to determine the amount of the substance.

Physico-chemical methods of analysis combine physical and chemical methods. When carrying out physicochemical methods, the result of a chemical reaction is observed by changes in the physical properties of a substance or its solution. Physicochemical methods have become widespread and are being intensively developed.

Qualitative (non-formalized) methods of analysis are based on the description of analytical procedures at the logical level, and not on strict analytical dependencies. These include methods: expert assessments, scenarios, morphological, comparison of systems of indicators, etc. The application of these methods is characterized by a certain subjectivity, since the intuition, experience and knowledge of the analyst are of great importance.

Expert assessments are quantitative or ordinal assessments of processes or phenomena that cannot be directly measured. They are based on the judgments of experts and therefore cannot be considered completely objective. Are being developed scientific methods such processing of individual expert assessments, so that they give in the aggregate more or less objective answers (using thoughtful forms of questions and answers, which are subsequently processed by a computer).

Scenario - a description of possible options for the development of the object under study under various combinations of certain conditions (selected in advance) for the purpose of further analysis and selection of the most realistic one.

Morphological analysis is used to predict complex processes. This is an expert method of a systematic review of all possible combinations of development of individual elements of the system under study. It is based on complete and rigorous classifications of objects, phenomena, properties and parameters of the system, which make it possible to build and evaluate possible scenarios for its development as a whole.

Quantitative (formalized) methods of analysis are based on fairly strict formalized analytical dependencies. Let's list them:

Classical methods of analysis - the method of chain substitutions, balance sheet, percentage numbers, differential, integral, discounting, etc.;

Methods of economic statistics - average and relative values, grouping, graphical, index, elementary methods for processing time series;

Mathematical and statistical methods for studying relationships - correlation analysis, regression analysis, analysis of variance, factorial analysis, principal components method, analysis of covariance, etc.;

Econometric methods - matrix methods, harmonic analysis, spectral analysis, methods of the theory of production functions, methods of the theory of input-output balance;

Methods of economic cybernetics and optimal programming - methods of system analysis, linear programming, non-linear programming, dynamic programming, etc.;

Methods of operations research and decision theory - methods of graph theory, game theory, tree method, Bayesian analysis, queuing theory, network planning and management methods.

Mathematical methods make it possible to replace approximate calculations with exact calculations, to carry out multidimensional comparative analysis which is practically impossible by hand.

3. Methods of financial analysis: horizontal, vertical and trend analysis

Horizontal analysis method- used to assess changes in indicators in dynamics. To determine the absolute change in the indicator, a value is calculated equal to:

∆З = З 1 - З 0,

where Z 1 - the value of the indicator in the reporting period;

З 0 - the value of the indicator in the base period.

To assess the growth rate of the indicator, the value is calculated:

T p (Z) \u003d Z 1: Z 0.

The value of the indicator shows how many times the value of the indicator has changed in the reporting period compared to the base period.

To assess the relative change, the growth rate is calculated using the formula:

T pr (Z) \u003d (Z 1: Z 0 - 1) x 100% \u003d ∆Z: Z 0 x 100%.

The growth rate of T pr (Z) shows how many percent the value of the indicator has changed in the reporting period compared to the base period.

Vertical analysis method- used to analyze complex economic indicators, allows you to determine the share of each component of a complex indicator in the total population.

To evaluate the structure, the formula is used:

where Di - i-th share component;

Zi - absolute i-th value a component included in a complex indicator;

Z - the value of this complex indicator.

To assess the dynamics of the structure of a complex economic indicator, a horizontal method is used, on the basis of which the absolute and relative changes in each component are determined:

∆Di \u003d Di 1 - Di 0; T pr (Di) \u003d ∆Di: Di ​​0 x 100%.

Vertical analysis of the book value of the organization allows you to determine the quality of the use of a particular type of resource in economic activity, to conduct a comparative analysis of the organization, taking into account industry specifics and other characteristics. Relative indicators of the Di type, in contrast to absolute ones, are more convenient when analyzing the activities of an organization in terms of inflation, and allow an objective assessment of changes in components in dynamics.

Trend analysis method- based on the use of data series of the dynamics of the studied factors, for example, the balance sheet, the structure of assets and liabilities of the organization. Usage this method allows you to assess the main directions of development of the organization both at the current moment and in subsequent periods.

For each main indicator characterizing the organization's activities, an analysis is made of changes in growth rates, average growth rates for the periods under consideration (month, quarter, half year, year), and the main directions of change in these indicators are identified. The results of calculating the average values ​​of the growth rate (growth rate), taking into account the links between the main indicators, allow us to calculate the forecast value of the indicator under study for the future. A forecast based on trend models allows, with a certain degree of reliability, to calculate the value of the predicted factor, choose the most rational management decisions and evaluate the consequences of these decisions for the financial and economic activities of the organization.