Reactions used in redox titrations. Redox titration

Redox titration methods are based on the use of reactions associated with electron transfer, that is, redox processes.

Oxidation-reduction reactions are reactions in which reactants gain or lose electrons. An oxidizing agent is a particle (ion, molecule, element) that adds electrons and moves from a higher oxidation state to a lower one, i.e. is being restored. A reducing agent is a particle that donates electrons and moves from a lower oxidation state to a higher one, i.e. oxidizes.

2КМnО 4 +10FeSO 4 +8Н 2 SO 4 ↔2МnSO 4 + 5Fe 2 (SO 4) 3 +К 2 SO 4 + 8Н 2 О

Fe 2+ - e ↔ Fe 3+

MnO 4 - + 5e + 8H + ↔ Mn 2+ + 4H 2 O

Redox titration methods are suitable for the determination of many organic compounds, including pharmaceuticals, the vast majority of which are potential reduction agents.

Depending on the titrant used, permanganatometry, iodometry, dichromatometry, and bromatometry are distinguished. In these methods, KMnO 4, I 2, K 2 Cr 2 O 7, KBrO 3, etc. are used as standard solutions, respectively.

Of all the types of chemical reactions used in quantitative analysis, oxidation-reduction reactions (ORRs) are the most complex in mechanism.

A distinctive feature of ORR is the transfer of electrons between reacting particles, as a result of which the oxidation state of the reacting particles changes.

In this case, two processes occur simultaneously - the oxidation of some and the reduction of others. Thus, any OVR written in general form

aOx 1 + bRed 2 = aRed 1 + bOx 2

Can be represented as two half-reactions:

Red 2 – a= Ox 2

The initial particle and the product of each half-reaction constitute an OB pair. For example, in the oxidation reaction of iron(II) with potassium permanganate, two OM pairs are involved: Fe 3 /Fe 2+ and MnO 4 - /Mn 2+.

During the titration process using the oxidation-reduction method, a change occurs in the RH potentials of the interacting systems. If the conditions differ from standard ones, i.e. The activities of potential-determining ions are not equal to 1 (a≠1), the equilibrium potential of the OM half-reaction aOx 1 + n= bRed 1 can be calculated using the Nernst equation:

E Ox 1/ Red 1 = E º + ,

R – universal gas constant (8.314 J/mol∙deg., F – Faraday’s constant (9.6585 cells/mol), E – OB potential of the system, E º – standard OB potential.

If we substitute the values of constant quantities, T = 298 K (i.e. 25 º C) and replace the natural logarithm with a decimal one, and activity with concentration, then the Nernst equation will take the following form:

E Ox 1/ Red 1 = E º + .

Oxidation-reduction reactions (ORR) are more complex than ion exchange reactions and have the following features:

1. The potential of the system depends on the value of the standard RH potential of the system, the concentrations of the oxidizing agent and reducing agent, the concentration of hydrogen ions and temperature.

2. Reactions often occur in several stages, each of them proceeding at a different rate.

3. The rate of ORR is lower than the rate of ion exchange reactions. Often special conditions are required to ensure reactions proceed to completion.

4. The presence of precipitants or complexing agents, causing a change in the concentrations of oxidized or reduced forms, leads to a change in the RH potential of the system.

The oxidation-reduction reactions on the basis of which titration is carried out must satisfy all the requirements for reactions during titration. To increase the rate of ORR, various techniques are used: increasing the temperature, increasing the concentration of reactants, changing the pH of the solution, or introducing a catalyst.

The equivalence point is most often fixed using Red/Ox – indicators, i.e. organic compounds that change their color depending on the potential of the system. With an excess of the oxidizing agent, an oxidized form of the indicator is formed, and an excess of the reducing agent leads to the formation of its reduced form. The process of transition from the oxidized form to the reduced form and back, accompanied by a change in color, can be repeated many times without destroying the indicator. Such indicators include diphenylamine (blue-violet in the oxidized state and colorless in the reduced state) and N-phenylanthranilic acid (oxidized form is red, reduced form is colorless).

For some reactions they use specific indicators are substances that change color when reacting with one of the titration components. For example, such an indicator is starch, which forms a blue adsorption compound with iodine.

In some cases, titration without an indicator is used if the color of the titrant is quite bright and changes sharply as a result of the reaction. An example is titration with potassium permanganate (KMnO 4), the raspberry solution of which becomes discolored when MnO 4 - is reduced to Mn 2+. When all the titrated substance has reacted, an extra drop of KMnO 4 solution will turn the solution pale pink.

Introduction

The titrimetric or volumetric method of analysis is one of the methods of quantitative analysis. This method is based on the accurate measurement of the volumes of solutions of two substances that react with each other. Quantitative determination using the titrimetric method of analysis is performed quite quickly, which makes it possible to carry out several parallel determinations and obtain a more accurate arithmetic average. All calculations of the titrimetric method of analysis are based on the law of equivalents.

Titration is the gradual addition of a titrated solution of a reagent (titrant) to the solution being analyzed to determine the equivalence point. The titrimetric method of analysis is based on measuring the volume of a reagent of a precisely known concentration spent on the reaction of interaction with the substance being determined. Equivalence point is the point of titration when an equivalent ratio of reactants is achieved.

The following requirements apply to reactions used in quantitative volumetric analysis:

The reaction must proceed in accordance with the stoichiometric reaction equation and must be practically irreversible. The result of the reaction should reflect the amount of the analyte. The equilibrium constant of the reaction must be sufficiently large.

The reaction must proceed without side reactions, otherwise the law of equivalents cannot be applied.

The reaction must proceed at a sufficiently high speed, i.e. in 1-3 seconds. This is the main advantage of titrimetric analysis.

There must be a way to fix the equivalence point. The end of the reaction should be determined quite easily and simply.

If a reaction does not satisfy at least one of these requirements, it cannot be used in titrimetric analysis.

Many methods for the detection, determination and separation of substances are based on oxidation-reduction (redox) reactions. Those titrimetric methods in which solutions of oxidizing or reducing agents are used as titrants are called redox (redoximetric) titration methods.

1. Theoretical foundations of methods

Of all the types of chemical reactions used in quantitative analysis, redox reactions are the most complex in mechanism. However, it is possible to establish some analogy for redox reactions and acid-base reactions: exchange of protons in acid-base interaction and exchange of electrons in redox reactions, a reducing agent - an electron donor is similar to an acid - a proton donor, an oxidizing agent is an analogue of a base , the oxidized and reduced forms form a conjugate pair like the acidic and basic forms; the ratio of the concentrations of these forms quantitatively characterizes the oxidizing capacity (potential) of the system and acidity (pH), respectively.

1.1 Redox systems

A distinctive feature of redox reactions is the transfer of electrons between reacting particles - ions, atoms, molecules and complexes, as a result of which the oxidation state of these particles changes, for example

Fe2+ ̶ e̅ = Fe3+.

Since electrons cannot accumulate in a solution, two processes must occur simultaneously - losses and acquisitions, that is, the process of oxidation of some particles and reduction of other particles. Thus, any redox reaction can always be represented in the form of two half-reactions:

aOx1 + bRed2 = aRed1 + bOx2

The parent particle and the product of each half-reaction constitute a redox couple or system. In the above half-reactions, Red1 is conjugated to Ox1 and Ox2 is conjugated to Red1.

Not only particles in solution, but also electrodes can act as electron donors or acceptors. In this case, the redox reaction occurs at the electrode-solution interface and is called electrochemical.

Redox reactions, like all chemical reactions, are reversible to one degree or another. The direction of reactions is determined by the ratio of the electron-donor properties of the components of the system of one redox half-reaction and the electron-acceptor properties of the second (provided that the factors influencing the equilibrium shift are constant). The movement of electrons during a redox reaction creates a potential. Thus, potential, measured in volts, serves as a measure of the redox ability of a compound.

To quantitatively assess the oxidative (reductive) properties of the system, an electrode made of a chemically inert material is immersed in the solution. At the phase interface, an electron exchange process occurs, leading to the emergence of a potential, which is a function of the activity of electrons in the solution. The higher the oxidizing capacity of the solution, the greater the potential value.

The absolute value of a system's potential cannot be measured. However, if you choose one of the redox systems as a standard one, then relative to it it becomes possible to measure the potential of any other redox system, regardless of the selected indifferent electrode. The H+/H2 system, the potential of which is assumed to be zero, is chosen as the standard one.

Rice. 1. Diagram of a standard hydrogen electrode

1. Platinum electrode.

2. Supply of hydrogen gas.

3. Acid solution (usually HCl<#"522214.files/image003.gif">

or negative if the system plays the role of a reducing agent, and a reduction half-reaction occurs at the hydrogen electrode:

The absolute value of the standard potential characterizes the “strength” of the oxidizing agent or reducing agent.

The standard potential - a thermodynamic standardized value - is a very important physicochemical and analytical parameter that allows one to evaluate the direction of the corresponding reaction and calculate the activities of reacting particles under equilibrium conditions.

To characterize a redox system under specific conditions, the concept of real (formal) potential E0 is used, which corresponds to the potential established at the electrode in a given specific solution when the initial concentrations of the oxidized and reduced forms of potential-determining ions are equal to 1 mol/l and the fixed concentration of all other components solution.

From an analytical point of view, real potentials are more valuable than standard potentials, since the true behavior of the system is determined not by the standard, but by the real potential, and it is the latter that allows one to predict the occurrence of a redox reaction under specific conditions. The actual potential of the system depends on the acidity, the presence of foreign ions in the solution and can vary over a wide range.

1.2 Nernst equation

For conditions other than standard (activities of potential-determining ions are not equal to unity), the equilibrium potential of the redox half-reaction

аOx + n e̅ = bRed

can be calculated using the Nernst equation:

where E0 is standard potential, V; R is the universal gas constant equal to 8.314 J∙mol-1∙K-1; T - absolute temperature, K; n is the number of electrons participating in the half-reaction; F is Faraday's constant, equal to 96500 C∙mol-1.

After substituting the indicated values (T = 298K) and replacing the natural logarithm with a decimal one, the Nernst equation takes the form:

If we take into account that a = γ[C], then

For dilute solutions a ≈ C; the activity of metals, pure solid phases and solvents is taken equal to unity, the activity of a gas is taken to be equal to its partial pressure.

The potential of a redox system is equal to its standard potential if aOx = aRed = 1. In general, the potential characterizing a redox system depends on the nature of its components (E0) and the ratio of activities (concentrations) of the reduced and oxidized forms. The E0 value reflects the effect on the potential of substances whose concentration in solution does not change during the redox reaction.

The Nernst equation is applicable to thermodynamically reversible redox half-reactions. For irreversible systems, the prelogarithmic coefficient 0.059/n differs from the theoretically calculated one.

If the reaction occurs with the participation of molecules or ions of the medium, then their concentrations are also introduced into the Nernst equation. So for a half-reaction, the Nernst equation can be written as follows:

The real potential of the redox pair of oxidizing titrants should have a potential value 0.4 - 0.5 V higher than the potential of the redox pair of the titrated reducing agent , only in this case the requirements for reactions in redoximetry are met. To regulate the potential of redox couples of the titrant and the analyte, a change in the pH of the medium, complexing additives, an increase in temperature, etc. are used.

The equilibrium redox potential depends on a number of factors:

) From the pH of the environment. Standard redox potential for the above reaction . As the pH of the solution increases, the redox potential of this pair will decrease.

) From the concentration (activity) of the oxidized and reduced forms of the oxidizing agent or reducing agent. With changes in the concentrations (activities) of the oxidized and reduced forms, the value of the redox potential may change. For example, for a couple provided the standard redox potential is 0.77 V. Nernst's half-reaction equation has the form:

By changing the concentrations of the oxidized or reduced forms of a substance, you can change the value of the redox potential.

3) From the process of complexation. The value of the redox potential changes significantly if the oxidized or reduced form of the substance in the analyzed solution participates in the process of complex formation.

The potential of a redox pair, for example, in the absence of complexation will be at 25 0C equal to:

Upon complexation with the ligand, the ion concentration will decrease:

The stability constant is equal to:

From this expression, the ion concentration

Substituting it into the original Nernst equation, after a series of transformations we obtain:

4) From the formation of poorly soluble substances. In the presence of ions capable of forming poorly soluble compounds, the potential of a redox couple can be calculated as follows:

2. Titration curves

In titrimetric methods, the calculation and construction of a titration curve makes it possible to estimate how successful the titration will be and allows the choice of an indicator. When constructing a redox titration curve, the system potential is plotted along the ordinate axis, and the titrant volume or titration percentage is plotted along the abscissa axis.

Consider, as an example, the titration of 100 ml of a 0.1 N solution of FeSO4 with a 0.1 N solution of KMnO4 in an acidic medium ([H+] = 1 mol/l):

At any point in the titration, the solution always contains two redox pairs: Fe3+/Fe2+ and MnO4-/Mn2+. The concentrations of the reactants are set in such a way that, at equilibrium, the potentials of the two systems are equal at any point on the titration curve. Therefore, two equations are suitable for calculating the potential:

The calculated potentials satisfy both equations, but the calculation can be simplified based on the following. While not all Fe2+ ions have yet been titrated, the concentrations of Fe3+ and Fe2+ are easy to calculate. The concentration of MnO4- ions that did not enter the reaction is much more difficult to calculate, since it is necessary to use the equilibrium constant of this redox reaction, which must be known. Therefore, at first, up to the equivalence point, it is more convenient to use the equation for the Fe3+/Fe2+ system.

When introducing excess permanganate, it is easy to calculate the concentrations of MnO4- and Mn2+ and the potential value due to this pair.

) Calculate the potential before titration begins. When calculating the first point on the titration curve before adding permanganate to the solution, it is necessary to take into account that only Fe2+ ions cannot be present in the solution, and Fe3+ ions are always present in low concentrations, but their equilibrium concentration is unknown. For this reason, when calculating redox titration curves, the potential value for this point, corresponding to the moment when the titrant has not yet been added to the test solution, is usually not given.

) Calculation of the potential during titration to the equivalence point. Let us calculate the potential of the system for the point on the curve when 50 ml of 0.1 N KMnO4 solution is added to 100 ml of 0.1 N FeSO4 solution (50% titration). In this case, there are three reaction components in the solution: Fe3+, Fe2+ and Mn2+; the concentration of the fourth (MnO4-) is very low. The equilibrium concentration of Mn2+ ions is equal to the total concentration of the KMnO4 solution minus the negligible concentration of unreacted permanganate ions:

This approximation is acceptable since the equilibrium constant of this reaction is large (K≈1064). The concentration of Fe3+ ions is the same:

Substituting the values of the equilibrium concentrations of iron (II) and iron (III), we obtain:

i.e., when titrating 50% of the analyte, the system potential is equal to the standard potential of the redox couple of the analyte.

Of particular interest are those points on the titration curve that correspond to 0.1 ml of deficiency and 0.1 ml of excess of KMnO4 (0.1% equivalent volume), since they determine the potential jump near the equivalence point. Let's calculate the first of them (the beginning of the jump). Since at this moment 99.9 ml of KMnO4 solution was added, 0.1 ml of Fe2+ remained in the solution untitered. Therefore, for this moment:

3) Calculation of the potential at the equivalence point. In the above equations for the potential values of the reacting redox pairs, we equalize the coefficients of the terms containing logarithms by multiplying the second term of the equation by 5. After this, we add both equations term by term, taking into account that [H+] = 1 mol/l:

-----------------

Since at the equivalence point MnO4- ions are introduced into the solution in an amount corresponding to the reaction equation, then at equilibrium there should be 5 Fe2+ ions for each MnO4- ion. Consequently, at the equivalence point, the concentration of Fe2+ ions is 5 times greater than the concentration of MnO4- ions, i.e. = 5. At the same time = 5. Dividing the second of these equalities by the first, we obtain:

And .= 0.6E = 0.77 + 5 ∙ 1.51,

E = (0.77 + 5 ∙ 1.51)/6 = 1.39B.

In general, the potential at the equivalence point is calculated using the formula

where a is the number of electrons accepted by the oxidizing agent; b is the number of electrons donated by the reducing agent.

) Calculation of the potential after the equivalence point. When 100.1 ml of KMnO4 solution is introduced (end of the jump), the solution, in addition to equivalent amounts of Fe3+ and Mn2+ ions, contains an excess of MnO4- ions. The concentration of iron (II) is very low, therefore:

and the potential of the system at this moment of titration is equal to

The potential jump is 1.48 - 0.95 = 0.53 V. The results of calculating the titration curve are summarized in table. 1 and are presented in Fig. 2.

As follows from Table 1 and Fig. 2, the titration curve is asymmetric. The titration jump is in the range of 0.95 - 1.48 V, and the equivalence point is not in the middle of the jump.

Table 1. Change in redox potential when titrating 100 ml of 0.1 N FeSO4 solution with 0.1 N KMnO4 solution.

Titration stages	Added KMnO4, ml	Excess, ml	Calculations E, V


			E = 0.77 + 0.059lg100.82
			E = 0.77 + 0.059lg1000.88
			E = 0.77 + 0.059lg10000.95
					E = (0.77 + 5∙1.51)/(5 + 1)
				E = 1.51 + (0.059/5)log0.0011.47
				E = 1.51 + (0.059/5)log0.011.48
				E = 1.51 + (0.059/5)log0.11.49
				E = 1.51 + (0.059/5)log11.51

Fig.2. Titration curve of 100 ml of 0.1 N FeSO4 solution with 0.1 N KMnO4 solution ([H+] = 1 mol/l).

With a twofold excess of titrant, the system potential is equal to the standard potential of the titrant redox couple.

For a more rigorous calculation of titration curves, real potentials should be used instead of standard ones.

2.2 Influence of titration conditions on the course of the curves

oxidative reduction titration

The titration curve is constructed based on the values of redox potentials, so all factors influencing the potential will affect the shape of the titration curve and the jump on it. Such factors include the values of the standard potential of the analyte and titrant systems, the number of electrons participating in half-reactions, the pH of the solution, the presence of complexing reagents or precipitants, and the nature of the acid. The greater the number of electrons involved in the redox reaction, the flatter the curve characterizes this titration. The greater the difference in the redox potentials of the oxidizing agent and the reducing agent, the greater the titration jump. If the difference in their redox potentials is very small, titration is impossible. Thus, titration of Cl- ions (E = 1.36V) with permanganate (E = 1.51) is practically impossible. It is often necessary to expand the potential interval in which the jump is located if it is small. In such cases, they resort to jump regulation.

The size of the jump is significantly affected by reducing the concentration of one of the components of the redox couple (for example, using a complexing reagent). Let us assume that phosphoric acid, fluorides or oxalates are introduced into the solution, forming complexes with iron (III) and not interacting with iron (II), and the potential of the Fe3+/Fe2+ pair decreases. If, for example, as a result of the reaction of competitive complexation, the concentration of Fe3+ ions in the solution decreases by 10,000 times, the potential jump on the titration curve will no longer begin at E = 0.95 V, but at E = 0.71 V. It will end, as before, at E = 1.48V. Thus, the region of the jump in the titration curve will be significantly expanded.

Increasing the temperature accordingly increases the potential of the titrant and analyte system.

So, when choosing optimal conditions for redox titration, one should first of all take into account their influence on the state of the redox system, and, consequently, on the real redox potential.

2.3 Titration of multicomponent systems

The analyzed solution may contain several reducing or oxidizing agents. Their differentiated determination is possible provided that the titration curve has several well-separated jumps of sufficient length. In this case, the difference between the standard potentials of the systems being determined must be at least 0.2 V.

For example, when titrating a solution containing Fe2+ and Ti3+ ions with potassium permanganate, the stronger reducing agent Ti3+ will be titrated first. Therefore, the first part of the titration curve is determined by the stoichiometric ratio of titanium (IV) and titanium (III), and the potential can be calculated using the equation:

The curve is identical to the case of titration of an individual solution of titanium (III).

Rice. 3. Titration curve of 50 ml of a solution containing 0.1 (mol∙eq)/l Ti3+ and 0.2 (mol∙eq)/l Fe2+ with a 0.1 N solution of KMnO4 ([H+] = 1 mol/l).

The potential at the moment of titration of Ti3+ can be calculated by adding the Nernst equations for the Fe3+/Fe2+ and TiO2+/Ti3+ systems term by term. Since the potentials of redox systems at equilibrium can be written:

Considering that ΔE of the redox pairs TiO2+/Ti3+ and Fe3+/Fe2+ is significantly greater than 0.2 V, we can assume that the main source of Fe3+ ions in the solution at this point is the reaction:

TiO2+ + Fe2+ + H+ = Fe3+ + Ti3+ + H2O

and therefore = . Substituting this relation into the previous potential equation gives:

If we assume that and are practically equal to their total concentrations, we can calculate the potential at the equivalence point.

After the first equivalence point, the solution contains significant amounts of Fe2+ and Fe3+ ions, and the potential values for constructing the titration curve should be calculated using the equation:

The titration curve in the second section is almost identical to the titration curve of a solution of Fe2+ ions (see Fig. 2).

Similarly, when titrating a solution containing ions of the same element in different oxidation states (VIV, VV, WV, WVI, MoIV, MoV, MoVI), a curve with two or more steps can be obtained.

2.4 Determination of the equivalence point

In redox titration methods, as well as in acid-base methods, various methods of indicating the equivalence point are possible.

Non-indicator methods are applicable when using colored titrants (solutions of KMnO4, I2), a slight excess of which gives the solution a visually detectable color.

Indicator methods can be chemical if they use chemical compounds as indicators that sharply change their color near the equivalence point (within the jump on the titration curve).

Sometimes acid-base indicators are used in redox titration methods: methyl orange, methyl red, Congo red, etc. These indicators at the end point of titration are irreversibly oxidized by excess oxidizing agent and at the same time change their color.

It is possible to use fluorescent and chemiluminescent indicators when titrating reducing agents with strong oxidizing agents. Fluorescent indicators include many substances (acridine, euchrysin, etc.) that emit in the visible region at certain pH values of the solution after irradiation with ultraviolet radiation. Chemiluminescent indicators are substances (luminol, lucigenin, siloxene, etc.) that emit in the visible region of the spectrum at the end point of titration due to exothermic chemical processes. Chemiluminescence is observed mainly during oxidation reactions with hydrogen peroxide, hypochlorites and some other oxidizing agents. The advantage of fluorescent and chemiluminescent indicators is that they can be used for titration of not only transparent and colorless, but also cloudy or colored solutions, for the titration of which conventional redox indicators are unsuitable.

Indicator methods can also be physicochemical: potentiometric, amperometric, conductometric, etc.

2.5 Redox indicators

To determine the equivalence point in redoximetry, various indicators are used:

) Redox indicators (redox indicators), changing color when the redox potential of the system changes.

2) Specific indicators that change color when an excess of titrant appears or the substance being determined disappears. Specific indicators are used in some cases. So starch is an indicator for the presence of free iodine, or rather triiodide ions. In the presence of starch, it turns blue at room temperature. The appearance of a blue color in starch is associated with adsorption on amylase, which is part of starch.

Sometimes ammonium thiocyanate is used as an indicator when titrating iron(III) salts; cations and ions form a red compound. At the equivalence point, all ions are reduced to and the titrated solution turns from red to colorless.

When titrating with a solution of potassium permanganate, the titrant itself plays the role of an indicator. With the slightest excess of KMnO4, the solution turns pink.

Redox indicators are divided into: reversible and irreversible.

Reversible indicators - reversibly change their color when the system potential changes. Irreversible indicators - undergo irreversible oxidation or reduction, as a result of which the color of the indicator changes irreversibly.

Redox indicators exist in two forms, oxidized and reduced, with one form having a different color than the other.

The transition of an indicator from one form to another and a change in its color occurs at a certain potential of the system (transition potential). The indicator potential is determined by the Nernst equation:

When performing redox titrations, it is necessary to select the indicator so that the potential of the indicator is within the potential jump on the titration curve. Many redox titration indicators have acidic or basic properties and can change their behavior depending on the pH of the environment.

One of the most famous and used redox indicators is diphenylamine:

The reduced form of the indicator is colorless. Under the influence of oxidizing agents, diphenylamine is first irreversibly converted to colorless diphenylbenzidine, which is then reversibly oxidized to blue-violet diphenylbenzidine violet.

A two-color indicator is ferroin, which is a complex of Fe2+ with o-phenanthroline

Titration by the indicator method is possible if for a given reaction the EMF is ≥ 0.4 V. For EMF = 0.4 - 0.2 V, instrumental indicators are used.

3. Classification of redox titration methods

According to a widely used classification, the name of the redox titration method comes from the name of the standard solution (titrant). Standard solutions used in redox titration methods are characterized by a wide range of redox potentials; therefore, the analytical capabilities of these methods are great. If the solution being titrated contains only one component with a sufficiently high ability to gain electrons, and the titrant is the only source of electrons (or vice versa), and there is a reliable way to indicate the end point of the titration, the direct titration method is applicable. If these conditions are not met, indirect titration methods are used. The redox reaction between the analyte and the titrant must satisfy the general requirements for reactions used in titrimetry.

If the redox reaction proceeds nonstoichiometrically or not fast enough, indirect titration methods are used: reverse titration and substitution titration. For example, in the cerimetric determination of Fe3+, the substitution titration method is used:

Fe3+ +Ti3+ = TiIV + Fe2+ + + CeIV = Fe3+ + Ce3+.3+ does not interfere with titration.

Redox titration is possible if the solution contains one suitable oxidation state of the component being determined. Otherwise, before titration begins, it is necessary to carry out preliminary reduction (oxidation) to a suitable oxidation state, as is done, for example, when analyzing a mixture of Fe2+ and Fe3+ by permanganatometry. Preliminary reduction (oxidation) should ensure a quantitative conversion of the element being determined to the desired oxidation state.

The reagent introduced for this purpose must be a compound whose excess can be easily removed before titration begins (by boiling, filtering, etc.). In some cases, redoximetry is used to determine compounds that do not change their oxidation state.

Thus, by titration by substitution, calcium, zinc, nickel, cobalt and lead ions are determined in permanganatometry, strong acids - in iodometry.

Table 2. Redox titration methods

Method name	Standard solution (titrant)	Equations of half-reactions of the titrant system	Features of the method
Standard solution - oxidizer
Permanga-natometry		MnO4−+ 8H+ + 5e̅ = Mn2++ 4H2O MnO4−+ 4H+ + 3e̅ = MnO2 + 2H2O MnO4−+ 2H2O + 3e̅ = MnO2+ 4OH−	Indicator-free method, used in a wide pH range
Bromatometry		BrO3−+ 6H+ + 6e̅ = Br−+ 3H2O	The indicator is methyl orange. Wednesday - highly acidic
Cerimetry		Ce4+ + e̅ = Ce3+	The indicator is ferroin. Environment - highly acidic
Chromatometry		Сr2O72−+ 14H+ + 6e̅ = 2Cr3++2H2O	The indicator is diphenylamine. Medium: highly acidic
Nitritometry		NO2- + 2H+ + e̅ = NO + H2O	External indicator - iodide-starch paper. Medium: slightly acidic
Yodimetry		I2 + 2e̅ = 2I -	Indicator - starch
Standard solution - reducing agent
Ascorbinometry		С6H6O6 +2H+ +2 e̅ = С6H8O6	Indicators - variamine blue or for determining Fe3+ ions, potassium thiocyanate. Environment - acidic
Titanometry		TiO2+ + 2H+ + e̅ =Ti3+ + H2O	The indicator is methylene blue. Environment - acidic
Iodometry		S4O62−+ 2e̅ = 2S2O32−	Indicator - crash-small. Auxiliary reagent - KI. Medium - slightly acidic or neutral

4. Permanganatometry

Permanganatometry is one of the most commonly used methods of redox titration. A solution of potassium permanganate is used as a titrant, the oxidizing properties of which can be adjusted depending on the acidity of the solution.

4.1 Features of the method

The most widespread in analytical practice is the permanganatometric method of determination in acidic media: the reduction of MnO4- to Mn2+ occurs quickly and stoicheometrically:

Quantitative reduction of permanganate in an alkaline medium to manganate occurs in the presence of barium salt. Ba(MnO4)2 is soluble in water, while BaMnO4 is insoluble, so further reduction of MnVI from the precipitate does not occur.

Permanganatometrically in an alkaline environment, as a rule, organic compounds are determined: formate, formaldehyde, formic, cinnamic, tartaric, citric acids, hydrazine, acetone, etc.

The end of titration is indicated by the pale pink color of the excess titrant KMnO4 (one drop of 0.004 M titrant solution gives a noticeable color to 100 ml of solution). Therefore, if the titrated solution is colorless, the achievement of the equivalence point can be judged by the appearance of a pale pink color of the excess KMnO4 titrant during direct titration or by the disappearance of color during reverse titration. When analyzing colored solutions, it is recommended to use the indicator ferroin.

The advantages of the permanganatometric method include:

1. Possibility of titration with KMnO4 solution in any environment (acidic, neutral, alkaline).

2. The applicability of a solution of potassium permanganate in an acidic medium for the determination of many substances that do not react with weaker oxidizing agents.

Stoicheometry of most redox reactions involving MnO4- − under optimally selected conditions with sufficient speed.

Possibility of titration without indicator.

Availability of potassium permanganate.

Along with the listed advantages, the permanganatometry method has a number of disadvantages:

1. KMnO4 titrant is prepared as a secondary standard, since the initial reagent - potassium permanganate - is difficult to obtain in a chemically pure state.

2. Reactions involving MnO4- are possible under strictly defined conditions (pH, temperature, etc.).

4.2 Application of the method

Definition of reducing agents. If the redox reaction between the determined reducing agent and MnO4- proceeds quickly, then titration is carried out in a direct way. This is how oxalates, nitrites, hydrogen peroxide, iron (II), ferrocyanides, arsenous acid, etc. are determined:

H2O2 + 2MnO4- + 6H+ = 5O2 + 2Mn2+ + 8H2O

54- + MnO4- + 8H+ = 53- + 2Mn2+ + 4H2O

AsIII + 2MnO4- + 16H+ = 5AsV + 2 Mn2+ + 8H2O

5Fe2+ + MnO4- +8H+ = 5Fe3+ + 2Mn2+ + 4H2O

For direct permanganatometric determination of Fe3+ ions, they must first be quantitatively reduced to Fe2+ using one of the reducing agents: SnCl2, Zn, N2H4.

When analyzing solutions containing iron (II) and iron (III), the Fe2+ content is determined in a separate sample of the initial solution of a mixture of ions by direct titration with a KMnO4 solution. In parallel, in the same sample of the analyzed mixture, Fe3+ is reduced to Fe2+ and the total amount of Fe2+ ions is titrated with a KMnO4 solution. From the results of determining the total iron content obtained by titrating the reduced solution, the result of determining the Fe2+ content before reduction is subtracted and the content of Fe3+ ions in the analyzed mixture is calculated.

When permanganatometric determination of nitrites, the titration order is reversed (reverse titration): a standard permanganate solution is titrated with the analyzed nitrite solution. This is due to the fact that nitrites decompose in an acidic environment to form nitrogen oxides. The oxidation reaction of nitrite with a KMnO4 solution can be written:

NO2- + 2MnO4- + 6H+ = 5NO3- + 2Mn2+ + 3H2O

In the case of delayed reactions, determination is carried out by back titration of excess permanganate. This is how formic, poly- and hydroxycarboxylic acids, aldehydes and other organic compounds are determined:

HCOO- + 2MnO4- + 3OH- = CO32- + 2MnO42- + 2H2O + (MnO4-)

excess remainder

MnO4- + 5C2O42- + 16H+ = 2Mn2+ +10CO2 + 8H2O

remainder

Determination of oxidizing agents. Add excess standard reducing agent solution and then titrate the remainder with KMnO4 solution (back titration method). For example, chromates, persulfates, chlorites, chlorates and other oxidizing agents can be determined by the permanganometric method by first treating with an excess of a standard Fe2+ solution, and then titrating the unreacted amount of Fe2+ with a KMnO4 solution:

Cr2O72- + 6Fe2+ + 14H+ = 2Cr3+ + 6Fe3+ + 7H2O + (Fe2+)

excess remainder

Fe2+ + MnO4- + 8H+ = 5Fe3+ + Mn2+ + 4H2O

remainder

The determination of substances that do not have redox properties is carried out indirectly, for example by substitution titration. To do this, the component to be determined is converted into the form of a compound with reducing or oxidizing properties, and then titration is carried out. For example, ions of calcium, zinc, cadmium, nickel, cobalt are precipitated in the form of poorly soluble oxalates:

M2+ + C2O4- = ↓MC2O4

The precipitate is separated from the solution, washed and dissolved in H2SO4:

MC2O4 + H2SO4 = H2C2O4 + MSO4

Then H2C2O4 (substituent) is titrated with KMnO4 solution:

2MnO4- + 5C2O42- + 16H+ = 2Mn2+ +10CO2 + 8H2O

4. Determination of organic compounds. A distinctive feature of the reactions of organic compounds with MnO4- is their low rate. Determination is possible if an indirect method is used: the analyzed compound is pre-treated with an excess of a strongly alkaline permanganate solution and the reaction is allowed to proceed for the required period of time. The permanganate residue is titrated with sodium oxalate solution:

C3H5(OH)3 + 14MnO4- + 20OH- = 3CO32- + 14MnO42- + 14H2O + (MnO4-), excess remainder

2MnO4- + 5C2O42- + 16H+ = 2Mn2+ +10CO2 + 8H2O

remainder

Table 3. Examples of determination of some inorganic and organic compounds by the permanganatometric method

Determined compound (ion)	Reactions used in the analysis	Analysis conditions
	5SbIII + 2MnO4- + 16H+ = 5SbV +2Mn2+ + 8H2O	Direct titration. Medium – 2M HCl
	5Sn2+ + 2MnO4- + 16H+ = 5Sn4+ + 2Mn2+ + 8H2O	Medium - 1M H2SO4 Eliminate access to O2
	5Ti3+ + MnO4- + 8H+ = 5Ti4+ + Mn2+ + 4H2O	Medium - 1M H2SO4
	5W3+ + 3MnO4- + 24H+ = 5W6+ + 3Mn2+ + 12H2O	Medium - 1M H2SO4
	5U4+ + 2MnO4- + 16H+ = 5U6+ + 2Mn2+ + 8H2O	Medium - 1M H2SO4
	5V4+ + MnO4- + 8H+ = 5V5+ + Mn2+ + 4H2O	Medium - 1M H2SO4
	10Br− + 2MnO4- + 16H+ = 2Mn2+ + 8H2O + 5Br2	Titration in 2M H2SO4 solution at boiling to remove Br2	CH3OH + 6MnO4-ex.	+ 8OH- = CO32- + 6MnO42- + 6H2O + (MnO4-)res.
HCOO- + 2(MnO4-)res. + 3Ba+ + 3OH- = BaCO3 + ↓2BaMnO4 + 2H2O	Back titration The remaining unreacted MnO4- after adding barium salt is titrated with sodium formate solution	Ca2+, Mg2+, Zn2+, Co2+, La3+, Th4+, Ba2+, Sr2+, Pb2+, Ag+

4.3 Preparation of a 0.05 N solution of potassium permanganate and its standardization with oxalic acid or ammonium (sodium) oxalate

It is impossible to prepare a titrated solution of potassium permanganate from an exact weighed crystalline solution, since it always contains a certain amount of other decomposition products. Therefore, the potassium permanganate solution is classified as a secondary standard solution. Initially, prepare a solution whose concentration is approximately equal to the required concentration. The sample is taken on a technochemical balance slightly larger than the calculated value. Since it is a strong oxidizing agent and changes its concentration in the presence of various reducing agents, the prepared solution of potassium permanganate is kept for 7-10 days in a dark place so that all redox processes with impurities contained in water take place. The solution is then filtered. Only after this the concentration of the solution becomes constant and it can be standardized by oxalic acid or ammonium oxalate. Solutions should be stored in dark glass bottles. A solution of potassium permanganate prepared in this way with a molar concentration equivalent to 0.05 mol/l and higher does not change its titer for quite a long time.

The standardization method is based on the oxidation of oxalic acid with permanganate ions in an acidic environment:

In this case, the half-reactions of oxidation and reduction have the form:

At room temperature this reaction proceeds slowly. And even at elevated temperatures, its speed is low if it is not catalyzed by manganese(II) ions. It is impossible to heat the acid above 70-80 0C, since in this case part of the acid is oxidized by atmospheric oxygen:

The reaction of potassium permanganate with oxalic acid is an autocatalytic reaction. The oxidation reaction of oxalic acid occurs in several stages. The first drops of potassium permanganate, even in a hot solution, discolor very slowly. To start it, at least traces of the following must be present in the solution:

The resulting manganate ion in an acidic solution quickly disproportionates:

Manganese (III) forms oxalate complexes of the composition; these complexes slowly decompose to form

Thus, until manganese (II) accumulates in sufficient concentrations in the solution, the reaction between proceeds slowly. When the concentration of manganese(II) reaches a certain value, the reaction begins to proceed at high speed.

The intense color of the potassium permanganate solution complicates the measurement of titrant volumes in the burette. In practice, it is convenient to take the surface of the liquid as the reference level, rather than the lower part of the meniscus.

Ammonium oxalate has some advantages compared to other installation substances:

crystallizes well and easily dissolves in water,

has a certain chemical composition and does not change during storage,

does not interact with air oxygen and CO2.

To set the concentration (titer or molar concentration equivalents) of a standard solution of potassium permanganate, calculate the weighed portion of oxalic acid or ammonium oxalate, necessary to prepare a solution with a molar concentration equivalent to 0.05 N:

ENa2C2O4 = M/2 = 134.02/2 = 67.01 g;

EN2C2O4∙2H2O = M/2 = 126.06/2 = 63.03 g;

EKMnO4 = M/5 = 158.03/5 = 31.61 g.

Knowing the mass of 1 mol equivalent of sodium oxalate, calculate the weight of this salt that must be taken to prepare a solution to determine the normality of the permanganate solution. In this case, solutions of sodium oxalate and permanganate should have approximately the same normality.

To prepare 100 ml of 0.05 N Na2C2O4 solution you need to take: 0.05∙67.01∙0.1 = 0.3351 g Na2C2O4. You should not strive to take exactly the right amount of salt to get exactly 0.05N. solution. You must first take a sample close to the calculated one on a technical balance, for example 0.34 g, and then accurately weigh it on an analytical balance (this significantly speeds up and simplifies the work). Let the sample taken be equal to 0.3445 g. Transfer it to a volumetric flask (avoid losses), dissolve it in distilled water, dilute the solution to the mark and then, capping the flask with a stopper, mix well. The normality of the prepared Na2C2O4 solution is established from the ratio:

3351 g Na2C2O4 - 0.05N

3445 g Na2C2O4 - x

x = 0.0514n

The calculated amount of acid (or salt) is weighed on an analytical balance. A weighed mass of acid (or salt) is dissolved in water in a volumetric flask, and the solution is thoroughly mixed. The solution is then titrated. Calculation of the concentration of potassium permanganate in all cases is carried out based on the law of equivalents:

For example, when titrating a 0.0514 N solution of H2C2O4 (Val = 10.0 ml) with a solution of KMnO4, the following results were obtained:

V1(KMnO4) = 11.0 ml

V2(KMnO4) = 10.9 ml

V3(KMnO4) = 11.0 ml

Then the normality of the potassium permanganate solution will be equal to:

4.4 Titration of the analyzed solution

As an example, consider the use of the permanganatometry method to determine the iron content in Mohr's salt. Mohr's salt is a double salt of iron (II) and ammonium sulfates FeSO4∙(NH4)2SO4∙6H2O. Since ammonium sulfate does not participate in the reaction with permanganate, the interaction reaction equation can only be written with FeSO4:

10FeSO4+2KMnO4+8H2SO4 = 5Fe2(SO4)3+K2SO4+2MnSO4+8H2O.

According to this equation:

E FeSO4 = M/1 = 151.92

E FeSO4∙(NH4)2SO4∙6H2O = M/1 = 392.15.

Iron(II) can be titrated with potassium permanganate in sulfuric acid or hydrochloric acid media. In the first case, no complications are observed. The presence of chloride ions in the titrated solution leads to excessive consumption of permanganate and an unclear end of the titration. This is because the reaction between iron(II) and permanganate induces a reaction between the ions

Moreover, in the absence of ions this reaction does not occur. Reactions of this type, which do not occur without each other, are called conjugate or induced. An induced reaction does not occur if phosphoric acid and manganese (II) are present in sufficient quantities in the solution. Therefore, before titration, a Reinhard-Zimmermann mixture consisting of sulfuric, phosphoric acids and manganese(II) sulfate is added to the solution. The presence in this mixture creates the required concentration of protons in the titrated solution. The presence is necessary for the binding of iron(III) into a colorless complex and the formation of manganese(III) phosphate complexes. If iron is not masked, the color of its complex chlorides will make it difficult to observe the pale pink color at the end of the titration with potassium permanganate.

The normality of iron (II) sulfate solution is determined by the equation:

С(KMnO4) ∙V(KMnO4) = С(FeSO4) ∙V(FeSO4)

Since the mass of 1 mole equivalent of iron is 55.85 g, the mass of iron contained in 100 ml of solution is equal to

If the initial sample is equal to a g (in 100 ml of solution), then the iron content in Mohr’s salt will be:

Theoretically calculated iron content in Mohr's salt

Conclusion

Of the titrimetric methods of analysis, redox titration is widespread; the scope of application of this method is wider than that of acid-base or complexometric methods. Due to the wide variety of redox reactions, this method makes it possible to determine a large number of different substances, including those that do not directly exhibit redox properties.

Permanganatometry is used to determine the total oxidability of water and soil. In this case, all organic components (including humic acids of soils and natural waters) react with MnO4-ion in an acidic environment. The number of millimole equivalents of KMnO4 used for titration is a characteristic of oxidation (for permanganate).

Permanganatometry is also used for the analysis of easily oxidized organic compounds (aldehydes, ketones, alcohols, carboxylic acids: oxalic, tartaric, citric, malic, as well as hydrazo groups). In the food industry, permanganatometry can be used to determine the sugar content in food products and raw materials, and the nitrite content in sausages.

In the metallurgical industry, the permanganatometry method is used to determine the iron content in salts, alloys, metals, ores and silicates.

Bibliography

1. Analytical chemistry. Chemical methods of analysis / ed. O.M. Petrukhina. M.: Chemistry, 1992, 400 p.

2. Vasiliev V.P. Analytical chemistry. In 2 hours. Part 1. Gravimetric and titrimetric methods of analysis. M.: Higher School, 1989, 320 p.

Fundamentals of analytical chemistry. In 2 books. Book 2. Methods of chemical analysis / ed. Yu.A. Zolotova. M.: Higher School, 2000, 494 p.

General characteristics of methods
Redox titration methods are based on the use of redox reactions (ORR). The analytical capabilities of the methods make it possible to determine oxidizing agents, reducing agents and substances that themselves do not exhibit redox properties, but react with oxidizing agents and reducing agents to form precipitation or complex compounds.
Working solutions are solutions of oxidizing agents (oxidative titration) and reducing agents (reductive titration). Since working solutions of reducing agents are unstable due to oxidation in air, reductive titration is used less frequently. In most cases, working solutions are prepared with a concentration of 0.05 mol eq/l. Almost all of them are secondary standards.
The analytical performance of the methods is similar to that of acid-base titration, but analysis often takes longer due to the slower rates of redox reactions.
The classification of methods is based on the working solutions used. For example, permanganatometry (KMnO 4), iodometry (I 2), dichromatometry (K 2 Cr 2 O 7), bromatometry (KBrOz), etc.
Requirements for oxidation-reduction reactions (ORR) in titrimetry
More than 100 thousand OVRs are known. However, not all of them are suitable for titration due to their characteristics:
a) ORR is the most complex type of chemical reaction in terms of mechanism;
b) they do not always proceed in exact accordance with the overall reaction equation; c) unstable intermediate compounds are often formed.
Therefore, the ORR, which is used for titration, must meet all the requirements mandatory for reactions in titrimetry, namely:
1) it must proceed in accordance with the stoichiometric reaction equation. Many ORRs proceed non-stoichiometrically. For example, reaction

5Fe 2+ + MnO 4 - + 8H+ = 5Fe 3+ + Mn 2+ + 4H 2 O

proceeds in accordance with the equation only in the presence of H 2 SO 4. If other acids (HC1, HNO3) are used to create the necessary environment, then side reactions will occur;
2) OVR must proceed to the end. If titration is carried out with an error
< 0.1 %, то должно выполняться условие: lgK>3(n 1 + n 2), where n 1 and n 2 are the number of electrons participating in half-reactions; K equilibrium constant of ORR. The ORR equilibrium constant is related to the standard EMF of the element E0, equal to the difference between the standard potentials of the oxidizer and the reducer by the following equation:

RT. lnK = E 0 nF,

where n is the number of electrons transferred from the reducing agent to the oxidizing agent F is Faraday’s constant, equal to 96500 C/mol. Under standard conditions, the equation takes the form:

For example, for the oxidation reaction of ferrous iron with potassium permanganate:

logK = then K = 10 62

A large numerical value of the equilibrium constant indicates that the equilibrium of the reaction occurring during titration is almost entirely shifted to the right;
3) she must go quickly. Many ORRs are slow and cannot be used for titration. Sometimes, to increase the speed, the solution is heated or a catalyst is introduced.
Titration methods. If the reaction meets all the requirements and it is possible to record the c.t.t., then direct titration is used. If the reaction proceeds nonstoichiometrically, slowly, then back titration and titration of the substituent are used.

8.1 Calculation of the factor and equivalence number of substances participating in OVR

It is usually necessary to determine what fraction of a particle is equivalent to one electron in a half-reaction. For example, the equivalence factors for permanganate and thiosulfate in specific reactions are:
MnO 4 - + 8H + + 5e - = Mn 2+ + H 2 O; feq.(KMnO 4) =1/5, z = 5
MnO 4 - + 4H + + Ze - =MnO 2 +2H 2 O; feq.(KMnO 4) = 1/3, z = 3

МnО 4 - +е - = МnО 4 2-; feq.(KMnO 4) = 1, z = 1

2S 2 O 3 -2e - = S 4 O 6 2 - ; feq.(S 2 O 3 -2) = 1, z = 1.
However, there are also more complex cases of calculating f eq. of a substance involved in ORR, if titration by residue, titration of a substituent, multi-stage analysis or titration involving an organic substance is carried out. In these cases, the easiest way is to calculate feq. of the substance being determined by proportion, based on the stoichiometry of the reaction and feq. the most “reliable” substance involved in it. If the analysis is multi-stage, then such a calculation begins with the last reaction, since it is this reaction that is carried out during titration.

8.2 Redox titration curves

The curves of the method are plotted in the coordinate system “potential - titrant volume (degree of titration)” and have an S-shaped appearance. If titrated with an oxidizing solution, an ascending curve is obtained, if titrated with a reducing solution, a descending curve is obtained.
Calculation of the potential at various stages of titration is carried out as follows.
1. Before titration begins, the potential cannot be calculated, since there is no redox couple in the solution yet, so the Nernst equation cannot be applied.
2. Before t.e. potential E is calculated using the Nernst equation for the redox couple of the analyte, since it is in excess and there is a certain amount of both oxidized and reduced forms: E = E 0 + (0.059/n 1). lg (/), where E 0 is the standard electrode potential of a pair of oxidized and reduced forms of the titrated substance, n 1 is the number of electrons passing from the reduced to the oxidized form of the substance being determined, log /) is the logarithm of the ratio of the concentrations of the oxidized and reduced forms of this substance. For example, when titrating iron (II) sulfate with a solution of potassium permanganate (Fig. 6), the potential is up to t.e. calculated for half-rection: Fe 2+ - e - = Fe 3+
.
3. In i.e. the potential is calculated using the formula: E = (n 1 . E 0 1 + n 2 . E 0 2)/(n 1 + n 2), where E 0 1 and E 0 2 are the standard electrode potentials of the oxidizer and reducer pairs of the titration reaction, and n 1 and n 2 are the number of electrons in half-reactions.
If H + ions are involved in the reaction, then the calculation is carried out according to the formula: E = (n 1 . E 0 1 + n 2 . E 0 2)/(n 1 + n 2) + 0.059/(n 1 + n 2) . log m, where m is the stoichiometric coefficient at H + in the overall reaction equation.

4. After t.e. the potential is calculated using the Hernst equation for the redox couple that includes the titrant, since it is in excess and there is a certain amount of both oxidized and reduced forms in the solution. For example, for a half-reaction:

МnО 4 - +8Н + + 5е - = Мn 2+ + 4Н 2 О potential is calculated by the formula:

Table 3 shows the changes in the redox potential when titrating 100 ml of a 0.1 N solution of FeSO 4 with a 0.1 N solution of KMnO 4 at C(H +) = 1 mol/l

Table 3. These changes in the redox potential when titrating 100 ml of a 0.1 N solution of FeSO 4 with a 0.1 N solution of KMnO 4 at C(H +) = 1 mol/l

Figure 6 shows the titration curve of a FeSO 4 solution with a KMnO 4 solution at = 1 mol/l (pH = 0), determined by the reaction:

10FeSO 4 + 2KMnO 4 + 8H 2 SO 4 = 5Fe 2 (SO 4) 3 + K 2 SO 4 + 2MnSO 4 + 8H 2 O

Fig.6. Titration curve of FeSO 4 solution with KMnO 4 solution

at = 1 mol/l (pH = 0)

Factors influencing the magnitude of the jump.
All factors influencing the potential also affect the magnitude of the jump:
a) the nature of the titrated substance and titrant. The greater the difference in the standard redox potentials of the titrated substance and titrant pairs (DE 0), the greater the jump. If DE 0 is low, titration is impossible. For titration with uncertainty< 0,1 % надо, чтобы DЕ 0 >0.35 V;
b) pH of the solution. If H + or OH - ions participate in the half-reaction, then their concentration is included in the Nernst equation to the degree corresponding to the stoichiometric coefficient, therefore the magnitude of the jump in such cases depends on the pH value of the solution; c) competing complexation or precipitation reactions involving the oxidized or reduced form. The jump can be increased if one of the components of the conjugated redox pair is bound into a complex or slightly soluble compound:
d) solution concentration. If H + or OH - ions do not participate in the reaction and the stoichiometric coefficients before the oxidized and reduced forms in the half-reaction are the same, then the magnitude of the jump does not depend on the concentrations of the substances, since when the solution is diluted, the ratio [Approx. forms]/[Rec. form] will remain constant. In other cases, dilution affects the magnitude of the jump;

e) the number of electrons participating in the half-reaction. The greater the number of electrons, the larger the jump;

e) temperature. The higher the temperature, the greater E 1 and E 2.
Assumptions made when calculating titration curves
If:
1) the stoichiometric coefficients for the oxidized and reduced forms are equal;
2) the Nernst equation does not include [H + ] or [OH - ] (or they are equal to 1 mol/l);
3) dilution of the solution during titration is not taken into account,

then you can replace [Ok. forms]/[Rec. shape] on the volume ratio.
In all other cases you need to:
a) set the volume of the reagent;
b) using general formulas, calculate the molar concentrations of the equivalent of an untitrated substance, reaction products, and titrant;
c) convert them to molar concentrations and substitute them into the Nernst equation.

8.3 Methods for fixing the titration end point (t.t.t.)

In redox titration methods, the following methods of fixing the c.t.t. are used.
1. Indicator-free titration. It is used when the oxidized and reduced forms of the working solution have different colors. For example. MnO 4 - (purple) Mn 2+ (colorless), I 2 (brown) - I - (colorless), In this case, a small excess of titrant after t.e. causes the solution to color and the titration is stopped. This method cannot be used when titrating colored solutions.
2. Application of specific indicators. Specific indicators are substances that form intensely colored compounds with one of the components of a redox couple. Reagents for qualitative reactions can often play this role. For example, starch is a specific indicator for I 2 (a blue compound is formed), CNS thiocyanate is a specific indicator for Fe 3+ ions (a complex, red).
3. Application of irreversible indicators. These are indicators that are irreversibly oxidized or reduced by an excess of the working solution in the chemical solution and at the same time change their color. For example, in bromatometry, the indicators methyl orange and methyl red are used as irreversible. When titrated with a solution of KBrO 3, Br 2 is formed, which oxidizes the indicators with the formation of colorless products, therefore, at the same time, the color of the solution changes.
4. Application of redox indicators. These are organic compounds that reversibly change color depending on the potential of the system (diphenylamine, anthranilic acid, etc.). They come in one and two colors.
Requirements for them: the color of the indicator must change quickly and reversibly, in a narrow range of potential values: the color of the oxidized and reduced forms of the indicator must be different.
Mechanism of action: the indicator can be reversibly oxidized or reduced, and its oxidized and reduced forms have different colors. When the potential changes, the equilibrium shifts towards the formation of one or another form of the indicator, so the color of the solution changes. Oxidation or reduction of the indicator can occur with or without the participation of H+ ions.
Without the participation of H + ions:
redox balance:
Ind(ok)+ne Ind(rec).
Nernst equation: E = E o + (0.059/n) log/
indicator transition interval. If we substitute into the Nernst equation the ratio of the concentrations of the oxidized and reduced forms of the indicator equal to 1/10 or 10/1, then after the transformations we obtain:
E 1 = E o + 0.059/n, E 2 = E o - 0.059/n, ∆E Ind = E 0 ± 0.059/n, where n is the number of electrons in the reaction of the transition of the oxidized form of the indicator to the reduced one.
Rule for choosing a redox indicator. The transition interval of the indicator must lie within the jump on the titration curve (or the standard potential of the indicator must practically coincide with the potential value in i.e.).
Due to the discrepancy between the standard potential of the indicator and the potential value in i.e. an indicator titration error occurs. If, during titration with an oxidizing agent, the solution is undertitrated, i.e. E° Ind. ox/Ind. red< E° т.э. , то относительная ошибка (погрешность) титрования ПT равна:

Where a = , f = V T /V 0 – degree of titration.

If, during titration with an oxidizing agent, the solution is overtitrated, i.e. E° Ind. ox/Ind. red > E° i.e. , then the relative error (error) of titration PT is equal to.

oxidation states

For example:

Methods for establishing T.E.

To determine the equivalence point during redox titration, use:

a) non-indicator methods. In the case where the solution of the titrated substance or titrant is colored, TE can be determined by the disappearance or appearance of this color, respectively;

b) specific indicators - changing color when the titrant appears or the substance being determined disappears. For example, for the J 2 /2J - system, the specific indicator is starch, which colors solutions containing J 2 blue, and for Fe 3+ ions the specific indicator is SCN - ions (thiocyanate ions), the resulting complex is colored blood-red ;

c) RH (redox) indicators – changing color when the RH potential of the system changes. Single-color indicators are diphenylamine, two-color indicators are ferroin.

Redox indicators exist in two forms - oxidized (Ind ok) and reduced (Ind rec), and the color of one form is different from the other. The transition of an indicator from one form to another and a change in its color occurs at a certain transition potential, which is observed when the concentrations of the oxidized and reduced forms of the indicator are equal and according to the Nernst-Peters equation:

The transition interval of redox indicators is very short, unlike acid-base indicators.

RH titration curves

RH titration curves depict the change in the RH potential of the system as the titrant solution is added.

Reductometry, when a solution of an oxidizing agent is titrated with a standard solution of a reducing agent

In reductometry, titration curves are calculated:

Oxidimetry, when a reducing agent solution is titrated with a standard oxidizing agent solution

In oxidimetry, titration curves are calculated:

Example. Let's calculate the titration curve of a 100 cm 3 solution of FeSO 4 with a molar concentration equivalent to 0.1 mol/dm 3 with a KMnO 4 solution of the same concentration.

Reaction equation:

The equilibrium constant of this reaction is

A large numerical value of the equilibrium constant indicates that the equilibrium of the reaction is almost entirely shifted to the right. After adding the first drops of titrant, two OM pairs are formed in the solution: , the potential of each of which can be calculated using the Nernst equation:

In this case, the reducing agent solution is titrated with an oxidizing agent solution, i.e. Titration refers to the oxidimetry method; the titration curve is calculated according to the appropriate scheme.

3) After T.E.

Calculation data for constructing a titration curve

No.	τ	Calculation formula	E, B
	0,10		0,71
0,50	0,77
0,90	0,83
0,99	0,89
0,999	0,95
			1,39
	1,001		1,47
1,01	1,49
1,10	1,50
1,50	1,505

Using the table data, we construct a titration curve:

For titration error ±0.1% titration jump

∆E = E τ =1.001 - E τ =0.999 = 1.47 – 0.95 = 0.52.

For titration error ± 1.0% titration jump

∆E = E τ =1.01 - E τ =0.99 = 1.49 – 0.89 = 0.60.

In the region of TE, when moving from a solution undertitrated by 0.1% to a solution overtitrated by 0.1%, the potential changes by more than 0.5 V. The potential jump makes it possible to use directly potentiometric measurements or RH indicators, the color of which changes with change in potential. In addition, in this case, a colored solution is used as a titrant, therefore T.E. can be determined by the appearance of a faint pink color from one excess drop of potassium permanganate.

PERMANGANOMETRY

The method is based on the oxidation of solutions of reducing agents with potassium permanganate KMnO 4. The oxidation of reducing agents can be carried out in various environments, and manganese (VII) is reduced in an acidic environment to Mn 2+ ions, in a neutral environment to manganese (IV) and in an alkaline environment to manganese (VI). Typically, in the permanganatometry method, the reaction is carried out in an acidic environment. In this case, a half-reaction occurs

A titrated solution cannot be prepared using an exact weighing, because it contains . Therefore, first prepare a solution of approximately the required concentration, leave it in a dark bottle for 7-10 days, filter off the precipitate, and then set the exact concentration of the resulting solution. Standardization of the solution is carried out using a titrated solution of oxalic acid ( ) or sodium oxalate ().

The indicator is the permanganate itself, colored red-violet. The end of the reaction is easily determined by the change in color from one excess drop of permanganate. In an acidic environment, the titrated solution turns pink due to excess MnO 4 - ions. A big disadvantage of redox reactions is their low speed, which complicates the titration process. Heat is used to speed up slow reactions. As a rule, with every 10° increase in temperature, the reaction rate increases by 2-3 times. The oxidation reaction with oxalic acid permanganate is carried out at a temperature of 70-80 °C. Under these conditions, titration proceeds normally, since the reaction rate increases significantly.

If heating cannot be used (volatilization of one of the substances, decomposition, etc.), the concentrations of the reacting substances are increased to speed up the reaction. The reaction rate can be affected by the introduction of a catalyst into the solution.

The oxidation reaction with oxalic acid permanganate can be catalytically accelerated by the addition of MnSO 4, the role of which is as follows:

The resulting manganese dioxide oxidizes oxalic acid, reducing to manganese (III):

Thus, manganese (II) added to the solution is completely regenerated and is not consumed in the reaction, but greatly accelerates the reaction. In permanganatometry, one of the products of the oxalic acid oxidation reaction is Mn 2+ ions, which, as they form in solution, accelerate the reaction process. Such reactions are called autocatalytic. The first drops of permanganate during the titration of a hot acidified solution of oxalic acid become discolored slowly. As a small amount of Mn 2+ ions is formed, further discoloration of the permanganate occurs almost instantly, since the formed Mn 2+ ions play the role of a catalyst.

Redox titration

Redox processes include chemical processes that are accompanied by changes oxidation states atoms of substances participating in the reaction.

Substances whose atoms reduce their oxidation state during a reaction due to the addition of electrons are called oxidizing agents, i.e. they are electron acceptors. In this case, the oxidizing agents themselves are reduced. Reducing agents, being electron donors, are oxidized.

The product of reduction of an oxidizing agent is called the reduced form, and the product of oxidation of a reducing agent is its oxidized form. The oxidizing agent with its reduced form constitutes a half-pair of the redox system, and the other half-pair is the reducing agent with its oxidized form. Thus, a reducing agent with an oxidized form and an oxidizing agent with its reduced form constitute two semi-pairs (redox pairs) of the redox system.

All OM processes (redox reactions) can be divided into three types

a) intermolecular, when during the OB reaction the transfer of electrons occurs between particles of different substances. For example

In this reaction, the role of the oxidizing agent in the presence of H 3 O + is played by ions, and the ions act as a reducing agent

b) dismutation (disproportionation), during which the transfer of electrons occurs between particles of the same substance. As a result of disproportionation, the oxidation state of one part of the atoms decreases at the expense of another part of the same atoms, the oxidation state of which becomes greater.

For example:

c) intramolecular, in which the transfer of electrons occurs between two atoms that are part of the same particle of a substance, leading to the decomposition of the substance into simpler ones.

(REDOXOMETRY, OXIDIMETRY)

Essence and classification of redox titration methods

Redoxometry methods are based on oxidation-reduction reactions. A lot of methods have been developed. They are classified according to the standard (working, titrant) solution used. The most commonly used methods are:

Permanganatometry is a method that is based on the oxidizing ability of a working solution of potassium permanganate KMnO4. Titration is carried out without an indicator. Used to determine only reducing agents during direct titration.

Iodometry is a method in which the working titrated solution is a solution of free iodine in CI. The method allows the determination of both oxidizing agents and reducing agents. Starch serves as an indicator.

Dichromatometry is based on the use of potassium dichromate K2Cr2O7 as a working solution. The method can be used for both direct and indirect determination of reducing agents.

Bromatometry is based on the use of potassium bromate KBrO3 as a titrant in the determination of reducing agents.

Iodatometry uses a solution of potassium iodate KIO3 as a working solution when determining reducing agents.

Vanadatometry makes it possible to use the oxidizing ability of ammonium vanadate NH4VO3. In addition to the listed methods, such methods as cerimetry (Ce4+), titanometry and others are also used in laboratory practice.

To calculate the molar mass equivalent of oxidizing agents or reducing agents, the number of electrons taking part in the redox reaction is taken into account (Me = M/ne, where n is the number of electrons e). To determine the number of electrons, it is necessary to know the initial and final oxidation states of the oxidizing agent and the reducing agent.

Of the large number of redox reactions, only those reactions are used for chemical analysis that:

· flow to the end;

· pass quickly and stoichiometrically;

· form products of a certain chemical composition (formula);

· allow you to accurately fix the equivalence point;

· do not react with by-products present in the test solution.

The most important factors influencing the reaction rate are:

· concentration of reacting substances;

· temperature;

· pH value of the solution;

· presence of a catalyst.

In most cases, the reaction rate is directly dependent on the temperature and pH of the solution. Therefore, many determinations by redox titration must be carried out at a certain pH value and under heating.

Redox titration indicators

oxidative reduction titration

When analyzing by redox titration methods, direct, reverse and substitution titration are used. The equivalence point of redox titration is fixed both using indicators and without indicators. The indicator-free method is used in cases where the oxidized and reduced forms of the titrant differ. At the equivalence point, the introduction of 1 drop of excess titrant solution will change the color of the solution. Determinations can be made using the permanganatometric method without an indicator, since at the equivalence point, one drop of potassium permanganate solution turns the titrated solution pale pink.

In the indicator method of fixing the equivalence point, specific and redox indicators are used. Specific indicators include starch in iodometry, which in the presence of free iodine turns intense blue due to the formation of a blue adsorption compound. Redox indicators are substances whose color changes when a certain redox potential value is reached. Redox indicators include, for example, diphenylamine NH(C6H5)2. When exposed to colorless solutions by its oxidizing agents, it turns blue-violet.

Redox indicators have the following requirements:

· the color of the oxidized and reduced forms must be different;

· the color change should be noticeable with a small amount of indicator;

· the indicator must react at the equivalence point with a very small excess of reducing agent or oxidizing agent;

· its action interval should be as short as possible;

· the indicator must be resistant to environmental components (O2, air, CO2, light, etc.).

The action interval of the redox indicator is calculated by the formula:

E = Eo ± 0.058/n,

where Eo is the normal redox potential of the indicator (in the reference book), n is the number of electrons accepted in the process of oxidation or reduction of the indicator.

Permanganatometry

Permanganatometry is based on the oxidation reaction of various reducing agents with a working solution of potassium permanganate, i.e. MnO4- ion. Oxidation with potassium permanganate can be carried out in acidic, neutral and alkaline environments

In a strongly acidic environment, permanganate ions (MnO4-) have a high redox potential, being reduced to Mn2+, and they are used to determine many reducing agents:

MnO4- + 8H+ + 5e = Mn2+ + 4H2O

E0 MnO4- / Mn2+ = 1.51 V

In an alkaline environment, MnO4- is reduced to manganate ion:

MnO4- + e = MnO42-

In a neutral or slightly alkaline environment, the permanganate ion is reduced to permanganic acid MnO(OH)2 or to MnO2:

МnО4- + 2Н2О + 3е = МnО2↓ + 4ОН-

E0 MnO4- / MnO2 = 0.59 V

When titrating with permanganate, indicators are not used, since the reagent itself is colored and is a sensitive indicator: 0.1 ml of 0.01 M KMnO4 solution turns 100 ml of water pale pink. As a result of the reaction of potassium permanganate with a reducing agent in an acidic medium, colorless Mn2+ ions are formed, which makes it possible to clearly determine the equivalence point.

The KMnO4 solution is a titrant with a set titer. In this regard, before using it in the analysis as a titrant, the KMnO4 solution is standardized according to the concentration of solutions of the starting substances of shawelic acid or sodium oxalate. A solution of potassium permanganate is very difficult to obtain in pure form. It is usually contaminated with traces of manganese(IV) oxide. Additionally, pure distilled water usually contains traces of substances that reduce potassium permanganate to form manganese(IV) oxide:

4 KMnO4 + 2H2O = 4 MnO2↓ + 4OH- + 3O2

When stored in solid form, potassium permanganate decomposes under the influence of light, also becoming contaminated with MnO2:

КМnО4 = К2МnО4 + МnО2↓ + О2

A solution of potassium permanganate can be prepared from a standard titer and a sample taken on a technical scale. In the first case, the contents of the ampoule are transferred quantitatively into a 2-liter volumetric flask, rinsing the ampoule and funnel with warm distilled water. Add a small volume of hot water to the volumetric flask to dissolve the crystals, then cool the resulting solution to room temperature, bring the volume of the solution to the mark and stir. The molar concentration of the resulting solution is 0.05 mol/l.

In the second case, weigh out a sample of potassium permanganate weighing 1.6 g on a technical scale in a beaker or on a watch glass, place it in a beaker and dissolve it in hot distilled water while thoroughly mixing the resulting solution, trying to ensure that all KMnO4 crystals dissolve. Then carefully pour the solution through a funnel into a 1-liter volumetric flask and mix thoroughly, after closing the flask with a ground-in stopper (do not use a rubber stopper). Leave the prepared KMnO4 solution for 7-10 days, then filter the solution through a funnel with glass wool or carefully pour it into another bottle using a siphon. It is imperative to store the KMnO4 solution in dark bottles, protected from light, to prevent decomposition.

The titer of a potassium permanganate solution prepared from a sample can be determined using oxalic acid H2C2O4*2H2O or sodium oxalate Na2C2O4.

Determination of nitrite ions in solution

In a neutral or alkaline environment, nitrites do not react with potassium permanganate; in a hot acidic solution they are oxidized to nitrates:

5КNO3 + 2КМnО4 + 3Н2SO4 = 2MnSO4 + 5КNO2 + K2SO4 + 3H2O

When slowly titrating an acidified solution of sodium nitrite with a solution of potassium permanganate, reduced results are obtained because nitrites are easily oxidized by acids to form nitrogen oxides:

2NO2- + 2H+ → 2 HNO2 → NO2- + NO + H2O

Therefore, to avoid losses, you can use the back titration method or the Lynge method - titration of an acidified solution of potassium permanganate with a solution of sodium nitrite.

Determination of calcium in calcium carbonate

Determination of calcium in solution by permanganatometric titration is possible by reverse or substitution titration. In the first case, a precisely measured excess of a titrated solution of oxalic acid is introduced into a solution containing calcium. The resulting CaC2O4 + H2SO4 precipitate, CaC2O4, is filtered off, and the residue that is not included in the oxalic acid reaction is titrated with a standard solution of potassium permanganate. Based on the difference between the introduced volume and the residue, it is determined how much oxalic acid was required for the precipitation of Ca2+, which will be equivalent to the calcium content in the solution.

According to the method of substitution titration, Ca2+ is isolated in the form of a precipitate of CaC2O4, which is filtered, washed and dissolved in H2SO4 or HC1.

CaC2O4 + H2SO4 → H2C2O4 + CaSO4

The resulting oxalic acid is titrated with a standard solution of potassium permanganate, the amount of which is equivalent to the calcium content in the solution.

Iodometry

The iodometric method of titrimetric analysis is based on the reaction:

I2 + 2e= 2I- ; Ео I2/3I- = 0.545 V