Course work
"ELECTROCHEMICAL METHODS
RESEARCH "
Introduction
1. Theoretical foundations of electrochemical research methods
1.1 History of the method
1.2 Description of electrochemical research methods
1.3 Potentiometry
1.4 Conductometry
1.5 Coulometry
1.6 Voltammetry
1.7 Electrogravimetry
2. Experimental part of electrochemical research methods
2.1 Determination of acid concentration by conductometric titration
2.2 Potentiometric titration
2.3 Electrolysis
2.4 Determination of electrode potentials
2.5 Determination of EMF of a galvanic cell
Conclusion
Bibliography
Introduction
In the modern world, the influence of scientific and technological progress on all spheres of our life is increasingly observed. In this regard, there is a need for more accurate and faster methods of analysis. Electrochemical research methods (ECMR) satisfy these requirements most strongly. They are the main physicochemical methods for studying substances.
ECMI is based on processes occurring at the electrodes or the interelectrode space. They are one of the oldest physicochemical research methods (some are described at the end of the 19th century). Their advantage is high accuracy and comparative simplicity. High accuracy is determined by very precise laws used in EMHI, for example, Faraday's law. It is of great convenience that in EHMI, electrical influences are used, and the fact that the result of this influence (response) is also obtained in the form of an electrical signal. This provides a high speed and accuracy of counting, opens up wide possibilities for automation. EHMIs are distinguished by good sensitivity and selectivity; in a number of cases, they can be attributed to microanalysis, since sometimes less than 1 ml of solution is sufficient for analysis.
Equipment for electrochemical analyzes is relatively cheap, affordable and easy to use. Therefore, these methods are widely used not only in specialized laboratories, but also in many industries.
Purpose of the work: study of electrochemical methods for studying the composition of matter.
To achieve this goal, it was necessary to solve the following tasks:
consider electrochemical research methods, their classification and essence;
to study potentiometric and conductometric titration, determination of electrode potentials and electromotive force (EMF) of a galvanic cell, as well as the electrolysis process in practice.
Object of research: the use of electrochemical methods in the analysis of the properties and composition of a substance.
Subject of research: mechanisms of electrochemical processes, potentiometry, conductometry, coulometry, voltammetry, electrogravimetry.
electrochemical titration galvanic
1.Theoretical foundations of electrochemical research methods
1 History of the method
It became possible to carry out systematic electrochemical studies only after the creation of a constant sufficiently powerful source of electric current. Such a source appeared at the turn of the 18-19th centuries. as a result of the work of L. Galvani and A. Volta. While researching the physiological functions of the frog, Galvani accidentally created an electrochemical circuit consisting of two different metals and the muscle of a prepared frog leg. When the foot, which was secured with a copper holder, was touched with an iron wire, also connected to the holder, the muscle contracted. Similar contractions occurred under the action of an electric discharge. Galvani explained this phenomenon by the existence of "animal electricity". Volta gave a different interpretation to these experiments, who considered that electricity arises at the point of contact of two metals, and the contraction of the frog's muscle is the result of an electric current passing through it. The current also occurred when a spongy material (cloth or paper) soaked in salt water was placed between two metal discs, for example, zinc and copper, and the circuit was closed. Consistently connecting 15-20 such "elements", Volta in 1800 created the first chemical current source - "volt pillar".
The effect of electricity on chemical systems immediately interested many scientists. Already in 1800 W. Nicholson and A. Carlyle reported that water decomposes into hydrogen and oxygen when an electric current is passed through it using platinum and gold wires connected to a "voltaic pillar". The most important of the early electrochemical studies were the work of the English chemist H. Davie. In 1807, he isolated the element potassium by passing a current through a slightly moistened solid potassium hydroxide. A battery of 100 galvanic cells was used as a voltage source. Metallic sodium was prepared in a similar manner. Later, Davy, using a mercury electrode, isolated magnesium, calcium, strontium and barium by electrolysis.
Assistant Davy M. Faraday investigated the relationship between the amount of electricity (current times time) flowing across the electrode / solution interface and the chemical changes it causes. A device (now known as a gas coulometer) was created to measure the amount of electricity by the volume of hydrogen and oxygen released in an electrolytic cell, and it was shown (1833) that the amount of electricity required to obtain a given amount of a substance does not depend on the size of the electrodes, the distance between them and the number of plates in the battery feeding the cell. In addition, Faraday discovered that the amount of a substance released during electrolysis is directly proportional to its chemical equivalent and the amount of electricity passed through the electrolyte. These two fundamental provisions are called Faraday's laws. Together with his friend W. Whewell, a specialist in classical philology, Faraday also developed a new terminology in electrochemistry. He called conductors immersed in a solution electrodes (previously they were called poles); introduced the concepts of "electrolysis" (chemical changes associated with the passage of current), "electrolyte" (conducting liquid in electrochemical cells), "anode" (the electrode on which the oxidation reaction takes place) and "cathode" (the electrode on which the reduction reaction occurs ). He called charge carriers in liquids ions (from the Greek "wanderer", "wanderer"), and ions moving to the anode (positive electrode) were called "anions", and to the cathode - "cations". Faraday's research on electromagnetic induction led to the creation of electrical generators, which made it possible to carry out electrochemical processes on an industrial scale.
Faraday explained the ability of solutions to pass an electric current by the presence of ions in them, however, he himself and other scientists, such as I. Gittorf and F. Kohlrausch, believed that ions appear under the influence of current. In 1884, S. Arrhenius suggested that in fact, ions are formed simply by dissolving salt in water. The works of S. Arrhenius, J. Van't Hoff and W. Ostwald were an important milestone in the development of the theory of electrolytes and ideas about the physicochemical properties of solutions and their thermodynamics. The agreement between theory and experimental data on ionic conductivity and equilibria in solution became more complete after P. Debye and E. Hückel took into account long-range electrostatic interactions between ions in 1923.
The first attempt to find out the reasons for the appearance of a potential difference between a solution and a metal was made in 1879 by H. Helmholtz, who showed that this potential difference is caused by an electric double layer, the positive side of which is on the metal, the negative side in the liquid. Thus, H. Helmholtz considered the double layer as a flat condenser. This model of a double layer remained outside the field of vision of electrochemists for a long time. The microcosm at the metal-solution boundary, where electrochemical processes take place, was still "waiting" for its time.
The French physicist J. Guy in 1910 and the English electrochemist D. Chapman in 1913 showed that electrolyte ions are not located in one plane (as G. Helmholtz imagined), but form a certain "diffuse" region (with distance from the surface metal ion concentration gradually changes). The theory of the structure of the Guy - Chapman double layer was further developed by the German scientist O. Stern. In 1924, he proposed to take into account the size of ions and the effect of adsorption of ions and dipole solvent molecules when describing the structure of the electric double layer. The study of the differential capacity of the double layer using new research methods allowed the Soviet scientist, academician A.N. Frumkin in 1934-1935. and the American scientist D. Graham in 1941 to establish the limits of applicability of the Guy-Chapman-Stern theory. A.N. Frumkin suggested that the discrepancy between theory and experimental data is due to the discrete nature of the charge distribution in the double layer. This idea, first expressed in 1935, was further developed in the 40-50s.
J. Gibbs and W. Nernst made a significant contribution to electrochemical thermodynamics and specifically to the elucidation of the nature of the electric potential (voltage) in an electrochemical cell and the balance between electrical, chemical and thermal energy. Yu. Tafel (1905), J. Butler (1924), M. Volmer (1930), A.N. Frumkin (1930-1933).
2 Description of electrochemical research methods
An electrochemical cell, which is a vessel with an electrolyte solution, in which at least two electrodes are immersed, serves as an instrument for EHMI. Depending on the problem to be solved, the shape and material of the vessel, the number and nature of electrodes, solution, analysis conditions (applied voltage (current) and the recorded analytical signal, temperature, stirring, purging with an inert gas, etc.) can be different. The substance to be determined can be included both in the composition of the electrolyte filling the cell and in the composition of one of the electrodes. If the redox reaction occurs spontaneously on the cell electrodes, that is, without applying a voltage from an external source, but only due to the potential difference (EMF) of its electrodes, then such a cell is called a galvanic cell. If necessary, the cell can be connected to an external voltage source. In this case, by applying sufficient voltage, the direction of the redox reaction and the current can be reversed to that of the galvanic cell. The redox reaction that occurs on the electrodes under the action of an external voltage source is called electrolysis, and an electrochemical cell that consumes the energy required for a chemical reaction in it is called an electrolytic cell.
EHMI is subdivided into:
) conductometry - measurement of the electrical conductivity of the test solution;
) potentiometry - measurement of the current-free equilibrium potential of the indicator electrode, for which the test substance is potentiopotential;
) coulometry - measuring the amount of electricity required for the complete transformation (oxidation or reduction) of the substance under study;
) voltammetry - measurement of stationary or non-stationary polarization characteristics of electrodes in reactions involving the test substance;
) electrogravimetry - measurement of the mass of a substance released from a solution during electrolysis.
EHMI can be subdivided according to the use of electrolysis. Coulometry, voltammetry and electrogravimetry are based on the principles of electrolysis; electrolysis is not used in conductometry and potentiometry.
EHMI are of independent importance for the direct conduct of chemical analysis, but can be used as ancillary in other methods of analysis. For example, it can be used in titrimetry to register the end of titration not with the help of a chemical color-variable indicator, but by the change in potential, electrical conductivity of the current, etc.
Let us consider in more detail the processes occurring during electrochemical studies.
The electrode is a system, in the simplest case, consisting of two phases, of which the solid has electronic, and the other - liquid has ionic conductivity. The solid phase with electronic conductivity is considered to be a type I conductor, and the liquid phase with ionic conductivity is considered to be of the II type. When these two conductors come into contact, an electric double layer (EDL) is formed. It can be the result of ion exchange between the solid and liquid phases, or the result of specific adsorption of cations or anions on the surface of the solid phase when it is immersed in water or solution.
With the ionic mechanism of DEL formation, for example, in the case when the chemical potential of atoms on the metal surface (solid phase) is greater than the chemical potential of ions in the solution, then the atoms from the metal surface will pass into the solution in the form of cations: Me? Me z + + ze -... The released electrons charge the surface of the solid phase negatively and, due to this, attract positively charged ions of the solution to the surface. As a result, two oppositely charged layers are formed at the interface, which are, as it were, the plates of a kind of capacitor. For the further transition of charged particles from one phase to another, they need to perform work equal to the potential difference of the plates of this capacitor. If the chemical potential of atoms on the surface of the solid phase is less than the chemical potential of ions in the solution, then the cations from the solution pass to the surface of the solid phase, charging it positively: Me z + + ze - ? Me. In both the first and second cases, these processes do not proceed endlessly, but until a dynamic equilibrium is established, which can be represented by a reversible redox transition of the Me - ze type -? Me z + or in general Ox + I0 ? Red z + .
The processes in which the return or attachment of electrons occurs on the electrodes are called electrode.
Nernst obtained a formula that relates the difference between the internal potentials of the DES with the activities (concentrations) of particles participating in the reversible redox transition:
where ?(Me) is the potential of the charged layer of the solid phase;
?(solution) - potential of the solution layer adjacent to the solid phase;
??0- standard electrode potential; - universal gas constant (8.31 J / K mol); - temperature, K; - Faraday number (96 488 C / mol); - the number of electrons participating in the redox transition;
a (Ox) and a (Red) are the activities of the oxidized (Ox) and reduced (Red) forms of the substance in the redox transition, mol / L.
Establish the internal potentials of the individual phases ?(Me) and ?(p - p), unfortunately, experimentally impossible. Any attempt to connect the solution using a wire to the measuring device causes the appearance of a new surface of contact between the metal-solution phases, that is, the emergence of a new electrode with its own potential difference affecting the measured one.
However, you can measure the difference ?(Me) - ?(p - p) using a galvanic cell. A galvanic cell is a system made up of two different electrodes, which has the ability to spontaneously convert the chemical energy of the redox reaction taking place in it into electrical energy. The electrodes that make up a galvanic cell are called half cells. The redox reaction proceeding in the galvanic cell is spatially separated. The oxidation half-reaction takes place at a half-cell called the anode (negatively charged electrode), and the reduction half-reaction occurs at the cathode.
The electromotive force (EMF) of a galvanic cell is algebraically composed of the differences in the internal potentials of its constituent electrodes. Therefore, if we take an electrode with a known value of the internal potential difference as one half-element ?(Me) - ?(solution), then the measured value of the EMF can be used to calculate the desired potential difference of the investigated electrode.
For this purpose, it is customary to use a standard (normal) hydrogen electrode (see Fig. 1). It consists of a platinum plate or wire coated with platinum black (fine platinum) immersed in an acid solution C = 1 mol / l, the hydrogen pressure above which is 0.1 MPa (1 atm). Under the catalytic influence of platinum black, a reversible redox transition occurs in the electrode. The difference in internal potentials for a hydrogen electrode in accordance with the Nernst formula is equal to:
Figure 1. Schematic of a standard hydrogen electrode
since = 1 mol / l, and p (H2 ) = 1 atm, then
?(Me) - ?(p - p) = ??0(2H + / H 2).
The value ??0(2H +/ H 2) = 0.00 V. Obviously, in this case, the measured value of the EMF of a galvanic cell, which includes a hydrogen electrode, is equal to the difference between the internal potentials of the second electrode. This EMF is usually called the electrode potential or redox potential and denoted by the letter E. The transition from internal potentials to redox potentials does not change the nature of the Nernst formula:
For most electrodes, the value of the electrode potential at single activities of the oxidized and reduced forms (E 0) is measured and given in reference books.
Under normal conditions and the transition from natural to decimal logarithms, the pre-logarithmic factor becomes 0.0591, and the formula takes the form
It should be remembered that the Nernst formula connects the equilibrium potential with the activities (concentrations) of the redox pair, i.e. potential that an insulated electrode acquires. Therefore, for analytical circuits, the measurement of the electrode potential should be carried out under conditions as close as possible to equilibrium: in the absence of current in the external circuit of the galvanic cell and after a time sufficient to achieve equilibrium. However, under real conditions, current can flow through the electrodes. For example, the current flows through the electrodes in a galvanic cell, the work of which is associated with the transition of charged particles through the interface "solution-solid phase", and this directional movement of particles is a current. The current flows through the electrodes during electrolysis, which is understood as a set of redox processes occurring on the electrodes in solutions and melts of electrolyte electrodes under the influence of an external electric current. During electrolysis, it is possible to carry out processes opposite to those occurring in a galvanic cell.
When current (i) flows through the electrode, its potential changes and acquires a certain value Еi, which differs from the electrode potential in equilibrium (isolated) conditions Ер. The process of displacement of the potential from Ер to Еi and the difference Еi-Ep are called polarization
E = Ei-Ep. (5)
Not all electrodes are subject to polarization processes. Electrodes, the potential of which does not change when current flows through them, are called non-polarizable, and electrodes, which are characterized by polarization, are called polarizable.
Non-polarizable ones include, for example, type II electrodes, polarizable ones - all metal and amalgam ones.
1.3 Potentiometry
Potentiometry is an electrochemical method for research and analysis of substances based on the dependence of the equilibrium electrode potential on the activity of the concentrations of the ion being determined, described by the Nernst equation (1).
The dependence of electrode potentials on the nature of electrode processes and the activities of the substances involved in them allows the use of EMF measurement (potentiometric method) to find the activity coefficients of electrolytes, standard electrode potentials, equilibrium constants, solubility products, pH solutions, etc. The advantages of the potentiometric method are accuracy, objectivity and speed.
It is known that
is an important characteristic of a solution and determines the possibility and nature of many reactions.
Potentiometric determination of pH is based on the use of so-called indicator electrodes, in the electrode reaction of which hydrogen ions are involved, and the potential depends on pH. By measuring the EMF of an element containing an indicator electrode with a test solution, the pH of this solution can be calculated. An electrode with a known potential should be taken as the second electrode.
EMF element
H 2| investigated solution || KCl, Hg2 Cl 2| Hg
Potentiometric pH determination allows you to find the pH of turbid and colored media. When using a hydrogen electrode as an indicator one can determine the pH of solutions in a wide range (from pH 1 to pH 14). The disadvantage is the need for long-term saturation of the electrode with hydrogen to achieve equilibrium. It cannot be used in the presence of surfactants and certain salts.
The schematic of the element used in this case is as follows:
| Hg 2Cl 2, KC l || test solution + quinhydrone | Рt,
its EMF is
(10)
The potentiometric method for determining the pH of a solution using a quinhydrone electrode is very simple. It is applicable for solutions with a pH from 1 to 8. In alkaline media, as well as in the presence of oxidizing or reducing agents, the quinhydrone electrode is unsuitable.
A so-called glass electrode is often used as an indicator electrode. It is a thin-walled glass ball with a reference electrode, for example, silver chloride, placed inside. Glass is a supercooled silicate solution containing alkali metal cations and type anions. The glass bead is preliminarily kept in a strong acid solution, where cations are exchanged between the glass and the solution and the glass is saturated with hydrogen ions. When determining pH, a glass electrode and another reference electrode are lowered into the test solution. As a result, the following chain is formed:
The potential jump Δ1 at the interface between the glass and the potassium chloride solution entering the reference electrode is constant due to the constancy of the concentration of this solution. The potential jump Δ2 depends on the concentration of the test solution and can be written
(11)
Where ?o and m are constants for a given glass electrode. Taking into account the potential jumps on the glass surface, we obtain
(12)
(13)
where . From here
(14)
Constants for a given glass electrode ?° and m are determined by preliminary graduation. To do this, place a glass electrode in several buffer solutions with a known pH and measure the EMF of the circuit. Subsequently, using formula (14), the pH of the solutions under study is found.
Let's move on to considering the coefficient of activity of the electrolyte. Consider a double concentration chain without transfer containing two electrolyte solutions:
Pt, H 2| HCl, AgCl | Ag | AgCl, HCl | H2 , Pt
a1 a2
where a1 and a2 - average ionic activities of HCl solutions. It can be used to determine the HCl activity factor. The EMF of this circuit is
(15)
Substitution of the numerical values R, F and T = 298 K and the transition to decimal logarithms gives
(16)
We substitute in the resulting equation
(17)
where m 1- average molality; ?1is the average coefficient of electrolyte activity.
We transfer the values determined experimentally to the left side of the equation, and we obtain
(18)
In view of the fact that in the limiting case of an infinitely dilute solution, it should be close to ideal, and ?1 ? 1, then B is
(19)
We build a graph of dependence (or, which is more convenient, since it gives a line close to a straight line) and extrapolate to. Thus, we determine B graphically (Fig. 2).
Figure 2. Determination of the coefficient of activity of the electrolyte
We calculate the activity coefficient according to the equation
(20)
4 Conductometry
Conductometry- a set of electrochemical analysis methods based on measuring the electrical conductivity of liquid electrolytes, which is proportional to their concentration.
Measurements of electrical conductivity (conductometry) allow solving a number of theoretical and practical problems. Such measurements can be carried out quickly and accurately. With the help of conductometry, it is possible to determine the constant and degree of dissociation of a weak electrolyte, the solubility and the product of the solubility of hardly soluble substances, the ionic product of water and other physicochemical quantities. In production, conductometric measurements are used to select electrolyte solutions with a sufficiently high conductivity to eliminate waste energy, to quickly and accurately determine the solute content, to automatically control the quality of various liquids, etc.
In conductometric titration, the course of the reaction is monitored by the change in electrical conductivity after each addition of the titrating reagent. It does not require the use of indicators and can be performed in non-transparent environments. In the process of conductometric titration, the ions of the titrated substance are replaced by the ions of the added reagent. The equivalence point is determined by a sharp change in the electrical conductivity of the solution, which is explained by the different mobility of these ions.
In fig. 3 shows the curves of the dependence of the specific electrical conductivity (x) on the volume V of the added reagent. When a strong acid is titrated with a strong base or a strong base with a strong acid (curve l), a minimum is formed on the titration curve, corresponding to the replacement of hydrogen or hydroxyl ions by less mobile ions of the resulting salt. When a weak acid is titrated with a strong base or a weak base with a strong acid (curve 2), the slope of the curve changes at the equivalence point, which is explained by the more significant dissociation of the formed salt as compared to the dissociation of the initial substance. In the case of titration of a mixture of strong (a) and weak (b) acids with a strong base (curve 3), two points of equivalence are observed.
Figure 3. Curves of conductometric titration.
Using ionic conductivity tables or measurements ?at different concentrations of the solution and subsequent extrapolation to zero concentration, one can find ?°. If we measure the electrical conductivity of a solution of a given concentration, then according to the equation
(22)
we obtain the relation
(23)
Figure 4. Orientation of polar solvent molecules near electrolyte ions
From equations
(24) and , (25)
assuming we get
(26)
(27)
It remains to take into account that the quantity ?due only to this electrolyte and does not include the electrical conductivity of the solvent, i.e.
5 Coulometry
Coulometry- an electrochemical research method based on measuring the amount of electricity (Q) passed through an electrolyzer during electrochemical oxidation or reduction of a substance on a working electrode. According to the combined Faraday's law, the mass of an electrochemically converted substance (P) in g is related to Q in Cl by the ratio:
(28)
where M is the molecular or atomic mass of a substance, n is the number of electrons involved in the electrochemical transformation of one molecule (atom) of a substance (M / n is the electrochemical equivalent of a substance), F is Faraday's constant.
Coulometry is the only physical and chemical research method in which standard samples are not required. A distinction is made between direct coulometry and coulometric titration. In the first case, an electrochemically active substance is determined, in the second case, regardless of the electrochemical activity of the substance to be determined, an electrochemically active auxiliary reagent is introduced into the test solution, the product of electrochemical transformation of which chemically interacts with the substance to be determined at a high rate and quantitatively. Both variants of coulometry can be carried out at a constant potential E of the working electrode (potentiostatic mode) or at a constant electrolysis current I NS (galvanostatic mode). The most commonly used are direct coulometry at constant E and coulometric titration at constant I NS ... For a coulometric study, the following conditions must be met: the electrochemical transformation of a substance must proceed with a 100% current efficiency, i.e. there should be no side electrochemical and chemical processes; reliable methods are needed to determine the amount of electricity and establish the moment of completion of an electrochemical or chemical reaction. In direct coulometry, a 100% current efficiency is ensured if the value of E is kept constant in the region of the limiting diffusion current I np on the voltammogram of the analyte. In this case, the analyzed solution should be free of foreign substances capable of electrochemically converting under the same conditions. The amount of electricity is usually determined using electronic current integrators. Sometimes they use less accurate instruments - coulometers of various types, as well as planometric and calculation methods. In the last two cases, the end of electrolysis is considered the moment when I NS falls to the background current I f , therefore, the amount of electricity required to complete the electrode reaction is equal to the difference Q about -Q f , where Q about - the total amount of electricity, Q f - the amount of electricity measured under the same conditions for the same electrolysis time t NS , but in the absence of the analyte. If the electrochemical reaction is of the first order, then
(29)
(30)
where I t and I o - electrolysis current, respectively, at time t and at ?= 0, is the electrode surface area, is the diffusion coefficient of the electrochemically active substance,
?is the thickness of the diffusion layer; is the volume of the solution in the cell.
The duration of electrolysis does not depend on the initial concentration of the substance, but it decreases markedly with an increase in the S / V ratio and with vigorous stirring of the solution. The electrolysis can be considered complete when I NS becomes equal to 0.1 I 0or 0.01 I 0(depending on the required analysis accuracy). In the planometric method, to establish Q, measure the area under the curve I ? - ?since
(31)
In the calculation method, the last equation is solved by substituting the expression for I ?... To find I 0and K "expression for I ?logarithm and, using several (5-7) points, construct a straight line lg I ?-?, the slope of which is K ", and the point of intersection with the ordinate corresponds to lg I 0, i.e. to determine Q, it is not necessary to carry out electrolysis to the end and measure I 0whose value is poorly reproduced.
Installations for coulometric research consist of a potentiostat or galvanostat, a recording potentiometer or current integrator, an electrolyzer and an indication system (in the case of using physical and chemical methods to establish the end of a chemical reaction in coulometric titration).
Electrolyzers are, as a rule, glass vessels, the cathode and anode chambers in which are separated by a diaphragm (for example, made of porous glass). As working and auxiliary (closing the electrolysis circuit) electrodes, noble metals (Pt, Au), electrodes of the second kind and, less often, carbon materials (graphite, glassy carbon, etc.) are used. The solution, in which the working electrode is immersed, is usually stirred with a magnetic stirrer; if necessary, the experiment is carried out in an inert gas atmosphere.
Advantages of coulometric titration: there is no need to standardize titrant solutions; the titrant is added in very small portions (almost continuously); the solution is not diluted; it is possible to generate electrochemically inactive titrants, for example complexone III, as well as unstable strong oxidants and reducing agents, in particular Mn (III), Pb (IV), Cr (II), V (II), Ti (III).
6 Voltammetry
Voltammetry- a set of electrochemical research and analysis methods based on the study of the dependence of the current in the electrolytic cell on the potential of the indicator microelectrode immersed in the analyzed solution, on which the investigated electrochemically active (electroactive) substance reacts.
In addition to the indicator, an auxiliary electrode with a significantly higher sensitivity is placed in the cell so that its potential practically does not change when the current passes (non-polarizable electrode). The potential difference of the indicator and auxiliary electrodes E is described by the equation
where U is the polarizing voltage, is the solution resistance.
An indifferent electrolyte (background) is introduced into the analyzed solution in a high concentration in order, firstly, to reduce the value of R and, secondly, to exclude the migration current caused by the action of an electric field on electroactive substances (outdated - depolarizers). At low concentrations of these substances, the ohmic voltage drop IR in the solution is very small. To fully compensate for the ohmic voltage drop, potentiostation and three-electrode cells are used, which additionally contain a reference electrode. In these conditions
Stationary and rotating electrodes are used as indicator microelectrodes - made of metal (mercury, silver, gold, platinum), carbon materials (for example, graphite), as well as dripping electrodes (made of mercury, amalgam, gallium). The latter are capillaries from which liquid metal flows out dropwise. Voltammetry using dripping electrodes, the potential of which changes slowly and linearly, is called polarography (the method was proposed by Ya. Heyrovsky in 1922). The reference electrodes are usually the electrodes of the second kind, for example, calomel or silver chloride. The dependence curves I = f (E) or I = f (U) (voltammograms) are recorded with special devices - polarographs of different designs.
Figure 5. Voltammogram obtained with a rotating disk electrode
Voltammograms obtained with a rotating or dripping electrode with a monotonic change (linear sweep) of the voltage have the form shown schematically in Figure 5. The section of current increase is called a wave. Waves can be anodic, if the electroactive substance is oxidized, or cathodic, if it is reduced. When oxidized (Ox) and reduced (Red) forms of a substance are present in the solution, which react quickly (reversibly) at the microelectrode, a continuous cathode-anode wave is observed on the voltammogram, crossing the abscissa axis at a potential corresponding to oxidation-reduction. the potential of the Ox / Red system in a given environment. If the electrochemical reaction on the microelectrode is slow (irreversible), the voltammogram shows an anodic wave of oxidation of the reduced form of the substance and a cathodic wave of reduction of the oxidized form (at a more negative potential). The formation of the limiting current area on the voltammogram is associated either with the limited rate of mass transfer of the electroactive substance to the electrode surface by convective diffusion (limiting diffusion current, I d ), or with a limited rate of formation of an electroactive substance from the analyte in solution. Such a current is called. limiting kinetic, and its strength is proportional to the concentration of this component.
The waveform for a reversible electrochemical reaction is described by the equation:
(33)
where R is the gas constant, T is the absolute temperature, is the half-wave potential, i.e. potential corresponding to half the wave height. The value is characteristic of a given electroactive substance and is used to identify it. When the electrochemical reaction is preceded by the adsorption of the analyte on the electrode surface, the voltammograms show not waves, but peaks, which is associated with the extreme dependence of adsorption on the electrode potential. The voltammograms recorded with a linear change (sweep) of the potential with a stationary electrode or on one drop of a dropping electrode also exhibit peaks, the descending branch of which is determined by the depletion of the near-electrode layer of the solution with an electroactive substance. In this case, the height of the peak is proportional to the concentration of the electroactive substance. In polarography, the limiting diffusion current (in μA) averaged over the lifetime of a drop is described by the Ilkovich equation:
(34)
where n is the number of electrons participating in the electrochemical reaction, C is the concentration of the electroactive substance, D is its diffusion coefficient, the lifetime of a mercury drop, m is the rate of mercury outflow.
Voltammetry is used: for the quantitative analysis of inorganic and organic substances in a very wide range of concentrations - from 10 -10 % up to tens of%; to study the kinetics and mechanism of electrode processes, including the stage of electron transfer, previous and subsequent chemical reactions, adsorption of initial products and products of electrochemical reactions, etc .; to study the structure of the electric double layer, the equilibrium of complexation in solution, the formation and dissociation of intermetallic compounds in mercury and on the surface of solid electrodes; to select the conditions for amperemetric titration, etc.
7 Electrogravimetry
Electrogravimetry is an electrochemical research method based on determining the increase in the mass of the working electrode due to the release of the determined component on it as a result of electrolysis. Typically, the analyte is deposited as a metal (or oxide) on a pre-weighed platinum cathode (or anode). The moment of completion of electrolysis is established using a specific sensitive qualitative reaction to the ion being determined. The working electrode is washed, dried and weighed. The mass of the released metal or oxide is determined from the difference in the masses of the electrode before and after electrolysis.
The theoretical potential of metal precipitation at the cathode can be calculated from the values of standard electrode potentials E 0... For example, when determining Cu (II) in an acidic solution, the corresponding reactions occur on the platinum cathode and anode:
Under electrolysis conditions, the cathode potential at 25 ° C is described by the Nernst equation:
(35)
At the beginning of electrolysis, when the cathode surface is not covered with copper, a (Cu) is infinitely small; in the presence of a current sufficient to fill the cathode surface with copper, a (Cu) approaches unity. In practice, for an electrochemical reaction to proceed at a noticeable rate, a higher voltage is required than the theoretically calculated evolution potential E. This is due to the overvoltage of oxygen at the platinum anode and the ohmic voltage drop in the cell.
Electrogravimetry is a selective method: if the initial concentrations of the components are equal, separate separation on the electrode is possible with a difference in their electrode potentials of the order of 0.3 V (for singly charged ions) or 0.1 V (for doubly charged ions).
Electrolysis can be carried out at a constant voltage between the electrodes, at a constant current strength, or at a controlled potential of the working electrode. In the case of electrogravimetry at a constant voltage, the potential of the working electrode is shifted to a more negative region due to polarization. The consequence of this is a decrease in selectivity due to the occurrence of an additional reaction (the release of other metals or gaseous H 2). This version of electrogravimetry is suitable for the determination of easily reducible substances in the presence of impurities that are more difficult to reduce than H ions +... At the end of electrolysis, gaseous H 2... Although, unlike coulometry, a 100% current efficiency of the analyte is not required, the release of H 2often leads to the formation of deposits with unsatisfactory physical properties. Therefore, it is recommended to introduce into the analyzed solution substances that are reduced more easily than H ions +(hydrazine, hydroxylamine) and thus preventing the release of H2 .
If electrolysis is carried out at a constant current strength, it is necessary to periodically increase the external voltage applied to the cell in order to compensate for the decrease in current caused by concentration polarization. As a result, the analysis becomes less selective. Sometimes, however, it is possible to bind interfering cations into strong complex compounds, which are reduced at a more negative potential than the analyte, or to remove the interfering ion in the form of a poorly soluble compound beforehand. The method is used, for example, to determine Cd in an alkaline solution of its cyanide, Co and Ni in an ammonium sulfate solution, Cu in a mixture of sulfuric and nitric acids.
Electrogravimetry has been known since the 1860s. and was used to determine the metals used for minting coins in various alloys and ores. This is a standardless method that can be regarded as the simplest version of coulometry. In terms of accuracy and reproducibility of results, electrogravimetry surpasses other methods in the determination of metals such as Cu, Sn, Pb, Cd, Zn. Despite the relative duration of the experiment, electrogravimetry is still used to analyze alloys, metals, and solutions for electrolyte baths.
2.Experimental part of electrochemical research methods
1 Determination of acid concentration by conductometric titration
The purpose of the laboratory work:determination of the concentration of acetic and hydrochloric acids by conductometric titration.
Equipment and reagents:general laboratory module, computer, burette, Mohr pipettes for 5 and 10 ml; solutions: 0.1 N NaOH, HCl and CH solutions 3COOH with unknown concentration.
Progress
When conducting conductometric titration, two experiments are carried out:
Experience number 1
Installing the burette and glass. Pour 10 ml of hydrochloric acid solution into the glass in the sensor of the device with a Mohr pipette. The solution level in the glass should be 3-5 mm higher than the upper electrode and sensor. We dilute the solution with water. We turn on the magnetic stirrer. We fill the burette with 0.1 N solution. NaOH. We make a measurement using a general laboratory module connected to a personal computer.
Process chemistry
Processing of results
1)During the measurement, the computer measures the conductivity of this solution, which are summarized in Table 1.
Table 1. Dependence of electrical conductivity on the volume of alkali used for titration of hydrochloric acid.
V (NaOH), ml 0246891010,51112131415L, mS 9,2929,329,2959,2899,2789,2719,269,259,2419,219,1359,2489,256
)We build a graph of the dependence of electrical conductivity on the volume of alkali, which was used for titration of hydrochloric acid (Figure 6).
Figure 6. Dependence of electrical conductivity on the volume of alkali used for titration of hydrochloric acid.
Veq (NaOH) = 13 ml
4)Using the law of equivalents, we calculate the concentration of hydrochloric acid:
hence (37)
Experience number 2
The experiment is carried out with 5 ml of acetic acid solution. Further actions are the same as in the previous experiment.
Process chemistry
Processing of results
1)During the measurement, the computer measures the conductivity of this solution, which are summarized in Table 2.
Table 2. Dependence of electrical conductivity on the volume of alkali used for the titration of acetic acid.
V (NaOH), ml 012344.555.5678910L, mS 6.63.84.65.76.67.08.08.38.58.99.09.19.2
)We build a graph of the dependence of electrical conductivity on the volume of alkali used for the titration of acetic acid (Figure 7).
Figure 7. Dependence of electrical conductivity on the volume of alkali used for the titration of acetic acid.
3)Find the equivalence point according to the graph:
Veq (NaOH) = 5 ml
)Using the law of equivalents, we calculate the concentration of acetic acid:
Output
In the course of this work, we determined by conductometric titration the concentration of hydrochloric and acetic acids:
2 Potentiometric titration
Target: Get to know the potentiometric titration method. Establish equivalence points when titrating a strong acid with a strong base, a weak acid with a strong base.
Equipment: pH meter, glass electrode, silver chloride electrode, 100 ml beaker; 0.1 n. HC1 solution; CH 3UNOO; 0.5 n. KOH solution; burette, magnetic stirrer.
Progress
Experience number 1
Pour 15 ml of a 0.1 N solution into a glass using a pipette. hydrochloric acid, lower the slider, place the glass on the magnetic stirrer and turn it on after lowering the electrodes (make sure that the glass electrode does not touch the slider).
The disconnected position of the pH meter "-1-14" and "0-t" are pressed. To change, press the "pH" button and remove the value on the lower scale. Then add a solution of 0.1 N. alkali 1-3 ml and fix the pH value. Install the microburettes so that the alkali flows out in drops. When approaching the point of equivalence, we add alkali in very small doses. During the experiment, the beaker is placed on a magnetic stirrer, and the solution is constantly stirred.
After a sharp change in the pH of the solution, add a small amount of alkali and constantly fix the pH.
Process chemistry
Processing of results
1)As a result of this experiment, we got the following results:
Table 3. Dependence of the pH value on the volume of alkali used for the titration of acetic acid.
V (KOH), ml 12345678910pH4.004.154.154.004.204.304.294.945.004.91
Continuation of table. 3
V (KOH), ml 1112131415161718192021pH5.075.105.125.205.355.407.307.608.048.409.00
)Based on the data obtained, we build a graph of the dependence of pH on the volume of alkali used for titration (Figure 8).
Figure 8. Hydrochloric acid titration curve
)According to the graph (Figure 8), we determine the equivalence point.
V eq (NaOH) = 16.5 ml
Experience number 2
We carry out a similar titration with 0.1 N. CH3 UNSD.
Chemism
Processing of results
1)As a result of this experiment, we received the following data:
Table 4. Dependence of the pH value on the volume of alkali used for the titration of acetic acid.
V (KOH), ml 123456789101112131415pH4,465,345,375,485,635,705,735,876,006,106,236,406,606,409,60
)Based on the data obtained, we build a graph of the dependence of pH on the volume of alkali used for titration (Figure 9).
Figure 9. Acetic acid titration curve
)According to the graph (Figure 9), we determine the equivalence point. eq (NaOH) = 14.2 ml
Output
In the course of this work, we determined the equivalence point of solutions of hydrochloric and acetic acids by potentiometric titration.
Equivalence point for hydrochloric acid solution:
V eq (NaOH) = 16.5 ml
Equivalence point for acetic acid solution: eq (NaOH) = 14.2 ml
3 Electrolysis
purpose of work: determination of the electrochemical equivalent of copper.
Equipment: rectifier, ammeter, bath with electrolyte and two copper electrodes, stopwatch, analytical balance, 5% CuSO solution 4, wires for mounting the device.
Progress
Electrochemical equivalent - the amount of a substance that has undergone a chemical transformation at the electrode when passing a unit of electricity, provided that all the passed electricity is spent only on the transformation of this substance.
(38)
where E is the electrochemical equivalent,
?- molar mass of the compound,
?q is the number of electrons required for the electrochemical transformation of one molecule of this compound.
Molar mass of the equivalent of a substance that underwent chemical transformation at the electrode (Meq ) is equal to:
(39)
where m is the mass of the deposited substance,
F - Faraday constant,
I - current strength,
t is the time during which the current flowed.
To determine the electrochemical equivalent E, we assemble a device, where the current from the source is passed through a rectifier and a bath with electrolyte, an ammeter, connected in series. When switched on, copper is released on the copper electrode, which is the cathode. The anode, also made of copper, dissolves. In order for copper to be deposited on the cathode, to form a dense layer and not peel off during the experiment, distorting the results, you should use a current not exceeding 0.05 A per 1 cm 2cathode surface. To do this, before the start of the experiment, using a millimeter ruler, determine the surface of the cathode and calculate the maximum permissible current.
Before starting the experiment, immerse the cathode in a 20-30% solution of nitric acid for 1-2 seconds, and then thoroughly rinse it with distilled water.
During the work, it is important not to touch the surface of the cathode immersed in the electrolyte, because even the smallest traces of fat impair the adhesion of the copper cathode deposit.
After that, we fix the cathode in a voltmeter, which we fill with a CuSO solution 4... We remove the cathode from the electrolyte bath, rinse with distilled water, dry it and weigh it on an analytical balance. After that, we put the cathode back into the electrolyte bath and proceed to the experiment. At the same time, turn on the current and set the stopwatch in motion. The experiment lasts 40-50 minutes. At the same time, turn off the current and stop the stopwatch. We remove the cathode from the electrolyte, rinse with distilled water, dry and weigh.
During electrolysis, the following chemical reactions took place:
)Dissociation of copper (II) sulfate solution:
2)Redox reactions on electrodes:
Processing of results
1)As a result of this laboratory work, we received the following data (table 5):
Table 5. Data on the laboratory work carried out.
Current (I), A1.8 Time during which the current flowed (t), s 2527 Weight of the cathode before the experiment, expressed in mass, g 24.42 Weight of the cathode after the experiment, expressed in mass, g 25.81 Weight of the deposited substance, expressed in mass (m ), g 1.39 2)Calculation of the electrochemical equivalent:
)Calculation of molar mass equivalent, absolute and relative error:
Output.
In the course of this work, we determined the electrochemical equivalent of copper, the molar mass of the equivalent of copper, as well as the absolute and relative error.
2.4 Determination of electrode potentials
purpose of work: to measure the potential of copper and zinc electrodes in solutions of their salts of various activities. Compare the measured values of the potentials with the calculations according to the Nernst equation.
Equipment: pH meter, copper electrode, zinc electrode, silver chloride electrode, U-tube with saturated KCl solution, sandpaper, CuSO solutions 4and ZnSO 4with varying concentration.
Progress
To measure potentials of the 1st kind, we assemble a circuit consisting of a measuring device, a measured electrode and a reference electrode. In fact, we measure the EMF of a galvanic cell
| AgCl, KCl || CuSO4 | Cu;
Zn | ZnSO4 || KCI, AgCl | Ag.
The potential of a silver chloride electrode (electrode of the second kind) is constant, depends only on the activity of Cl ions and is equal to Ag | AgCl (saturated solution KC1) = 0.2 V. It is a reference electrode.
To eliminate the diffuse potential, we use bridges filled with a saturated KCl solution.
We use a pH meter to measure potentials. We connect the silver chloride electrode to a special socket "reference electrode" (on the VSP panel of the device), and the measuring electrode through a special plug to the socket "measurement - 1", "measurement - 2".
Process chemistry
For electrochemical cell Ag | AgCl, KCl || CuSO4 | Cu:
For galvanic cell Zn | ZnSO4 || KCI, AgCl | Ag:
Processing of results
1)As a result of measuring the potentials of a copper electrode at different activities of Cu ions 2+we got the following data:
¾ for a copper electrode (table 6):
Table 6. Data on the laboratory work carried out for the copper electrode.
?meas, BCn, mol * eq-1 * l-1 ?lg a ?calculated, В0,2100,10,38-1,72120,2862230,3510,20,36-1,44370,2944110,3600,50,25-1,20410,3014780,3611,00,23-0,93930, 309291
¾ for a zinc electrode (table 7):
Table 6. Data on the laboratory work carried out for the zinc electrode.
?meas, BCn, mol * eq-1 * l-1 ?lg a ?calculated, B-0.0650.10.25-1.9031-0.81914-0.0650.20.28-1.5528-0.80881-0.0290.50.38-1.0223-0, 79316-0.0501.00.40-0.6990-0.78362
2) We build a graph of the dependence of the electrode potential on lg a (Cu2 +).
¾ for a copper electrode (Figure 10):
Figure 10. Dependence of the electrode potential on the logarithm of the activity of copper (II) ions
¾ for a zinc electrode (Figure 11):
Figure 11. Dependence of the electrode potential on the logarithm of the activity of zinc ions
.We calculate the potentials of the electrodes according to the Nernst equation (1):
¾ for copper electrode:
¾ for zinc electrode:
Output: in the course of this work, we measured the potentials of copper and zinc electrodes at various concentrations of CuSO 4and ZnSO 4accordingly, and also calculated these electrode potentials according to the Nernst equation, as a result of which they concluded that with an increase in concentration, the electrode potentials at the copper and zinc electrodes increase.
5 Determination of EMF of a galvanic cell
Purpose: to determine the EMF of a galvanic cell.
Equipment: zinc and copper electrode, CuSO solutions 4and ZnSO 4, silver chloride electrode, pH meter, sandpaper, U-shaped tube with saturated solution KC1, 0.1N. and 1n. CuSO solution 4, 0.1n. and 1n. ZnSO4 solution ,
Progress
Pour half of the CuSO solutions into two glasses 4and ZnSO 4... In the first we place an electrode made of copper, in the second - made of zinc.
We pre-clean the electrodes with sandpaper and rinse them. We connect the wires to the pH meter on the rear panel to the inputs "Measure 1" and "El. compare ". We close the external circuit using a U-shaped tube filled with a saturated solution of KCl in agar-agar.
Before measurement, the device warms up for 30 minutes. When the circuit is assembled, we proceed to measurements, press the "mV" button and look at the instrument readings on the lower scale "1-14". For a more accurate determination of the EMF, press the button of the desired range. To convert measured values to volts, the numerator of the value is multiplied by 0.1.
To perform the work, we measure the EMF of the elements in solutions with a concentration of 1N. and 0.1N. and compare this data with the calculations. Find the absolute and relative error.
Process chemistry
For this cell
| ZnSO4 || KCI, AgCl | Ag
the following reactions are characteristic:
The overall equation of the reaction proceeding in a copper-zinc galvanic cell:
Processing of results
1)As a result of this work, we received the following results (table 6):
Table 6. Data on the conducted laboratory work
Solutions ?unit, V ?calculated, V Relative error,% 0.1n. CuSO4 and 0.1N. ZnSO41.0871.0991.0921n. CuSO4 and 0.1N. ZnSO41,0821,0931,0061n. CuSO4 and 1N. ZnSO41.0601.070.935
)We calculate the EMF:
The calculation of the potentials is carried out according to the Nernst equation (1). Standard electrode potentials are taken from the reference data.
For solutions 0.1N. CuSO 4 and 0.1N. ZnSO 4:
For solutions 1N. CuSO 4 and 0.1N. ZnSO 4:
For solutions 1N. CuSO 4 and 1n. ZnSO 4:
Output: in this work, we have determined the EMF of a galvanic cell in solutions of various concentrations:
at a concentration of 0.1N. CuSO4 and 0.1N. ZnSO4,
at a concentration of 1N. CuSO4 and 0.1N. ZnSO4,
at a concentration of 1N. CuSO4 and 1N. ZnSO4;
and also determined the relative error: 1.092%, 1.006%, 0.935%, respectively. As a result, it was concluded that with an increase in the concentration of solutions, E.DS. at the galvanic cell decreases.
Conclusion
In this work, we considered the main methods of electrochemical research, analyzed their classification, basic electrochemical processes, and also proved the relevance of these methods. Most of the work was devoted to the description of electrode processes. Potentiometry, conductometry, coulometry, voltammetry and electrogravimetry were studied in detail.
In the course of practical research, we carried out: determination of the concentration of unknown acids by conductometric titration, determination of the equivalence point of solutions of hydrochloric and acetic acids by potentiometric titration, determination of the electrochemical equivalent of copper, determination of the potentials of copper and zinc electrodes, and determination of the EMF of a galvanic cell.
We were convinced of the speed and accuracy of these methods, but at the same time, on our own experience, we identified some significant drawbacks: to obtain accurate data, very precise adjustment and calibration of devices is required, the results obtained depend on various external factors (pressure, temperature, etc.) and others. conditions can vary significantly, as well as the fragility and high cost of devices.
And yet, these are far from all known methods of electrochemical research. All the above methods are only a small part of the electrochemical research methods used in science and technology. And they are used so widely in all branches of industry that without them, neither the existence nor the further development of civilization is possible. Despite its considerable age, electrochemical research methods are experiencing rapid development with great prospects for the future. According to forecasts of a number of leading scientists, their role will grow rapidly.
It remains only to contribute in every possible way to development in this direction, and perhaps in the future we will discover such secrets and areas of application of electrochemical research methods that could only be dreamed of.
Bibliography
Agasyan P.K., Khamrakulov T.K. Coulometric method of analysis. Moscow: Chemistry. 2010.168 s.
Brainina H.Z., Neiman E.Ya. Solid-phase reactions in electroanalytical chemistry. Moscow: Chemistry. 2009.264 p.
Galyus Z. Theoretical foundations of electrochemical analysis: translation from Polish. Moscow: Mir. 1974.552 s.
Heyrovsky Y., Kuta Y. Fundamentals of polarography: translation from Czech. Edited by S.G. Mayranovsky. Moscow: Mir. 1965.559 s.
Golikov G.A. Physical Chemistry Manual: Textbook for specialized chemical engineering universities. Moscow: Higher School. 2008.383 p.
Zozulya A.N. Coulometric analysis, 2nd edition, Leningrad: Chemistry. 1968.160 s.
Knorre D.G., L.F. Krylov. V.S. Musicians. Physical Chemistry: Textbook for Biological Faculties of Universities and Pedagogical Universities. 2nd edition. Moscow: Higher School. 1990.416 s.
Levin A.I. Theoretical foundations of electrochemistry. Moscow: Metallurgizdat. 1963.432 s.
Loparin B.A. Theoretical foundations of electrochemical methods of analysis. Moscow: Higher School. 1975.295 s.
Plembek D. Electrochemical methods of analysis: theoretical foundations and applications. Moscow: Mir. 2009.496 p.
Yu.I. Solovyov History of Chemistry: The Development of Chemistry from Ancient Times to the End of the 19th Century. A guide for teachers. 2nd edition. Moscow: Enlightenment. 2007.368 p.
Figurovsky N.A. History of Chemistry: Textbook for students of pedagogical institutes in chemical and biological specialties. Moscow: Enlightenment. 1979.311 s.
Physical chemistry: discipline program and educational guidelines / compiled by A.N. Kozlov, N.P. Uskov. Ryazan: Ryazan State University named after S.A. Yesenin. 2010. 60 s.
Physical chemistry. Theoretical and practical guidance. Textbook for universities / Edited by academician B.P. Nikolsky. 2nd edition. Leningrad: Chemistry, 1987, 880 p.
Harned G. Ouer B. Physical chemistry of electrolyte solutions. Moscow: IIN. 2011.629 s.
Ewing G. Instrumental Methods of Chemical Analysis. Moscow: Mir. 2011.620 s.
Book: multivolume edition
Measurement methods in electrochemistry / editors E. Eger and A. Zalkind, translated from English by V.S. Markin and V.F. Pastushenko, under the editorship of Doctor of Chemical Sciences Yu.A. Chizmadzheva. Moscow: Mir, 1977.Vol. 1-2.
Skoog D., West D. Fundamentals of analytical chemistry. Moscow: Mir, 1979.Vol. 2
Atkins P. Physical chemistry. Moscow: Mir, 1980.Vol. 1-2.
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2. ELECTROCHEMICAL ANALYSIS METHODS
Electrochemical methods of analysis and research are based on the study and use of processes occurring on the surface of the electrode or in the near-electrode space. Any electrical parameter (potential, current strength, resistance, etc.), functionally related to the concentration of the analyzed solution and amenable to correct measurement, can serve as an analytical signal.
Distinguish direct and indirect electrochemical methods. Direct methods use the dependence of the current strength (potential, etc.) on the concentration of the analyte. In indirect methods, the current strength (potential, etc.) is measured in order to find the end point of the titration of the analyte with a suitable titrant, i.e. the dependence of the measured parameter on the titrant volume is used.
For any kind of electrochemical measurements, an electrochemical circuit or an electrochemical cell is required, of which the analyzed solution is an integral part.
2.1. Potentiometric analysis method
2.1.1. Basic laws and formulas
Potentiometric methods are based on measuring the potential difference between the indicator electrode and the reference electrode, or, more precisely, electromotive forces(EMF) of various circuits, since it is the EMF that is the potential difference that is experimentally measured.
Equilibrium potential of the indicator electrode associated with the activity and concentration of substances involved in the electrode process, the Nernst equation:
E = E ° + R T / (n F) ln (and oxide/and revolt)
E = E ° + R T / (n F) ln ([ oxide] ү oxid / ( [ revolt] ү rest)),
R - universal gas constant equal to 8.31 J / (mol. K); T is the absolute temperature; F - Faraday constant (96500 C / mol); n - the number of electrons taking part in the electrode reaction; and oxide, and revolt- the activity of the oxidized and reduced forms of the redox system, respectively;[ oxide] and[ revolt] - their molar concentrations; ү oxide, ү rest - activity coefficients; E ° is the standard potential of the redox system.
Substituting T= 298.15 K and the numerical values of the constants in the equation, we get:
E = E ° + (0.059 / n) lg (and oxide/and revolt)
E = E ° + (0.059 / n) lg ([ oxide] ү oxid / ([ revolt] ү rest))
Direct Potentiometry Methods are based on the application of the Nernst equation to find the activity or concentration of a participant in the electrode reaction from the experimentally measured EMF of the circuit or the potential of the electrode. The most widespread among direct potentiometric methods is the method for determining pH, but the recent creation of reliably working ion-selective electrodes has significantly expanded the practical possibilities of direct methods. The pH is also measured by potentiometric titration.
A glass electrode is most often used to determine pH. The main advantages of a glass electrode are ease of operation, quick establishment of equilibrium and the ability to determine pH in redox systems. The disadvantages include the fragility of the electrode material and the complexity of work when switching to strongly alkaline and strongly acidic solutions.
In addition to the concentration of hydrogen ions, the content of several tens of different ions can be determined by a direct potentiometric method with ion-selective electrodes.
Potentiometric titration based on the determination of the equivalence point from the results of potentiometric measurements. A sharp change (jump) in the potential of the indicator electrode occurs near the point of equivalence. Just like in others titrimetric methods, potentiometric titration reactions must proceed strictly stoichiometrically, have a high speed and go all the way.
For potentiometric titration, a circuit is assembled from the indicator electrode in the analyzed solution and the reference electrode. Calomel or silver chloride electrodes are most often used as reference electrodes.
The type of indicator electrode used for potentiometric titration depends on the properties titrimetric mixture and its interaction with the electrode. In acid-base titration, a glass electrode is used, in redox titration, an inert (platinum) electrode or an electrode reversible with respect to one of the ions contained in titrimetric mixtures; in the precipitation - a silver electrode; v complexometric- metal electrode, reversible to the titrated metal ion.
To find the equivalence point, a differential curve is often plotted in coordinates D E/ D V - V ... The equivalence point is indicated by the maximum of the obtained curve, and the abscissa reading corresponding to this maximum gives the titrant volume, spent for titration to the point of equivalence. Determination of an equivalence point before a differential curve is much more accurate than using a simple dependence E - V.
The main advantages of the potentiometric titration method are high accuracy and the ability to carry out determinations in dilute solutions, in turbid and colored media, as well as to determine several substances in one solution without preliminary separation. The area of practical application of potentiometric titration when using non-aqueous solvents is significantly expanding. They make it possible to analyze multicomponent systems that cannot be determined in an aqueous solution, to analyze substances that are insoluble or decompose in water, etc. Potentiometric titration can be easily automated. The industry produces several types of auto titrators using potentiometric sensors.
The disadvantages of potentiometric titration include not always rapid establishment of the potential after adding the titrant and the need in many cases to carry out a large number of readings during titration.
In potentiometric analysis, the main measuring instruments are potentiometers of various types. They are designed to measure the EMF of the electrode system. Since the emf depends on the activity of the corresponding ions in the solution, many potentiometers also make it possible to directly measure the pX value - the negative logarithm of the X ion activity. ionomers... If the potentiometer and electrode system are designed to measure the activity of only hydrogen ions, the device is called a pH meter.A.A. Vikharev, S.A. Zuikova, N.A. Chemeris, N.G. Domina
Physicochemical methods of analysis (PCMA) are based on the use of the relationship between the measured physical properties of substances and their qualitative and quantitative composition. Since the physical properties of substances are measured using various devices - "instruments", then these methods of analysis are also called instrumental methods.
The most practical applications among FHMA are:
- electrochemical methods- based on the measurement of potential, current, amount of electricity and other electrical parameters;
- spectral and other optical methods- based on the phenomena of absorption or emission of electromagnetic radiation (EMP) by atoms or molecules of a substance;
- chromatographic methods- based on sorption processes occurring under dynamic conditions with directional movement of the mobile phase relative to the stationary one.
The advantages of PCMA include high sensitivity and low detection limit - mass up to 10-9 μg and concentration up to 10-12 g / ml, high selectivity (selectivity), which makes it possible to determine the components of mixtures without their preliminary separation, as well as rapid analysis, the ability to their automation and computerization.
Electrochemical methods are widely used in analytical chemistry. The choice of the analysis method for a particular object of analysis is determined by many factors, including, first of all, the lower limit of the definition of an element.
The data on the lower limit of detection of various elements by some methods are presented in the table.
Limits of determination (μg / ml) of elements by various methods
| Element | MAC | AAS | PTP | WILLOW | Ionometry | Ampere.titles. |
| Ag | 0.1 - dithizone | 0,07 | 0,2 | 0.00001 | 0.02 | 0.05 |
| As | 0.05 - molybd. Blue | 0,2 | 0,04 | 0,02 | - | 0,05 |
| Au | 0.04-methyl phiol. | 0,3 | 0,005 | 0,001 | - | 0,05 |
| Bi | 0.07-dithizone | 0,005 | 0,00001 | - | 0,5 | |
| Cd | 0.04-dithizone | 0,05 | 0,002 | 0,00001 | 0,03 | 0,5 |
| Cr | 0,04-diphenylcarbazide | 0,2 | 0,02 | - | - | |
| Cu | 0.03-dithizone | 0,2 | 0,002 | 0,00002 | 0,01 | 0,05 |
| Hg | 0.08-dithizone | - | 0,00005 | |||
| Pb | 0.08-dithizone | 0,6 | 0,003 | 0,00002 | 0,03 | |
| Sb | 0.08-rhodamine | 0,004 | 0,00004 | - | 0,5 | |
| Fe | 0.1-thiocyanate | 0,2 | 0,003 | 0,0002 | 0,3 | 0,5 |
| Se | 0.08-diaminophthalene | 0,3 | 0,2 | 0,00002 | - | 0,5 |
| Sn | 0,07-phenyl-flurium | 0,4 | 0,003 | 0,00004 | - | 0,5 |
| Te | 0.1-bismutol | 0,7 | 0,02 | - | - | |
| Tl | 0.06-rhodamine | 0,6 | 0,01 | 0,00002 | - | 0,5 |
| Zn | 0.02-dithizone | 0,02 | 0,003 | 0,0003 | - | 0,5 |
| F - | - | - | - | - | 0,02 | 5-10 |
| NH 4 +, NO 3 - | - | - | - | - | 0,1 | 1-5 |
MAS - molecular absorption spectrometry (photometry);
AAS - atomic absorption spectrometry (flame photometry);
PTP - alternating current polarography;
IVA - stripping voltammetry.
The errors of determination in FKhMA are about 2-5%; the analysis requires the use of complex and expensive equipment.
Distinguish direct and indirect methods of physical and chemical analysis. Direct methods use the dependence of the measured analytical signal on the concentration of the analyte. In indirect methods, the analytical signal is measured in order to find the end point of the titration of the analyte with a suitable titrant, that is, the dependence of the measured parameter on the volume of the titrant is used.
Electrochemical methods of analysis based on the study and use of processes occurring on the surface of the electrode or in the near-electrode space. Any electrical parameter (potential, electric current, amount of electricity, etc.), functionally related to the concentration of the analyte and amenable to correct measurement, can serve as an analytical signal.
By the nature of the measured analytical signal, electrochemical methods of analysis are divided into potentiometry, voltammetry, coulometry and a number of other methods:
Characteristic dependence of the electrochemical signal on the independent variable
| Method | Measured signal | Signal versus independent variable |
| Potentiometry, ionometry | potential E = f (C) С-concentration of the analyte | |
| Potentiometric titration | potential E = f (V), V- volume of titrant reagent |
 |
| polarography, voltammetry | current I = f (E), E - electrode polarization potential |  |
| stripping voltammetry | current I n = f (E) |  |
| chronopotentiometry | potential E = f (t), t is the electrode polarization time at I = const. |
 |
| amperometric titration with one indicator electrode | current I = f (V), V - volume of titrant reagent |  |
| amperometric titration with two indicator electrodes | current I = f (V) V - volume of titrant reagent | |
| coulometry | Q = f (C), С - amount of substance |  |
| conductometry | G = f (C), С - concentration of ions in solution |  |
| conductometric titration | electrical conductivity G = f (V), V - volume of titrant reagent |  |
Potentiometry
Potentiometric measurements are based on the dependence of the equilibrium potential of the electrode on the activity (concentration) of the ion being determined. For measurements, it is necessary to assemble a galvanic cell from a suitable indicator electrode and reference electrode, and also have a device for measuring the potential of the indicator electrode (EMF of a galvanic cell), in conditions close to thermodynamic, when the indicator electrode has an equilibrium (or close to it) potential, that is, without draining a noticeable current from the galvanic cell when the circuit is closed. In this case, you cannot use a conventional voltmeter, but you should use potentiometer- an electronic device with a large input resistance (1011 - 1012 Ohm), which excludes the course of electrode electrochemical reactions and the occurrence of current in the circuit.
The indicator electrode is an electrode, the potential of which depends on the activity (concentration) of the detected ion in the analyzed solution.
The reference electrode is an electrode whose potential remains constant under the conditions of the analysis. The potential of the indicator electrode is measured with respect to the reference electrode E(EMF of a galvanic cell).
There are two main classes of indicator electrodes used in potentiometry - electron exchange and ion exchange.
Electron exchange electrodes- these are electrodes, on the surface of which electrode reactions with the participation of electrons take place. These electrodes include electrodes of the first and second kind, redox electrodes.
First class electrodes- these are electrodes reversible by a cation in common with the material of the electrode, for example, metal M, immersed in a solution of a salt of the same metal. On the surface of such an electrode, a reversible reaction M n + + ne↔ M and its real potential depends on the activity (concentration) of metal cations in solution in accordance with the Nernst equation:
For a temperature of 250С (298 K) and for conditions when the activity of ions is approximately equal to the concentration (γ → 1):
Type I electrodes can be made of various metals, for example, Ag (silver), Cu (copper), Zn (zinc), Pb (lead), etc.
Schematically, electrodes of the first kind are written as M | M n+, where the vertical line shows the boundary between the solid (electrode) and liquid (solution) phases. For example, a silver electrode immersed in a solution of silver nitrate is depicted as follows - Ag | Ag +; if necessary, indicate the concentration of the electrolyte - Ag | AgNO 3 (0.1 M).
The electrodes of the first kind also include gas hydrogen electrode Pt (H 2) | H + (2H + + 2e↔ H 2, E 0 = 0):
Type II electrodes Are electrodes reversible by anion, for example, a metal coated with a poorly soluble salt of this metal, immersed in a solution containing the anion of this poorly soluble salt M, MA | A n-... On the surface of such an electrode, a reversible reaction MA + ne↔ M + A n- and its real potential depends on the activity (concentration) of the anion in the solution in accordance with the Nernst equation (at T= 298 K and γ → 1):
Examples of type II electrodes are silver chloride (AgCl + e↔ Ag + Cl -) and calomel (Hg 2 Cl 2 + 2e↔ 2Hg + 2Cl -) electrodes:
Redox electrodes- these are electrodes that consist of an inert material (platinum, gold, graphite, glassy carbon, etc.) immersed in a solution containing oxidized (Ox) and reduced (Boc) forms of the analyte. On the surface of such an electrode, a reversible reaction Ok + ne↔ Boc and its real potential depends on the activity (concentration) of the oxidized and reduced forms of the substance in solution in accordance with the Nernst equation (at T= 298 K and γ → 1):
If hydrogen ions participate in the electrode reaction, then their activity (concentration) is taken into account in the corresponding Nernst equations for each specific case.
Ion exchange electrodes- these are electrodes on the surface of which ion-exchange reactions take place. Such electrodes are also called ion-selective or membrane. The most important component of such electrodes is semipermeable membrane- a thin solid or liquid film that separates the inner part of the electrode (internal solution) from the analyzed one and has the ability to transmit only ions of one type X (cations or anions). Structurally, the membrane electrode consists of an internal reference electrode (usually silver chloride) and an internal electrolyte solution with a constant concentration of the potential-determining ion, separated from the external (investigated) solution by a sensitive membrane.
The real potential of ion-selective electrodes, measured relative to any reference electrode, depends on the activity of those ions in solution that are sorbed by the membrane:
where const - a constant depending on the nature of the membrane ( asymmetry potential) and the potential difference between the external and internal reference electrodes, n and a(NS n±) - charge and activity of the potential-determining ion. If the potential of the ion selective electrode is measured relative to a standard hydrogen electrode, then the constant is the standard electrode potential E 0.
For membrane electrodes the value electrode slope may differ from theoretical Nernst's values (0.059 V); in this case, the real value of the electrode function is θ defined as the tangent of the slope of the calibration graph. Then:
The potential of a membrane electrode in a solution containing, in addition to the determined ion X, a foreign ion B, which affects the electrode potential, is described the Nikolsky equation(modified Nernst equation):
where z- charge of an extraneous (interfering) ion, KХ / В - selectivity coefficient of the membrane electrode.
Selectivity factor K X / B characterizes the sensitivity of the electrode membrane to the determined X ions in the presence of interfering B ions. K X / B<1, то электрод селективен относительно ионов Х и, чем меньше числовое значение коэффициента селективности, тем выше селективность электрода по отношению к определяемым ионам и меньше мешающее действие посторонних ионов. Если коэффициент селективности равен 0,01, то это означает, что мешающий ион В оказывает на величину электродного потенциала в 100 раз меньшее влияние, чем определяемый ион той же молярной концентрации.
The selectivity coefficient is calculated as the ratio of the activities (concentrations) of the determined and interfering ions, at which the electrode acquires the same potential in solutions of these substances, taking into account their charges:
Knowing the value of the selectivity coefficient, it is possible to calculate the concentration of the interfering ion, which affects the potential of the ion-selective electrode (example).
Example. What concentration of nitrate ions must be created in a 1 ∙ 10-3 M sodium fluoride solution so that the ion-selective fluoride electrode is equally sensitive to both ions, if its electrode selectivity coefficient?
Solution.
Since then
This means that the concentration of nitrate ions in the analyzed solution above 0.5 mol / L has a significant effect on the determination of the fluoride ion in its millimolar solutions.
A classic example of a solid-membrane ion selective electrode is a glass electrode with a hydrogen function for measuring the concentration of hydrogen ions in a solution (glass pH electrode). For such electrodes, the membrane is a special glass of a certain composition, and the internal electrolyte is a 0.1 M solution of hydrochloric acid:
Ag, AgCl | 0.1 M HCl | glass membrane | test solution
An ion-exchange process takes place on the surface of the glass membrane:
SiO-Na + (glass) + H + (solution) → -SiO-H + (glass) + Na + (solution)
as a result of which a dynamic equilibrium is established between hydrogen ions in glass and a solution H + (glass) ↔ H + (solution), which leads to the emergence of a potential:
E = const + θ lg a(H +) = const – θ pH
A glass electrode with a high content of Al2O3 in the membrane measures the activity of sodium ions in solution (glass Na-electrode, sodium selective electrode). In this case, the internal solution is a 0.1 M sodium chloride solution:
Ag, AgCl | 0.1 M NaCl | glass membrane | test solution
On the surface of the glass membrane of the sodium selective electrode, an equilibrium is established between the sodium ions in the glass and the Na + (glass) ↔ Na + (solution) solution, which leads to the emergence of a potential:
E = const + θ lg a(Na +) = const – θ pNa
The most perfect electrode with a crystalline membrane is a fluoride selective electrode, the membrane of which is made of a single crystal plate of lanthanum fluoride (LaF3), activated to increase conductivity with europium fluoride (EuF 2):
Ag, AgCl | 0.1 M NaCl, 0.1 M NaF | LaF 3 (EuF 2) | test solution
The potential of a fluoride electrode is determined by the ion-exchange process on its surface F- (membrane) ↔ F- (solution):
E = const - θ lg a(F-) = const + θ pF
The values of the constant and slope of the electrode function θ for ion-selective electrodes is determined from the calibration graph E ÷рХ as a segment on the ordinate and the tangent of the slope of a straight line, respectively. For a glass pH electrode, this operation is replaced by the adjustment of instruments (pH meters) to standard buffer solutions with precisely known pH values.
A schematic view of glass and fluoride-selective electrodes are shown in the figures:
Paired with an indicator electrode to measure its potential (EMF of a galvanic cell), a reference electrode with a known and stable potential, independent of the composition of the test solution, is used. Most often, silver chloride and calomel electrodes are used as a reference electrode. Both electrodes belong to the second kind and are characterized by high stability in operation.
The potentials of silver chloride and calomel electrodes depend on the activity (concentration) of chloride ions (at T= 298 K and γ → 1):
As reference electrodes, electrodes with a saturated solution of potassium chloride are most often used - at 250C the potential of a saturated silver chloride reference electrode is +0.201 V, and a saturated calomel electrode is +0.247 V (relative to a standard hydrogen electrode). The potentials for silver chloride and calomel reference electrodes containing 1 M and 0.1 M potassium chloride solutions can be found in the reference tables.
A schematic view of saturated silver chloride and calomel comparison electrodes are shown in the figure:
Silver chloride reference electrodes (a) and calomel (b)
1 - asbestos fiber providing contact with the analyzed solution
2 - KCl solution (saturated)
3 - contact hole
4 - KCl solution (saturated), AgCl (tv.)
5 - hole for injecting KCl solution
6 - paste from a mixture of Hg2Cl2, Hg and KC1 (saturated)
Potentiometric analysis is widely used to directly determine the activity (concentration) of ions in a solution by measuring the equilibrium potential of an indicator electrode (EMF of a galvanic cell) - direct potentiometry (ionometry) as well as to indicate the end point of the titration ( ktt) by the change in the potential of the indicator electrode during the titration ( potentiometric titration).
In all receptions direct potentiometry the dependence of the indicator electrode on the activity (concentration) of the ion being determined is used, which is described by the Nernst equation. The results of the analysis imply the determination of the concentration of the substance, and not its activity, which is possible when the ion activity coefficients are equal to unity (γ → 1) or their constant value (constant ionic strength of the solution), therefore, in further considerations, only concentration dependences are used.
The concentration of the determined ion can be calculated from the experimentally found potential of the indicator electrode, if the constant component is known for the electrode (standard potential E 0) and the slope of the electrode function θ ... In this case, a galvanic cell is composed, consisting of an indicator electrode and a reference electrode, its EMF is measured, the potential of the indicator electrode (relative to the SHE) and the concentration of the detected ion are calculated.
V grading plot method prepare a series of standard solutions with a known concentration of the ion to be determined and constant ionic strength, measure the potential of the indicator electrode relative to the reference electrode (EMF of a galvanic cell) in these solutions and plot the dependence E÷ p WITH(A) (calibration graph). Then measure the potential of the indicator electrode in the analyzed solution E x (under the same conditions) and determine p WITH x (A) and calculate the concentration of the analyte in the analyzed solution.
V method of standard (comparison) measure the potential of the indicator electrode in the analyzed solution ( E x) and in a standard solution of the analyte ( E Art). The concentration of the determined ion is calculated based on the Nernst equations for the analyzed sample and the standard sample. Electrode slope for indicator electrode θ
Using method of additions first measure the potential of the indicator electrode in the analyzed solution ( E x), then add to it a certain volume of a standard solution of the analyte and measure the potential of the electrode in the resulting solution with the addition ( E x + d). The concentration of the determined ion is calculated based on the Nernst equations for the analyzed sample and the sample with the additive. Electrode slope for indicator electrode θ must be known or determined in advance according to the calibration schedule.
At potentiometric titration measure and record the EMF of the electrochemical cell (potential of the indicator electrode) after adding each portion of the titrant. Then, based on the results obtained, titration curves are plotted - integral in coordinates E ÷ V (a) and differential in coordinates ∆ E/∆V ÷ V (b), and determine the endpoint of titration ( ktt) graphically:
In potentiometric titration, all the main types of chemical reactions are used - acid-base, redox, precipitation and complexation. They have the same requirements as in visual titrimetry, supplemented by the presence of a suitable indicator electrode for recording changes in the concentration of potential-determining ions during titration.
The determination error during potentiometric titration is 0.5-1%, which is significantly lower than with direct potentiometric measurements (2-10%), however, higher detection limits are observed - more than 10 -4 mol / L.
Coulometry
Coulometry combines analysis methods based on measuring the amount of electricity consumed in an electrochemical reaction. An electrochemical reaction leads to a quantitative electroconversion (oxidation or reduction) of the analyte at the working electrode (direct coulometry) or to the production of an intermediate reagent (titrant) that reacts stoichiometrically with the analyte (indirect coulometry, coulometric titration).
Coulometric methods are based on Faraday's law, which establishes a relationship between the amount of electrically converted (oxidized or reduced) substance and the amount of electricity consumed in this case:
where m Is the mass of the electrically converted substance, g; Q- the amount of electricity spent on the electrical transformation of a substance, C; F- Faraday number, equal to the amount of electricity required for the electrical conversion of one mol-equivalent of a substance, 96500 C / mol; M- molar mass of the substance, g / mol; n- the number of electrons involved in the electrochemical reaction.
A necessary condition for conducting coulometric analysis is the almost complete consumption of electricity for the transformation of the analyte, that is, the electrochemical reaction should proceed without side processes with 100% current output.
In practice, coulometric analysis is implemented in two versions - at a constant potential ( potentiostatic coulometry) and at constant current strength ( amperostatic coulometry).
Potentiostatic coulometry apply for direct coulometric measurements, when the analyte is directly subjected to electrolysis. In this case, the potential of the working electrode using potentiostats is kept constant and its value is selected on the basis of polarization curves in the region of the limiting current of the analyte. During electrolysis at a constant potential, the current decreases in accordance with a decrease in the concentration of the electroactive substance according to the exponential law:
where Ι - current strength at the moment of time t, A; Ι 0 — current strength at the initial moment of electrolysis, A; k- a constant depending on the electrolysis conditions.
Electrolysis is carried out until the residual current is reached. Ι , the value of which is determined by the required accuracy - for a permissible error of 0.1%, electrolysis can be considered complete at Ι = 0,001Ι 0. To shorten the electrolysis time, a working electrode of a large surface should be used with vigorous stirring of the analyzed solution.
Total electricity Q required for the electrical transformation of the analyte is determined by the equation:
Electricity can be quantified by measuring the area under the current-time curve with mechanical or electronic integrators, or with chemical coulometers. Coulometer Is an electrolytic cell in which an electrochemical reaction of known stoichiometry takes place with 100% current efficiency. The coulometer is switched on in series with the coulometric cell under study, therefore, during the electrolysis, the same amount of electricity flows through both cells. If, at the end of electrolysis, the amount (mass) of the substance formed in the coulometer is measured, then according to Faraday's law, the amount of electricity can be calculated. The most commonly used are silver, copper and gas coulometers.
Amperostatic coulometry apply for coulometric titration at a constant current, during which the analyte reacts with a titrant formed as a result of an electrochemical reaction on the working electrode, and therefore, called electrogenerated titrant.
To ensure a 100% current efficiency, a significant excess of the auxiliary substance is required, from which the titrant is generated, which excludes the occurrence of competing reactions on the working electrode. In this case, the titrant is generated in an amount equivalent to the analyte, and the content of the analyte can be calculated from the amount of electricity consumed to generate the titrant.
Electricity quantity Q in coulometry at constant amperage Ι calculated by the formula:
where t- electrolysis time, for the determination of which practically all methods of establishing the end point in titrimetry are suitable (visual - indicators, instrumental - potentiometry, amperometry, photometry). With the current strength in amperes and the electrolysis time in seconds, we get the amount of electricity in pendants (example).
Example. The coulometric titration of the ascorbic acid solution with iodine generated from potassium iodide with a current of 5.00 mA took 8 min 40 s. Calculate the mass of ascorbic acid in the analyzed solution. Propose a method for fixing the endpoint of the titration.
Solution. The amount of electricity spent on the oxidation of iodide and, accordingly, ascorbic acid is equal to:
Q = Ι t= 5.00 ∙ 10 -3 ∙ 520 = 2.60 Cl.
Ascorbic acid is oxidized by iodine to dehydroascorbic acid with the donation of two electrons (C 6 H 8 O 6 - 2 e→ С 6 Н 6 О 6 + 2Н +), then according to Faraday's law:
The endpoint of the titration is determined by the appearance of excess iodine in the solution. Consequently, it can be recorded visually with the help of starch added to the analyzed solution (the appearance of a blue color), amperometrically with a dropping mercury or platinum microelectrode by the appearance of a limiting iodine current, and potentiometrically by a sharp increase in the potential of the platinum electrode.
Voltammetry
Voltammetric method of analysis based on the use of the phenomenon of polarization of the microelectrode, obtaining and interpreting volt-ampere (polarization) curves reflecting the dependence of the current on the applied voltage. The voltammetric curve (voltammogram) allows you to simultaneously obtain qualitative and quantitative information about substances that are reduced or oxidized at the microelectrode (depolarizers), as well as about the nature of the electrode process. Modern voltammetry is a highly sensitive and express method for the determination of substances, suitable for the analysis of various objects of inorganic and organic nature, including pharmaceuticals. The minimum detectable concentration in voltammetry reaches values of 10 -8 mol / l with a method error of less than 5%. Voltammetry under optimal experimental conditions makes it possible to determine several components simultaneously in the analyzed solution.
In voltammetry, two electrodes are used - worker a polarizable electrode with a small surface (indicator microelectrode) and auxiliary non-polarizable electrode with a large surface (reference electrode). Working electrodes are microelectrodes made of mercury (dropping mercury electrode, RCE), platinum (PE), and conductive carbon materials (graphite, glassy carbon).
When a direct current passes through an electrolytic cell, the process is characterized by the ratio (Ohm's law for an electrolyte solution):
E = Ea - Eк + IR
Where E- applied external voltage; Ea- potential of the anode; Ek- potential of the cathode; I- current in the circuit; R- internal resistance of the electrolytic cell.
In voltammetric measurements, the analyzed solution contains an indifferent (background) electrolyte of high concentration (100 times or more higher than the concentration of the analyte - the resistance of the solution is small), and the current in voltammetry does not exceed 10 -5 A, therefore, the voltage drop in the cell IR can be neglected.
Since in voltammetry one of the electrodes (auxiliary) is not polarized and the potential for it remains constant (it can be taken equal to zero), the voltage applied to the cell manifests itself in a change in the potential of only the working electrode, and then E = Ea for a working microanode ( anodic polarization) and E =-Eк for the working microcathode ( cathodic polarization). Thus, the recorded volt-ampere curve reflects the electrochemical process that occurs only at the working electrode. If the solution contains substances that can be electrochemically reduced or oxidized, then when a linearly varying voltage is applied to the cell, the voltammogram has a waveform 1 (in the absence of an electrochemical reaction, the dependence of the current on voltage is linear 2 in accordance with Ohm's law):
The section of voltammetry, in which the RCE serves as a working microelectrode, is called polarography, in honor of the Czech electrochemist J. Geyrovsky, who proposed this method in 1922. Voltammograms obtained in a cell with a dropping mercury electrode are called polarograms.
To register classical polarograms, a cell with a RCE (working electrode) and a saturated calomel electrode (auxiliary electrode, reference electrode) is connected to a constant voltage source and the potential is changed at a rate of 2-5 mV / s.
A dropping mercury electrode is almost ideally polarizable in a wide potential range, limited in the anodic region by the electrode reactions of mercury oxidation (+0.4 V), and in the cathodic reactions of the reduction of hydrogen ions (from -1 to -1.5 V, depending on the acidity of the medium) or background cations (from -2 V for alkali metal cations to -2.5 V for R 4 N +). This makes it possible to study and determine on EEC substances that are reduced at very high negative potentials, which is impossible on electrodes made of other materials. It should be noted that hereinafter, the values of the potentials are given relative to the saturated calomel electrode and, if necessary, can be recalculated with respect to another reference electrode, for example, saturated silver chloride.
Before registering the polarogram on the RCE, it is necessary to remove dissolved oxygen, since it is electroactive in the negative potential range, giving two reduction waves at -0.2 and -0.9 V. This can be done by saturating the solution with an inert gas (nitrogen, argon, helium). Oxygen is removed from alkaline solutions using sodium sulfite (O 2 + 2Na 2 SO 3 → 2Na 2 SO 4).
The classical polarogram (polarographic wave) in an idealized form is presented below:
The main characteristics of a polarographic wave are the magnitude of the diffusion current ( I d, μA), half-wave potential ( E 1/2, V) is the potential at which the current is equal to half of the diffusion current, and the slope of the ascending section (0.059 / n Is the slope of the electrode function). These parameters allow using polarography as a method of analysis (current is proportional to concentration) and research (half-wave potential and electrode function depend on the nature of the substance).
At the initial section of the polarographic wave (A-B), the current with a change in potential increases very slowly - this is the so-called residual current (I ost) . The main contribution to the residual current is made by the formation of an electric double layer ( charging current), which cannot be excluded and whose value increases with increasing potential. The second term of the residual current is the current due to electroactive impurities, which can be reduced by using pure reagents and water.
Upon reaching point B ( isolation potential- upon reduction at the cathode, the release potential is called recovery potential E vos, during oxidation at the anode - oxidation potential E ok) an electrochemical reaction begins on the electrode, into which an electroactive substance (depolarizer) enters, as a result of which the current sharply increases (section B-C) to a certain limiting value, then remaining practically constant (section C-D). The current corresponding to this section is called limiting current(I pr), and the difference between the limiting and residual current is diffusion current (I d = I NS - I ost). In the V-G section, with an increase in the potential, the limiting and residual currents slightly increase, and the value of the diffusion current remains constant. The rise in current at point G is due to a new electrochemical reaction (for example, the reduction of cations in the background electrolyte).
The diffusion current got its name due to the fact that in this potential region, as a result of an electrochemical reaction in the near-electrode layer, there is an almost complete absence of a depolarizer and its enrichment with a substance occurs due to the diffusion of the depolarizer from the depth of the solution, where its concentration remains constant. Since the diffusion rate under given specific conditions remains constant, the diffusion current also remains constant in its value.
Dependence of the magnitude of the diffusion current on the concentration of the depolarizer for the r.c.e. is expressed by the Ilkovich equation:
I d = 605nD 1/2 m 2/3 t 1/6 s
where D is the diffusion coefficient of the electroactive ion; n is the number of electrons participating in the reaction; m 2/3 t 1/6 - characteristic of the capillary from which mercury flows; с - concentration of the analyte (depolarizer).
When working with the same capillary and depolarizer, the value 605nD 1/2 m 2/3 t 1/6 = const, therefore there is a linear relationship between the wave height and the concentration of the substance
Quantitative polarographic analysis is based on this linear relationship. The relationship between the electrode potential and the resulting current is described by the polarographic wave equation (Ilkovich-Heyrovsky equation):
where E and I are, respectively, the potential and the current value for a given point of the polarographic curve; I d is the value of the diffusion current; E 1/2 is the half-wave potential.
E 1/2 is the potential at which a current value equal to half of I d is reached. It does not depend on the concentration of the depolarizer. E 1/2 is very close to the normal redox potential of the system (Eo), that is, it is a qualitative characteristic determined only by the nature of the ions being reduced and by which the qualitative composition of the analyzed solution can be determined.
Polarogram (voltammogram) contains valuable analytical information - half-wave potential E 1/2 is the qualitative characteristic of the depolarizer (qualitative analytical signal), while the diffusion current I d is linearly related to the concentration of the analyte in the volume of the analyzed solution (quantitative analytical signal) - I d = KC.
The magnitude E 1/2 can be calculated from the polarographic wave equation or determined graphically:
Found value E 1/2, taking into account the used background electrolyte, makes it possible to identify the depolarizer on the basis of tabular data. If the analyzed solution contains several substances, the half-wave potentials of which differ by more than 0.2 V, then the polarogram will show not one wave, but several - according to the number of electroactive particles. It should be borne in mind that the reduction (oxidation) of multiply charged particles can occur stepwise, giving several waves.
To exclude the movement of the substance to the electrode due to thermal and mechanical convection (stirring), the measurement is carried out in a thermostated solution and in the absence of stirring. The elimination of the electrostatic attraction of the depolarizer by the field of the electrode (migration) is facilitated by a large excess of the electrically inactive background electrolyte, the ions of which screen the electrode charge, reducing the driving force of migration to practically zero.
When using a dripping mercury electrode, the polarogram shows current oscillation(its periodic slight increase and decrease). Each such oscillation corresponds to the appearance, growth, and detachment of a drop of mercury from the capillary of the microelectrode. Devices for eliminating oscillations are provided in polarographs.
Polarograms can be distorted due to polarographic maxima- a sharp increase in the current above its limit value, followed by a decline:
The appearance of the maxima is due to the mixing of the solution as a result of the movement of the surface of the mercury droplet due to the uneven distribution of the charge, and, accordingly, the surface tension (maxima of the first kind), as well as the appearance of vortices when mercury flows out of the capillary (maxima of the second kind). The maxima distort the polarogram and make it difficult to decipher it. To remove the peaks of the first kind, a surfactant is introduced (for example, agar-agar, gelatin, camphor, fuchsin, synthetic surfactants), which, being adsorbed on the surface of the mercury drop, equalizes the surface tension and eliminates the movement of the surface layers of mercury. To remove the peaks of the second kind, it is sufficient to reduce the pressure of mercury in the capillary by lowering the height of the mercury column.
Voltammetry with solid working electrodes differs from polarography with the use of RCE in a different range of polarization of the microelectrode. As shown above, the dropping mercury electrode, due to the high hydrogen overvoltage on it, can be used in the region of high negative potentials, but due to the anodic dissolution of mercury at +0.4 V, it cannot be used for research in the field of positive potentials. On graphite and platinum, the discharge of hydrogen ions proceeds much easier; therefore, the region of their polarization is limited by significantly lower negative potentials (-0.4 and -0.1 V, respectively). At the same time, in the region of anodic potentials, platinum and graphite electrodes are suitable up to a potential of +1.4 V (then the electrochemical reaction of water oxygen oxidation 2Н 2 О - 4 e→ О 2 + 4Н +), which makes them suitable for research in the range of positive potentials.
Unlike RCE, during the recording of the voltammogram, the surface of the solid microelectrode does not renew and is easily contaminated with the products of the electrode reaction, which leads to a decrease in the reproducibility and accuracy of the results; therefore, before recording each voltammogram, the surface of the microelectrode should be cleaned.
Stationary solid electrodes have not found wide application in voltammetry due to the slow establishment of the limiting current, which leads to a distortion of the voltammogram shape, however, on rotating microelectrodes conditions for stationary diffusion arise in the near-electrode layer, therefore, the current strength is established quickly and the voltammogram has the same shape as in the case of RCE.
The value of the limiting diffusion current on a rotating disk electrode (regardless of the material) is described by the convective diffusion (Levich) equation:
I d = 0.62nFSD 2/3 w 1/2 n -1/6 s
where n is the number of electrons participating in the electrode process;
F is the Faraday number (96,500 coulombs);
S is the electrode area;
D is the diffusion coefficient of the depolarizer;
w is the angular velocity of rotation of the electrode;
n is the kinematic viscosity of the test solution;
с - concentration of the depolarizer, mol / l.
In case of difficulties in decoding polarograms, the "witness" method is used - after registering the polarogram of the analyzed solution, standard solutions of the proposed compounds are alternately added to the electrolytic cell. If the assumption was correct, then the wave height of the corresponding substance increases; if the assumption is incorrect, an additional wave will appear at a different potential.
The concentration of the depolarizer in the analyzed solution can be determined by the methods of the calibration graph, the method of the standard (comparison) and the method of additions. In this case, in all cases, standard solutions should be used, the composition of which is as close as possible to the composition of the analyzed solution, and the conditions for registering polarograms should be the same. The methods are applicable in the concentration range where the directly proportional dependence of the diffusion current on the depolarizer concentration is strictly observed. In practice, in quantitative determinations, as a rule, the value of the diffusion current in μA is not recorded, but the height of the polarographic wave is measured. h as shown in the previous figure, which is also a linear function of concentration h = KC.
By calibration curve method register polarograms of a series of standard solutions and build a calibration graph in coordinates h ÷ C(or I d ÷ WITH), according to which for the found value h x in the analyzed solution, find the concentration of the analyte in it WITH NS.
V method of standard (comparison) under the same conditions, record polarograms of the analyte and standard solutions of the analyte with concentrations WITH x and WITH st, then:
Using method of additions first, the polarogram of the analyzed solution is recorded with a volume V x with concentration WITH x and measure the height of the wave h x. Then, a certain volume of a standard solution of the analyte is added to the electrolytic cell to the analyzed solution. V d with concentration WITH d (it is preferable that V x >> V and WITH NS<WITH e), record the polarogram of the solution with the concentration WITH x + d and measure the height of the resulting wave h x + d. Simple transformations allow using these data to calculate the concentration of the analyte in the analyzed solution (example).
Example. When polarographing 10.0 ml of nicotinamide solution, a wave with a height of 38 mm was obtained. After adding to this solution 1.50 ml of a standard solution containing 2.00 mg / ml nicotinamide, the wave increased to 80.5 mm. Calculate the drug content (mg / ml) in the analyzed solution.
Solution. Wave height of nicotinamide in the analyzed solution h x in accordance with the Ilkovich equation is equal to:
and after adding a standard solution ( h x + d):
If we divide the first equation term by term by the second, we get:
Solving the equation for WITH x and substituting the values of the quantities from the condition of the problem.
Introduction
The use of electrochemical methods in quantitative analysis is based on the use of dependences of the values of the measured parameters of electrochemical processes (the difference in electrical potentials, current, amount of electricity) on the content of the analyte in the analyzed solution participating in the given electrochemical process. Electrochemical processes are processes that are accompanied by the simultaneous occurrence of chemical reactions and changes in the electrical properties of the system, which in such cases can be called electrochemical system. In analytical practice, an electrochemical system usually contains electrochemical cell, including a vessel with an electrically conductive solution to be analyzed, in which the electrodes are immersed.
Classification of electrochemical methods of analysis
Electrochemical analysis methods are classified in different ways. ... Classification based on the nature of the source of electrical energy in the system. There are two groups of methods. - Methods without imposing external (extraneous) potential. The source of electrical energy is the electrochemical system itself, which is a galvanic cell (galvanic circuit). These methods include potentiometric methods; the electromotive force (EMF) and electrode potentials in such a system depend on the content of the analyte in the solution. - Methods with the imposition of external (extraneous) potential. These methods include:
O conductometric analysis- based on measuring the electrical conductivity of solutions as a function of their concentration;
O voltammetric analysis- based on current measurement as a function of the applied known potential difference and solution concentration;
O coulometric analysis- based on measuring the amount of electricity passing through the solution as a function of its concentration;
O electrogravimetric analysis- based on measuring the mass of the product of an electrochemical reaction.
Classification according to the method of application of electrochemical methods. Distinguish between direct and indirect methods.
- Direct methods. The electrochemical parameter is measured as a known function of the concentration of the solution, and the content of the analyte in the solution is found according to the indication of the corresponding measuring device.
- Indirect methods. Titration methods in which the end of the titration is recorded based on the measurement of the electrical parameters of the system.
In accordance with this classification, there are, for example, direct conductometry and conductometric titration, direct potentiometry and potentiometric titration etc.
This manual contains laboratory work only for the following electrochemical methods:
Direct potentiometry;
Potentiometric titration;
Coulometric titration.
All these methods are pharmacopoeial and are used to control the quality of medicines.
General characteristics of potentiometric analysis
Method principle
Potentiometric analysis (potentiometry) is based on measuring the EMF and electrode potentials as a function of the concentration of the analyzed solution.
If in an electrochemical system - in a galvanic cell - a reaction occurs on the electrodes:
with carry n electrons, then the Nernst equation for the EMF E this reaction has the form:
where is the standard EMF of the reaction (the difference between the standard electrode potentials); R- universal gas constant; T- the absolute temperature at which the reaction proceeds; F- Faraday number; -
activity of reagents - participants in the reaction.
Equation (1) is valid for the EMF of a reversibly working galvanic cell.
For room temperature, equation (1) can be represented in the form:
(2)
Under conditions when the activity of the reagents is approximately equal to their concentration, equation (1) turns into equation (3):
(3)
where are the concentrations of reagents.
For room temperature, this equation can be represented as:
(4)
For potentiometric measurements in an electrochemical cell, two electrodes are used:
. indicator electrode, whose potential depends on the concentration of the determined (potential-determining) substance in the analyzed solution;
. reference electrode, the potential of which under the conditions of the analysis remains constant.
That is why the value of the EMF determined by equations (14) can be calculated as the difference in the real potentials of these two electrodes.
In potentiometry, electrodes of the following types are used: electrodes of the first, second kind, redox, membrane.
First-class electrodes. These are electrodes that are cation-reversible in common with the electrode material. There are three types of electrodes of the first kind:
a) Metal M immersed in a salt solution of the same metal. A reversible reaction occurs on the surface of such electrodes:
The real potential of such an electrode of the first kind depends on the activity 
metal cations and is described by equations (5-8). In general, for any temperature:
(5)
For room temperature:
(6)
At low concentrations 
when activity 
cations
metal is approximately equal to their concentration,
(7)
For room temperature:
(8)
b) Gas electrodes such as a hydrogen electrode, including a standard hydrogen electrode. The potential of a reversibly operating gas hydrogen electrode is determined by the activity of hydrogen ions, i.e. the pH value of the solution, and at room temperature is equal to:
since for a hydrogen electrode the standard potential is taken to be zero 
, and in accordance with the electrode reaction
the number of electrons participating in this reaction is equal to one: n= 1;
v) Amalgam electrodes, which are an amalgam of a metal immersed in a solution containing cations of the same metal. Potential
The number of such electrodes of the first kind depends on the activity 
ka-
metal ions in solution and activity a (M) metal in amalgam:
Amalgam electrodes are highly reversible. Type II electrodes are anion reversible. There are the following types of electrodes of the second kind:
A. A metal, the surface of which is covered with a slightly soluble salt of the same metal, immersed in a solution containing the anions that make up this poorly soluble salt. An example is the silver chloride electrode 
, or calomel electrode 
,
A silver chloride electrode consists of a silver wire coated with a salt that is poorly soluble in water and immersed in an aqueous solution of potassium chloride. A reversible reaction occurs on the silver chloride electrode:
The calomel electrode consists of metallic mercury coated with a paste of poorly soluble mercury (I) chloride 
- calomels, contact
ting with an aqueous solution of potassium chloride. A reversible reaction occurs on the calomel electrode:
The real potential of electrodes of the second kind depends on the activity of anions and for a reversibly working electrode on which the reaction takes place
is described by the Nernst equations (9-12).
Generally at any acceptable temperature T:
. (9)
For room temperature:
For conditions in which the activity of anions is approximately equal to their concentration 
:
. (11)
For room temperature:
(12)
For example, the real potentials, respectively, of silver chloride and calomel electrodes at room temperature can be represented as:
In the latter case, 2 electrons are involved in the electrode reaction (n= 2) and 2 chloride ions are also formed, therefore the factor at the logarithm is also 0.059.
Electrodes of the second kind of the considered type have high reversibility and are stable in operation, therefore they are often used as reference electrodes capable of stably maintaining a constant potential value;
b) gas electrodes of the second kind, for example, chlorine electrode,
Gas electrodes of the second kind in quantitative potential
cyometric analysis is rarely used.
Redox electrodes. They consist of an inert material (platinum, gold, tungsten, titanium, graphite, etc.) immersed in a solution containing oxidized Ox and reduced Red forms of this substance. There are two types of redox electrodes:
1) electrodes, the potential of which does not depend on the activity of hydrogen ions, for example, etc .;
2) electrodes, the potential of which depends on the activity of hydrogen ions, for example, a quinhydrone electrode.
On a redox electrode, the potential of which does not depend on the activity of hydrogen ions, a reversible reaction occurs:
The real potential of such a redox electrode depends on the activity of the oxidized and reduced form of a given substance and for a reversibly working electrode is described, depending on the conditions (by analogy with the above potentials), by the Nernst equations (13-16):
(13) (14) (15) 
(16)
where all designations are traditional.
If hydrogen ions participate in the electrode reaction, then their activity (concentration) is taken into account in the corresponding Nernst equations for each specific case.
Membrane, or ion-selective, electrodes- electrodes reversible for certain ions (cations or anions) sorbed by a solid or liquid membrane. The real potential of such electrodes depends on the activity of those ions in the solution that are sorbed by the membrane.
Membrane electrodes with a solid membrane contain a very thin membrane, on both sides of which there are different solutions containing the same detectable ions, but with different concentrations: a solution (standard) with a precisely known concentration of the ions to be determined and an analyzed solution with an unknown concentration of the ions to be determined. Due to the different concentration of ions in both solutions, ions on different sides of the membrane are sorbed in different amounts, and the electric charge arising from the sorption of ions on different sides of the membrane is also different. As a result, a membrane potential difference arises.
The determination of ions using membrane ion-selective electrodes is called ionometry.
As mentioned above, during potentiometric measurements, the electrochemical cell includes two electrodes - an indicator
and a reference electrode. The magnitude of the EMF generated in the cell is equal to the potential difference between these two electrodes. Since the potential of the reference electrode remains constant under the conditions of potentiometric determination, the EMF depends only on the potential of the indicator electrode, i.e. from the activity (concentration) of certain ions in the solution. This is the basis for the potentiometric determination of the concentration of a given substance in the analyzed solution.
For potentiometric determination of the concentration of a substance in a solution, both direct potentiometry and potentiometric titration are used, although the second method is used much more often than the first.
Direct potentiometry
Determination of the concentration of a substance in direct potentiometry. It is usually carried out by the method of a calibration graph or by the method of adding a standard.
. Calibration graph method. Prepare a series of 5-7 standard solutions with a known content of the analyte. The concentration of the analyte and the ionic strength in standard solutions should not differ greatly from the concentration and ionic strength of the analyzed solution: under these conditions, the determination errors are reduced. The ionic strength of all solutions is maintained by the constant introduction of an indifferent electrolyte. The reference solutions are sequentially introduced into the electrochemical (potentiometric) cell. Typically, this cell is a glass beaker in which the indicator and reference electrodes are placed.
Measure the EMF of the standard solutions by thoroughly rinsing the electrodes and the glass with distilled water before filling the cell with each standard solution. Based on the data obtained, a calibration graph is plotted in coordinates 
where with- concentration determined
th substance in the reference solution. Typically, such a graph is a straight line.
Then, the analyzed solution is introduced into the electrochemical cell (after washing the cell with distilled water) and the EMF of the cell is measured. According to the calibration schedule, find 
, where is the concentration of the analyte in the analyzed solution.
. Standard addition method. A known volume V (X) of the analyzed solution with concentration is introduced into the electrochemical cell and the EMF of the cell is measured. Then, in the same solution, add precisely measured small the volume of a standard solution with a known, up to
with a sufficiently high concentration of the analyte and again determine the EMF of the cell.
Calculate the concentration of the analyte in the analyzed solution according to the formula (17):
(17)
where - difference between two measured values of EMF; - the number of electrons involved in the electrode reaction.
Application of direct potentiometry. The method is used to determine the concentration of hydrogen ions (pH of solutions), anions, metal ions (ionometry).
When using direct potentiometry, the selection of a suitable indicator electrode and accurate measurement of the equilibrium potential play an important role.
When determining the pH of solutions, electrodes are used as indicator, the potential of which depends on the concentration of hydrogen ions: glass, hydrogen, quinhydrone and some others. Most often, a membrane glass electrode, reversible for hydrogen ions, is used. The potential of such a glass electrode is determined by the concentration of hydrogen ions; therefore, the EMF of a circuit including a glass electrode as an indicator is described at room temperature by the equation:
where is the constant K depends on the material of the membrane, the nature of the reference electrode.
The glass electrode allows you to determine pH in the range of pH 0-10 (more often in the range of pH 2-10) and has high reversibility and stability in operation.
Quinhydron electrode, often used earlier - a redox electrode, the potential of which depends on the concentration of hydrogen ions. It is a platinum wire immersed in an acid solution (usually HC1) saturated with quinhydrone, an equimolecular compound of quinone with hydroquinone (dark green powder, slightly soluble in water). Schematic designation of a quinhydrone electrode:
A redox reaction takes place on the quinhydrone electrode:
The potential of a quinhydrone electrode at room temperature is described by the formula:
The quinhydron electrode makes it possible to measure the pH of solutions in the range of pH 0-8.5. At pH< 0 хингидрон гидролитически расщепляется; при рН >8.5 hydroquinone, which is a weak acid, enters into a neutralization reaction.
The quinhydrone electrode must not be used in the presence of strong oxidizing and reducing agents.
Membrane ion-selective electrodes are used in ionometry as indicator for the determination of various cations
Etc.) and anions 
,
and etc.).
The advantages of direct potentiometry include the simplicity and speed of measurements. Measurements require small volumes of solutions.
Potentiometric titration
Potentiometric titration is a method for determining the volume of titrant spent on titrating an analyte in an analyzed solution by measuring the EMF (during titration) using a galvanic circuit composed of an indicator electrode and a reference electrode. In potentiometric titration, the analyzed solution in the electrochemical cell is titrated with a suitable titrant, fixing the end of the titration by a sharp change in the EMF of the measured circuit - the potential of the indicator electrode, which depends on the concentration of the corresponding ions and changes sharply at the equivalence point.
Measure the change in the potential of the indicator electrode during the titration, depending on the volume of the added titrant. Based on the data obtained, a potentiometric titration curve is plotted and the volume of consumed titrant in TE is determined from this curve.
Potentiometric titration does not require the use of indicators that change color near the TE.
The electrode pair (reference electrode and indicator electrode) is made up so that the potential of the indicator electrode depends on the concentration of ions involved or formed in the reaction proceeding during the titration. The potential of the reference electrode must remain constant during titration. Both electrodes are installed directly in the electrochemical cell or placed in separate vessels with conductive solutions (the indicator electrode is in the analyzed solution), which are connected by an electrolytic bridge filled with an indifferent electrolyte.
The titrant is added in equal portions, each time measuring the potential difference. At the end of the titration (near the TE), the titrant is added dropwise, also measuring the potential difference after the addition of the next portion of the titrant.
The potential difference between the electrodes is measured using high resistance potentiometers.
Potentiometric titration curves
Potentiometric titration curve is a graphical representation of the change in the EMF of an electrochemical cell depending on the volume of added titrant.
Potentiometric titration curves are plotted in different coordinates:
Titration curves in coordinates 
, sometimes such curves are called integral titration curves;
Differential titration curves - in coordinates
Titration curves by Gran's method - in coordinates
where is the EMF of the potentiometric cell, 
- the volume of the added
th titrant, is the change in potential corresponding to the addition of the titrant.
In fig. 3-8 show schematically different types of potentiometric titration curves.
Based on the constructed titration curves, the titrant volume is determined
in the TE, as shown in Fig. 3-8. Titrant volume 
added to TE, you can determine
not only graphically, but also by calculation using the formula (18):
where is the volume of added titrant corresponding to the last measurement before TE; is the volume of added titrant corresponding to the first measurement after TE;
Rice. 3-8. Types of potentiometric titration curves (E - measured EMF, - volume of added titrant, 
- the volume of the titrant, at-
added at the equivalence point): a - titration curve in coordinates 
; b, c - differential titration curves; d - titration curve according to the Gran's method
Table 3-9 shows the results of determinations and calculations in potentiometric titration as an example (pharmacopoeial).
Let us calculate by the formula (18) the value V(TE) using the data table. 3-9. Obviously, the maximum value 
= 1000. Therefore, = 5.20 and = 5.30; = 720,. = -450. Hence:
Table 3-9. An example of processing the results of potentiometric titration
The use of potentiometric titration. The method is universal, it can be used to indicate the end of the titration in all types of titrations: acid-base, redox, compleximetric, precipitation, when titrating in non-aqueous media. Glass, mercury, ion-selective, platinum, silver electrodes are used as indicator electrodes, and calomel, silver chloride, and glass electrodes are used as reference electrodes.
The method is highly accurate and highly sensitive; allows titration in turbid, colored, non-aqueous media, separate determination of mixture components in one analyzed solution, for example, separate determination of chloride and iodide ions during argentometric titration.
Many medicinal substances are analyzed by potentiometric titration methods, for example, ascorbic acid, sulfa drugs, barbiturates, alkaloids, etc.
Assignment for self-preparation for laboratory studies on the topic "Potentiometric Analysis"
The purpose of studying the topic
Based on knowledge of the theory of potentiometric analysis and the development of practical skills, learn to reasonably choose and practically apply the methods of direct potentiometry and potentiometric titration for the quantitative determination of a substance; be able to conduct a statistical assessment of the results of potentiometric analysis.
Target tasks
1. Learn to quantitatively determine the content of fluoride ion in solution by direct potentiometry using a fluoride-selective electrode.
2. To learn how to quantitatively determine the mass fraction of novocaine in the preparation by potentiometric titration.
Two laboratory sessions are allocated for the study of the topic. In one lesson, students perform the first laboratory work and solve typical computational problems in the main sections of potentiometric analysis; in another lesson, students perform a second laboratory work. The sequence of the lessons does not really matter.
Bibliography
1. Tutorial. - Book 2, chapter 10. - pp. 447-457; 493-507; 510-511.
2.Kharitonov Yu.Ya. Grigorieva V.Yu. Examples and tasks in analytical chemistry. - M .: GEOTAR-Media, 2007. - P. 214-225; 245-259; 264-271.
3. Lectures on the topic: "Potentiometric analysis".
4.Efremenko O.A. Potentiometric analysis. - M .: MMA im. THEM. Sechenov, 1998.
You need to know for the lesson
1. The principle of methods of potentiometric analysis. Nernst equation.
2. Varieties of methods of potentiometric analysis.
3. Installation diagram for direct potentiometry.
4. Indicator electrodes and reference electrodes used in direct potentiometry.
5. The essence of determining the concentration of a substance by the method of direct potentiometry using a calibration graph.
6. The essence of determining the content of fluoride ion in solution by direct potentiometry using a fluoride-selective electrode.
For the lesson you need to be able to
1. Calculate the weight of the sample for the preparation of a standard solution of the substance.
2. Prepare standard solutions by dilution method.
3. Build calibration curves and use them for quantitative determination of a substance.
Self-test questions
1. What is the principle behind the direct potentiometry method?
3. What electrochemical parameter is measured when determining a substance by the method of direct potentiometry?
4. Give a diagram of the setup for determining a substance by the direct potentiometry method.
5. What electrodes are called indicator? What are the most commonly used indicator ion-selective electrodes?
6. What electrodes are called reference electrodes? Which reference electrode is accepted as the international standard? How does it work? What are the most commonly used reference electrodes? How do they work:
a) saturated calomel electrode;
b) saturated silver chloride electrode?
7. What is the essence of potentiometric determination of a substance by the method of a calibration graph?
8. Name the range of the determined concentrations and the percentage (relative) error in the determination of the substance by the direct potentiometry method.
9. What is the principle behind the determination of fluoride ion by direct potentiometry? List the main stages of the analysis.
Laboratory work "Determination of the content of fluoride ion in solution using a fluoride-selective electrode"
purpose of work
Learn to apply the method of direct potentiometry using an ion-selective electrode for the quantitative determination of a substance using a calibration graph.
Target tasks
1. Preparation of a standard solution of sodium fluoride, the concentration of which is exactly equal to the specified one.
2. Preparation by dilution method of a series of standard solutions of sodium fluoride, in composition and ionic strength close to the analyzed solution.
3. Measurement of the electromotive force (EMF) of a galvanic cell composed of an indicator fluoride selective electrode and a silver chloride reference electrode as a function of fluoride ion concentration.
4. Construction of a calibration graph in coordinates: "EMF - an indicator of the concentration of fluoride ion".
5. Determination of the content of fluoride ion in the analyzed solution using a calibration graph.
Material security
Reagents
1. Sodium fluoride, chemically pure.
2. Acetate buffer solution, pH ~ 6.
3. Distilled water. Glassware
1. Volumetric flask, 100 ml - 1 pc.
2. Volumetric flask, 50 ml - 6 pcs.
3. Measuring pipette, 5 ml - 1 pc.
4. Beaker chemical for 200-250 ml - 1 pc.
5. Beaker chemical 50 ml - 2 pcs.
6. Byux - 1 pc.
7. Funnel - 1 pc.
8. Glass stick - 1 pc.
9. Wash bottle for 250 or 500 ml - 1 pc.
Devices
2. Indicator electrode, fluoride-selective. Before operation, the fluoride electrode is kept in 0.01 mol / L sodium fluoride solution for 1-2 hours.
3. Reference electrode, auxiliary laboratory silver chloride EVL-IMZ or similar. Before use, the silver chloride electrode is filled through the side hole with a concentrated, but unsaturated, approximately 3 mol / l solution of potassium chloride. When a saturated solution of potassium chloride is used, salt crystallization is possible in the immediate vicinity of the contact zone of the electrode with the measured solution, which prevents the passage of current and leads to irreproducible readings of the measuring device. After filling the electrode with 3 mol / L potassium chloride solution, the side hole is closed with a rubber stopper, the electrode is immersed in a potassium chloride solution of the same concentration and kept in this solution for ~ 48 h. During operation, the plug from the side hole of the electrode must be removed. The flow rate of the potassium chloride solution through the electrolytic switch of the electrode at a temperature of 20 ± 5 ° C is 0.3-3.5 ml / day.
4. A stand for fixing two electrodes.
5. Magnetic stirrer.
Other materials
1. Strips of filter paper 3 5 cm.
2. Millimeter paper 912 cm.
3. Ruler.
The essence of the work
The determination of the fluoride ion by the direct potentiometry method is based on measuring the electromotive force of a galvanic cell, in which a fluoride-selective electrode serves as an indicator electrode, and a silver chloride or calomel electrode as a reference electrode, as a function of the concentration of fluoride ions in solution.
The sensitive part of the fluoride electrode (Fig. 3-9) is a membrane made of a single crystal of lanthanum (III) fluoride, activated with europium (II).
Rice. 3-9. Diagram of the device of a fluoride-selective electrode: 1 - single crystal membrane 
2 - internal half-cell (usually silver chloride -
ny); 3 - internal solution with constant ion activity (0.01 mol / l and imol / l); 4 - electrode body; 5 - wire for connecting the electrode to the measuring device
The equilibrium potential of the fluoride electrode in accordance with the Nernst equation for anion-selective electrodes depends on the activity (concentration) of the fluoride ion in the solution:
(19) or at 25 ° C:
(20)
where is the standard potential of the fluoride electrode, V; 
-
respectively, activity, activity coefficient, molar concentration of fluoride ion in solution.
The first term on the right-hand side of equation (20) is a constant value. For solutions with approximately the same ionic strength, the activity coefficient of the fluoride ion, and hence the second term on the right-hand side of Eq. (20), is also a constant. Then the Nernst equation can be represented as:
E= const - 0.0591gc (F -) = const + 0.059pF, (21)
where pF = -1gc (F -) is an indicator of the concentration of fluoride ion in the solution.
Thus, for constant ionic strength solutions, the equilibrium potential of the fluoride electrode is linearly dependent on the concentration of the fluoride ion. The existence of such a dependence makes it possible to determine the concentration of fluoride ion using a calibration graph, which is plotted in coordinates 
for a series of standard solutions of sodium fluoride, in composition and ionic strength close to the analyzed solution.
The fluoride electrode is used in the pH range of 5-9, since at pH< 5 наблюдается неполная ионизация или образование 
and at pH> 9 - the interaction of the electrode material with hydroxydion:
To maintain a constant pH value and create a constant ionic strength in standard and analyzed solutions, a buffer solution (for example, acetate or citrate) is usually used. When analyzing solutions with a complex salt composition, the buffer solution also serves to eliminate the interfering influence of extraneous cations by binding them into stable acetate, citrate, or other complex compounds. For the same purpose, additional complexing reagents (for example, EDTA) are introduced into the buffer solution.
The selectivity of determination with a fluoride electrode is very high; only hydroxide ions interfere and those few cations that form more stable complex compounds with the fluoride ion than with the components of the buffer solution 
The range of determined concentrations of fluoride ion is very wide: from 10 -6 to 1 mol / l; in this case, the percentage determination error is ± 2%.
The fluoride selective electrode is widely used in the analysis of various objects: drinking water, pharmaceuticals, biological materials, environmental pollution control, etc.
Since in this work, sodium fluoride solutions that do not contain foreign ions are analyzed, the buffer solution can be omitted. In this case, a slight deviation of the calibration graph from the linear dependence should be expected, since in standard solutions with an increase in the concentration of the fluoride ion, the ionic strength increases, and the activity coefficient of the fluoride ion does not remain constant.
Work order
1. (see Appendix 1).
2. Acquaintance with the purpose, principle of operation and the "Operating Instructions for the EV-74 universal ion meter" (or a similar device) (see Appendices 2, 3).
3.
ATTENTION! This work provides for the use of an EV-74 type ionomer. When using devices of a different type, it is necessary to give an additional description of them.
3.1. A galvanic cell is assembled from an indicator fluoride selective electrode and a silver chloride reference electrode.
ATTENTION! When working with ion-selective electrodes, care must be taken not to damage the working surface of the electrode - the membrane, which should be smooth, free from scratches and deposits.
Before installation, shake the fluoride electrode vigorously like a medical thermometer, holding it upright with the membrane facing down. This is done in order to remove air bubbles invisible from the outside, which can form between the membrane surface and the internal solution of the electrode (see Fig. 3-9) and lead to instability of the meter readings.
The fluoride electrode is fixed in a stand next to the reference electrode.
ATTENTION! Holders for attaching electrodes to the tripod are usually pre-installed properly; it is not recommended to change their position. In order to fix the fluoride electrode or change the solution in the cell, you must first carefully remove the magnetic stirrer from under the cell.
When fixing, the fluoride electrode is brought into the tripod leg from below so that its lower end is level with the lower end of the reference electrode. The electrode is connected to the ionomer through the "Measure" socket located on the rear panel of the device (Appendix 3, p. 1.1). The reference electrode must be connected to the ionomer through the "Aux." Socket.
The electrodes are repeatedly washed with distilled water from a washing bottle over a glass with a capacity of 200-250 ml, after which a 50 ml glass with distilled water is placed under the electrodes, which is installed in the center of the table of a magnetic stirrer. Correctly attached electrodes should not touch the walls and bottom
glasses, as well as a magnetic rod, which is used later to stir the solution.
3.2. The ionomer is connected to the network under the supervision of a teacher, guided by the instruction manual for the device (Appendix 3, items 1.2-1.7). Allow the appliance to warm up for 30 minutes.
4. Preparation of a standard 0.1000 mol / L sodium fluoride solution. Calculate, with an accuracy of 0.0001 g, the mass of a sample of sodium fluoride required for the preparation of 100 ml of a 0.1000 mol / l solution according to the formula:
where c, - respectively, molar concentration (mol / l) and volume (l) of a standard solution of sodium fluoride; - molar mass of sodium fluoride, g / mol.
First, a clean and dry weighing bottle is weighed on an analytical balance with an accuracy of ± 0.0002 g, and then a sample of reagent grade is weighed in this weighing bottle. sodium fluoride, the mass of which must be accurately calculated.
The weighed portion is quantitatively transferred into a volumetric flask with a capacity of 100 ml through a dry funnel, rinsing salt particles from the walls of the bottle and funnel with an acetate buffer solution (pH ~ 6). The solution from the bottle is poured into a flask on a glass rod, leaning it against the edge of the bottle. Complete dissolution of the salt is achieved, after which the volume of the solution is brought up to the mark of the flask with the buffer solution. The contents of the flask are mixed.
5. Preparation of a series of constant ionic strength sodium fluoride standard solutions. A series of standard solutions with a fluoride ion concentration equal to 10 -2, 10 -3, 10 -4, 10 -5 and 10 -6 mol / l are prepared in 50 ml volumetric flasks from a standard 0.1000 mol / l sodium solution fluoride by successive dilution with buffer solution.
So, to prepare a 10 -2 mol / L solution, 5 ml of 0.1000 mol / L sodium fluoride solution is pipetted into a 50 ml volumetric flask, after rinsing the pipette with a small amount of this solution 2-3 times, the volume of the solution is adjusted to the mark with the buffer solution. , the contents of the flask are stirred. In the same way, a 10 -3 mol / l solution is prepared from a 10 -2 mol / l solution, etc. up to 10 -6 mol / l sodium fluoride solution.
6. Measurement of the electromotive force of a galvanic cell as a function of the concentration of fluoride ion. In a beaker with a capacity of 50 ml, the prepared standard solutions are sequentially placed on
sodium fluoride, starting with the most diluted one, after rinsing the glass with the measured solution 2-3 times. Carefully dry the surface of the fluoride and silver chloride electrodes with filter paper, after which the electrodes are immersed in the solution to be measured, the magnetic rod is lowered and the cell is installed in the center of the magnetic stirrer table. If instructed by the teacher, open the side hole of the silver chloride electrode by removing the rubber stopper from it. Turn on the magnetic stirrer and measure the EMF of the element (positive potential of the fluoride electrode) using an EV-74 ion meter in a narrow measurement range - 14, as indicated in Appendix 3, p. 2.1-2.5. The measurement results are entered in table. 3-10.
Table 3-10. Results of measuring the electromotive force of a galvanic cell as a function of the concentration of fluoride ion
7. Construction of a calibration graph. According to the table. 3-10, a calibration graph is plotted on graph paper, plotting the concentration of fluoride ion along the abscissa, and the EMF of the element in millivolts on the ordinate (E, mV). If dependence (21) is satisfied, then a straight line is obtained, the slope of which to the abscissa axis is 59 ± 2 mV (at 25 ° C). The graph is glued to the laboratory journal.
8. Determination of the content of fluoride ion in the analyzed solution using a calibration graph. The analyzed solution containing fluoride ion is obtained from the teacher in a 50 ml volumetric flask. The volume of the solution is made up to the mark with an acetate buffer solution. The contents of the flask are stirred and the EMF of an element composed of fluoride and silver chloride electrodes is measured in the resulting solution.
At the end of the measurements, close the hole of the silver chloride electrode with a rubber stopper and turn off the device, as indicated in Appendix 3, clause 2.6.
According to the calibration graph, an indicator of the concentration of the fluoride ion is found, corresponding to the EMF of the element in the analyzed solution, then the molar concentration is determined and the content of the fluoride ion in the solution is calculated by the formula:
where 
- titer of fluoride ion in the analyzed solution, g / ml; - molar
ny concentration of fluoride ion, found using the calibration graph, mol / l; 
- molar mass of fluoride ion, g / mol.
The titer is calculated with an accuracy of three significant figures.
9. Determination of the content of fluoride ion in the analyzed solution according to the equation of the calibration graph. The pF value for the analyzed solution can be found from the equation of the calibration graph, which seems to be more accurate than using the calibration graph. This equation is:
where 
chains with test solution 
;
chains at = 0 -
line cut by the ordinate 
;
- tangent of an angle
the slope of the straight line to the abscissa axis:
where n- the number of standard solutions. Thus:
Having determined according to the schedule and calculated 
count on
according to the formula:
Then the molar concentration is determined and the content of the fluoride ion in the solution is calculated according to the formula indicated above.
Control questions
1. Name the components of a galvanic cell used to determine the concentration (activity) of a fluoride ion in a solution by direct potentiometry.
2. What is the mathematical relationship underlying the determination of the concentration (activity) of the fluoride ion in the solution by the direct potentiometry method?
3. Describe the design of the fluoride-selective electrode. What factors determine its potential?
4. Why is it necessary to create the same ionic strength in the analyzed and standard solutions when determining the concentration of fluoride ion by the method of direct potentiometry?
5. What is the optimal pH range for fluoride ion determination using a fluoride selective electrode?
6. How is the optimal pH value and constant ionic strength maintained during the determination of fluoride ion in solutions with a complex salt composition?
7. What ions interfere with the determination of fluoride ion in solution using a fluoride-selective electrode? How is their interfering influence eliminated?
8. List the main stages of determining the concentration of fluoride ion in a solution by the potentiometric method using a calibration curve.
9. In what coordinates is the calibration graph plotted when determining the concentration of the fluoride ion by the direct potentiometry method?
10. What should be equal to the slope (tangent of the slope) of the calibration graph plotted in coordinates 
, for standard solutions of sodium fluoride with the same ionic strength at 25 ° C?
11. How to calculate the concentration of fluoride-ion in solution using the data of the calibration graph, built in coordinates 
, if the EMF of the element in the analyzed solution is known?
12. How to prepare a standard solution from a crystalline substance of sodium fluoride with a concentration exactly equal to the specified one, for example, 0.1000 mol / l?
13. How to prepare a standard sodium fluoride solution from a more concentrated solution?
14. Name the range of the determined concentrations and the percentage error in determining the fluoride ion using a fluoride-selective electrode by the method of the calibration curve.
15. Name the areas of application of the fluoride-selective electrode.
Lesson 2. Potentiometric titration
You need to know for the lesson
1. The principle of methods of potentiometric analysis. Nernst equation. Varieties of methods of potentiometric analysis.
2. Schematic diagram of a potentiometric titration setup.
3. Indicator electrodes used in potentiometric titration, depending on the type of titration reaction; reference electrodes.
4. Methods for indicating the equivalence point in potentiometric titration.
5. Advantages of potentiometric titration over titrimetric analysis with visual indication of the equivalence point.
6. The essence of the determination of novocaine by potentiometric titration.
For the lesson you need to be able to
1. Prepare the solution to be analyzed by dissolving a weighed portion of the test sample with a precisely known mass.
2. Calculate the mass fraction of the substance in the analyzed sample based on the titration results.
3. Write the equation of the reaction taking place during titration.
Self-test questions
1. What is the principle behind the potentiometric titration method?
2. What equation expresses the dependence of the electrode potential on the concentration (activity) of the potential-determining components in the solution?
3. What electrochemical parameter is measured when determining a substance by potentiometric titration?
4. Give a definition to the terms "indicator electrode", "reference electrode".
5. What is the reason for the sharp change in the electromotive force of the galvanic cell (potential of the indicator electrode) in the titrated solution near the equivalence point?
6. Name the known methods for determining the equivalence point based on potentiometric titration data.
7. For what types of chemical reactions can the potentiometric titration method be used? What electrodes are used for this?
8. What is the advantage of potentiometric titration over titrimetric analysis with visual indication of the equivalence point?
9. Name the range of the determined concentrations and the percentage (relative) error in the determination of the substance by potentiometric titration.
10. What is the chemical reaction underlying the determination of a substance containing a primary aromatic amino group by nitrite titration? What are the conditions for holding it? Applied indicators?
11. What is the principle underlying the determination of novocaine by potentiometric titration? List the main stages of the analysis.
Laboratory work "Determination of the mass fraction of novocaine in the preparation"
purpose of work
Learn to use the potentiometric titration method for the quantitative determination of a substance.
Target tasks
1. Approximate potentiometric titration of novocaine with sodium nitrite solution.
2. Precise potentiometric titration of novocaine with sodium nitrite solution.
3. Finding the end point of potentiometric titration.
4. Calculation of the mass fraction of novocaine in the preparation.
Material security
Reagents
1. Sodium nitrite, standard ~ 0.1 mol / l solution.
2. Novocaine powder.
3. Potassium bromide, powder.
4. Concentrated hydrochloric acid (= 1.17 g / ml).
5. Distilled water. Glassware
1. Volumetric flask, 100 ml.
2. Volumetric flask, 20 ml.
3. 25 ml burette.
4. Measuring cylinder for 20 ml.
5. Measuring cylinder for 100 ml.
6. Beaker for titration, 150 ml.
7. Byux.
8. Funnel.
9. 250 ml or 500 ml wash bottle.
Devices
1. Universal ionomer EV-74 or similar.
2. Platinum indicator electrode ETPL-01 M or similar.
3. Reference electrode, auxiliary laboratory silver chloride EVL-1MZ or similar.
Preparation of the silver chloride electrode for use - see above, previous laboratory work.
4. A stand for fixing two electrodes and a burette.
5. Magnetic stirrer.
6. Analytical balance with weights.
7. Weights technochemical with weights.
Other materials: see "Material Support" in previous work.
The essence of the work
Potentiometric titration is based on the indication of the equivalence point by a sharp change (jump) in the potential of the indicator electrode during the titration.
To determine novocaine, a substance containing a primary aromatic amino group, a nitritometric titration method is used, according to which novocaine is titrated with a standard 0.1 mol / L sodium nitrite solution in a hydrochloric acid medium in the presence of potassium bromide (accelerates the reaction) at a temperature not higher than 18-20 ° C. Under such conditions, the titration reaction proceeds quantitatively and rather quickly:
The progress of the diazotization reaction is monitored using a platinum indicator electrode, which, together with a suitable reference electrode (silver chloride or calomel), is immersed in the solution to be titrated, and the electromotive force is measured 
element depending on
the difference from the volume of the added titrant
The potential of the indicator electrode according to the Nernst equation depends on the concentration (activity) of the substances participating in the titration reaction. Near the point of equivalence (TE), the concentration of potential-determining substances changes sharply, which is accompanied by a sharp change (jump) in the potential of the indicator electrode. The EMF of an element is determined by the potential difference between the indicator electrode and the reference electrode. Since the potential of the reference electrode remains constant, a jump in the potential of the indicator electrode causes a sharp change in the EMF of the element, which indicates the achievement of TE. For greater accuracy of the TE determination, the titrant is added dropwise at the end of the titration.
Graphical methods, usually used to find TE, in this case is hardly advisable to use, since the titration curve plotted in coordinates 
, is asymmetric with respect to TE; it is rather difficult to establish TE with a sufficiently high accuracy.
The percentage error in the determination of novocaine in the preparation by potentiometric titration does not exceed 0.5%.
Similar to the determination of novocaine by potentiometric titration, many other organic compounds and drugs containing a primary aromatic amino group can be determined, for example, sulfacil, norsulfazole, derivatives of n-aminobenzoic acid, etc.
Note. The diazotization reaction is slow. Various factors affect the rate of its flow. An increase in acidity leads to a decrease in the reaction rate; therefore, during titration, try to avoid a large excess of hydrochloric acid. To accelerate the reaction, potassium bromide is introduced into the reaction mixture. Temperature has the usual effect
on the reaction rate: an increase in temperature by 10 ° C leads to an increase in the rate of about 2 times. However, titration, as a rule, is carried out at a temperature not higher than 18-20 ° C, and in many cases even lower, when the reaction mixture is cooled to 0-10 ° C, since the diazo compounds formed as a result of the reaction are unstable and decompose at a higher temperature.
Titration using the diazotization reaction is carried out slowly: first at a rate of 1–2 ml / min, and at the end of titration — 0.05 ml / min.
Work order
ATTENTION! This work provides for the use of a universal ionomer EV-74. When using devices of a different type, it is necessary to additionally give their description in the laboratory methodological instructions.
1. Acquaintance with the "Safety instructions for working with electrical appliances"(see Appendix 1).
2. Acquaintance with the purpose, principle of operation and "Operating instructions for the universal ion meter EV-74"(see Appendices 2, 3) or a similar device.
3. Preparation of the ionomer for measurements.
3.1. A galvanic cell is assembled from a platinum indicator electrode and a silver chloride reference electrode.
The platinum electrode is fixed in a stand next to the reference electrode.
ATTENTION! Holders designed for attaching electrodes and burettes to the tripod are usually pre-installed properly. It is not recommended to change their position. In order to fix the platinum electrode or replace the solution in the cell, first carefully remove the magnetic stirrer from under the cell.
For fixing, the platinum electrode is brought into the tripod leg from below so that its lower end is slightly higher (by about 0.5 cm) than the lower end of the reference electrode. The indicator electrode is connected to the ionomer through the "Measure" socket located on the rear panel of the device (see Appendix 3, p. 1.1). The reference electrode must be connected to the ionomer through the "Aux." Socket.
The electrodes are repeatedly washed with distilled water from a washing bottle over a 200-250 ml beaker, after which a 150 ml beaker with distilled water is placed under the electrodes, which is installed in the center of the magnetic stirrer table. Correctly fixed electrodes should not touch the walls and bottom of the glass, as well as the magnetic rod used later to stir the solution.
3.2. The ionomer is connected to the network under the supervision of a teacher, guided by the instruction manual for the device (Appendix 3, p. 1.2-1.7). Allow the appliance to warm up for 30 minutes.
4. Preparation of the analyzed solution of novocaine. Prepare about 0.05 mol / l novocaine solution in 2 mol / l hydrochloric acid solution. To do this, about 0.9 g of the drug (the sample is weighed in a weighing bottle on an analytical balance with an accuracy of ± 0.0002 g) is placed in a 100 ml volumetric flask, 20-30 ml of distilled water, 16.6 ml of concentrated hydrochloric acid solution ( = 1.17 g / ml). The mixture is stirred until the drug is completely dissolved, the volume of the solution is brought to the mark with distilled water, the contents of the flask are stirred.
5. Indicative titration. In a glass with a capacity of 150 ml with a pipette, place 20 ml of the analyzed solution of novocaine, add 60 ml of distilled water using a cylinder and about 2 g of potassium bromide. Electrodes - indicator platinum and auxiliary silver chloride - are immersed in the titrated solution, the magnetic rod is lowered and the cell is installed in the center of the magnetic stirrer table. If instructed by the teacher, open the side hole of the silver chloride electrode by removing the rubber stopper from it. A 25 ml burette is filled with a standard 0.1 mol / L sodium nitrite solution and fixed in a stand so that the lower end of the burette is lowered into the beaker 1–2 cm below its edge. Turn on the magnetic stirrer. Stirring is not stopped during the entire titration process.
The device is switched on in the millivoltmeter mode to measure positive potentials (+ mV). In an approximate titration, the EMF of the system is measured over a wide range (-119) as indicated in Appendix 3, p. 2.1-2.5, the titrant solution is added in portions of 1 ml, each time measuring the EMF of the system after the reading of the device assumes a steady value.
A sharp change in the EMF (titration jump) is observed, and then another 5-7 ml of the titrant is added in portions of 1 ml and the measured value changes insignificantly. At the end of the titration, turn off the magnetic stirrer. The measurement results are entered in table. 3-11.
Based on the results of the approximate titration, the titrant volume is established, after the addition of which a titration jump is observed. This volume is considered to be close to the endpoint titration (CTT) volume.
In the table. 3-11 in the example, the volume of titrant consumed for approximate titration is 11 ml.
Table 3-11. Indicative titration (example)
Based on the results of the approximate titration, a titration curve is plotted in coordinates. The asymmetric nature of the curve is noted, which makes it difficult to determine the CTT graphically with appropriate accuracy.
6. Accurate titration. A new portion of the analyzed solution of novocaine, distilled water, potassium bromide in the same quantities as in the approximate titration are placed in a clean 150 ml beaker. The electrodes, previously washed with distilled water, are immersed in the solution, the magnetic bar is lowered and the magnetic stirrer is turned on. For accurate titration, the EMF measurement is carried out over a narrow range (49) as indicated in Appendix 3, clause 2.5.
First, to the titrated solution at a rate of 1 ml / min, add such a volume of titrant, which should be 1 ml less than the volume spent on approximate titration, after which the EMF of the element is measured. In the example shown, the volume of titrant added is: 11 - 1 = 10 ml.
Then the titrant is added in portions of 2 drops, each time measuring the EMF after the reading of the device assumes a steady-state value. A sharp change in the EMF (titration jump) is observed, and then the titration is continued in portions of 2 drops and a decrease and a small change are confirmed. At the end of the titration, the total volume of the added titrant is noted with an accuracy of hundredths of a milliliter.
Turn off the magnetic stirrer. The titration results are entered in table. 3-12.
Accurate titration is carried out at least three times. At the end of the measurements, close the hole of the silver chloride electrode with a rubber stopper and turn off the device, as indicated in Appendix 3, clause 2.6.
7.
Calculation of the analysis result. Based on the exact titration data, first the volume of one drop is calculated and then the volume of the titrant corresponding to 
by the formulas:
where is the volume of the titrant, after the addition of which the titration is continued dropwise, ml; is the volume of the titrant at the end of the titration, ml; n- the total number of titrant drops added; - the number of titrant drops added before the titration jump appeared; - the number of drops that make up the portion of the titrant solution that caused the titration jump.
Table 3-12. Accurate titration (example)
Example. Calculation according to the table. 3-12.
The volume of titrant consumed for titration is determined for each i-th titration.
Mass fraction (percentage) of novocaine in the preparation 
calculate
melt with an accuracy of hundredths of a percent according to the formula:
where with- molar concentration of the titrant: standard sodium nitrite solution, mol / l; - the volume of the titrant spent on the i-th exact titration, ml;
The volume of an aliquot of novocaine solution, ml; - the total volume of the analyzed solution of novocaine, ml; M- molar mass of novocaine, equal to 272.78 g / mol; m- weight of a sample of a preparation containing novocaine, g.
The obtained values of the mass fraction of novocaine in the preparation are processed by the method of mathematical statistics, presenting the analysis result in the form of a confidence interval for a confidence level of 0.95.
Control questions
1. What is the principle of determining novocaine by potentiometric titration?
2. What is the chemical reaction underlying the determination of novocaine by potentiometric titration?
3.What electrodes can be used to monitor the progress of the diazotization reaction during titration of novocaine with sodium nitrite solution?
4. What caused the jump in EMF (jump in the potential of the indicator electrode) in the region of the equivalence point during titration of novocaine with sodium nitrite solution?
5. Under what conditions does the diazotization reaction (with the participation of novocaine) proceed quantitatively and quickly enough?
6. At what rate is the potentiometric titration of novocaine carried out with sodium nitrite solution?
7. What is the form of the titration curve of novocaine with sodium nitrite solution, plotted in the coordinates "EMF - titrant volume"?
8. Is it advisable to use graphic methods for determining the equivalence point in potentiometric titration of novocaine?
10. What is the percentage (relative) error in the determination of novocaine in the preparation by potentiometric titration?
11. What are the advantages of the potentiometric method of indicating the equivalence point in comparison with the visual one in the determination of novocaine by nitrite titration?
12. What substances can be determined by potentiometric titration by analogy with the determination of novocaine?
Annex 1
Safety instructions for working with electrical appliances
Work with ungrounded appliances;
Leave the turned on device unattended;
Relocating the included device;
Work near open current-carrying parts of the device;
Switch the device on and off with wet hands.
2. In the event of a power outage, turn off the appliance immediately.
3. In case of fire of wires or an electrical appliance, it is necessary to immediately de-energize them and extinguish the fire with a dry fire extinguisher, blankets of asbestos, sand, but not with water.
Appendix 2
Purpose and principle of operation of the universal ionomer EV-74
1. Purpose of the device
Universal ionometer EV-74 is designed to determine, complete with ion-selective electrodes, the activity (activity indicator - pX) of singly and doubly charged ions (for example, 
, 
and others), as well as for measuring redox potentials (electromotive force) -corresponding electrode systems in aqueous solutions of electrolytes.
The ionomer can also be used as a high resistance millivoltmeter.
2. The principle of operation of the device
The work of the ionomer is based on converting the electromotive force of the electrode system into a direct current proportional to the measured value. The conversion is carried out using a high-resistance autocompensating type converter.
The electromotive force of the electrode system is compared to the opposite voltage drop across the precision resistance R, through which the amplifier current flows The voltage is applied to the amplifier input:
With a sufficiently large gain, the voltage differs little from the electromotive force, and due to this, the current flowing through the electrodes during the measurement is very small, and the current flowing through the resistance R, proportional to the electromotive force of the electrode system:
By measuring the current with a microammeter A, it is possible to determine as well in the test solution.
Appendix 3
Operating instructions for the universal ion meter EV-74 for measuring redox potentials (EMF) of electrode systems
Measurements can be carried out both in millivolts and in pX units on the instrument scale. When measuring the EMF, no correction for the temperature of the test solution is introduced.
1. Preparation of the EV-74 ionomer for measurements.
1.1. Select the required electrodes and fix them in the tripod. The indicator electrode is connected to the "Meas." directly or using an adapter plug, and the reference electrode - to the "Aux." on the back of the instrument. The electrodes are washed and immersed in a glass of distilled water.
1.2. Check the presence of grounding of the device case.
1.3. Set the mechanical zero of the indicating device, for which, by turning the zero corrector with a screwdriver, set the arrow to the zero (initial) mark of the scale.
1.4. Press the lower button "t °" to select the type of work and the upper button "-119" to select the measurement range.
1.5. Connect the device to a 220 V network using a cord.
1.6. Turn on the device using the "Network" toggle switch. When voltage is applied, the switch-on indicator light comes on.
1.7. The device warms up for 30 minutes.
2. Measurement of oxidation-reduction potentials (EMF) of electrode systems.
2.1. The electrodes are immersed in a glass with the test solution, after removing the excess of distilled water from the surface of the electrodes with filter paper.
2.2. Turn on the magnetic stirrer.
2.3. Press the button 
and a button for the selected measuring range.
2.4. The button "anion | cation; + | - ", if positive potentials are measured, and pressed when negative potentials are measured.
2.5. The readings of the device are allowed to stabilize and the potential value in millivolts is read on the appropriate scale of the indicating device, multiplying the reading of the device by 100:
When measuring on a wide range of "-119", the reading is carried out on the lower scale with digitization from -1 to 19;
When measuring on a narrow range of "-14", the reading is carried out on the upper scale with digitization from -1 to 4;
When measuring on one of the narrow ranges "49", "914", "1419", the reading is carried out on the upper scale with digitization from 0 to 5, and the reading of the device is added to the value of the lower limit of the selected range.
Example. The range switch is set to position "49", and the arrow of the device is set at a value of 3.25. In this case, the measured value is: (4 + 3.25). 100 = 725 mV.
2.6. At the end of the measurements, press the "t °" and "-119" buttons, turn off the device using the "Network" toggle switch and disconnect the device and the magnetic stirrer from the network. The electrodes and the rod of the magnetic stirrer are washed with distilled water and handed over to the laboratory assistant.
Lesson 3. Coulometric analysisMethod principle
Coulometric analysis (coulometry) based on the use of the relationship between mass m the substance reacted during electrolysis in the electrochemical cell, and the amount of electricity Q passed through the electrochemical cell during the electrolysis of only this substance. In accordance with the unified law of electrolysis M. Faraday, the mass m(in grams) is related to the amount of electricity Q(in pendants) with the ratio:
(1)
where M- molar mass of the substance reacted during electrolysis, g / mol; n- the number of electrons participating in the electrode reaction; F= 96 487 C / mol - Faraday number.
The amount of electricity (in pendants) passed through the electrochemical cell during electrolysis is equal to the product of the electric current (in amperes) by the electrolysis time (in seconds):
(2)
If the amount of electricity is measured, then according to (1), you can calculate the mass m. This is true when the entire amount of electricity passed during electrolysis through an electrochemical cell is consumed only for the electrolysis of a given substance; side-
certain processes should be excluded. In other words, the current output (efficiency) must be 100%.
Since, in accordance with the unified law of electrolysis by M. Faraday (1), to determine the mass m (g) of a substance reacted during electrolysis, it is necessary to measure the amount of electricity Q, spent on the electrochemical conversion of the analyte, in pendants, then the method is called coulometry. The main task of coulometric measurements is to determine the amount of electricity as accurately as possible. Q.
Coulometric analysis is carried out either in amperostatic (galvanostatic) mode, i.e. with constant electric current i= const, or at a controlled constant potential of the working electrode (potentiostatic coulometry), when the electric current changes (decreases) during electrolysis.
In the first case, to determine the amount of electricity Q it is enough to measure as accurately as possible the electrolysis time, direct current and calculate the value Q by formula (2). In the second case, the quantity Q determined either by calculation or using chemical coulometers.
Distinguish between direct and indirect coulometry (coulometric titration).
Direct coulometry
The essence of the method
Direct coulometry at constant current is rarely used. Coulometry with a controlled constant potential of the working electrode or direct potentiostatic coulometry is used more often.
In direct potentiostatic coulometry, a directly determined substance is subjected to electrolysis. The amount of electricity consumed for the electrolysis of this substance is measured, and the mass is calculated using equation (1) m analyte.
During electrolysis, the potential of the working electrode is kept constant, 
what devices are usually used for - potentiostats.
Constant potential value E are selected in advance on the basis of consideration of the volt-ampere (polarization) curve plotted in the coordinates "current i- potential E ", obtained under the same conditions in which electrolysis will be carried out. Usually choose
potential value E, corresponding to the region of the limiting current for the substance to be determined and slightly exceeding its half-wave potential (by ~ 0.05-0.2 V). At this potential value, the background electrolyte should not undergo electrolysis.
A platinum electrode is most often used as a working electrode, on which electrochemical reduction or oxidation of the analyte occurs. In addition to the working electrode, the electrochemical cell includes 1 or 2 other electrodes - a reference electrode, for example, silver chloride, and an auxiliary electrode, for example, made of steel.
As the electrolysis process proceeds at a constant potential, the electric current in the cell decreases, since the concentration of the electroactive substance participating in the electrode reaction decreases. In this case, the electric current decreases with time according to the exponential law from the initial value at the moment of time to the value at the moment of time
(3)
where the coefficient depends on the nature of the reaction, the geometry of the electrochemical cell, the area of the working electrode, the diffusion coefficient of the analyte, the stirring rate of the solution and its volume.
The graph of function (3) is schematically shown in Fig. 3-10.
Rice. 3-10. Variation of tox with time in direct potentiostatic coulometry
The current output will be quantitative when the current decreases to zero, i.e. with an infinite time. In practice, electrolysis
The analyte is considered quantitative when the current reaches a very small value, not exceeding ~ 0.1% of the value. In this case, the determination error is about ~ 0.1%.
Since the amount of electricity is defined as the product of current and time of electrolysis, it is obvious that the total amount of electricity Q, spent on electrolysis of the analyte is equal to:
(4)
those. is determined by the area bounded by the coordinate axes and the exponent in Fig. 3-10.
To find the mass m of the reacted substance is required according to (1) to measure or calculate the amount of electricity Q.
Methods for determining the amount of electricity passed through a solution in direct potentiostatic coulometry
The value Q can be determined by calculation methods or using a chemical coulometer.
. Calculation of the value of Q from the area under the curve of the dependence of i on Measure the area bounded by the coordinate axes and the exponent (3) (see Fig. 3-10). If the current i expressed in amperes, and time in seconds, then the measured area is equal to the amount of electricity Q in pendants.
For determining Q without noticeable error, the method requires almost complete completion of the electrolysis process, i.e. long time. In practice, the area is measured at a value m corresponding to i= 0.001 (0.1% of.
. Calculation of the Q value based on the relationship from In accordance with (3) and (4) we have:
insofar as:
Thus, 
and to determine the value Q necessary
find values 
According to (3) 
... After taking the logarithm of this equation,
we get a linear dependence on
(5)
If you measure several values at different points in time (for example, using a curve of the type shown in Fig. 3-10 or directly experimentally), you can build a graph of function (5), schematically shown in Fig. 3-11 and representing a straight line.
The segment cut off by a straight line on the ordinate is equal to the tangent of the angle of inclination of the straight line to the abscissa is: 
Knowing the values 
and therefore, it is possible to calculate the value
Well 
and then the mass m according to the formula (1).
Rice. 3-11. Time dependence of electrolysis in direct potentiostatic coulometry
... Determination of the Q value using a chemical coulometer. In this method, a chemical coulometer is connected in series with an electrochemical cell in the electric circuit of the coulometric installation, in which the analyte is electrolyzed. Electricity quantity Q, passing through a coulometer and an electrochemical cell connected in series is the same. The design of the coulometer makes it possible to experimentally determine the value Q.
The most commonly used are silver, copper and gas coulometers, less often some others. The use of silver and copper coulometers is based on the electrogravimetric determination of the mass of silver or copper deposited on a platinum cathode during electrolysis.
Knowing the mass of the metal precipitated at the cathode in the coulometer, we can calculate the amount of electricity Q using equation (1).
Coulometers, especially silver and copper, allow you to determine the amount of electricity Q with high accuracy, however, working with them is quite laborious and time-consuming.
In coulometry, electronic integrators are also used, which allow registering the amount of electricity. Q, spent on electrolysis, according to the indications of the corresponding device.
Application of direct coulometry
The method possesses high selectivity, sensitivity (up to 10 -8 -10 -9 g or up to ~ 10 -5 mol / l), reproducibility (up to ~ 1-2%), allows to determine the content of trace impurities. The disadvantages of the method include the high complexity and duration of the analysis, the need for expensive equipment.
Direct coulometry can be used to determine metal ions, organic nitro and halogen derivatives, chloride, bromide, iodide, thiocyanate anions, metal ions in lower oxidation states when they are converted to higher oxidation states, for example:
Etc.
In pharmaceutical analysis, direct coulometry is used to determine ascorbic and picric acids, novocaine, oxyquinoline, and in some other cases.
Direct coulometry is rather laborious and time consuming. In addition, in a number of cases, side processes begin to occur noticeably even before the completion of the main electrochemical reaction, which reduces the current efficiency and can lead to significant analysis errors. That is why indirect coulometry is often used - coulometric titration.
Coulometric titration
The essence of the method
In coulometric titration, the analyte X, which is in solution in the electrochemical cell, reacts with the titrant T, a substance that is continuously formed (generated) on the generator electrode during the electrolysis of an auxiliary substance also present in the solution. The end of the titration is the moment when all the analyte X completely reacts with the generated titrant T;
house, introducing into the solution an appropriate indicator that changes color near the TE, or using instrumental methods - potentiometric, amperometric, photometric.
Thus, during coulometric titration, the titrant is not added from the burette to the solution to be titrated. The role of the titrant is played by the substance T, which is continuously generated during the electrode reaction on the generator electrode. Obviously, there is an analogy between the usual titration, when a titrant is introduced from the outside into the titrated solution and, as it is added, reacts with the substance to be determined, and the generation of substance T, which, as it is formed, also reacts with the substance to be determined, therefore, the method under consideration is called coulometric titration ".
Coulometric titration is carried out in amperostatic (galvanostatic) or potentiostatic mode. More often coulometric titration is carried out in amperostatic mode, maintaining the electric current constant during the entire electrolysis time.
Instead of the volume of titrant added in coulometric titration, the time t and the current are measured i electrolysis. The process of formation of a substance T in a coulometric cell during electrolysis is called generation of titrant.
Coulometric constant current titration
In coulometric titration in amperostatic mode (at constant current), the time during which the electrolysis was carried out and the amount of electricity are measured Q, consumed during electrolysis is calculated by the formula (2), after which the mass of the analyte X is found according to the ratio (1).
So, for example, the standardization of a solution of hydrochloric acid by the coulometric titration method is carried out by titrating hydrogen ions 
for a standardized solution containing HCl, hydroxide ions OH generated at a platinum cathode - during electrolysis of water:
The resulting titrant - hydroxide ions - reacts with ions 
in solution:
Titration is carried out in the presence of phenolphthalein indicator and is stopped when a light pink color of the solution appears.
Knowing the magnitude of the direct current in amperes) and the time (in seconds) spent on titration, calculate the amount of electricity by the formula (2) Q(in pendants) and according to the formula (1) - the mass (in grams) of the reacted HCl contained in an aliquot of the standardized HCl solution introduced into the coulometric cell (into the generator vessel).
In fig. 3-12 schematically shows one of the variants of an electrochemical cell for coulometric titration with a visual (by changing the color of the indicator) indication of the end of titration, with a generator cathode and an auxiliary anode.
The generator platinum electrode 1 (in this case, the anode) and the auxiliary platinum electrode 2 (in this case, the cathode) are placed, respectively, in the generation (generator) vessel 3 and auxiliary vessel 4. The generation vessel 3 is filled with a test solution containing the substance to be determined X, background electrolyte with an auxiliary electroactive substance and indicator. The excipient itself can play the role of a supporting electrolyte; in such cases, there is no need to add another supporting electrolyte to the solution.
The generation and auxiliary vessels are connected by an electrolytic (salt) bridge 5 filled with a strong indifferent electrolyte to ensure electrical contact between the electrodes. The ends of the electrolytic bridge tube are closed with filter paper plugs. The generation vessel has a magnetic bar 6 for stirring the solution by means of a magnetic stirrer.
The electrochemical cell is included in the electrical circuit of the coulometric titration setup capable of maintaining a constant current of the required value (for example, a universal power supply such as a UIP-1 laboratory instrument and similar equipment is used).
Before coulometric titration, the electrodes are thoroughly washed with distilled water, a solution with an auxiliary electroactive (under these conditions) substance is introduced into the generation vessel, and, if necessary, a background electrolyte and an indicator.
Since the background solution prepared in this way may contain electroreductive or electrooxidizing impurities, then first carry out preelectrolysis background solution for the purpose of electroreduction or electrooxidation of impurities. To do this, close the electrical circuit of the installation and conduct electrolysis for
some (usually short) time until the color of the indicator changes, after which the circuit is opened.
Rice. 3-12. Diagram of an electrochemical cell for coulometric titration with visual indicator fixation of the end of titration: 1 - working generator platinum electrode; 2 - auxiliary platinum electrode; 3 - a generation vessel with a test solution; 4 - an auxiliary vessel with a solution of a strong indifferent electrolyte; 5 - electrolytic bridge; 6 - magnetic stirrer rod
After the completion of pre-electrolysis, an accurately measured volume of the analyzed solution is introduced into the generation vessel, the magnetic stirrer is turned on, the electrical circuit of the installation is closed, simultaneously turning on the stopwatch, and electrolysis is carried out at constant current until the color of the indicator (solution) abruptly changes, when the stopwatch is immediately stopped and the electrical installation chain.
If the analyzed solution introduced into the coulometric cell for titration contains impurities of electroreductive or electrooxidizing substances, the transformation of which requires a certain amount of electricity during electrolysis, then after pre-electrolysis (before adding the analyzed solution to the cell), carry out blank titration, introducing into the coulometric cell instead of the analyzed solution exactly the same volume of solution, which contains all the same substances and in the same quantities as the added analyzed solution, with the exception of the analyte X. In the simplest case, distilled water is added to the background solution in a volume equal to the volume of an aliquot of the analyzed solution with the analyte.
The time spent on blank titration is subsequently subtracted from the time spent on titrating the test solution with the analyte.
Conditions for carrying out coulometric titration. Must provide 100% current efficiency. To do this, at least the following requirements must be met.
1. The auxiliary reagent, from which the titrant is generated on the working electrode, must be present in the solution in a large excess with respect to the analyte (~ 1000-fold excess). Under these conditions, side electrochemical reactions are usually eliminated, the main of which is the oxidation or reduction of the background electrolyte, for example, hydrogen ions:
2. The magnitude of the constant current i= const during electrolysis should be less than the value of the diffusion current of the auxiliary reagent in order to avoid the occurrence of a reaction with the participation of ions of the background electrolyte.
3. It is necessary to determine as accurately as possible the amount of electricity consumed during electrolysis, for which it is required to accurately record the beginning and end of the time count and the magnitude of the electrolysis current.
End of titration indication. In coulometric titration, TE is determined either by visual indicator or instrumental (spectrophotometric, electrochemical) methods.
For example, when titrating a sodium thiosulfate solution with electrogenerated iodine, an indicator — a starch solution — is added to the coulometric cell. After reaching the TE, when all the thiosulfate ions have been titrated in the solution, the very first portion of the electrogenerated iodine stains the solution blue. The electrolysis is interrupted.
In the case of electrochemical indication of TE, a pair of electrodes, included in an additional indicator electric circuit, are placed in the test solution (in the generation vessel). The end of the titration can be recorded using an additional indicator electric circuit potentiometrically (pH-metric) or biamperometrically.
With biamperometric indication of TE, titration curves are plotted in coordinates by measuring the current i in additional indi-
electric circuit as a function of electrolysis time in a coulometric cell.
Coulometric constant potential titration
Potentiostatic mode is used less frequently in coulometric titration.
Coulometric titration in potentiostatic mode is carried out at a constant potential value corresponding to the discharge potential of the substance on the working electrode, for example, during the cathodic reduction of metal cations M n + on the platinum working electrode. As the reaction proceeds, the potential remains constant until all metal cations have reacted, after which it sharply decreases, since there are no potential-determining metal cations in the solution.
Application of coulometric titration. In coulometric titration, you can use all types of reactions of titrimetric analysis: acid-base, redox, precipitation, complexation reactions.
Small amounts of acids (up to ~ 10 -4 -10 -5 mol / l) can be determined by coulometric acid-base titration with electrogenerated ions formed during the electrolysis of water at the cathode:
It is possible to titrate bases with hydrogen ions generated at the anode during water electrolysis:
In redox bromometric coulometric titration, it is possible to determine compounds of arsenic (III), antimony (III), iodides, hydrazine, phenols and other organic substances. Bromine electrically generated at the anode acts as a titrant:
By precipitation coulometric titration, halide ions and organic sulfur-containing compounds can be determined by electrogenerated silver cations, zinc cations, by electrogenerated ferrocyanide ions, etc.
Complexometric coulometric titration of metal cations can be carried out with EDTA anions electrogenerated at a mercury (II) complexonate cathode.
Coulometric titration has high accuracy, a wide range of applications in quantitative analysis, allows you to determine small amounts of substances, low-stability compounds (since they enter into reactions immediately after their formation), for example, copper (I), silver (II), tin (II) , titanium (III), manganese (III), chlorine, bromine, etc.
The advantages of the method also include the fact that the preparation, standardization and storage of the titrant is not required, since it is continuously formed during electrolysis and is immediately consumed in the reaction with the analyte.
Objectives of studying the topic
Based on knowledge of the theoretical foundations of the coulometric titration method and the development of practical skills, learn how to reasonably choose and practically apply this method of analysis for the quantitative determination of a substance; be able to carry out a statistical assessment of the results of coulometric titration.
Target tasks
1. Learn to quantitatively determine the mass of sodium thiosulfate in solution by coulometric titration.
2. Learn to standardize a hydrochloric acid solution by coulometric titration.
3. Solution of typical computational problems.
One of the two laboratory sessions described in this manual is devoted to the study of the topic. It is recommended to carry out the laboratory work "Determination of the mass of sodium thiosulfate in solution by coulometric titration".
Self-study assignment
You need to know for the lesson
1. The principle of coulometry methods.
2. The essence of the coulometric titration method for determining:
a) sodium thiosulfate;
b) hydrochloric acid.
You must be able to
1. Write the equations of electrochemical reactions occurring on electrodes during coulometric titration:
a) sodium thiosulfate;
b) hydrochloric acid.
2. Write the equations of electrochemical reactions occurring in solution during coulometric titration:
a) sodium thiosulfate;
b) hydrochloric acid.
3. Calculate the amount of electricity and the mass (concentration) of the substance based on the results of coulometric titration.
4. To process the results of parallel determinations of a substance by the method of mathematical statistics.
Bibliography
1. Tutorial. - Book 2, chapter 10. - S. 481-492; 507-509; 512-513.
2.Kharitonov Yu.Ya., Grigorieva V.Yu. Examples and tasks in analytical chemistry.- M .: GEOTAR-Media, 2009.- pp. 240-244; 261-264; 277-281.
COURSE WORK
By discipline: ______ ___________
EXPLANATORY NOTE
_______ Potentiometry and Potentiometric Titration ________
(Full name) (signature)
GRADE: _____________
Date: ___________________
CHECKED
Project Manager: A. V. Tsybizov /________________/
(Full name) (signature)
St. Petersburg
Department of Metallurgy of Non-Ferrous Metals
COURSE WORK
By discipline _________ Physicochemical methods for the analysis of substances __________
(name of the discipline according to the curriculum)
EXERCISE
For a group student: ONG-10-1 Fandofan A.A. . (group code) (full name)
1. Project theme: Potentiometry and potentiometric titration.
3. List of graphic material: Presentation of results in the form of graphs, tables, figures.
4. Completion date of the completed project 10.12.12
Project Manager: A. V. Tsybizov /________________/
(Full name) (signature)
Date of issue of the assignment: 24.10.12
annotation
This explanatory note is a report on the implementation of the course project. The aim of the work is to learn how to navigate in the main flow of information on analytical chemistry, to work with classical and periodical literature in the field of analytical chemistry of non-ferrous metals, to technically competently understand and evaluate the proposed methods and methods of analysis.
Pages 17, figures 0.
The Summary
This explanatory note is a report on the implementation of a course project. The aim is to learn to navigate the mainstream media in analytical chemistry, to work with classical literature and periodicals in the field of analytical chemistry of non-ferrous metals, technically competent to understand and evaluate the proposed methods and analysis techniques.
Pages 17, figures 0.
Abstract .. 3
Introduction. 5
Brief description of electrochemical methods of analysis .. 6
Potentiometry .. 7.
Direct potentiometry .. 10
Potentiometric titration. 13
Conclusion. 16
References .. 17
Introduction
The purpose of the work is to learn how to navigate the main flow of information on analytical chemistry, to work with classical and periodical literature in the field of analytical chemistry of non-ferrous metals, to technically competently understand and evaluate the proposed methods and methods of analysis.
Taking into account the peculiarities of analytical control in nonferrous metallurgy (many determined elements, including elements of waste rock, satellite elements; complex combinations of elements in minerals; a very wide range of element concentrations, etc.), the most widespread methods of physical and chemical analysis in factory and research laboratories, should include such classical methods as titrimetry (including complexometry), gravimetry (for high concentrations of elements and arbitration analysis) and especially intensively developing recently optical methods of analysis (spectrophotometry, extraction-photometric method, atomic -absorption analysis, X-ray spectral analysis) and electrochemical (potentiometry, voltammetry).
The variety of raw materials presents us with a wide range of metals and elements that need to be quantified: basic metals of nonferrous and ferrous metallurgy (copper, nickel, lead, zinc, tin, aluminum, magnesium, titanium, antimony, arsenic, iron, cadmium, silver, chromium etc.), rock-forming elements (silicon, calcium, sodium, chlorine, fluorine, sulfur, phosphorus, etc.) and rare metals (lithium, rubidium, cesium, zirconium, hafnium, vanadium, niobium, tantalum, molybdenum, tungsten, rhenium , gallium, indium, thallium, germanium, selenium, tellurium, etc.).
Brief description of electrochemical methods of analysis
Electrochemical methods of analysis and research are based on the study and use of processes occurring on the surface of the electrode or in the near-electrode space. Any electrical parameter (potential, current strength, resistance, etc.), functionally related to the concentration of the analyzed solution and amenable to correct measurement, can serve as an analytical signal.
A great convenience is that electrochemical methods use electrical influences, and the fact that the result of this influence (response) is also obtained in the form of an electrical signal. This ensures high speed and accuracy of readout, opens up wide possibilities for automation. Electrochemical methods of analysis are distinguished by good sensitivity and selectivity, in some cases they can be attributed to microanalysis, since sometimes less than 1 ml of solution is sufficient for analysis.
For any kind of electrochemical measurements, an electrochemical circuit or an electrochemical cell is required, of which the analyzed solution is an integral part. The substance to be determined can be included both in the composition of the electrolyte filling the cell and in the composition of one of the electrodes. If the analytical redox reaction occurs spontaneously on the cell electrodes, that is, without applying a voltage from an external source, but only due to the potential difference (EMF) of its electrodes, then such a cell is called a galvanic cell.
Distinguish between straight and indirect electrochemical methods . Direct methods use the dependence of the current strength (potential, etc.) on the concentration of the analyte. In indirect methods, the current strength (potential, etc.) is measured in order to find the end point of the titration of the analyte with a suitable titrant, i.e. the dependence of the measured parameter on the titrant volume is used.
According to the types of analytical signal, EMA is subdivided into: 1) conductometry - measurement of the electrical conductivity of the test solution; 2) potentiometry- measurement of the current-free equilibrium potential of the indicator electrode, for which the test substance is potenti-determining; 3) coulometry - measuring the amount of electricity required for the complete transformation (oxidation or reduction) of the substance under study; 4) voltammetry - measurement of stationary or non-stationary polarization characteristics of electrodes in reactions involving the test substance;
5) electrogravimetry - measurement of the mass of a substance released from a solution during electrolysis.
Potentiometry
Potentiometry (from Latin potentia-force, power and Greek metreo-I measure) is an electrochemical method for determining various physicochemical quantities, based on measuring the equilibrium electrode potential of an indicator electrode immersed in the test solution. The potential of the indicator electrode, which is determined by the activity of the components of the electrochemical reaction, is measured with respect to the reference electrode. Potentiometry is widely used in analytical chemistry to determine the concentration of substances in solutions (potentiometric titration), to measure the concentration of hydrogen ions (pH-metry), as well as other ions (ionometry).
Potentiometry is based on the dependence of the equilibrium electrode potential E from thermodynamic activity a components of the electrochemical reaction:
aA + bB + ... + n e m M + R P + ...
This relationship is described by the Nernst equation:
E = E° + R T/(n F) ln ( a ox / a rev)
E = E° + R T /(n F) ln ([oxid] ү oxid / ([recovery] ү recovery)), where
R- universal gas constant equal to 8.31 J / (mol. K); T- absolute temperature; F- Faraday constant (96500 C / mol); n- the number of electrons taking part in the electrode reaction; a ox, a rest — activities of the oxidized and reduced forms of the redox system, respectively; [oxide] and [rest] are their molar concentrations; ү oxide, ү rest - activity coefficients; E° - standard potential of the redox system.
Substituting T= 298.15 K and the numerical values of the constants in the equation, we get:
E = E° + (0.059 / n) lg ( a ox / a rev)
E = E° + (0.059 / n) lg ([oxid] ү oxid / ([recovery] ү recovery))
For potentiometric measurements, constitute a galvanic cell with an indicator electrode , whose potential depends on the activity of at least one of the components of the electrochemical reaction, and the electromotive force (emf) of this element is measured with a reference electrode.
In potentiometry, galvanic cells are used without transfer, when both electrodes are placed in the same test solution, and with transfer, when the electrodes are in different solutions that have an electrolytic contact with each other. The latter is carried out in such a way that the solutions can be mixed with each other only by diffusion. Usually they are separated by a porous ceramic or plastic partition or a firmly ground glass sleeve. Elements without transfer are used mainly for measuring equilibrium constants of chemical. reactions, electrolyte dissociation constants. stability constants of complex compounds, solubility products, standard electrode potentials, as well as activities and activity coefficients of ions. Transferred elements are used to determine "apparent" equilibrium constants (since they do not take into account the liquid potential), activities and activity coefficients of ions, as well as in potentiometric methods of analysis.
Direct potentiometry
Direct potentiometry methods are based on the application of the Nernst equation to find the activity or concentration of a participant in an electrode reaction from an experimentally measured EMF of a circuit or an electrode potential. Direct potentiometry is used to directly determine a ions (for example, Ag + in a solution of AgNO 3) according to the EMF value of the corresponding indicator electrode (for example, silver); in this case, the electrode process must be reversible. Historically, the first methods of direct potentiometry were methods for determining the pH . A glass electrode is most often used to determine pH. The main advantages of a glass electrode are ease of operation, quick establishment of equilibrium and the ability to determine pH in redox systems. The disadvantages include the fragility of the electrode material and the complexity of work when switching to strongly alkaline and strongly acidic solutions.
The emergence of membrane ion-selective electrodes led to the emergence of ionometry (рХ -metry), where рХ = - lg ahah - activity of component X of the electrochemical reaction. Sometimes pH metering is considered as a special case of ionometry. The calibration of the potentiometer instrument scales according to the pX values is difficult due to the lack of appropriate standards. Therefore, when using ion-selective electrodes, the activity (concentration) of ions is determined, as a rule, using a calibration graph or by the method of additions. The use of such electrodes in non-aqueous solutions is limited due to the instability of their body and membrane to the action of organic solvents.
Direct potentiometry also includes redoxmetry - measurement of standard and real redox potentials and equilibrium constants of redox reactions. The redox potential depends on the activities of oxidized (O and reduced ( a re) forms of matter. Redoxmetry is also used to determine the concentration of ions in solutions. The mechanism and kinetics of precipitation and complexation reactions are studied by direct potentiometry using metal electrodes.
Also use the method of the calibration graph. . To do this, a calibration graph is built in advance in EMF coordinates - lg WITH an using standard solutions of the analyzed ion having the same ionic strength of the solution.
In this case f an(activity coefficient) and E diff(diffusion potential) remain constant and the graph becomes linear. Then, using the same ionic strength, the EMF of the circuit with the analyzed solution is measured and the concentration of the solution is determined from the graph. An example of the definition is shown in Fig. 1.
Fig. 1. Calibration graph for concentration determination by direct potentiometry
Direct potentiometry has important advantages. In the course of measurements, the composition of the analyzed solution does not change. In this case, as a rule, no preliminary separation of the analyte is required. The method can be easily automated, which makes it possible to use it for continuous monitoring of technological processes.
