As a result, a diffusion potential arises. Membrane diffusion potential

outer cell membrane- plasmalemma - basically a lipid layer, which is a dielectric. Since there is a conductive medium on both sides of the membrane, this whole system from the point of view of electrical engineering is capacitor. Thus, alternating current through living tissue can pass both through active resistances and through electrical capacitances formed by numerous membranes. Accordingly, the resistance to the passage of alternating current through the living tissue will be provided by two components: active R - resistance to the movement of charges through the solution, and reactive X - resistance to the current of electric capacitance on membrane structures. The reactance has a polarization nature, and its value is related to the value of the electric capacitance by the formula:

where C is the electric capacitance, w is the circular frequency, f is the frequency of the current.

These two elements can be connected in series or in parallel.

Equivalent electrical circuit of living tissue- this is a connection of elements of an electrical circuit, each of which corresponds to a certain element of the structure of the tissue under study.

If we take into account the basic structures of the fabric, then we get the following scheme:

Figure 2 - Equivalent electrical circuit of living tissue

R c - resistance of the cytoplasm, R mf - intercellular resistance, Cm is the electrical capacitance of the membrane.

Concept of impedance.

Impedance- the total complex resistance of the active and reactive components of the electrical circuit. Its value is related to both components of the formula:

where Z is the impedance, R is the active resistance, X is the reactance.

The value of the impedance with a series connection of reactive and active resistance is expressed by the formula:

The value of the impedance with a parallel connection of reactive and active resistance is written as:

If we analyze how the impedance value changes with a change in R and C, then we will come to the conclusion that with a series and parallel connection of these elements, with an increase in the active resistance R, the impedance increases, and with an increase in C, it decreases and vice versa.

The impedance of living tissue is a labile value, which depends, firstly, on the properties of the measured tissue, namely:

1) on the structure of the tissue (small or large cells, dense or loose intercellular spaces, the degree of lignification of cell membranes);

2) tissue hydration;

4) the state of the membranes.

Secondly, the impedance is affected by the measurement conditions:

1) temperature;

2) frequency of the tested current;

3) electrical circuit diagram.

When membranes are destroyed by various extreme factors, a decrease in the resistance of the plasmalemma, as well as the apoplast, will be observed due to the release of cellular electrolytes into the intercellular space.

The direct current will go mainly through the intercellular spaces and its value will depend on the resistance of the intercellular space.

Figure 3 - Change in capacitance (C) and resistance (R) of the tissue when changing the frequency of alternating current (f)

The preferred path of alternating current depends on the frequency of the applied voltage: with increasing frequency, an increasing proportion of the current will go through the cells (through the membranes), and the complex resistance will decrease. This phenomenon - a decrease in impedance with an increase in the frequency of the testing current - is called conductivity dispersion.

The steepness of the dispersion is characterized by the polarization coefficient. The dispersion of the electrical conductivity of living tissues is the result of polarization at low frequencies, as with direct current. Electrical conductivity is related to polarization - as the frequency increases, polarization phenomena affect less. The dispersion of electrical conductivity, as well as the ability to polarize, is inherent only in living tissues.

If we look at how the polarization coefficient changes during tissue death, then in the first hours it decreases quite strongly, then its fall slows down.

Mammalian liver has a polarization coefficient of 9-10, frog liver 2-3: the higher the metabolic rate, the higher the polarization coefficient.

Practical value.

1. Determination of frost resistance.

2. Definition of water supply.

3. Determination of the psycho-emotional state of a person (device "Tonus")

4. Component of the lie detector - polygraph.

Membrane diffusion potential

Diffusion potential- the electric potential arising from the microscopic separation of charges due to differences in the speed of movement of various ions. A different speed of movement through the membrane is associated with different selective permeability.

For its occurrence, contact of electrolytes with different concentrations and different mobility of anions and cations is necessary. For example, hydrogen and chlorine ions (Fig. 1.). The interface is equally permeable to both ions. The transition of H + and Cl - ions will be carried out in the direction of lower concentration. The mobility of H + when moving through the membrane is much higher than Cl -, because of this, a large concentration of ions will be created on the right side of the electrolyte interface, a potential difference will arise.

The emerging potential (membrane polarization) inhibits further ion transport, so that, in the end, the total current through the membrane will stop.

In plant cells, the main flows of ions are the flows of K + , Na + , Cl - ; they are contained in significant quantities inside and outside the cell.

Taking into account the concentrations of these three ions, their permeability coefficients, it is possible to calculate the value of the membrane potential due to the uneven distribution of these ions. This equation is called the Goldmann equation, or the constant field equation:

Where φM - potential difference, V;

R - gas constant, T - temperature; F - Faraday number;

P - ion permeability;

0 - ion concentration outside the cell;

I is the concentration of the ion inside the cell;

Speaking of a galvanic cell, we considered only the interface between a metal and a solution of its salt. Let us now turn to the interface between solutions of two different electrolytes. In galvanic cells at the boundaries of contact between solutions, so-called diffusion potentials. They also appear at the interface between solutions of the same electrolyte in the case when the concentration of the solutions is not the same. The reason for the potential in such cases is the unequal mobility of ions in solution.

The potential jump at the boundary between solutions of different composition or concentration is called the diffusion potential. The value of the diffusion potential depends, as experience shows, on the difference in the mobilities of the ions, as well as on the difference in the concentrations of the contacting solutions.

The diffusion potential can be determined experimentally as well as calculated. Thus, the value of the diffusion potential (ε D) arising from the contact of solutions of different concentrations of the same electrolyte, which gives singly charged ions, is calculated by the formula

Where l K And l a- mobility of ions of one electrolyte; l K ’ And l a'- mobility of ions of another electrolyte.

With accurate calculations, emf. galvanic circuits, a correction for the value of the diffuse potential must be introduced, including a saturated solution of potassium chloride between electrolyte solutions. Since the mobility of potassium and chlorine ions are approximately the same ( l K + = 64.4 10 -4 and l Cl - \u003d 65.5 10 -4 S m 2), then the diffusion potential caused by such an electrolyte will practically be equal to zero.

Diffusion potentials can also arise in biological objects when, for example, cell membranes are damaged. In this case, the selectivity of their permeability is disturbed and electrolytes begin to diffuse into or out of the cell, depending on the difference in concentrations. As a result of the diffusion of electrolytes, the so-called damage potential, which can reach values ​​of the order of 30-40 millivolts. Moreover, the damaged tissue is charged negatively in relation to the undamaged one.

The diffusion potential can greatly increase if electrolyte solutions of different concentrations are separated by a special membrane that is permeable only for ions of the same sign.

In some cases, the appearance of the membrane potential is due to the fact that the pores of the membrane do not correspond to the sizes of ions of a certain sign. Membrane potentials are very stable and can remain unchanged for a long time. In the tissues of plant and animal organisms, even within a single cell, there are membrane and diffusion potentials due to the chemical and morphological heterogeneity of the intracellular content. Various causes that change the properties of cell microstructures lead to the release and diffusion of ions, i.e., to the appearance of various biopotentials and biocurrents. The role of these biocurrents has not yet been fully studied, but the available experimental data indicate their importance in the processes of self-regulation of a living organism.

concentration circuits.

Galvanic cells are known in which electrical energy is generated not due to a chemical reaction, but due to the difference in the concentrations of solutions into which electrodes from the same metal are immersed. Such galvanic cells are called concentration(Fig. 4.12). An example is a circuit composed of two zinc electrodes immersed in ZnSO 4 solutions of various concentrations:

In this scheme, C 1 and C 2 are the concentrations of electrolytes, and C 1 > C 2 Since the metal of both electrodes is the same, their standard potentials (ε o Zn) are also the same. However, due to the difference in the concentration of metal cations, the equilibrium

in solution in both half-cells is not the same. In a half cell with a less concentrated solution (C 2), the equilibrium is slightly shifted to the right, i.e.

In this case, zinc sends more cations into the solution, which leads to the appearance of some excess electrons on the electrode. Along the external circuit, they move to the second electrode, immersed in a more concentrated solution of zinc sulfate ZnSO 4 .

Thus, an electrode immersed in a solution of a higher concentration (C 1) will be positively charged, and an electrode immersed in a solution of a lower concentration will be negatively charged.

During the operation of the galvanic cell, the concentration of C 1 gradually decreases, the concentration of C 2 increases. The element works until the concentrations at the anode and cathode are equal.

Calculation of emf Let us consider the concentration elements using the zinc concentration element as an example.

Let's assume that the concentration of C 1 \u003d l mol / l, and C 2 \u003d 0.01 mol / l. The activity coefficients of Zn 2+ in solutions of these concentrations are, respectively: f 1 = 0.061, and f 2 = 0.53. To calculate emf. chain, we use equation (4.91). Based on the Nernst equation, we can write

Given that

Equation (4.100) shows that the concentration of ions in a given solution can be easily calculated by making a circuit, one of the electrodes of which is immersed in the solution under study, and the other in a solution with a known activity of the same ions. For this purpose, it is only necessary to measure the emf. chain, which can be easily done with the appropriate setup. Concentration chains are widely used in practice to determine the pH of solutions, the product of the solubility of sparingly soluble compounds, and also to determine the valency of ions and instability constants in the case of complexation.

Reference electrodes.

As already noted, the potentials of the various electrodes are measured with respect to the potential of the normal hydrogen electrode. Along with hydrogen in electrochemistry, another reference electrode is currently widely used - the so-called calomel electrode, which, as experience has shown, has a constant and well reproducible potential.

Thus, a platinum plate or wire that has absorbed molecular hydrogen and immersed in a solution containing hydrogen ions is a hydrogen electrode. Since platinum itself does not participate in the electrode reaction (its role is only that it absorbs hydrogen and, being a conductor, makes it possible for electrons to move from one electrode to another), chemical

the symbol for platinum in the hydrogen electrode scheme is usually enclosed in brackets: (Pt)H 2 |2H+.

There are various designs of vessels for the hydrogen electrode, two of which are shown in Fig. 4.13.

An equilibrium is established on the surface of the hydrogen electrode:

As a result of these processes, a double electric layer is formed at the boundary between platinum and a solution of hydrogen ions, which causes a potential jump. The value of this potential at a given temperature depends on the activity of hydrogen ions in the solution and on the amount of gaseous hydrogen absorbed by platinum, which is proportional to its pressure:

where a H + is the activity of hydrogen ions in solution; P H2 is the pressure under which gaseous hydrogen enters to saturate the electrode. Experience shows that the greater the pressure to saturate platinum with hydrogen, the more negative the potential of the hydrogen electrode takes.

An electrode consisting of platinum saturated with hydrogen at a pressure of 101.325 kPa and immersed in an aqueous solution with a hydrogen ion activity equal to one is called a normal hydrogen electrode.

By international agreement, the potential of the normal hydrogen electrode is conventionally assumed to be zero, and the potentials of all other electrodes are compared with this electrode.

Indeed, at pH 2 - 101.325 kPa, the expression for the potential of the hydrogen electrode will have the form

Equation (4.103) is valid for dilute solutions.

Thus, when a hydrogen electrode is saturated with hydrogen at a pressure of 101.325 kPa, its potential depends only on the concentration (activity) of hydrogen ions in the solution. In this regard, the hydrogen electrode can be used in practice not only as a reference electrode, but also as an indicator electrode, the potential of which is directly dependent on the presence of H + -ions in the solution.

The preparation of the hydrogen electrode presents considerable difficulties. It is not easy to achieve that the pressure of hydrogen gas when platinum is saturated is exactly 101.325 kPa. In addition, gaseous hydrogen must be supplied for saturation at a strictly constant rate, in addition, completely pure hydrogen must be used for saturation, since even very small amounts of impurities, especially H 2 S and H 3 As, “poison” the platinum surface and thereby prevent the establishment of equilibrium H 2 ↔2H + +2e - . Obtaining high purity hydrogen is associated with a significant complication of the equipment and the process itself. Therefore, in practice, a simpler calomel electrode is more often used, which has a stable and perfectly reproducible potential.

Calomel electrode. The inconvenience associated with the practical use of the hydrogen reference electrode led to the need to create other, more convenient reference electrodes, one of which is the calomel electrode.

To prepare the calomel electrode, thoroughly purified mercury is poured onto the bottom of the vessel. The latter is covered with a paste on top, which is obtained by grinding Hg 2 Cl 2 calomel with a few drops of pure mercury in the presence of a solution of potassium chloride KCl. A solution of KCl saturated with calomel is poured over the paste. Metallic mercury added to the paste prevents the calomel from oxidizing to HgCl 2 . A platinum contact is immersed in mercury, from which a copper wire already goes to the terminal. The calomel electrode is schematically written as follows: Hg|Hg 2 Cl 2 , KC1. A comma between Hg 2 Cl 2 and KCl means that there is no interface between these substances, since they are in the same solution.

Consider how the calomel electrode works. Calomel, dissolving in water, dissociates with the formation of Hg + and Cl - ions:

In the presence of potassium chloride, which contains the chloride ion of the same name as calomel, the solubility of calomel decreases. Thus, at a given concentration of KCl and a given temperature, the concentration of Hg+ ions is constant, which, in fact, ensures the necessary stability of the potential of the calomel electrode.

The potential (ε k) in the calomel electrode occurs on the contact surface of metallic mercury with a solution of its ions and can be expressed by the following equation:

Since PR at a constant temperature is a constant value, an increase in the concentration of the chlorine ion can have a significant effect on the concentration of mercury ions, and, consequently, on the potential of the calomel electrode.

From equation (4.105)

Combining the values ​​\u200b\u200bconstant at a given temperature ε 0 H g and W lg (PR) into one value and denoting it through ε o k, we obtain the equation for the potential of the calomel electrode:

Using a calomel electrode, one can experimentally determine the potential of any electrode. So, to determine the potential of a zinc electrode, they make up a galvanic circuit of zinc immersed in a solution of ZnSO 4 and a calomel electrode

Let us assume that the experimentally determined emf. this circuit gives the value E \u003d 1.0103 V. The potential of the calomel electrode ε to \u003d 0.2503 V. The potential of the zinc electrode E \u003d ε to -ε Zn, from where ε Zn \u003d ε K -E, or e Zn \u003d 0.2503- 1.0103 = -0.76 V.

By replacing the zinc electrode with a copper one in a given element, one can determine the potential of copper, etc. In this way, the potentials of almost all electrodes can be determined.

silver chloride electrode. In addition to the calomel electrode, silver chloride electrode is also widely used as a reference electrode in laboratory practice. This electrode is a silver wire or plate soldered to a copper wire and soldered into a glass tube. Silver is electrolytically coated with a layer of silver chloride and placed in a solution of KCl or HCl.

The potential of the silver chloride electrode, as well as the calomel electrode, depends on the concentration (activity) of chloride ions in the solution and is expressed by the equation

4.109

where ε xs is the potential of the silver chloride electrode; e o xs is the normal potential of the silver chloride electrode. Schematically, a silver chloride electrode is written as follows:

The potential of this electrode occurs at the silver-silver chloride solution interface.

In this case, the following electrode reaction takes place:

Due to the extremely low solubility of AgCl, the potential of the silver chloride electrode has a positive sign with respect to the normal hydrogen electrode.

In 1 n. solution of KCl, the potential of the silver chloride electrode on the hydrogen scale at 298 K is 0.2381 V, and in 0.1 n. solution ε x c \u003d 0.2900 V, etc. Compared to the calomel electrode, the silver chloride electrode has a significantly lower temperature coefficient, i.e., its potential changes to a lesser extent with temperature.

indicator electrodes.

To determine the concentration (activity) of various ions in a solution by the electrometric method, in practice, galvanic cells are used, composed of two electrodes - a reference electrode with a stable and well-known potential and an indicator electrode, the potential of which depends on the concentration (activity) of the ion being determined in the solution. Calomel and silver chloride electrodes are most often used as reference electrodes. The hydrogen electrode for this purpose, due to its bulkiness, is used much less frequently. Much more often, this electrode is used as an indicator electrode in determining the activity of hydrogen ions (pH) in the studied solutions.

Let us dwell on the characteristics of indicator electrodes, which have received the widest distribution in recent years in various areas of the national economy.

Quinhydrone electrode. One of the widely used electrodes in practice, the potential of which depends on the activity of hydrogen ions in solution, is the so-called quinhydrone electrode (Fig. 4.16). This electrode compares favorably with the hydrogen electrode in its simplicity and ease of use. It is a platinum wire 1, lowered into a vessel with a test solution 2, in which an excess amount of quinhydrone powder 3 is previously dissolved. Quinhydrone is an equimolecular compound of two organic compounds - quinone C 6 H 4 O 2 and hydroquinone C b H 4 (OH) 2, crystallizing in the form of small dark green needles with a metallic sheen. Quinone is a diketone and hydroquinone is a dihydric alcohol.

The composition of quinhydrone includes one quinone molecule and one hydroquinone molecule C 6 H 4 O 2 ·C 6 H 4 (OH) 2. When preparing a quinhydrone electrode, quinhydrone is always taken in an amount that guarantees the saturation of the solution with it, i.e., it must remain partially undissolved in the precipitate. It should be noted that a saturated solution is obtained by adding a very small pinch of quinhydrone, since its solubility in water is only about 0.005 mol per 1 liter of water.

Consider the theory of the quinhydrone electrode. When dissolved in water, the following processes occur: quinhydrone decomposes into quinone and hydroquinone:

Hydroquinone, being a weak acid, dissociates to an insignificant degree into ions according to the equation

In turn, the resulting quinone ion can be oxidized to quinone under the condition that electrons are removed:

The overall reaction taking place at the cathode is

The equilibrium constant of this reaction

4.109

Due to the fact that in a solution saturated with quinhydrone, the concentrations of quinone and hydroquinone are equal, the concentration of the hydrogen ion is constant.

The quinhydrone electrode can be considered as a hydrogen electrode at a very low hydrogen pressure (approximately 10 -25 MPa). It is assumed that in this case, the reaction proceeds near the electrode

The resulting gaseous hydrogen saturates under this pressure a platinum wire or a plate dipped into the solution. The electrons formed according to reaction (d) are transferred to the platinum, whereby a potential difference arises between the platinum and the adjacent solution. Thus, the potential of this system depends on the ratio of the concentrations of the oxidized and reduced forms and on the concentration of hydrogen ions in the solution. With this in mind, the equation for the electrode potential of the quinhydrone electrode has the form

From formula (4.111) it can be seen that the potential of the quinhydrone electrode is directly dependent on the concentration (more precisely, on the activity) of hydrogen ions in solution. As a result of practical measurements, it was found that the normal potential of the quinhydrone electrode (and n + \u003d 1) is 0.7044 V at 291 K. Therefore, substituting into equation (4.111) instead of ε 0 xg and W their numerical values, we obtain the final potential equation quinhydrone electrode:

4.113

where ε 0 st is the standard potential of the glass electrode.

Studies have shown that, in addition to hydrogen ions, alkali metal ions, which are part of the glass, are also involved in the exchange reaction. At the same time, they are partially replaced by hydrogen ions, and they themselves go into solution. An equilibrium of the ion exchange process is established between the surface layer of the glass and the solution:

where M +, depending on the type of glass, can be lithium, sodium or other alkali metal ions.

The equilibrium condition for this reaction is expressed by the law of mass action:

the exchange constant equation can be rewritten in the following form:

Replacement A n+ / A n st + in the equation of the electrode potential of glass (4.113) by its value from equation (4.117) leads to the following expression:

i.e., the electrode has a hydrogen function and therefore can serve as an indicator electrode in determining pH.

If in solution A n+<<К обм A m +, then

A glass electrode with a metallic function can be used as an indicator electrode to determine the activity of the corresponding alkali metal ions.

Thus, depending on the type of glass (more precisely, on the size of the exchange constant), the glass electrode can have a hydrogen and a metal function.

The stated ideas about the glass electrode underlie the thermodynamic theory of the glass electrode, developed by B. P. Nikolsky (1937) and based on the idea of ​​the existence of ion exchange between glass and solution.

Schematically, a glass electrode with a hydrogen function can be written as follows:

A silver chloride electrode was taken here as the internal electrode.

Due to the fact that in the glass electrode equation (4.121) the value of F in practice turns out to be somewhat less than the theoretical one and ε 0 st depends on the type of glass and even on the method of preparing the electrode (i.e., it is an unstable value), the glass electrode (as well as antimony) before determining the pH of the test solution, pre-calibrate against standard buffer solutions, the pH of which is precisely known.

The advantage of a glass electrode over hydrogen and quinhydrone electrodes is that it makes it possible to determine the pH of a solution of any chemical compound in a fairly wide range of values.

As already mentioned, concentration chains are of great practical importance, since they can be used to determine such important quantities as the activity coefficient and activity of ions, the solubility of sparingly soluble salts, transfer numbers, etc. Such circuits are practically easy to implement, and the relationships connecting the EMF of the concentration circuit with the activities of ions are also simpler than for other circuits. Recall that an electrochemical circuit containing the boundary of two solutions is called a chain with transfer and its diagram is depicted as follows:

Me 1 ½ solution (I) solution (II) ½ Me 2 ½ Me 1,

where the dotted vertical line indicates the existence of a diffusion potential between two solutions, which is a galvanic potential between points that are in phases of different chemical composition, and therefore cannot be accurately measured. The value of the diffusion potential is included in the sum for calculating the EMF of the circuit:

The small value of the EMF of the concentration chain and the need to accurately measure it make it especially important either to completely eliminate or to accurately calculate the diffusion potential that occurs at the interface between two solutions in such a chain. Consider the concentration chain

Me½Me z+ ½Me z+ ½Me

Let's write the Nernst equation for each of the electrodes of this circuit:

for the left

for right

Let us assume that the activity of metal ions at the right electrode is greater than at the left one, i.e.

Then it is obvious that j 2 is more positive than j 1 and the EMF of the concentration circuit (E k) (without diffusion potential) is equal to the potential difference j 2 – j 1 .

Hence,

, (7.84)

then at T = 25 0 С , (7.85)

where and are the molar concentrations of Me z + ions; g 1 and g 2 are the activity coefficients of the Me z + ions, respectively, at the left (1) and right (2) electrodes.

a) Determination of the average ionic activity coefficients of electrolytes in solutions

For the most accurate determination of the activity coefficient, it is necessary to measure the EMF of the concentration circuit without transfer, i.e. when there is no diffusion potential.

Consider an element consisting of a silver chloride electrode immersed in an HCl solution (molality Cm) and a hydrogen electrode:

(–) Pt, H 2 ½HCl½AgCl, Ag (+)

Processes occurring on the electrodes:

(–) H 2 ® 2H + + 2

(+) 2AgCl + 2 ® 2Ag + 2Cl –

current-forming reaction H 2 + 2AgCl ® 2H + + 2Ag + 2Cl -

Nernst equation

for hydrogen electrode: (= 1 atm)

for silver chloride:

It is known that

= (7.86)

Given that the average ionic activity for HCl is

And ,

where C m is the molar concentration of the electrolyte;

g ± is the average ionic activity coefficient of the electrolyte,

we get (7.87)

To calculate g ± according to the EMF measurement data, it is necessary to know the standard potential of the silver chloride electrode, which in this case will also be the standard value of the EMF (E 0), since the standard potential of the hydrogen electrode is 0.

After transforming equation (7.6.10), we obtain

(7.88)

Equation (7.6.88) contains two unknown quantities j 0 and g ± .

According to the Debye-Hückel theory for dilute solutions of 1-1 electrolytes

lng ± = -A ,

where A is the coefficient of the limiting Debye law and, according to the reference data for this case, A = 0.51.

Therefore, the last equation (7.88) can be rewritten in the following form:

(7.89)

To determine, build a dependency graph from and extrapolate to C m = 0 (Fig. 7.19).

Rice. 7.19. Graph for determining E 0 when calculating g ± p-ra Hcl

The segment cut off from the y-axis will be the value j 0 of the silver chloride electrode. Knowing , it is possible to find g ± from the experimental values ​​of E and the known molality for a solution of HCl (C m), using equation (7.6.88):

(7.90)

b) Determination of the solubility product

Knowing the standard potentials makes it easy to calculate the solubility product of a sparingly soluble salt or oxide.

For example, consider AgCl: PR = L AgCl = a Ag + . aCl-

We express L AgCl in terms of standard potentials, according to the electrode reaction

AgCl - AgCl+ ,

going on the electrode II kind

Cl–/AgCl, Ag

And reactions Ag + + Ag,

running on the electrode Ikind with a current-generating reaction

Cl - + Ag + ®AgCl

; ,

because j 1 = j 2 (electrode is the same) after conversion:

(7.91)

= PR

The values ​​​​of standard potentials are taken from the reference book, then it is easy to calculate the PR.

c) Diffusion potential of the concentration chain. Definition of carry numbers

Consider a conventional concentration chain using a salt bridge in order to eliminate the diffusion potential

(–) Ag½AgNO 3 ½AgNO 3 ½Ag (+)

The emf of such a circuit without taking into account the diffusion potential is:

(7.92)

Consider the same circuit without the salt bridge:

(–) Ag½AgNO 3 AgNO 3 ½Ag (+)

EMF of the concentration circuit, taking into account the diffusion potential:

E KD \u003d E K + j D (7.93)

Let 1 faraday of electricity pass through the solution. Each type of ion carries a portion of this amount of electricity equal to its transfer number (t+ or t-). The amount of electricity that the cations and anions will carry will be equal to t +. F and t - . F respectively. At the interface between two AgNO 3 solutions of different activity, a diffusion potential (j D) arises. Cations and anions, overcoming (j D), perform electrical work.

Based on 1 mol:

DG \u003d -W el \u003d - zFj D \u003d - Fj d (7.94)

In the absence of a diffusion potential, the ions perform only chemical work when crossing the boundary of the solution. In this case, the isobaric potential of the system changes:

Similarly for the second solution:

Then according to equation (7.6.18)

(7.99)

We transform the expression (7.99), taking into account the expression (7.94):

(7.100)

(7.101)

Transfer numbers (t + and t -) can be expressed in terms of ionic conductivities:

;

Then (7.102)

If l - > l + , then j d > 0 (diffusion potential helps the movement of ions).

If l + > l – , then j d< 0 (диффузионный потенциал препятствует движению ионов, уменьшает ЭДС). Если l + = l – , то j д = 0.

If in equation (7.99) we substitute the value j d from equation (7.101), then we get

E KD \u003d E K + E K (t - - t +), (7.103)

after conversion:

E KD \u003d E K + (1 + t - - t +) (7.104)

It is known that t + + t – = 1; then t + = 1 – t – and the expression

(7.105)

If we express E KD in terms of conductivities, we get:

E KD = (7.106)

Measuring E KD experimentally, one can determine the transfer numbers of ions, their mobilities and ionic conductivities. This method is much simpler and more convenient than the Gettorf method.

Thus, using the experimental determination of various physicochemical quantities, it is possible to carry out quantitative calculations to determine the EMF of the system.

Using concentration chains, one can determine the solubility of sparingly soluble salts in electrolyte solutions, the activity coefficient and diffusion potential.

Electrochemical kinetics

If electrochemical thermodynamics is concerned with the study of equilibria at the electrode-solution boundary, then the measurement of the rates of processes at this boundary and the elucidation of the patterns to which they obey is the object of study of the kinetics of electrode processes or electrochemical kinetics.

Electrolysis

Faraday's laws

Since the passage of electric current through electrochemical systems is associated with a chemical transformation, there must be a certain relationship between the amount of electricity and the amount of reacted substances. This dependence was discovered by Faraday (1833-1834) and was reflected in the first quantitative laws of electrochemistry, called Faraday's laws.

Electrolysis – the occurrence of chemical transformations in an electrochemical system when an electric current is passed through it from an external source. By electrolysis, it is possible to carry out processes, the spontaneous occurrence of which is impossible according to the laws of thermodynamics. For example, the decomposition of HCl (1M) into elements is accompanied by an increase in the Gibbs energy of 131.26 kJ/mol. However, under the action of an electric current, this process can easily be carried out.

Faraday's first law.

The amount of the substance reacted on the electrodes is proportional to the strength of the current passing through the system and the time of its passage.

Mathematically expressed:

Dm = keI t = keq, (7.107)

where Dm is the amount of the reacted substance;

ke is a certain coefficient of proportionality;

q is the amount of electricity equal to the product of the force

current I for time t.

If q = It = 1, then Dm = k e, i.e. the coefficient k e is the amount of substance that reacts when a unit of electricity flows. The coefficient of proportionality k e is called electro-chemical equivalent . Since different values ​​\u200b\u200bare chosen as the unit of the amount of electricity (1 C \u003d 1A. s; 1F \u003d 26.8 A. h \u003d 96500 K), then for the same reaction one should distinguish between electrochemical equivalents related to these three units : A. with k e, A. h k e and F k e.

Faraday's second law.

During the electrochemical decomposition of various electrolytes by the same amount of electricity, the content of the products of the electrochemical reaction obtained on the electrodes is proportional to their chemical equivalents.

According to Faraday's second law, with a constant amount of electricity passed, the masses of the reacted substances are related to each other as their chemical equivalents A.

. (7.108)

If we choose a faraday as the unit of electricity, then

Dm 1 \u003d F k e 1; Dm 2 = F k e 2 and Dm 3 = F k e 3 , (7.109)

(7.110)

The last equation allows you to combine both Faraday's laws in the form of one general law, according to which the amount of electricity equal to one faraday (1F or 96500 C, or 26.8 Ah) always changes electrochemically one gram equivalent of any substance, regardless of its nature .

Faraday's laws are applicable not only to aqueous and non-aqueous salt solutions at ordinary temperature, but are also valid in the case of high-temperature electrolysis of molten salts.

Substance output by current

Faraday's laws are the most general and precise quantitative laws of electrochemistry. However, in most cases, a smaller amount of a given substance undergoes an electrochemical change than that calculated on the basis of Faraday's laws. So, for example, if a current is passed through an acidified solution of zinc sulfate, then the passage of 1F electricity usually releases not 1 g-eq of zinc, but approximately 0.6 g-eq. If chloride solutions are subjected to electrolysis, then as a result of passing 1F electricity, not one, but a little more than 0.8 g-eq of chlorine gas is formed. Such deviations from Faraday's laws are associated with the occurrence of side electrochemical processes. In the first of the analyzed examples, two reactions actually take place on the cathode:

zinc precipitation reaction

Zn 2+ + 2 = Zn

and the reaction of formation of gaseous hydrogen

2H + + 2 \u003d H 2

The results obtained during the release of chlorine will also not contradict Faraday's laws, if we take into account that part of the current is spent on the formation of oxygen and, in addition, the chlorine released at the anode can partially again pass into solution due to secondary chemical reactions, for example, according to the equation

Cl 2 + H 2 O \u003d HCl + HClO

To take into account the influence of parallel, side and secondary reactions, the concept was introduced current output R . The current output is the fraction of the amount of electricity flowing that is accounted for by a given electrode reaction.

R = (7.111)

or in percentage

R = . 100 %, (7.112)

where q i is the amount of electricity consumed for this reaction;

Sq i - the total amount of electricity passed.

Thus, in the first of the examples, the current efficiency of zinc is 60%, and that of hydrogen is 40%. Often the expression for the current output is written in a different form:

R = . 100 %, (7.113)

where q p and q p are the amount of electricity, respectively, calculated according to the Faraday law and actually spent on the electrochemical transformation of a given amount of substance.

You can also define the current efficiency as the ratio of the amount of the changed substance Dm p to that which would have to react if all the current was spent only on this reaction Dm p:

R = . 100 %. (7.114)

If only one of several possible processes is desired, then its current output must be as high as possible. There are systems in which all the current is spent on only one electrochemical reaction. Such electrochemical systems are used to measure the amount of electricity passed and are called coulometers, or coulometers.

Diffusion potential is the potential difference that occurs at the interface between two unequal electrolyte solutions. It is due to the diffusion of ions across the interface and causes slower diffusing ions to slow down and slower diffusing ions to accelerate, be they cations or anions. Thus, soon an equilibrium potential is established at the interface and reaches a constant value , which depends on the transport number of ions, their charge and electrolyte concentration.

E. d. s. concentration chain (see)

expressed by the equation

is the sum of two electrode potentials and the diffusion potential The algebraic sum of two electrode potentials is theoretically equal to

hence,

Let's assume that then

or, in general, for an electrode reversible with respect to the cation,

and for an electrode reversible with respect to the anion,

For electrodes reversible with respect to the cation, when if then is positive and is added to the sum of the electrode potentials; if then is negative and e. d.s. element in this case is less than the sum of the electrode potentials. Attempts were made to eliminate the diffusion potential by introducing a salt bridge containing a concentrated solution and other salts for which . In this case, since the solution is concentrated, diffusion is due to the electrolyte of the salt bridge itself, and instead of the diffusion potential of the cell, we have two diffusion potentials acting in opposite directions and having a value close to zero. In this way, it is possible to reduce diffusion potentials, but it is almost impossible to completely eliminate them.

The practically measured exact EMF value usually differs from the theoretically calculated one using the Nernst equation by some small value, which is associated with potential differences that occur at the point of contact of various metals (“contact potential”) and various solutions (“diffusion potential”).

Contact potential(more precisely, the contact potential difference) is associated with a different value of the electron work function for each metal. At each given temperature, it is constant for a given combination of metal conductors of a galvanic cell and is included in the EMF of the cell as a constant term.

Diffusion potential occurs at the boundary between solutions of different electrolytes or identical electrolytes with different concentrations. Its occurrence is explained by the different rate of diffusion of ions from one solution to another. The diffusion of ions is due to the different values ​​of the chemical potential of the ions in each of the half-cells. Moreover, its speed changes in time due to a continuous change in concentration, and hence m . Therefore, the diffusion potential has, as a rule, an uncertain value, since it is influenced by many factors, including temperature.

In normal practical work, the value of the contact potential is minimized by using mounting conductors made of the same material (usually copper), and the diffusion potential is minimized by using special devices called electrolytic(saline)bridges or electrolytic keys. They are tubes of various configurations (sometimes equipped with taps) filled with concentrated solutions of neutral salts. For these salts, the mobility of the cation and anion should be approximately equal to each other (for example, KCl, NH 4 NO 3, etc.). In the simplest case, an electrolytic bridge can be made from a strip of filter paper or an asbestos flagellum moistened with a KCl solution. When using electrolytes based on non-aqueous solvents, rubidium chloride is usually used as a neutral salt.

The minimum values ​​of the contact and diffuse potentials achieved as a result of the measures taken are usually neglected. However, in electrochemical measurements requiring high accuracy, the contact and diffusion potentials should be taken into account.

The fact that a given galvanic cell has an electrolytic bridge is displayed by a double vertical line in its formula, which stands at the point of contact between two electrolytes. If there is no electrolytic bridge, then a single line is put in the formula.