Lecture 15
1. The concept of electrochemistry. Atoms are made up of charged particles - nuclei (+) and electrons (-), but in general they are electrically neutral. The presence of electric charges may not be noticeable. But sometimes we encounter electrification. We comb our hair, but the hair on the head scatters. Clothes stick to the body, and even crackling electrical discharges are heard. This reveals one universal phenomenon - the occurrence of electric charges at the phase boundaries. The contacting surfaces sometimes spontaneously, sometimes with the expenditure of work (the case of electrification by friction) acquire opposite electric charges. In addition to the obvious examples, surface charges are the cause of electric current in batteries; operation of thermoelements; charges on the membranes of nerve cells ensure the conduction of nerve impulses; charges on nanoparticles stabilize dispersed systems, etc. The very name electricity arose from the ability of amber to electrify (in Greek hlektro - amber.)
The branch of physical chemistry that studies the relationship between chemical and electrical phenomena is called electrochemistry. The main problems of electrochemistry are the occurrence of electrical phenomena in chemical reactions and the occurrence of chemical reactions when exposed to electricity.
Two Italian physicians, Luigi Galvani (1737–1798, Bologna) and Alessandro Volta (1745–1827), are considered the founders of electrochemistry. Root galvano BME has 15 articles.
Galvanocaustics
Galvanization
Galvanotropism, etc.
The name galvanic cell comes from the surname Galvani.
An electrochemical system is a heterogeneous system in which an electric current arises due to a spontaneous reaction (galvanic cell) or a non-spontaneous reaction occurs due to the expenditure of electrical work (electrolyzer). A double action of the system is possible: in a charged state, it acts as a current source, and in the process of charging, as an electrolyzer. Such a device is called a battery. All the curious know this.
An electrochemical reaction is a reaction accompanied by the transfer of charges through the phase boundary.
2. Varieties of surface potentials. Depending on the nature of the contacting phases, several types of surface potentials are distinguished.
– Contact potential occurs at the interface between two metals. In the case of contact between zinc and copper, zinc, which donates electrons more easily, is positively charged, and copper is negatively charged. Excess charges are concentrated on the metal interface, forming a double electric layer.
If such a bimetal is immersed in an acid, then the electrons that reduce H + ions leave the copper surface, and at the same time zinc ions pass from the metal surface into a solution:
– Diffusion potential occurs at the interface between two liquid electrolytes. These can be solutions of one substance with different concentrations, or solutions of different substances, or a solution and a solvent. It is obvious that such a boundary is unstable. Diffusion of ions occurs, which leads to the appearance of a potential difference. Let us assume that the system consists of solutions of potassium chloride and hydrogen chloride of the same concentration of 1 mol/l. Diffusion of K + ions into the HCl solution and counter diffusion of H + ions into the KCl solution take place. The diffusion of hydrogen ions occurs at a higher rate (the direction is shown by a longer arrow), as a result of which there is an excess of positive charge on the side of the KCl solution, and on the side of the acid solution - negative. There is a potential jump φ diff.
– Membrane potential occurs on a membrane characterized by selective permeability with respect to ions of different nature. Imagine solutions of chloride of different concentrations separated by a membrane that allows chloride ions to pass through, but not sodium ions to pass through. Then a certain amount of Cl ions - from a solution with a higher concentration will pass into a solution with a lower concentration. The remaining excess of Na + ions attracts Cl - ions, and stops the transfer through the membrane. A certain potential jump is established, corresponding to the state of equilibrium.
– Electrode potential occurs at the interface between metal (conductor of the 1st kind) – electrolyte (conductor of the 2nd kind). The electrode potential is of the greatest importance in electrochemistry, since the work of chemical current sources is based on this phenomenon. A system consisting of a metal and an electrolyte is called an electrode. Next, we will talk about a number of varieties of electrodes. Now, as an example, consider an ion-metal electrode (electrode of the 1st kind) Cu / Cu 2+ . A plate of metallic copper is immersed in a copper salt solution, such as CuSO 4 . The electrode is conventionally written as Cu | Cu 2+ , where the vertical line means the interface between the metal and the electrolyte.
The concentration of copper ions in the metal and, accordingly, their chemical potential is higher than in solution. Therefore, a certain number of Cu 2+ ions pass from the metal surface into the electrolyte. An excess of electrons remains on the metal. Positively charged ions are attracted to the metal surface from the electrolyte side. There is a double electric layer (DES). As a result of the movement of ions in the solution, a certain number of ions move away from the surface, being in the diffusion layer. The equilibrium value of the potential jump in the double electric layer is established. This potential jump j is called the electrode potential.
Consider what determines the magnitude of the electrode potential. Separation of charges in DES means the cost of electrical work, and the transfer of particles of matter in the form of ions from the metal to the solution is a spontaneous chemical process that overcomes electrical resistance. In a state of equilibrium
W el \u003d -W chem
Let's transform this equation for one mole of metal ions Me z+ (in our example, this is Cu 2+):
where F- Faraday's constant 96485.3383 C mol -1 (according to the latest data). In physical terms, this is a charge of 1 mole of elementary charges. Metal ion activity a(Me z+) in the case of sufficiently dilute solutions can be replaced by the concentration With(Me z+). Dividing the written expression by zF we obtain an equation for calculating the electrode potential:
At a(Me z +) = 1; j \u003d j o \u003d DG ° / zF. We make a substitution:
This equation is called the Nernst equation. According to this equation, the electrode potential depends on the activity (concentration) of electrolyte ions a(Me z+), temperature E and the nature of the system Me / Me z+ , which is implied in the value of the standard electrode potential j o.
Let's take for comparison another electrode, obtained by immersing a zinc plate in a solution of zinc sulfate, denoted by the symbol Zn | Zn 2+:
Zinc is a more active metal than copper. A greater number of Zn 2+ ions pass from the metal surface into the electrolyte, and a greater excess of electrons remains on the metal (ceteris paribus). As a result, it turns out that
j o (Zn 2+)< j о (Cu 2+)
In the activity series known to you, the metals are arranged in order of increasing standard electrode potentials.
3. Galvanic cell
Consider a system composed of two electrodes - copper and zinc. The electrolytes are connected by a curved tube filled with potassium chloride solution. Through such a bridge, ions can move ions. The mobilities of K + and Cl - ions are practically the same, and thus the diffusion potential is minimized. Metals are connected by copper wire. Contact between metals can be opened if necessary. A voltmeter can also be placed in the circuit. This system is an example of a galvanic cell, or a chemical current source. The electrodes in a galvanic cell are called half elements.
With an open contact between metals, equilibrium values of the electrode potentials are established at the metal-electrolyte interfaces. There are no chemical processes in the system, but there is a potential difference between the electrodes
Δφ \u003d j o (Cu 2+) - j o (Zn 2+)
With a closed contact, electrons begin to move from the zinc plate, where their surface concentration is higher and the potential is lower, to the copper plate. The potential decreases on copper and increases on zinc. The balance has been broken. On the copper surface, electrons react with ions in the electrical double layer to form atoms:
Cu 2+ + 2e – = Cu
The potential on copper approaches equilibrium again. On the surface of zinc, the lack of electrons is compensated by the transition of ions to the electric double layer, and from it to the electrolyte:
Zn = Zn2+ + 2e –
The potential on zinc approaches equilibrium again. The processes on the electrodes maintain the potential difference between them, and the flow of electrons does not stop. There is an electric current in the circuit. In the copper half-cell, copper is deposited on the metal surface, and the concentration of Cu 2+ ions in the solution decreases. In the zinc half-cell, the mass of the metal decreases, and the concentration of Zn 2+ ions in the solution simultaneously increases. The galvanic cell works as long as the conductor is closed, and until the initial components are used up - metallic zinc and copper salt. Adding up the reactions taking place on the electrodes, we obtain the total reaction equation in the galvanic cell:
Zn + Cu 2+ \u003d Zn 2+ + Cu, Δ r H= -218.7 kJ; Δr G= -212.6 kJ
If the same reaction is carried out under normal conditions between zinc and copper sulfate, then all the energy is released in the form of heat equal to 218.7 kJ. The reaction in the galvanic cell gives an electrical work of 212.6 kJ, leaving only 6.1 kJ for heat.
The potential difference between the electrodes in a galvanic cell is a measurable quantity called electromotive force, EMF. This is a positive value:
The potentials of the electrodes and the EMF of the element do not depend on the size of the system, but only on the materials and conditions. Therefore, current sources have different sizes depending on the purpose, which we see on commercially available batteries. Electrodes for practical and scientific measurements can be micro-sized, allowing them to be introduced into the cell to measure membrane potentials.
The considered galvanic cell in the standard state has an EMF = 1.1 V.
EMF = |j o (Cu 2+ /Cu) - j o (Zn 2+ /Zn)| = 1.1 V.
The following conditional notation of the galvanic circuit is used:
|
|
Anode is the electrode where oxidation takes place.
The cathode is the electrode at which the reduction takes place.
The potential difference of the electrodes is measured with a voltmeter, but the electrode potential of an individual electrode cannot be experimentally determined. Therefore, the potential of a conditionally selected electrode is taken as zero, and the potentials of all other electrodes are expressed relative to it. A standard hydrogen electrode was taken as the zero electrode. It consists of a platinum plate coated with platinum black and immersed in an acid solution, into which hydrogen is passed under a pressure of 101.3 kPa. The electrode is written as follows:
By convention, jº(Pt, H 2 | H+)=0V.
If the hydrogen electrode in the studied galvanic cell turned out to be the cathode, then the second electrode in this cell is the anode, and its potential is negative. In the opposite case, when the hydrogen electrode turned out to be the anode, the second electrode has a positive potential (cathode). In a series of metal activities, hydrogen is between metals with negative and positive standard potentials. Standard electrode potentials, expressed relative to the hydrogen electrode, are given in the tables. We can find the potentials from the table and calculate the EMF of a copper-zinc galvanic cell:
j o (Cu 2+ / Cu) = +0.34 V; j o (Zn 2+ / Zn) \u003d -0.76 V; EMF = 0.34 V - (-0.76 V) = 1.1 V.
Living systems at all levels of organization are open systems. Therefore, the transport of substances through biological membranes is a necessary condition for life. The transfer of substances through membranes is associated with the processes of cell metabolism, bioenergetic processes, the formation of biopotentials, the generation of a nerve impulse, etc. Violation of the transport of substances through biomembranes leads to various pathologies. Treatment is often associated with the penetration of drugs through cell membranes. The effectiveness of the drug largely depends on the permeability of the membrane for it. The concept of electrochemical potential is of great importance for describing the transport of substances.
chemical potential given substance m to is the value numerically equal to the Gibbs energy per mole of this substance. Mathematically, the chemical potential is defined as the partial derivative of the Gibbs energy, G, with respect to the amount of the k-th substance, at a constant temperature T, pressure P and the amounts of all other substances m l (l¹k).
m k = (¶G/¶m k) P , T , m
For a dilute solution of the concentration of substance C:
m = m0 + RTlnC
where m 0 is the standard chemical potential, numerically equal to the chemical potential of a given substance at its concentration of 1 mol / l in solution.
Electrochemical potential m- a quantity numerically equal to the Gibbs energy G per one mole of a given substance placed in an electric field.
For dilute solutions
m = m o + RTlnC + ZFj (1)
where F = 96500 C/mol is the Faraday number, Z is the charge of the electrolyte ion (in elementary units of charge), j is the potential of the electric field, T [K] is the temperature.
The transport of substances across biological membranes can be divided into two main types: passive and active.
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EE "VSU them. P. M. Masherova UDC 577 (075) BBC 28.071-73 B 63 Published by decision of the Scientific and Methodological Council
Biophysics as a science. Subject of biophysics
Theoretical questions: 1. Subject and tasks of biophysics. Levels of biophysical research; research methods and requirements for them. 2. History
Subjects of the problem of biophysics. History of the development of biophysics
Biophysics is a science that studies the physical and physico-chemical processes that occur in biosystems at different levels of organization and are the basis of physiological acts. Its occurrence was
Methodology of Biophysics
Let's introduce the definition of the following terms: object of biophysical research, biological system, technique, method, methodology. Biological system - a set of interconnected certain arr
Thermodynamics of biological processes
Theoretical questions: 1. Subject and methods of thermodynamics. Basic concepts of thermodynamics. 2. State parameters (intensive and extensive) Function with
I. Prigogine's theorem. Onsager equations
I. Prigogine's postulate is that the total change in the entropy dS of an open system can occur independently or due to exchange processes with the environment (deS
Relationship between entropy and information. The amount of biological information, its value
According to the Boltzmann formula, entropy is defined as the logarithm of the number of microstates possible in a given macroscopic system: S = kB ln W
Biomembranology. Structure and properties of biological membranes
Theoretical questions: 1. The structure of cell membranes. 2. Types of biological membranes. 3. Proteins in the structure of cell membranes, their structure
Main functions of biological membranes
An elementary living system capable of independent existence, development and reproduction is a living cell - the basis of the structure of all animals and plants. The most important conditions for existence
Structure of biological membranes
The first model of the structure of biological membranes was proposed in 1902. It was noticed that substances that are highly soluble in lipids penetrate the membranes best, and on the basis of this, it was made
Phase transitions of lipids in membranes
A substance at different temperatures, pressures, concentrations of chemical components can be in different physical states, such as gaseous, liquid, solid, plasma. Crystalline
Physics of the processes of transport of substances through biological membranes
Theoretical questions: 1. Ways of penetration of substances through cell membranes. 2. Driving forces of membrane transport. 3. Types of transport
Passive transport of substances across the membrane
Passive transport is the transfer of a substance from places with a large value of the electrochemical potential to places with its lower value.
Active transport of substances. Ussing experience
Active transport is the transfer of a substance from places with a lower electrochemical potential to places with a higher value. active transport in the membrane
Electrogenic ion pumps
According to modern concepts, there are ion pumps in biological membranes that operate due to the free energy of ATP hydrolysis - special systems of integral proteins (
Membrane potential
One of the most important functions of a biological membrane is the generation and transfer of biopotentials. This phenomenon underlies the excitability of cells, the regulation of intracellular processes, the functioning of the nervous system,
Propagation of a nerve impulse along an excitable fiber
If an action potential is formed in any part of the excitable membrane, the membrane is depolarized, excitation spreads to other parts of the membrane. Consider the propagation of excitations
Properties of ion channels in cell membranes
The excitable membrane model according to the Hodgkin-Huxley theory assumes a regulated transport of ions across the membrane. However, the direct transition of the ion through the lipid bilayer is very difficult. Therefore led
Types of controlled channels and pumps
1) The “gates” of the channel are connected by a system of “levers” to a dipole, which can turn
Participation of membranes in the transmission of intercellular information
An important property of all living beings is the ability to perceive, process and transmit information using biological membranes. Despite the huge variety of different systems for obtaining
G proteins and second messengers
From the first link - the receptor (R), the signal goes to the so-called N- or G-proteins - membrane proteins that are activated when guanosine triphosphate (GTP) is bound. G proteins are capable of transmitting information
Molecular basis of nerve impulse conduction in nerve fibers and synapses
Nature has created two fundamentally different ways of intercellular signaling. One of them is that messages are transmitted by means of electric current; the second uses molecules, p
Special mechanisms of transport of substances through the biomembrane (endo- and exocytosis)
Transport proteins allow the penetration of many small polar molecules through cell membranes, but they are not able to transport macromolecules, for example, proteins, polynucleo
Biophysics as a science
1. Remizov A.N. Medical and biological physics: textbook. for universities / A.N. Remizov, A.G. Maksina, A.Ya. Potapenko. - M., 2003. - S. 14-17. 2. Biophysics: textbook. for universities / V. F. Antonov [and
Biophysics of membranes. Structure and functions of biological membranes. Dynamics of biomembranes. Model lipid membranes
1. Remizov A.N. Medical and biological physics: textbook. for universities / A.N. Remizov, A.G. Maksina, A.Ya. Potapenko. - M., 2003. - S. 184-190. 2. Rubin A.B. Biophysics of cellular processes. M.
Transport of substances across biological membranes. Bioelectric Potentials
1. Remizov A.N. Medical and biological physics: textbook. for universities / A.N. Remizov, A.G. Maksina, A.Ya. Potapenko. - M., 2003. - S. 191-213. 2. Biophysics: textbook. for universities / V.F. Antonov [
The chemical potential of the neutral component is a function of the temperature, pressure, and chemical composition of the phase in which it resides. The chemical potential is defined as follows:
where G - Gibbs free energy, A - Helmholtz free energy, U - internal energy, I - enthalpy, S - entropy, V - volume, T - temperature, pressure. In measurements, the difference in chemical potentials in various thermodynamic states is always determined, and never the absolute value of the chemical potential in a given state. However, when tabulating the results, it is convenient to assign a certain value to each thermodynamic state. This can be done by assigning an arbitrary value to the chemical potential in some state and determining its value in another state by comparison with the given standard state.
For example, the chemical potentials of pure elements at and pressure of one atmosphere can be taken equal to zero. As soon as the standard state is precisely established and the values of chemical potentials in other states are tabulated, the experimental results become unambiguous. We will return to this issue again when discussing data on electrochemical cells.
The electrochemical potential of an ion was introduced by Guggenheim, and the difference in its values in two phases was defined as the work on the reversible transfer of one gram ion from one phase to another at constant temperature and volume. It depends on the temperature, pressure, chemical composition and electrical state of the phase. It remains to be seen how well these independent variables are defined. Let us consider the following cases in which ion transport may appear:
1. Constant temperature and pressure, the same chemical composition of the phases. Differences between phases can only be electrical in nature.
a) For the transfer of one gram ion of component i from phase to phase a, the work of transfer is equal to
where the difference between the two phases can be characterized by the difference in the electric potentials of both phases (the second relation).
b) For the transfer of component 1 gram ions and component 2 gram ions, provided that
the work done is zero. Such electrically neutral combinations of ions do not depend on the electrical state of the phase, and this fact can be used to verify the above definition of the potential difference. Since for neutral combinations the total work of transfer will be equal to zero, so that equality (13-3) is satisfied, we have
If we apply equality (13-2) to the ionic component 1, then we can combine equalities (13-2) - (13-4) and express the difference
electrochemical potentials of ionic component 2 in the form
Therefore, the electric potential difference defined by equation (13-2) does not depend on which of the two charged components (1 or 2) is used in equation (13-2). In this sense, the electrical potential difference is defined correctly and coincides with the usual idea of the potential difference.
2. Constant temperature and pressure, different chemical compositions of both phases. When transferring neutral combinations of ions that satisfy equality (13-3), there is no dependence on the electrical state of any of the phases. Thus, the work of transfer will depend only on the difference in chemical compositions. The work of transfer of a charged component will still be given by the equality
but it can no longer be expressed simply in terms of electrical potential differences, since the chemical environment of the transferred component will be different in both phases.
It should be noted that a quantitative characteristic or measure of the difference in the electrical states of two phases with different chemical compositions has not yet been established. It is possible (and even reasonable for some computational purposes) to define such an electrical variable, but this is inevitably connected with an element of arbitrariness and is not essential for the consideration of thermodynamic phenomena. Several different ways of making this determination are discussed in Chap. 3. The usual definition of electric potential is based on electrostatics rather than thermodynamics, so the use of electrochemical potentials is more appropriate here.
Of interest is the question of the state of the phase, as well as whether both phases are in the same state. If two phases have different compositions, then the question of whether they are in the same electrical state is irrelevant from the point of view of thermodynamics. On the other hand, if both phases are chemically identical, then it is convenient to quantitatively describe their electrical states in a way that coincides with the usual definition of potential.
Electrode processes. The concept of potential jumps and electromotive force (EMF). Electrochemical circuits, galvanic elements. Standard hydrogen electrode, standard electrode potential. Classification of electrochemical circuits and electrodes.
LECTURE 9
The mutual transformation of electrical and chemical forms of energy occurs in electrochemical systems, including:
ª conductors of the second kind - substances with ionic conductivity (electrolytes).
ª conductors of the first kind - substances with electronic conductivity.
At the interface between two phases, an electric charge is transferred, i.e. there is a potential jump ().
A system consisting of contacting conductors of the first and second kind is called electrode.
The processes occurring at the phase boundary of conductors of the I and II kind in the electrodes are calledelectrode processes .
The electrode is a system consisting of at least two phases.
Let us consider how a potential jump occurs - the electrode potential - at the interface between the metal and the salt solution of this metal. When a metal plate is immersed in a salt solution, some of the metal ions from the surface of the plate can go into the solution adjacent to the surface of the plate. The metal is charged negatively, and the resulting electrostatic forces prevent the further flow of this process. The system is in equilibrium. The reverse process of transition of metal cations from solution to the plate is also possible. These processes lead to the appearance of a double electric layer and a potential jump.
The direction of the process of transfer of metal ions is determined by the ratio of the electrochemical potentials of ions () in the solution phase and the condensed phase. The process continues until the electrochemical potentials in the two phases are equalized.
The electrochemical potential consists of two terms
m chem. - chemical potential that characterizes the chemical response to a change in the environment of a given particle.
m el - the electrical component of the electrochemical potential or the potential energy of the electric field, which characterizes the response to the electric field.
For a certain kind of charged particles (i)
z i is the charge of the ion,
– internal potential, corresponding to the work of transfer of an elementary negative charge from infinity in vacuum deep into the phase.
Equilibrium of an electrochemical system characterized by the equality of electrochemical (rather than chemical) potentials of charged particles in different phases.
In the equilibrium system solution (I) / metal (II), we have:
In a non-equilibrium system, the work of transfer of one mol-equiv. ions from phase I to phase II is
Since then
In equilibrium, taking into account (1), we have:
where is the jump at the interface (absolute electrode potential). Denote
where is the potential jump at the phase boundary at a i = 1 (standard electrode potential).
The standard potential is a value characteristic of a given electrode process. It depends on the temperature and the nature of the electrode. Then for an electrode of type Me Z+ /Me:
A potential jump also occurs at the interface between two solutions, this is the diffusion potential.
In general terms (for any type of electrodes):
or for 298K
It should be remembered that if gases are involved in the electrode reaction, then the activity is assumed to be equal to the partial pressure; for the condensed phase of constant composition, a=1.
Equations (1), (2) are called Nernst equations for the electrode potential. The electric potential difference can be experimentally measured only between two points of the same phase where μ i = const. When an elementary charge moves between two points that are in different phases, in addition to the electric one, work must be performed associated with a change in the chemical environment of the charge. The magnitude of this chemical component of the work cannot be determined, so the absolute value of the electrode potential cannot be measured. Empirically, it is possible to determine only the magnitude of the EMF of a galvanic cell consisting of two electrodes.
Rules for recording electrodes and electrochemical circuits.
Systems consisting of two or more electrodes, connected in a special way and capable of producing electrical work, that is, serving as a source of electrical energy, are called galvanic cells.
Electromotive force of a galvanic cell(EMF GE) is the sum of jumps in electrode potentials at all phase boundaries in the equilibrium condition (the current in the external circuit is zero).
a) The following recording rules are accepted for electrodes: substances in solution are indicated to the left of the vertical bar, substances forming another phase (gas or solid) are indicated to the right.
If one phase contains several substances, then their symbols are separated by commas.
For example,
The equation of the electrode reaction for a separate electrode is written in such a way that substances in the oxidized form and electrons are located on the left, and substances in the reduced form are on the right:
b) When recording galvanic cells, an electrode with a more negative potential is located on the left; the solutions of both electrodes are separated from each other by a vertical dotted line if they are in contact with each other, and by two solid lines if there is a salt bridge between the solutions, for example, a saturated KCl solution, with which the diffusion potential is eliminated. Thus, the positively charged electrode is always indicated on the right, and the negatively charged electrode is always indicated on the left.
Electrode , on which it flows oxidation process, is called anode ().
The electrode on which flows recovery process, is called cathode ().
The reactions at the cathode and anode are called electrode reactions.
The total chemical process occurring in a galvanic cell consists of electrode processes and is expressed by the equation:
If electrode processes and a chemical reaction in a galvanic cell can be carried out in the forward (during the operation of the cell) and reverse (when electric current is passed through the cell) directions, then such electrodes and a galvanic cell are called reversible.
In what follows, only reversible electrodes and galvanic cells will be considered.
Let us consider in more detail the mechanism of the occurrence of galvanic potentials using the example of a hydrogen electrode. The hydrogen electrode belongs to the electrodes of the first kind. Hydrogen electrode is a platinized platinum immersed in an acid solution, for example HC1, and blown with a stream of hydrogen gas. The reaction takes place on the electrode
where H+ q denotes the solvated proton in aqueous solution (ie the hydronium ion H e O +), and e(Pt) is the electron remaining in the platinum. At such an electrode, a hydrogen molecule dissociates to form a hydronium ion in solution and a conduction electron in platinum. In this case, platinum metal is charged negatively, and the solution is positively charged. As a consequence, there is an electrical potential difference between the platinum and the solution. A double layer appears, consisting of negative and positive charges, resembling a flat electric capacitor. The hydrogen electrode is reversible with respect to the cation.
When considering the equilibrium for the given dissociation reaction, it is necessary to take into account that the resulting H + cation, leaving platinum, does work against electric forces. This work is done due to the thermal energy of the solution. It is equal to the stored electrical energy. Therefore, the chemical potential of aquated protons, p(H ^ q), will not be equal to the simple sum p°(Hgq) + R71ntf(Hg q), since the solution has an electric potential different from platinum. Taking into account the work against the forces of the electric field in the process of proton transfer, for p(H * a) we obtain
where cp(Pt) is the electric potential of the platinum electrode; (p) - electric potential of the solution; d(HM - activity of hydrogen cations in solution; F- Faraday number (F= 96485 C/mol); value cf (R)- f (P0 is the galvanic potential at the interface of platinum - solution D^f. The Faraday number arose because chemical potentials are usually calculated per mole, and not per electron. Work against the forces of the electric field P [f (/>) - - f(P0] is performed due to the thermal energy of the solution. It is this work that ensures the charging of the electrodes, the discharge of which, when the external circuit is closed, is accompanied by the production of electrical energy.
A quantity of type p(H + q) is called electrochemical potential. Equating in equilibrium the chemical potentials for substances in the left and right parts of the reaction (16.1), we obtain
where p)
