Ministry of Education of the Russian Federation Tomsk Polytechnic University ________________________________________________________________________________ N. A. Kolpakova, V. A. Kolpakov, S. V. Romanenko PHYSICAL CHEMISTRY Textbook Part I Tomsk 2004 UDC 541.1 Physical chemistry. Textbook / N.A. Kolpakova, V.A. Kolpakov, S.V. Romanenko. - Tomsk: Ed. TPU, 2004. - Part 1. - 168 p. The textbook covers the following sections of "Physical Chemistry": the basic laws of thermodynamics, chemical and phase equilibrium, thermodynamics of non-electrolyte solutions. The manual was prepared at the Department of Physical and Analytical Chemistry of TPU and is intended for students of correspondence courses in chemical specialties. Published by order of the Editorial and Publishing Council of Tomsk Polytechnic University Reviewers: Kurina L.N. – Prof. Department of Physical Chemistry, TSU, Doctor of Chem. sciences; Buinovsky A.S. - Head. cafe Chemistry TPU STU, doctor of chem. Sciences. © Tomsk Polytechnic University, 2004 © Authors, 2004 CHAPTER 1 . INTRODUCTION TO PHYSICAL CHEMISTRY 1.1. BRIEF HISTORICAL OUTLINE OF THE DEVELOPMENT OF PHYSICAL CHEMISTRY The name and definition of the content of physical chemistry was first given by M.V. Lomonosov (1752): “Physical chemistry is a science that, on the basis of the positions and experiments of physical scientists, must explain the reason for what happens through chemical operations in complex bodies” . The teaching of physical chemistry in Russia as an independent science was introduced by prof. N. N. Beketov in 1860 at Kharkov University. Lomonosov's most important theoretical and experimental studies led him to discoveries that have not lost their significance even now. Lomonosov came close to the correct definition of the principle of conservation of matter and motion, the kinetic nature of heat, and also noted the impossibility of a spontaneous transfer of heat from a colder body to a warmer one, which is currently one of the formulations of the second law of thermodynamics. Over the next century, research was carried out, on the basis of which many important discoveries and generalizations were made. K. V. Scheele in Sweden (1773) and Fontana in France (1777) discovered the adsorption of gases; T. E. Lovits in Russia (1785) discovered adsorption from solutions. A. L. Lavoisier and P. S. Laplace in France (1779–1784) studied the heat capacities of substances and the heat effects of reactions. At the beginning of the XIX century. G. Davy in England and L. J. Tenard in France discovered catalytic reactions, and J. J. Berzelius in Sweden (1835) further developed the idea of ​​catalysis. The foundations of electrochemistry were laid by research on galvanic cells, electrolysis, and current transfer in electrolytes. Galvani and A. Volta in Italy created in 1799 a galvanic cell. VV Petrov in Russia (1802) discovered the phenomenon of an electric arc. T. Grotgus in Russia in 1805 laid the foundations for the theory of electrolysis. In 1800, G. Davy advanced the electrochemical theory of the interaction of substances: he widely used electrolysis for chemical research. M. Faraday, a student of Davy, in 1833-1834 formulated the quantitative laws of electrolysis. B. S. Jacobi in Russia, solving the problems of the practical use of the electrolysis process, discovered in 1836 galvanoplasty. In the first half of the XIX century. thanks to the works of D. Dalton in England (1801–1803), J. L. Gay-Lussac in France (1802) and A. Avogadro in Italy (1811), who discovered the most important laws of the gaseous state, atomistic ideas were widely developed. The works of G. I. Hess (1802–1856) on thermochemistry belong to the same period. C. Guldberg and P. Waage in Norway (1864–1867), J. W. Gibbs in the USA (1873–1878) developed the thermodynamic doctrine of chemical equilibrium, and A. L. Le Chatelier in France (1884) discovered the general principle of displacement equilibrium under changing external conditions. In the works of the Dutch chemist J. H. van't Hoff, the thermodynamic theory of chemical equilibrium was developed. He also developed the quantitative theory of dilute solutions (1885–1889). The transfer of electricity in solutions was studied in Germany by I. V. Gittorf and F. V. G. Kohlrausch. The Swedish scientist S. A. Arrhenius developed in 1883–1887. theory of electrolytic dissociation. A. M. Butlerov, who created the theory of the structure of organic compounds, left a deep mark on the development of physical chemistry. The great Russian chemist D. I. Mendeleev (1834–1907) discovered the existence of a critical temperature (1860), derived the general equation of state for gases (1874) and developed the chemical theory of solutions (1887). D. P. Konovalov (1889), a student of Mendeleev, is one of the founders of the theory of solutions. At the end of the XIX century. a number of major discoveries were made in the field of the doctrine of the structure of matter, which proved the complexity of the structure of the atom and played a huge role in the development of physical chemistry. These include the discoveries of the electron by J. B. Perrin (1895) and J. Thomson (1897), the quantum nature of light by R. Planck (1900), the existence of light pressure by P. N. Lebedev (1899), the study (since 1898 of ) phenomena of radioactivity P. Curie and M. Sklodowska-Curie. By the beginning of the XX century. physical chemistry was defined as the science that studies the structure of matter, chemical thermodynamics, including thermochemistry and the theory of equilibrium, solutions, chemical kinetics and electrochemistry. New theoretical methods were applied, and studies of the structure of atoms, molecules, and crystals came to the fore. The doctrine of the structure of matter, especially the structure of atoms and molecules, developed most rapidly in the 20th century. A major achievement in this area was the nuclear theory of the atom, proposed by E. Rutherford (1911) and developed in the first quantitative theory of the hydrogen atom, developed by the Danish physicist N. Bohr (1913). The study of the nature of the chemical bond and the structure of molecules developed in parallel with the study of the structure of the atom. By the early 1920s, W. Kossel and G. N. Lewis had developed the fundamentals of the electronic theory of chemical bonding. VG Geitler and F. London (1927) developed the quantum-mechanical theory of chemical bonding. Based on the largest discoveries of physics in the field of atomic structure and using the theoretical methods of quantum mechanics and statistical physics, as well as new experimental methods, such as X-ray analysis, spectroscopy, mass spectroscopy, magnetic methods, the method of labeled atoms and others , physicists and physical chemists have made great strides in studying the structure of molecules and crystals and in understanding the nature of the chemical bond. The theory of the rates of chemical reactions, i.e., chemical kinetics, has been greatly developed, and is now associated specifically with studies of the structure of molecules and the strength of bonds between atoms in a molecule. New branches of physical chemistry have arisen and are successfully developing: magnetochemistry, radiation chemistry, physical chemistry of high polymers, physical chemistry of silicates, gas electrochemistry, etc. Like other sciences, physical chemistry and its individual branches arose or began to develop especially successfully in periods when one or another practical need necessitated the rapid development of some branch of industry, and for this development a solid theoretical foundation was required. Here it is necessary to note the major studies of N. S. Kurnakov on physicochemical analysis, the work in the field of electrochemistry by A. N. Frumkin, the creation of the theory of chain reactions by N. N. Semenov, and the development of the theory of heterogeneous catalysis by A. A. Balandin. Physical chemistry plays a leading role in solving numerous problems facing chemical science and practice. At present, physical chemistry is an independent discipline with its own research methods and is the theoretical basis for applied chemical engineering disciplines. 1.2. SUBJECT AND OBJECTIVES OF PHYSICAL CHEMISTRY Physical chemistry is the science of regularities of chemical processes and physical phenomena. The main task of physical chemistry is the study and explanation of the main regularities that determine the direction of chemical processes, their speed, the influence of the medium, impurities, radiation, and the conditions for obtaining the maximum yield of a useful product. The study of physical chemistry makes it possible to understand the laws of chemistry, as well as to predict and control chemical phenomena. Modern physical chemistry makes it possible to solve the problems of efficient production control, intensification and automation of production processes. It serves as the theoretical foundation of chemical technology. Such important production processes in chemical technology as the synthesis and oxidation of ammonia, the contact production of sulfuric acid, the production of ethanol from natural gas, oil cracking, and many others are based on the results of physicochemical studies of the reactions underlying these processes. 5 processes. Without physical chemistry, it is impossible to solve the problem of creating substances with desired properties, develop new current sources, and many other issues of efficient production. Therefore, knowledge of physical chemistry for future process engineers opens up great opportunities for solving various problems encountered in the practical activities of an engineer at factories and research institutes. The name of the science - "physical chemistry" - reflects both the history of its emergence at the junction of two sciences - physics and chemistry, as well as the fact that it widely uses the theoretical laws and experimental methods of physics in the study of chemical phenomena. 1.3. CLASSIFICATION OF METHODS OF PHYSICAL CHEMISTRY Several theoretical methods are used in physical chemistry.  The quantum chemical method uses the properties of elementary particles to describe chemical transformations. Using the laws of quantum mechanics, the properties and reactivity of molecules are described, as well as the nature of the chemical bond based on the properties of the elementary particles that make up the molecules.  The thermodynamic (phenomenological) method is based on several laws (postulates), which are a generalization of experimental data. It makes it possible, on their basis, to find out the energy properties of the system, to predict the course of the chemical process and its result by the moment of equilibrium.  The quantum-statistical method explains the properties of substances on the basis of the properties of the molecules that make up these substances.  The kinetic method allows you to establish the mechanism and create a theory of chemical processes by studying the change in the rate of chemical reactions from various factors. Physical chemistry is characterized by the widespread use of mathematics, which not only makes it possible to most accurately express theoretical laws, but is also a necessary tool for establishing them. 6 CHAPTER 2 . BASIC LAWS OF THERMODYNAMICS The word "thermodynamics" comes from the Greek therme - heat and dynamis - force. Thermodynamics is the science of the transformation of various types of energy from one into another. Chemical thermodynamics studies the transformation of various types of energy occurring during the course of chemical reactions. 2.1. BASIC CONCEPTS OF CHEMICAL THERMODYNAMICS A system is a separate body or a group of bodies interacting and separated from the environment by a real or imaginary shell (boundary). An open system is a system that exchanges substances (mass) and energy (for example, heat) with the external environment. An isolated system (or closed system) is a system that does not exchange heat and work with the environment. The energy and volume of an isolated system are constant in time. An example of such a system is, for example, a thermos. If the boundary does not pass heat, then the process occurring in the system is called adiabatic. When a system exchanges heat and work with the environment, changes occur both in the system and in the environment. Thermodynamic systems can be homogeneous or heterogeneous. If there are no interfaces inside the system separating parts of the system with different composition or structure, then this system is called homogeneous. Accordingly, a system consisting of various parts differing in structure or chemical composition is called heterogeneous. These parts are called phases. Thus, a phase is a part of a heterogeneous system limited by the interface and characterized by the same physical and chemical properties at all points. Each system consists of one or more substances. Individual chemicals that can be isolated from the system and exist outside of it on their own as a separate phase are called constituent substances of the system. For example, in a glass there is water in which a platinum plate is lowered. Above the glass is a mixture of gases: oxygen, hydrogen and nitrogen. This system is three-phase, it contains five constituent substances. 7 The thermodynamic state of a system is a set of values ​​of independent variables (system parameters) that determine its properties. Any property of a system can be called a thermodynamic state parameter if it is considered as one of the independent variables that determine the state of the system. Thermodynamics considers matter as a continuous medium and uses for research such thermodynamic parameters that are the result of the action of a large number of particles (macroparameters). For example, the macroparameters of a chemical reaction that proceeds even under “normal conditions” are temperature, pressure, volume, concentration, strength of gravitational, magnetic, electric and electromagnetic fields, etc. “Normal conditions” is a temperature of 20– 25 °C, atmospheric pressure, i.e. about 101 kPa, acceleration of gravity - on average about 9.8 m/s2, magnetic field strength - on average about 40 A/m, electric field strength - on average about 130 V/m, visible light illumination - about 500 lux on average. To characterize the thermodynamic state of a system, it is necessary to know not all properties, but only the smallest number of them, the so-called independent parameters of the system. As a rule, when describing a chemical process occurring on the Earth, we do not indicate the characteristics of the field, since they are constant and therefore do not affect the composition and yield of the reaction products. If the chemical process is carried out under conditions of strong magnetic or electric fields, or under intense irradiation with ultraviolet, X-rays, or even visible light, then the field parameters will have a significant effect on the composition and yield of the reaction products. In this case, the field parameters must be specified. Thermodynamic parameters are divided into extensive and intensive. Quantities proportional to the mass (or amount of substance) of the considered working fluid or thermodynamic system are called extensive, they are volume, internal energy, enthalpy, etc. Intensive quantities do not depend on the mass of the thermodynamic system. These are, for example, temperature and pressure. Pressure is a physical quantity equal to the ratio of a force uniformly distributed over the surface of a body to the surface area located perpendicular to the force: p \u003d S The unit of pressure in SI - pascal (Pa) is the pressure caused by a force of 1 N, uniformly distributed on a surface of 1 m2 located perpendicular to the direction of force: 1 N/m2 = 1 Pa. In practice, multiple and sub-multiple units of pressure are used: kilopascal 8 (103 Pa = 1 kPa); megapascal (106 Pa = 1 MPa); hectapascal (102 Pa = 1 hPa), as well as an off-system unit - bar (1 bar = 105 Pa). According to the conclusions of the molecular-kinetic theory, the pressure of a gas is the result of impacts of randomly continuously moving molecules against the vessel wall. The simplest relationships between the parameters and the behavior of molecules were obtained for an ideal gas. An ideal gas is a gas consisting of elastic molecules, between which there are no interaction forces, which have a negligibly small volume in comparison with the volume occupied by the gas. Any real gas at a relatively low pressure (close to atmospheric) behaves practically like an ideal one (strictly at p → 0). The equation of state of an ideal gas - the Mendeleev - Clapeyron equation has the form: pV = nRT, where p is the gas pressure, Pa; V - volume, m3; n is the amount of gas, mol; R is the universal gas constant equal to 8.314 J/(mol K); T is the absolute temperature, K. The temperature characterizes the thermal state of the system. Experimentally, the concepts of a warmer and colder body can be established, but the temperature cannot be measured directly. It is determined from the numerical values ​​of other physical parameters that depend on temperature, which is the basis for constructing empirical temperature scales. Various physical quantities can serve as such parameters (thermometric parameters). Among them are the volume of a body at constant pressure, pressure at a constant volume, electrical conductivity, thermoelectromotive force, geometric parameters of bodies, brightness of the glow, etc. A device for measuring temperature is called a thermometer. To build any empirical temperature scale, three assumptions are used: 1) the size of a degree is set by choosing the numerical value of ∆T between two reference temperature points - temperature standards; 2) the position of the temperature zero in empirical scales is arbitrary; 3) it is assumed that the thermometric function is linear in a given temperature range. The phase transitions of pure substances are used as reference points. For example, for the empirical Celsius scale, the melting and boiling points of water at atmospheric pressure (0 and 100 degrees, respectively) are taken as reference points. The interval between these temperatures is divided into one hundred equal parts (degrees Celsius - °C). Although an objective temperature scale can be constructed using any theoretically defined thermometric function, thermodynamics uses the ideal gas equation of state as such a function. The gas thermometer makes it possible to carry out the most accurate (close to the absolute temperature scale - the Kelvin scale) temperature measurements. However, determining the temperature on the scale of a gas thermometer is a rather difficult job, which is carried out only to establish the absolute temperatures of a few reference points of phase transitions, taken as reference ones. Intermediate temperatures are usually determined by empirical thermometric methods. The International Practical Temperature Scale (IPTS), adopted in 1954, is the most accurate approximation to the absolute temperature scale at the present stage. In contrast to empirical scales, the MPSH uses one experimental reference temperature point. The temperature of the triple point of water (when ice, water and water vapor are in equilibrium at the same time) was used as such a point. The temperature of the triple point of water is taken in the IPTS as 273.16 K (exactly). At atmospheric pressure, ice melts 0.01° lower. The reference point on the Celsius scale - 0 °C - corresponds to 273.15 K. The numerical value of temperatures for all other reference points (except for the triple point of water) is continuously refined as the accuracy of working with a gas thermometer increases. In 1968, twelve reference points were recommended as reference temperature points, spanning the range from the triple point of hydrogen to the melting point of gold. Currently, Celsius temperature (t) is expressed as a relationship with absolute temperature (T), which is: T = 273.15 + t. The properties of a system that can be unambiguously expressed as functions of temperature, pressure, and concentration of the substances that make up the system are called thermodynamic functions. For example, heat capacity, internal energy, entropy, etc. If the change in the thermodynamic function depends only on the initial and final state of the system and does not depend on the path of the process, then such a function is called the state function of the system. A thermodynamic process is any change in a system associated with a change in at least one of the thermodynamic parameters. A circular process or cycle is a process in which a thermodynamic system, having left some initial state and undergoing a series of changes, returns to the same state; in this process, the change in any state parameter is equal to zero. 10

The classification of sciences is based on the classification of the forms of motion of matter and their interrelation and difference. Therefore, in order to outline the boundaries of physical chemistry with a number of branches of physics and chemistry, one should consider the connection and difference between the chemical and physical forms of motion.

For the chemical form of motion, i.e., for a chemical process, a change in the number and arrangement of atoms in the molecule of the reacting substances is characteristic. Among many physical forms of movement (electromagnetic field, movement and transformations of elementary particles, physics of atomic nuclei, etc.) has a particularly close connection with chemical processes intramolecular form of movement (vibrations in a molecule, its electronic excitation and ionization). The simplest chemical process - an elementary act of thermal dissociation of a molecule takes place with an increase in the intensity (amplitude and energy) of vibrations in a molecule, especially vibrations of nuclei along the valence bond between them. Achieving a known critical value of the energy of vibrations in the direction of a certain bond in the molecule leads to the breaking of this bond and the dissociation of the molecule into two parts.

More complex reactions involving several (usually two) molecules can be considered as a combination of two molecules during their collision into an unstable and short-lived complex (the so-called active complex) and the rapid destruction of this complex into new molecules, since this complex turns out to be unstable during internal vibrations. through certain connections.

Thus, an elementary chemical act is a special, critical point of the oscillatory motion of molecules. The latter in itself cannot be considered a chemical movement, but it is the basis for primary chemical processes.

For the chemical transformation of significant masses of matter, i.e., many molecules, the collision of molecules and the exchange of energies between them (the transfer of the energy of the movement of molecules of the reaction products to the molecules of the initial substances by means of collisions) are necessary. Thus, the real chemical process is closely related to the second physical form of movement - chaotic motion of molecules of macroscopic bodies, which is often called thermal motion.

The reciprocal relations of the chemical form of motion with the two physical forms of motion have been outlined above briefly and in the most general terms. Obviously, there are the same connections of the chemical process with the radiation of the motion of an electromagnetic field, with the ionization of atoms and molecules (electrochemistry), etc.

The structure of matter . This section includes the structure of atoms, the structure of molecules and the doctrine of states of aggregation.

The doctrine of the structure of atoms has more to do with physics than with physical chemistry. This doctrine is the basis for studying the structure of molecules.

In the study of the structure of molecules, the geometry of molecules, intramolecular movements and forces that bind atoms in a molecule are studied. In experimental studies of the structure of molecules, the method of molecular spectroscopy (including radio spectroscopy) has received the greatest use; electrical, X-ray, magnetic, and other methods are also widely used.

In the theory of aggregate states, interactions of molecules in gases, liquids, and crystals are considered, as well as the properties of substances in various aggregate states. This branch of science, which is very important for physical chemistry, can be considered a part of physics (molecular physics).

The entire section on the structure of matter can also be considered as part of physics.

Chemical thermodynamics . In this section, on the basis of the laws of general thermodynamics, the laws of chemical equilibrium and the doctrine of phase equilibria, which is usually called the rule of phases, are expounded. Part of chemical thermodynamics is thermochemistry, in which the thermal effects of chemical reactions are considered.

The doctrine of solutions aims to explain and predict the properties of solutions (homogeneous mixtures of several substances) on the basis of the properties of the substances that make up the solution.

The solution of this problem requires the construction of a general theory of the interaction of heterogeneous molecules, i.e., the solution of the main problem, molecular physics. For the development of a general theory and particular generalizations, the molecular structure of solutions and their various properties depending on the composition are studied.

The doctrine of surface phenomena . Various properties of surface layers of solids and liquids (interfaces between phases) are studied; one of the main phenomena studied in surface layers is adsorption(accumulation of substances in the surface layer).

In systems where the interfaces between liquid, solid and gaseous phases are highly developed (colloidal solutions, emulsions, mists, smokes), the properties of the surface layers become of primary importance and determine many of the unique properties of the entire system as a whole. Such microheterogeneous systems are being studied colloid chemistry, which is a major independent section of physical chemistry and an independent academic discipline in higher chemical educational institutions.

Electrochemistry. The interaction of electrical phenomena and chemical reactions (electrolysis, chemical sources of electric current, the theory of electrosynthesis) is studied. Electrochemistry usually includes the study of the properties of electrolyte solutions, which with equal right can be attributed to the study of solutions.

Chemical kinetics and catalysis . We study the rate of chemical reactions, the dependence of the reaction rate on external conditions (pressure, temperature, electric discharge, etc.), the relationship of the reaction rate with the structure and energy states of molecules, the effect on the reaction rate of substances that are not involved in the stoichiometric reaction equation (catalysis).

Photochemistry. The interaction of radiation and substances involved in chemical transformations (reactions occurring under the influence of radiation, for example, photographic processes and photosynthesis, luminescence) is studied. Photochemistry is closely related to chemical kinetics and the study of the structure of molecules.

The above list of the main sections of physical chemistry does not cover some of the recent areas and smaller sections of this science, which can be considered as parts of larger sections or as independent sections of physical chemistry. Such, for example, are radiation chemistry, the physicochemistry of macromolecular substances, magnetochemistry, gas electrochemistry, and other branches of physical chemistry. Some of them are now rapidly growing in importance.

Methods of physical and chemical research

The basic methods of physical chemistry are naturally the methods of physics and chemistry. This is - first of all, an experimental method - the study of the dependence of the properties of substances on external conditions and the experimental study of the laws of the flow of chemical reactions in time and the laws of chemical equilibrium.

The theoretical understanding of the experimental material and the creation of a coherent system of knowledge of the properties of substances and the laws of chemical reactions is based on the following methods of theoretical physics.

Quantum mechanical method (in particular, the method of wave mechanics), which underlies the study of the structure and properties of individual atoms and molecules and their interaction with each other. Facts relating to the properties of individual molecules are obtained mainly with the help of experimental optical methods.

Statistical physics method , which makes it possible to calculate the properties of a substance; consisting of many molecules (“macroscopic” properties), based on knowledge of the properties of individual molecules.

Thermodynamic method , which allows one to quantitatively relate various properties of a substance (“macroscopic” properties) and calculate some of these properties based on the experimental values ​​of other properties.

Modern physicochemical research in any particular field is characterized by the use of a variety of experimental and theoretical methods to study the various properties of substances and to elucidate their relationship with the structure of molecules. The entire set of data and the above theoretical methods are used to achieve the main goal - to determine the dependence of the direction, speed and limits of chemical transformations on external conditions and on the structure of molecules participating in chemical reactions.

PHYSICAL, the science of the general laws that determine the structure and chem. transformations in-in at dec. ext. conditions. Researching chem. phenomena with the help of theoretical and experiment. methods of physics.

As independent, physical science took shape to. 18th century The term "physical" belongs to M.V. Lomonosov, who in 1752 gave the students of St. Petersburg University a course in physics for the first time. He owns the trail. definition: "Physical is a science that explains, on the basis of the provisions and experiments of physics, what happens in mixed bodies during chemical operations." The first scientific journal intended for the publication of articles on physics was founded in 1887 by W. Ostwald and J. van't Hoff.

F physical is the main theoretical. the foundation of modern , based on such important branches of physics as , statistical. physics and, nonlinear dynamics, field theory, etc. It includes the doctrine of the structure of islands, incl. oh and . As separate sections in the physical, they also often single out physical (including), the doctrine of, physical chemistry high-mol. conn. and others. They closely adjoin the physical and are sometimes considered as independent of it. sections , and . Most sections of the physical have fairly clear boundaries for the objects and methods of research, for methodological. features and equipment used.

Modern the stage of development of the physical is characterized by an in-depth analysis of the general laws of chem. conversions to a pier. level, widespread use of mat. , range extension ext. effects on chem. system (high and cryogenic temperatures, high, strong radiation and magnetic effects), the study of ultrafast processes, methods of energy storage in chemical. in-wah, etc.

The application of quantum theory is primarily in the explanation of chem. phenomena entailed means. increased attention to the level of interpretation and led to the selection of two directions in . A direction based on quantum mechanics. theory and operating on microscopic. level of explanation of phenomena, often called chem. physics, and the direction that operates with ensembles of a large number of particles, where statistical. laws, - physical. With such a subdivision, the boundary between physical chemistry and chem. physics can't. carried out sharply, which is especially evident in the theory of chemical rates. districts.

The doctrine of the structure of the Islands and summarizes an extensive experiment. material obtained by using such physical. methods, such as molecular, studying the interaction. electromagnetic radiation with in-tion in decomp. wavelength ranges, photo-and, and X-ray diffraction methods, methods based on magneto-optical. effects, etc. These methods make it possible to obtain structural data on the electron, on the equilibrium positions and amplitudes of oscillations of nuclei in and condenser. in-ve, about the energy system. levels and transitions between them, about changing the geom. configurations when changing the environment or its individual fragments, etc.

Along with the task of correlating the properties of in-in with their structure, modern. Physical science is also actively involved in the inverse problem of predicting the structure of compounds with given properties.

A very important source of information about their characteristics in decomp. states and characteristics of chem. transformations are the results of quantum chemical. calculations. gives a system of concepts and ideas, which is used in the physical when considering the behavior of chem. compounds per pier. level and when establishing correlations between the characteristics that form the in-in, and St. you of this in-va. Thanks to the results of quantum chemistry. calculations pov-stey potential energy chemical. systems in different and experiment. the possibilities of recent years, especially development, physical came close to a comprehensive study of St. Comm. in excited and highly excited states, to the analysis of structural features Comm. in such states and the specifics of the manifestation of these features in the dynamics of chemical. transformations.

The limitation of the usual one is that it allows one to describe only equilibrium states and reversible processes. Real irreversible processes are the subject of the problem that arose in the 1930s. 20th century . This area of ​​the physical studies non-equilibrium macroscopic. systems in which the rate of occurrence is locally kept constant (such systems are locally close to equilibrium). It allows us to consider systems with chem. p-tions and mass transfer (), heat, electric. charges, etc.

studies chemical transformations. in-in time, i.e. the speed of chemical. p-tions, the mechanisms of these transformations, as well as the dependence of the chemical. process from the conditions of its implementation. She sets patterns of changeniya of the composition of the transforming system in time, reveals the relationship between the rate of chemical. p-tion and external conditions, and also studies the factors affecting the speed and direction of chemical. districts.

Most chem. p-tions is a complex multi-stage processes, consisting of individual elementary chem. transformation, transport and transfer of energy. Theoretical chem. kinetics includes the study of the mechanisms of elementary p-tions and calculates such processes based on the ideas and apparatus of the classical. mechanics and quantum theory, is engaged in the construction of models of complex chemical. processes, establishes a relationship between the structure of the chemical. compounds and their reactions. ability. Identification of the kinetic patterns for complex p-tions (formal kinetics) is often based on the mat. and allows you to test hypotheses about the mechanisms of complex p-tions, as well as to establish a system of differentials. ur-tions, describing the results of the implementation of the process at decomp. ext. conditions.

For chem. kinetics is characterized by the use of many physical. research methods that make it possible to carry out local excitations of reactants, to study fast (up to femtosecond) transformations, to automate the registration of kinetic. data with their simultaneous processing on a computer, etc. Intensively accumulates kinetic. information through kinetic , incl. for chem. districts in extreme conditions.

A very important section of the physical, closely related to the chemical. kinetics is the doctrine of, i.e., the change in the speed and direction of chemical. p-tion when exposed to in-in (

Thermodynamic system- a body or a group of bodies that are in interaction, mentally or actually isolated from the environment.

homogeneous system- a system within which there are no surfaces separating parts of the system (phases) that differ in properties.

heterogeneous system- a system within which there are surfaces that separate parts of the system that differ in properties.

Phase- a set of homogeneous parts of a heterogeneous system, identical in physical and chemical properties, separated from other parts of the system by visible interfaces.

isolated system A system that does not exchange matter or energy with its environment.

closed system- a system that exchanges energy with the environment, but does not exchange matter.

open system- a system that exchanges both matter and energy with the environment.

State Options are quantities characterizing some macroscopic property of the system under consideration.

Thermodynamic process– any change in the thermodynamic state of the system (changes in at least one state parameter).

Reversible process- a process that allows the system to return to its original state without leaving any changes in the environment.

equilibrium process- a process in which the system passes through a continuous series of states that are infinitely close to the state of equilibrium. Characteristic features of the equilibrium process:

1) an infinitesimal difference between acting and opposing forces: Fex-Fin > 0;

2) performance by the system in the direct process of maximum work | W| = max;

3) an infinitely slow flow of the process associated with an infinitely small difference in the acting forces and an infinitely large number of intermediate states t > ?.

Spontaneous process- a process that can proceed without the expenditure of work from the outside, and as a result, work can be obtained in an amount proportional to the change in the state of the system that has occurred. A spontaneous process can take place reversible or irreversibly.

Non-spontaneous process- a process, the flow of which requires the cost of work from the outside in an amount proportional to the change in the state of the system.

Energy is a measure of the system's ability to do work; a general qualitative measure of the motion and interaction of matter. Energy is an inherent property of matter. Distinguish potential energy due to the position of the body in the field of some forces, and kinetic energy caused by a change in the position of the body in space.

Internal energy of the system U is the sum of the kinetic and potential energies of all particles that make up the system. One can also define the internal energy of a system as its total energy minus the kinetic and potential energy of the system as a whole. [ U]= J.

Heat Q - a form of energy transfer through the disordered movement of molecules, through chaotic collisions of molecules of two contiguous bodies, i.e. through heat conduction (and at the same time through radiation). Q > 0 if the system receives heat from the environment. [ Q]= J.

Work W - a form of energy transfer by the ordered movement of particles (macroscopic masses) under the action of any forces. W > 0 if the environment does work on the system. [W] = J.

All work is divided into mechanical work of expansion (or contraction) and other types of work (useful work): ? W = -pdV + ?W?.

Standard State of Solids and Liquids is the stable state of a pure substance at a given temperature under pressure p = 1 atm.

Standard state pure gas- the state of the gas, obeying the equation of state of an ideal gas at a pressure of 1 atm.

Standard values– quantities defined for substances in the standard state (denoted by superscript 0).

1.1. First law of thermodynamics

Energy is indestructible and uncreated; it can only change from one form to another in equivalent proportions.

The first law of thermodynamics is a postulate - it cannot be proven logically or deduced from any more general provisions.

The first law of thermodynamics establishes the relationship between heat Q, work W and change in the internal energy of the system? U.

isolated system

The internal energy of an isolated system remains constant.

U= const or dU= 0

closed system

The change in the internal energy of a closed system occurs due to the heat imparted to the system and/or the work done on the system.

?U=Q+W or dU=? Q+? W

open system

The change in the internal energy of an open system occurs due to the heat imparted to the system and/or the work done on the system, as well as due to a change in the mass of the system.

?U = Q + W + ?U m or dU=? Q+? W+ i?U i dn i

Internal energy is a state function; this means that the change in internal energy? U does not depend on the path of the system transition from state 1 to state 2 and is equal to the difference between the values ​​of internal energy U 2 And U 1 in these states:

?U \u003d U 2 - U 1

For some process:

?U = ?(v i U i) npod - ?(v i U i) ref

1.2. Application of the first law of thermodynamics to homogeneous one-component closed systems

Isochoric process (V = const; ?V = 0)

In the simplest case, no useful work is done.

dU=? Q+? W=? Q- pdV dU = ?Q v = C V dT = nC V dT

All the amount of heat received by the system goes to change the internal energy.

– heat capacity at constant volume, i.e., the amount of heat required to raise the temperature of the system by one degree at a constant volume. [ C V] = J / deg.

C V is the molar heat capacity at constant volume, J/(mol? deg). For ideal gases:

C V = 2 / 3 R is a monatomic gas;

C V = 5 / 2 R is a diatomic gas.

isobaric process (R = const) dU=? Q+? W = ?Q – pdV ?Q p = dU + pdV = d(U + pV) = dH

H \u003d U + pV - enthalpy is the system state function.

?Н = ?(? i U i) prod - ?(? i U i) ref

?Q p = dU + pdV =dH = C p dT – the thermal effect of an isobaric process is equal to the change in the enthalpy of the system.

– heat capacity at constant pressure. [FROM] = J/deg.

C p is the molar heat capacity at constant pressure, J/(mol? deg).

For ideal gases: C p = C V + R; C p, C V =[J/(mol K)].

Thermal effect (heat) of a chemical reaction- the amount of heat released or absorbed during the reaction at a constant temperature.

Qv = ?UV Qp = ?Up The dependence of the thermal effect of the reaction on temperature. Kirchhoff's law

The temperature coefficient of the thermal effect of a chemical reaction is equal to the change in the heat capacity of the system during the reaction.

Kirchhoff's law:

For a chemical process, the change in heat capacity is given by the change in the composition of the system:

?C p= ?(? i C p,i) prod – ?(? i C p,i) ref or? C V =?(? i C V,i) prod – ?(? i C V,i) ref

Integral form of Kirchhoff's law:

?H T2 \u003d ?H T1 + ?C p (T 2 - T 1) or? U T2 \u003d? U Ti +? C V (T 2 - T 1)

1.3. The second law of thermodynamics. Entropy

1) Heat cannot spontaneously transfer from a less heated body to a more heated one.

2) A process is impossible, the only result of which is the conversion of heat into work.

3) There is some system state function called entropy the change of which is related to the absorbed heat and the temperature of the system as follows:

in a non-equilibrium process

in an equilibrium process

S is entropy, J / deg,

is the reduced heat.

Statistical interpretation of entropy

Each state of the system is assigned thermodynamic probability(defined as the number of microstates that make up a given macrostate of the system), the greater, the more disordered or indeterminate this state is. Entropy is a state function that describes the degree of disorder in a system.

S=k ln W is the Boltzmann formula.

The system tends to spontaneously transition to a state with the maximum thermodynamic probability.

Absolute Entropy Calculation

The change in entropy during a chemical process is determined only by the type and state of the initial substances and reaction products and does not depend on the reaction path:

?S = ?(? i S i) prod - ?(?iSi) ref

The absolute entropy values ​​under standard conditions are given in the reference literature.

1.4. Thermodynamic potentials

Potential is the value whose decrease determines the work done by the system.

Only those processes that lead to a decrease in the free energy of the system can proceed spontaneously; the system comes to a state of equilibrium when the free energy reaches its minimum value.

F = U – TS – Helmholtz free energy – isochoric-isothermal potential(J) - determines the direction and limit of the spontaneous flow of the process in a closed system under isochoric-isothermal conditions.

dF = dU – TdS or? F = ?U - T?S

G = H – TS = U + pV – TS – Gibbs free energy – isobaric-isothermal potential(J) - determines the direction and limit of the spontaneous flow of the process in a closed system under isobaric-isothermal conditions.

dG = dH – TdS or? G = ?H - T?S ?G= ?(? i G i) prod - ?(? i G i) ref ?G0 = ?(? i ?G arr 0) prod - ?(? i ?G arr 0) ref Conditions for spontaneous processes in closed systems

Isobaric-isothermal (P = const, T = const):

?G< 0, dG < 0

Isochoric-isothermal (V = const, T = const):

?F< 0, dF< 0

Thermodynamic equilibrium such a thermodynamic state of a system with a minimum free energy is called, which, under constant external conditions, does not change in time, and this invariability is not due to any external process.

Thermodynamic equilibrium conditionsin a closed system

Isobaric-isothermal (P = const, T = const):

?G = 0, dG= 0, d 2 G > 0

Isochoric-isothermal (V = const, T = const):

?F=0, dF = 0, d 2 F >0 Chemical reaction isotherm equations:

For reaction v 1 A 1 + v 2 A 2+ … = v? 1 B 1 + v? 2 B 2 + …

Here C i ,p i- concentration, pressure of reacting substances at any moment of time, different from the state of equilibrium.

Influence of external conditions on chemical equilibrium

Le Chatelier-Brown equilibrium shift principle

If an external influence is exerted on a system that is in a state of true equilibrium, then a spontaneous process arises in the system that compensates for this impact.

Effect of Temperature on the Equilibrium Position

Exothermic reactions: ?H°< 0 (?U° < 0). Повышение температуры уменьшает величину константы равновесия, т. е. смещает равновесие влево.

Endothermic reactions: ?H° > 0 (?U°> 0). An increase in temperature increases the value of the equilibrium constant (shifts the equilibrium to the right).

2. Phase equilibria

Component- a chemically homogeneous component of the system, which can be isolated from the system and exist outside it. The number of independent components of the system is equal to the number of components minus the number of possible chemical reactions between them.

Number of degrees of freedom is the number of system state parameters that can be simultaneously arbitrarily changed within certain limits without changing the number and nature of phases in the system.

Phase rule J. Gibbs:

The number of degrees of freedom of an equilibrium thermodynamic system C is equal to the number of independent components of the system K minus the number of phases Ф plus the number of external factors affecting the equilibrium: C \u003d K - F + n.

For a system that is affected by external factors only temperature and pressure, can be written: C \u003d K - F+ 2.

Continuity principle- with a continuous change in the parameters of the state, all the properties of individual phases also change continuously; the properties of the system as a whole change continuously until the number or nature of the phases in the system changes, which leads to an abrupt change in the properties of the system.

According to conformity principle, on the system state diagram, each phase corresponds to a part of the plane - the field of the phase. The lines of intersection of the planes correspond to the equilibrium between the two phases. Any point on the state diagram (the so-called. figurative point) corresponds to a certain state of the system with certain values ​​of the state parameters.

2.1. Water Status Diagram

K = 1. Three phase equilibria are possible in the system: between liquid and gas (line OA), solid and gas (line OB), solid and liquid (line OC). The three curves have an intersection point O called triple point of water,– correspond to the equilibrium between the three phases and С = 0; three phases can be in equilibrium only at strictly defined values ​​of temperature and pressure (for water, the triple point corresponds to a state with P = 6.1 kPa and T = 273.16 K).

Inside each of the areas of the diagram (AOB, BOC, AOC) the system is single-phase; C = 2 (the system is bivariant).

On each of the lines, the number of phases in the system is two, and, according to the phase rule, the system is monovariant: C \u003d 1 - 2 + 2 \u003d 1, i.e., there is only one pressure value for each temperature value.

The effect of pressure on the phase transition temperature is described by the Clausius-Clapeyron equation:

V2, V1 is the change in the molar volume of a substance during a phase transition.

The equilibrium curve "solid matter - liquid" on the state diagram of water is tilted to the left, and on the state diagrams of other substances - to the right, since the density of water is greater than the density of ice, i.e. melting is accompanied by a decrease in volume (AV< 0). In this case, an increase in pressure will lower the temperature of the phase transition "solid - liquid" (water - anomalous substance). For all other substances (so-called. normal substances) ?V pl> 0 and, according to the Clausius-Clapeyron equation, an increase in pressure leads to an increase in the melting temperature.

3. Properties of solutions

3.1. Thermodynamics of solutions

Solution- a homogeneous system consisting of two or more components, the composition of which can continuously change within certain limits without an abrupt change in its properties.

Diffusion in solutions

Diffusion- a spontaneous process of leveling the concentration of a substance in a solution due to the thermal movement of its molecules or atoms.

Fick's law: the amount of a substance diffusing per unit time through a unit surface area is proportional to its concentration gradient:

where j is the diffusion flux; D is the diffusion coefficient.

Einstein-Smoluchowski equation:

where? is the viscosity of the medium; R is the radius of diffusing particles.

Solubility of gases in gases

Dalton's law: the total pressure of a gas mixture is equal to the sum of the partial pressures of all its constituent gases:

R total = ? pi And pi = xi P total

Henry Dalton's law: The solubility of a gas in a liquid is directly proportional to its pressure over the liquid: C i = kp i , where C i is the concentration of the gas solution in the liquid; k is the coefficient of proportionality, depending on the nature of the gas.

As a rule, when a gas dissolves in a liquid, heat is released (to< 0), so with increasing temperature, the solubility decreases.

Sechenov's formula:

X \u003d X 0 e -kC el

where X And X 0 is the solubility of a gas in a pure solvent and an electrolyte solution with concentration FROM.

3.2. Colligative properties of non-electrolyte solutions

colligative (collective) called the properties of solutions relative to the properties of the solvent, depending mainly on the number of dissolved particles.

Saturated vapor pressure of dilute solutions

A vapor in equilibrium with a liquid is called saturated. The pressure of this steam p 0 called pressure or elasticity of saturated steam pure solvent.

Raoult's first law. The partial pressure of the saturated vapor of a solution component is directly proportional to its mole fraction in the solution, and the coefficient of proportionality is equal to the saturated vapor pressure over the pure component:

p i = p i 0 x i

For a binary solution consisting of components A and B: the relative decrease in the vapor pressure of the solvent over the solution is equal to the mole fraction of the solute and does not depend on the nature of the solute:

Solutions for which Raoult's law holds are called ideal solutions.

Vapor pressure of ideal and real solutions

If the components of a binary (consisting of two components) solution are volatile, then the vapor above the solution will contain both components. General Composition, mol. fractions in (x in) steam pressure:

p = pA0 x A + pB0 x B = p A 0 (1 – x B) + p B 0 x B = p A 0 – x B (p A 0 – p B 0)

If the molecules of a given component interact with each other more strongly than with the molecules of another component, then the true partial vapor pressures over the mixture will be greater than those calculated using Raoult's first law (positive deviations, ?Н TV > 0). If homogeneous particles interact with each other weaker than heterogeneous particles, the partial vapor pressures of the components will be less than the calculated (negative deviations, ?H solution< 0).

Crystallization temperature of dilute solutions

Raoult's second law. The decrease in the freezing point of the solution? T deputy is directly proportional to the molar concentration of the solution:? T deputy \u003d T 0 - T \u003d KS m, where T 0 - freezing point of pure solvent; T is the freezing point of the solution; TO is the cryoscopic constant of the solvent, deg/kg mol,

T 0 2 is the freezing temperature of the solvent; M is the molecular weight of the solvent, ?Nm is the molar heat of fusion of the solvent.

Boiling point of dilute solutions

Boiling temperature is the temperature at which the saturated vapor pressure becomes equal to the external pressure.

An increase in the boiling point of solutions of non-volatile substances? T K \u003d T k - T k 0 proportional to the decrease in saturated vapor pressure and directly proportional to the molar concentration of the solution: EU m , where E - ebullioscopic constant solvent, deg/kg mol,

Osmotic pressure of dilute solutions

Osmosis- predominantly one-sided passage of solvent molecules through a semipermeable membrane into a solution or solvent molecules from a solution with a lower concentration to a solution with a higher concentration.

The pressure that must be applied to the solution to prevent the solvent from moving into the solution through the membrane separating the solution from the pure solvent is numerically equal to osmotic pressure?(Pa).

Van't Hoff principle: The osmotic pressure of an ideal solution is equal to the pressure that the solute would exert if it, being in a gaseous state at the same temperature, occupied the same volume that the solution occupies: = CRT.

Isotonic solutions– two solutions with the same osmotic pressure (?1 = ?2).

Hypertonic saline- a solution whose osmotic pressure is greater than that of another (? 1 > ? 2).

Hypotonic solution- a solution whose osmotic pressure is less than that of another (? 1< ? 2).

3.3. Electrolyte solutions

Degree of dissociation? is the ratio of the number of molecules n, decayed into ions, to the total number of molecules N:

Isotonic coefficient i Van Hoff is the ratio of the actual number of particles in the electrolyte solution to the number of particles in this solution without dissociation.

If from N molecules dissociated n, and each molecule broke up into ions, then

For non-electrolytes i = 1.

For electrolytes 1< i? ?.

3.4. Colligative properties of electrolyte solutions:

Arrhenius theory of electrolytic dissociation

1. Electrolytes in solutions decompose into ions - they dissociate.

2. Dissociation is a reversible equilibrium process.

3. The forces of interaction of ions with solvent molecules and with each other are small (i.e., solutions are ideal).

The dissociation of electrolytes in solution occurs under the action of polar solvent molecules; the presence of ions in a solution determines its electrical conductivity.

According to the degree of dissociation, electrolytes are divided into three groups: strong(? ? 0,7), medium strength(0,3 < ? < 0,7) и weak(? ? 0,3).

Weak electrolytes. Dissociation constant

For some electrolyte that decomposes into ions in solution in accordance with the equation:

A a B b - aA x- + bB y+

For binary electrolyte:

- Ostwald dilution law: the degree of dissociation of a weak electrolyte increases with dilution of the solution.

Solute activity– empirical value that replaces the concentration, – activity (effective concentration) but, related to concentration via activity coefficient f, which is a measure of the deviation of the properties of a real solution from an ideal one:

a = fC; a + = f+ C + ; a_ = f_C_.

For binary electrolyte:

is the average activity of the electrolyte;

is the average activity coefficient.

Debye-Hückel limit law for binary electrolyte: lg f = -0.51z2I?, where z is the charge of the ion for which the activity coefficient is calculated;

I is the ionic strength of the solution I = 0.5? (C i r i 2).

4. Electrical conductivity of electrolyte solutions

Conductors of the first kind- metals and their melts, in which electricity is carried by electrons.

Conductors of the II kind– solutions and melts of electrolytes with ionic type of conductivity.

Electricity is the orderly movement of charged particles.

Any conductor through which current flows represents a certain resistance R, which, according to Ohm's law, is directly proportional to the length of the conductor l and inversely proportional to the cross-sectional area S; proportionality factor is resistivity material? - resistance of a conductor having a length of 1 cm and a cross section of 1 cm 2:

Value W, the opposite of resistance is called electrical conductivity- a quantitative measure of the ability of an electrolyte solution to conduct an electric current.

Electrical conductivity? (k) - electrical conductivity of a conductor of the first kind 1 m long with a cross-sectional area of ​​\u200b\u200b1 m 2 or the electrical conductivity of 1 m 3 (1 cm 3) of an electrolyte solution (conductor of the second kind) with a distance between the electrodes of 1 m (1 cm) and an electrode area of ​​1 m 2 (1 cm 2).

Molar electrical conductivity of the solution) ? is the electrical conductivity of a solution containing 1 mol of a solute and placed between electrodes located at a distance of 1 cm from each other.

The molar electrical conductivity of both strong and weak electrolytes increases with decreasing concentration (i.e., with increasing dilution of the solution V = 1 / C) reaching some limit value? 0 (? ?), called molar electrical conductivity at infinite dilution.

For a binary electrolyte with singly charged ions at a constant temperature and a field strength of 1 V m -1:

? = ?F(u + + and?),

where F is the Faraday number; and + , and? - absolute mobilities (m 2 V -1 s -1) cation and anion - the speed of movement of these ions under standard conditions, with a potential difference of 1 V per 1 m of the length of the solution.

? + = Fu + ; ?? = Fu?,

where? + , ?? – mobility cation and anion, Ohm m 2 mol -1 (Ohm cm 2 mol -1).

? = ?(? + + ??)

For strong electrolytes? ?1 and ? = ? + + ??

With infinite dilution of the solution (V > ?, ? + > ? ? + , ?? > ? ? ?, ? > 1) for both strong and weak electrolytes? ? = ? ? + – ? ? ? - Kohlrausch's law: is the molar electrical conductivity at infinite dilution equal to the sum of the electrolytic mobilities? ? + , ? ? ? cation and anion of a given electrolyte.

Ions H + and OH? have an abnormally high mobility, which is associated with a special mechanism of charge transfer by these ions - relay mechanism. Between hydronium ions H 3 O + and water molecules, as well as between water molecules and OH? protons are continuously exchanged according to the equations:

H 3 O + + H 2 O > H 2 O + H 3 O +

H 2 O + OH? >OH? + H 2 O

5. Electrochemical processes

5.1. Electrode potentials. Galvanic elements. EMF

When two chemically or physically dissimilar materials come into contact (metal 1 (conductor of the first kind) - metal 2 (conductor of the first kind), metal (conductor of the first kind) - metal salt solution (conductor of the second kind), electrolyte solution 1 (conductor of the second kind) - electrolyte solution 2 (conductor of the second kind), etc.) between them arises electric double layer (DES). DES is the result of an ordered distribution of oppositely charged particles at the interface.

The formation of a DEL leads to a potential jump?, which, under conditions of equilibrium, a metal (conductor of the first kind) - a solution of a metal salt (conductor of the second kind) is called galvanic potential.

System: metal (Me) - an aqueous solution of a salt of a given Me - is called electrode or half element and is shown schematically as follows:

The electrode (p / e) is written so that all substances in solution are placed to the left, and the electrode material is placed to the right of the vertical line.

? > 0, if the reduction reaction occurs on the electrode Me n+ + ne? - Me 0 ,

? < 0, если на электроде протекает реакция окисления Ме 0 - Ме n+ + ne?.

Electrode potential E Me n+ / Me is the equilibrium potential difference that occurs at the phase boundary conductor of the first kind / conductor of the second kind and measured relative to a standard hydrogen electrode.

Nernst Equation, where n is the number of electrons involved in the electrode reaction; FROM Me n+ is the concentration of cations; E Me n+ /Me is the standard electrode potential.

contact potential? ?- equilibrium potential jump that occurs at the interface between two conductors of the first kind.

Diffusion potential? dif is the equilibrium potential difference that occurs at the phase boundary conductor of the second kind / conductor of the second kind.

Galvanic cell (g.e.)- an electrical circuit consisting of two or more p.e. and producing electrical energy due to the chemical reaction taking place in it, and the stages of oxidation and reduction of the chemical reaction are spatially separated.

The electrode on which the oxidation process occurs during the operation of a galvanic cell is called anode, the electrode on which the recovery process is taking place, - cathode.

IUPAC rules for recording galvanic cells and the reactions occurring in them

1. In g. e. work is done, so the EMF of the element is considered a positive value.

2. The value of the EMF of the galvanic circuit E is determined by the algebraic sum of potential jumps at the interfaces of all phases, but since oxidation occurs at the anode, the EMF is calculated by subtracting the value of the anode (left electrode) potential from the numerical value of the cathode (right electrode) potential - right pole rule. Therefore, the element circuit is written so that the left electrode is negative (oxidation occurs), and the right electrode is positive (reduction process occurs).

3. The interface between the conductor of the first kind and the conductor of the second kind is indicated by one line.

4. The boundary between two conductors of the second kind is depicted by a dotted line.

5. An electrolyte bridge at the boundary of two conductors of the II kind is indicated by two dotted lines.

6. The components of one phase are written separated by commas.

7. The equation of the electrode reaction is written so that the substances in the oxidized form (Ox) are located on the left, and in the reduced form (Red) on the right.

Daniel-Jacobi galvanic cell consists of zinc and copper plates immersed in the corresponding solutions of ZnSO 4 and CuSO 4 , which are separated by a salt bridge with a KCl solution: an electrolytic bridge provides electrical conductivity between the solutions, but prevents their mutual diffusion.

(-) Zn | Zn2+ :: Cu2+ | Cu(+)

Reactions on the electrodes:

Zn0 > Zn2+ + 2e? Cu 2+ + 2е? > Cu 0

Total redox process:

Cu 2+ + Zn 0 > Cu 0 + Zn 2+

The work of the current of a galvanic cell (and, consequently, the potential difference) will be maximum during its reversible operation, when the processes on the electrodes proceed infinitely slowly and the current strength in the circuit is infinitely small.

The maximum potential difference that occurs during the reversible operation of a galvanic cell is electromotive force (EMF) of a galvanic cell E.

element emf E Zn/Cu = ? Cu2+ /Cu+? Zn2+ /Zn + ? to +? diff.

Excluding? diff and? to: E Zn/Cu = ? Cu2+ /Cu+? Zn2+ /Zn = E Cu 2+ /Cu + E Zn 2+ /Zn - galvanic cells consisting of two identical metal electrodes immersed in salt solutions of this metal with different concentrations С 1 > С 2 . In this case, the cathode will be an electrode with a higher concentration, since the standard electrode potentials of both electrodes are equal.

concentration chains

The only result of the work of the concentration element is the transfer of metal ions from a more concentrated solution to a less concentrated one.

The work of an electric current in a concentration galvanic cell is the work of a diffusion process, which is carried out reversibly as a result of its spatial division into two reversible electrode processes opposite in direction.

5.2. Electrode classification

Electrodes of the first kind. A metal plate immersed in a salt solution of the same metal. During the reversible operation of the element in which the electrode is included, the process of transition of cations from metal to solution or from solution to metal takes place on a metal plate.

Electrodes of the second kind. The metal is covered with a sparingly soluble salt of this metal and is in solution containing another soluble salt with the same anion. Electrodes of this type are reversible with respect to the anion.

Reference electrodes– electrodes with precisely known and reproducible potential values.

Hydrogen electrode is a platinum plate washed with hydrogen gas, immersed in a solution containing hydrogen ions. The hydrogen adsorbed by platinum is in equilibrium with gaseous hydrogen.

Pt, N 2 / N +

Electrochemical equilibrium on the electrode:

2H++ 2e? - H 2 .

The potential of a standard hydrogen electrode (with an activity of H + 1 mol/l ions and a hydrogen pressure of 101.3 kPa) is assumed to be zero.

Electrode potential of non-standard hydrogen electrode:

Calomel electrode consists of a mercury electrode placed in a KCl solution of a certain concentration and saturated with Hg 2 Cl 2 calomel:

Hg / Hg 2 Cl 2 , KCl

Calomel electrode is reversible with respect to chloride anions

Silver chloride electrode– reversible with respect to chlorine anions:

Ag/AgCl, KCl

If the KCl solution is saturated, then E AgC l \u003d 0.2224 - 0.00065 (t - 25), V.

indicator electrodes. Electrodes that are reversible with respect to the hydrogen ion are used in practice to determine the activity of these ions in solution.

Quinhydrone electrode is a platinum wire lowered into a vessel with the test solution, into which an excess amount of quinhydrone C 6 H 4 O 2 C 6 H 4 (OH) 2 is first placed - a compound of quinone C 6 H 4 O 2 and hydroquinone C 6 H 4 (OH ) 2 capable of interconversion in an equilibrium redox process in which hydrogen ions participate:

C 6 H 4 O 2 + 2H + + 2e? > C 6 H 4 (OH) 2

Most commonly used glass electrode in the form of a tube ending in a thin-walled glass ball. The ball is filled with a buffer solution with a certain pH value, in which an auxiliary electrode (usually silver chloride) is immersed. To measure pH, the glass electrode is immersed in the test solution in tandem with the reference electrode. The glass electrode ball is pre-treated for a long time with an acid solution. In this case, hydrogen ions are introduced into the walls of the ball, replacing the alkali metal cations. The electrode process is reduced to the exchange of hydrogen ions between two phases - the test solution and glass: H solution - H st + .

standard capacity E st 0 for each electrode has its own value, which changes over time; therefore, the glass electrode is calibrated before each pH measurement against standard buffer solutions with exactly known pH.

Redox electrodes

An electrode consisting of an inert conductor of the 1st kind, placed in an electrolyte solution containing one element in various oxidation states, is called redox or redox electrode.

Electrode reaction: Oh n+ + ne? - red.

In this case inert Me takes an indirect part in the electrode reaction, being an intermediary in the transfer of electrons from the reduced form of Me (Red) to the oxidized form (Ox) or vice versa.

6. Surface phenomena and adsorption

6.1. Surface Tension and Gibbs Adsorption

Surface phenomena called the processes occurring at the interface and due to the peculiarities of the composition and structure of the surface (boundary) layer.

Gs = ?s,

where Gs is the surface Gibbs energy of the system, J; ? - coefficient of proportionality, called surface tension, J / m 2; s is the interfacial surface, m2.

Surface tensionabout is a quantity measured by the Gibbs energy per unit area of ​​the surface layer. It is numerically equal to the work that must be done against the forces of intermolecular interaction to form a unit interface at a constant temperature.

From the Dupre model, surface tension equal to the force tending to reduce the interface and related to the unit length of the contour that bounds the surface

The ability of solutes to change the surface tension of a solvent is called surface activity g:

Classification of substances according to the effect on the surface tension of the solvent

1. Surfactants (surfactants)– lower the surface tension of the solvent (? solution< ? 0) g >0 (in relation to water - organic compounds of amphiphilic structure).

2. Surface Inactive Substances (SIDs)– slightly increase the surface tension of the solvent (? solution > ? 0) g< 0 (неорганические кислоты, основания, соли, глицерин, ?-аминокислоты и др).

3. Surface-inactive substances (NSV)- practically do not change the surface tension of the solvent (? rr = ? 0) g = 0 (in relation to water, substances are sucrose and a number of others).

Duclos-Traube rule: in any homologous series at low concentrations, elongation of the carbon chain by one CH 2 group increases the surface activity by 3–3.5 times:

For aqueous solutions of fatty acids (Shishkovsky equation):

where b And TO are empirical constants, b the same for the entire homologous series, K increases for each subsequent member of the series by 3–3.5 times.

The process of spontaneous change in the concentration of a substance at the interface between two phases is called adsorption. Adsorbent a substance is called, on the surface of which there is a change in the concentration of another substance - adsorbate.

Gibbs adsorption isotherm:

The excess of the adsorbate in the surface layer compared to its initial amount in this layer characterizes excess or the so-called Gibbs, adsorption(G).

6.2. Adsorption at the solid-gas interface

physical adsorption arises due to van der Waals interactions of an adsorbed molecule with the surface, is characterized by reversibility and a decrease in adsorption with increasing temperature, i.e., exothermicity (the thermal effect of physical adsorption is usually close to the heat of liquefaction of the adsorbate, 10–80 kJ/mol).

Chemical adsorption (chemisorption) carried out by chemical interaction of adsorbent and adsorbate molecules, usually irreversible; is an localized i.e., the adsorbate molecules cannot move over the surface of the adsorbent. Since chemisorption is a chemical process requiring an activation energy of the order of 40-120 kJ/mol, an increase in temperature contributes to its occurrence.

Henry's equation(monomolecular adsorption on a homogeneous surface at low pressures or low concentrations):

G = Ks or G \u003d Kr,

TO is the adsorption equilibrium constant, which depends on the nature of the adsorbent and adsorbate; C, r is the concentration of the dissolved substance or gas pressure.

Langmuir's theory of monomolecular adsorption

1. Adsorption is localized and is caused by forces close to chemical ones.

2. Adsorption occurs on a homogeneous surface of the adsorbent.

3. Only one layer of adsorbed molecules can form on the surface.

4. The process of adsorption is reversible and equilibrium.

Langmuir adsorption isotherm:

where Г 0 – monolayer capacity is a constant equal to the limiting adsorption observed at relatively high equilibrium concentrations, mol/m 2 ; b is a constant equal to the ratio of the adsorption rate constant and the desorption rate constant.

Freundlich equation(adsorption on an inhomogeneous surface): Г = K F with n , where. K F is a constant numerically equal to adsorption at an equilibrium concentration equal to unity; n is the constant that determines the curvature of the adsorption isotherm (n= 0,1–0,6).

Molecular adsorption from solutions:

where C 0 is the initial concentration of the adsorbate; FROM is the equilibrium concentration of the adsorbate; V is the volume of the adsorbate solution; m is the mass of the adsorbent.

Area S 0 , per molecule in a saturated adsorption layer, landing area:

m 2 /molecule.

Adsorption layer thickness:

where M is the molecular weight of the surfactant; ? is the surfactant density.

Rebinder's rule: on polar adsorbents, polar adsorbates from low-polarity solvents are better adsorbed; on polar adsorbents, non-polar adsorbates from polar solvents.

The orientation of surfactant molecules on the surface of the adsorbent is shown schematically in the figure:

6.3. Adsorption from electrolyte solutions

Exchange adsorption- the process of ion exchange between a solution and a solid phase, in which the solid phase absorbs ions of any sign (cations or anions) from the solution and instead of them can release an equivalent number of other ions of the same sign into the solution. Forever specific i.e., for a given adsorbent, only certain ions are capable of exchange; exchange adsorption is usually irreversible.

Package-Peskov-Faience Rule: on the surface of a crystalline solid, an ion is specifically adsorbed from an electrolyte solution, which is able to complete its crystal lattice or can form a poorly soluble compound with one of the ions that make up the crystal.

7. Colloidal (dispersed) systems

Colloidal (dispersed) system a heterogeneous system is called, in which one of the phases is represented by small particles uniformly distributed in the volume of another homogeneous phase. These are ultramicroheterogeneous systems consisting of particles dispersed phase- aggregates of crushed particles, the size of which lies within 10 -9 -10 -5 m, and continuous dispersion medium, in which these particles are distributed.

signs colloidal state of matter - dispersion and heterogeneity.

The degree of dispersion? is the reciprocal of the mean diameter or, for non-spherical particles, the reciprocal of the mean equivalent diameter d(m -1):

Specific surface area is the ratio of the total surface area of ​​the dispersed phase S DF to its total volume or to its mass:

7.1. Classification and methods for obtaining disperse systems

Classification according to the state of aggregation of phases

A dispersed system in which both the dispersed phase and the dispersion medium are gases does not exist, since the gases are infinitely soluble in each other.

Classification of systems according to the particle size of the dispersed phase:

1) highly dispersed, 10 -9_ 10 -7 m (ruby glass);

2) medium dispersed, 10 -7_ 10 -5 m (instant coffee);

3) coarse, > 10 -5 m (raindrops).

Methods for obtaining colloidal systems dispersion

Physical dispersion: mechanical grinding using colloid mills; electrical spraying of substances; ultrasonic dispersion and other methods. To prevent the formed particles from sticking together, the dispersion is carried out in the presence of stabilizer– electrolyte or substance adsorbed at the interface (surfactants).

Chemical dispersion (peptization): conversion of a freshly prepared precipitate into a colloidal state using a peptizer.

Condensation

Physical Condensation: 1) the method of replacing the solvent, which consists in the fact that a liquid that mixes with the solvent is added to the true solution of the substance, in which the substance itself is poorly soluble; due to a decrease in the solubility of the substance in the new solvent, the solution becomes supersaturated, and part of the substance condenses, forming particles of the dispersed phase; 2) vapor condensation method; the original substance is in a pair; as the temperature decreases, the vapor becomes supersaturated and partially condenses, forming a dispersed phase.

Chemical condensation: any chemical reaction resulting in the formation of a poorly soluble compound; in order to obtain a colloidal solution, the reaction must be carried out in a dilute solution at a low particle growth rate, one of the starting materials is taken in excess and is a stabilizer.

7.2. Optical properties of dispersed systems

When light falls on a disperse system, the following phenomena can be observed:

light passage particles of the dispersed phase (observed for transparent systems in which the particles are much smaller than the wavelength of the incident light (r<< ?);

light refraction particles of the dispersed phase (if these particles are transparent);

light reflection particles of the dispersed phase (if the particles are opaque);

refraction and reflection light is observed for systems in which the particles are much larger than the wavelength of the incident light (r >> ?). Visually, this phenomenon is expressed in the turbidity of these systems;

light scattering observed for systems in which the particles of the dispersed phase are smaller, but commensurate with the wavelength of the incident light (r ? 0.1 ?);

adsorption(absorption) of light by the dispersed phase with the conversion of light energy into heat.

Rayleigh equation:

where I, I 0 are the intensity of the scattered and incident light; V is the volume of one particle; ? – partial concentration (number of particles per unit volume); ? is the wavelength; n 1 , n 0 are the refractive indices of the particles and the medium, respectively.

The phenomenon of different colors of a colloidal solution in transmitted and scattered (reflected) light is called opalescence. In the case of colored solutions, there is an overlay of their own color and the color caused by opalescence (phenomenon dichroism of light).

7.3. Molecular kinetic properties

Colloidal systems are characterized Brownian motion- continuous random movement of particles of microscopic and colloidal sizes. This movement is the more intense, the higher the temperature and the lower the mass of the particle and the viscosity of the dispersion medium.

Diffusion is a spontaneous process of particle concentration equalization.

Fick's law:

Due to the large size of colloidal particles, diffusion in colloidal systems is slower than in true solutions.

Osmotic pressure:

where mtot is the mass of the dissolved substance; m is the mass of one particle; V is the volume of the system; N A is the Avogadro number; T is the absolute temperature; ? – partial concentration; k is the Boltzmann constant.

For spherical particles:

where? m is the mass of the dispersed phase per unit volume of the solution; ? is the density of the dispersion medium; r is the particle radius.

7.4. The structure of a micelle

Lyophobic micelle system is called a heterogeneous microsystem, which consists of a microcrystal of the dispersed phase, surrounded by solvated stabilizer ions.

Potential-determining called ions adsorbed on the surface of a particle of the solid phase (unit) and give it a charge. The aggregate, together with potential-determining ions, is micelle core.

Counterions are ions grouping near the micelle core.

The location of counterions in a dispersion medium is determined by two opposite factors: thermal motion (diffusion) and electrostatic attraction.

The counterions that make up the dense adsorption layer, are called "connected" and together with the core make up colloidal particle or granule. A colloidal particle (granule) has a charge, the sign of which is due to the sign of the charge of potential-determining ions.

The counterions that form diffuse layer,- "mobile", or "free".

A colloidal particle with a surrounding diffuse layer of solvated counterions is micelle. Unlike a colloidal particle, a micelle is electrically neutral and does not have strictly defined dimensions.

In a micelle with an ionic stabilizer, there is a DES at the phase boundary, a potential difference arises between the dispersed phase and the dispersion medium - thermodynamic potential f (interphase), which is determined by the properties of a given disperse system, as well as by the charge and concentration of potential-determining ions adsorbed on the solid phase.

The movement of charged colloidal particles in a stationary liquid to one of the electrodes under the action of an external electric field is called electrophoresis.

The surface on which the movement occurs is called sliding surface. The magnitude of the potential jump at the boundary of phases that are in motion relative to each other during electrophoresis and in Brownian motion, i.e., on the sliding surface, is called electrokinetic or?-potential (zeta potential).

7.5. Stability and coagulation

Stability of dispersed systems characterizes the ability of the dispersed phase to maintain a state of uniform distribution of particles throughout the volume of the dispersion medium.

There are two types of relative stability of dispersed systems: sedimentation and aggregation.

Sedimentation resistance- the ability of the system to resist the action of gravity. Sedimentation is the settling of particles in solution under the influence of gravity.

Condition sedimentation equilibrium: the particle moves at a constant speed, i.e. evenly, the force of friction balances the force of gravity:

6??rU = 4/3?r 3 (? - ? 0)g,

where? is the density of the dispersed phase, ? 0 is the density of the dispersion medium, g is the acceleration of gravity, ? is the viscosity of the medium.

Aggregative stability characterizes the ability of the particles of the dispersed phase to resist their sticking together and thereby maintain their size.

In violation of aggregative stability occurs coagulation is the process of sticking together of particles with the formation of large aggregates. As a result of coagulation, the system loses its sedimentation stability, since the particles become too large and cannot participate in Brownian motion.

Reasons for coagulation:

> temperature change;

> action of electric and electromagnetic fields;

> action of visible light;

> exposure to elementary particles;

> mechanical impact;

> adding electrolyte, etc.

Of greatest practical interest is coagulation with electrolytes.

Types of coagulation with electrolytes

concentration coagulation occurs under the influence indifferent electrolytes. indifferent is called an electrolyte, upon introduction of which the interfacial potential<р не изменяется. Данный электролит не содержит таких ионов, которые были бы способны к специфической адсорбции на частицах по правилу Па-нета-Фаянса, т. е. не способны достраивать кристаллическую решетку агрегата:

The state in which the diffuse layer disappears and the colloidal particle becomes electrically neutral is called isoelectric– electrokinetic potential (?) is equal to zero, coagulation occurs. The micelle formula in this state takes the form: (mnAg + nNO 3 ?) 0 .

Neutralization coagulation occurs when added to the sol non-indifferent electrolyte. Non-indifferent an electrolyte is called that is capable of changing the interfacial (?) and linearly related electrokinetic (?) potentials, i.e. this electrolyte contains ions that can be specifically adsorbed on the surface of the aggregate, complete its crystal lattice, or chemically interact with potential-determining ions.

The reversible process in which the coagulate again goes into a colloidal state is called peptization or disaggregation.

coagulation rules

1. All strong electrolytes added to the sol in sufficient quantities cause it to coagulate. The minimum electrolyte concentration that causes coagulation of the sol in a certain short period of time is called coagulation threshold:

where C el is the concentration of electrolyte-coagulant; V el is the volume of added electrolyte; V sol (usually 10 ml) is the volume of the sol.

2. The ion whose charge coincides in sign with the charge of the counterions of the micelle of the lyophobic sol has a coagulating effect (the charge of the coagulating ion is opposite to the charge of the colloidal particle). This ion is called coagulant ion.

3. The coagulating ability of an ion - coagulant is the greater, the greater the charge of the ion:

Significance rule:

? 1: ? 2: ? 3 = 1/1 6: 1/2 6: 1/3 6 = 729: 11: 1

The coagulating ability of an ion with the same charge is the greater, the larger its crystal radius. Ag + > Cs + > Rb + > NH 4 + > K + > Na + > Li+ - lyotropic series.

Colloidal protection is called increasing the aggregative stability of the sol by introducing into it an IUD (high molecular weight compound) or a surfactant (surfactant).

guard number called the minimum number of milligrams of dry matter that is necessary to protect 10 ml of sol when an electrolyte is added to it in an amount equal to the coagulation threshold.

PHYSICAL CHEMISTRY

The subject of physical chemistry. Its meaning

The relationship of chemical and physical phenomena studies physical chemistry. This branch of chemistry is the boundary between chemistry and physics. Using the theoretical and experimental methods of both sciences, as well as its own methods, physical chemistry is engaged in a multifaceted study of chemical reactions and the physical processes accompanying them. Since, however, even a multifaceted study is never complete and does not cover the phenomenon in an exhaustive way, the laws and laws of physical chemistry, like those of other natural sciences, always simplify the phenomenon and do not fully reflect it.

The rapid development and growing importance of physical chemistry are associated with its boundary position between physics and chemistry. The main general task of physical chemistry is the prediction of the time course of the process and the final result (equilibrium state) under various conditions based on data on the structure and properties of the substances that make up the system under study.

Brief outline of the history of the development of physical chemistry

The term "physical chemistry" and the definition of this science were first given by M.V. Lomonosov, who in 1752-1754. read a course in physical chemistry to the students of the Academy of Sciences and left the manuscript of this course "Introduction to True Physical Chemistry" (1752). Lomonosov carried out many studies, the topics of which correspond to the "Plan for the course of physical chemistry" (1752) compiled by him and the program of experimental work "Experience in Physical Chemistry" (1754). Under his leadership, a student workshop in physical chemistry was also held.

Lomonosov gave the following definition of physical chemistry: "Physical chemistry is a science that explains, on the basis of the provisions and experiments of physics, what happens in mixed bodies during chemical operations." This definition is close to modern.

For the development of physical chemistry, the discovery of two laws of thermodynamics in the middle of the 19th century (S. Carnot, Yu.R. Mayer, G. Helmholtz, D.P. Joule, R. Clausius, W. Thomson) was of great importance.

The number and variety of research, lying in the field that borders between physics and chemistry, constantly increased in the 19th century. The thermodynamic theory of chemical equilibrium was developed (K.M. Guldberg, P. Waage, D.W. Gibbs). The studies of L.F. Wilhelmi laid the foundation for the study of the rates of chemical reactions (chemical kinetics). The transfer of electricity in solutions was studied (I.V. Gittorf, F.V.G. Kolrausch), the laws of equilibrium of solutions with steam were studied (D.P. Konovalov) and the theory of solutions was developed (D.I. Mendeleev).

The recognition of physical chemistry as an independent science and academic discipline was expressed in the establishment at the University of Leipzig (Germany) in 1887 of the first department of physical chemistry headed by W. Ostwald and in the foundation of the first scientific journal on physical chemistry there. At the end of the 19th century, the University of Leipzig was the center for the development of physical chemistry, and the leading physical chemists were W. Ostwald, J. H. Van't Hoff, S. Arrhenius and W. Nernst. By this time, three main sections of physical chemistry were defined - chemical thermodynamics, chemical kinetics and electrochemistry.

The most important areas of science, the development of which is a necessary condition for technical progress, include the study of chemical processes; physical chemistry plays a leading role in the development of this problem.

Sections of physical chemistry. Research methods

Chemical thermodynamics. In this section, on the basis of the laws of general thermodynamics, the laws of chemical equilibrium and the doctrine of phase equilibria are expounded.

The doctrine of solutions aims to explain and predict the properties of solutions (homogeneous mixtures of several substances) on the basis of the properties of the substances that make up the solution.

The doctrine of surface phenomena. Various properties of surface layers of solids and liquids (interfaces between phases) are studied; one of the main studied phenomena in the surface layers is adsorption(accumulation of matter in the surface layer).

In systems where the interfaces between liquid, solid, and gaseous phases are highly developed (emulsions, mists, smokes, etc.), the properties of the surface layers become of primary importance and determine many of the unique properties of the entire system as a whole. Such dispersed (microheterogeneous) systems are being studied colloid chemistry, which is a major independent branch of physical chemistry.

The above list of the main sections of physical chemistry does not cover some areas and smaller sections of this science, which can be considered as parts of larger sections or as independent sections of physical chemistry. It should be emphasized once again the close interrelationship between the various branches of physical chemistry. In the study of any phenomenon, one has to use an arsenal of ideas, theories and methods for studying many branches of chemistry (and often other sciences). Only with an initial acquaintance with physical chemistry is it possible for educational purposes to distribute the material into the indicated sections.

Methods of physical and chemical research. The basic methods of physical chemistry are naturally the methods of physics and chemistry. This is, first of all, an experimental method - the study of the dependence of the properties of substances on external conditions, the experimental study of the laws of the flow of various processes and the laws of chemical equilibrium.

The theoretical understanding of experimental data and the creation of a coherent system of knowledge is based on the methods of theoretical physics.

The thermodynamic method, which is one of them, makes it possible to quantitatively relate various properties of a substance (“macroscopic” properties) and calculate some of these properties based on the experimental values ​​of other properties.

CHAPTER I
THE FIRST LAW OF THERMODYNAMICS

Warmth and work

Changes in the forms of motion during its transition from one body to another and the corresponding transformations of energy are very diverse. The forms of the transition of motion itself and the transitions of energy connected with it can be divided into two groups.

The first group includes only one form of motion transition by chaotic collisions of molecules of two adjoining bodies, i.e. by conduction (and at the same time by radiation). The measure of the movement transmitted in this way is heat .

The second group includes various forms of movement transition, the common feature of which is the movement of macroscopic masses under the action of any external forces that have a directed character. Such are the rise of bodies in a gravitational field, the transition of a certain amount of electricity from a larger electrostatic potential to a smaller one, the expansion of a gas under pressure, etc. The general measure of the movement transmitted by such means is Job .

Heat and work characterize qualitatively and quantitatively two different forms of transmission of motion from one part of the material world to another.

The transmission of motion is a kind of complex motion of matter, the two main forms of which we distinguish. Heat and work are measures of these two complex forms of motion of matter, and they should be considered as types of energy.

The common property of heat and work is that they matter only during the time intervals in which these processes take place. In the course of such processes, in some bodies the movement in one form or another decreases and the corresponding energy decreases, while in other bodies the movement in the same or other forms increases and the corresponding types of energy increase.

We are not talking about the stock of heat or work in any body, but only about the heat and work of a known process. After its completion, there is no need to talk about the presence of heat or work in the bodies.

Internal energy

For a non-circular process, the equality (I, 1) is not observed, since the system does not return to its original state. Instead, the equalities for a non-circular process can be written (omitting the coefficient k):

Since the limits of integration are generally arbitrary, then for elementary quantities dW And dQ:

d Q¹d W,

Consequently:

d Q– d W ¹ 0

Denote the difference dQ - dW for any elementary thermodynamic process through dU:

dUº d Q– d W(I, 2)

or for the final process:

– (I, 2a)

Returning to the circular process, we obtain (from Equation I, 1):

= – = 0 (I, 3)

Thus, the value dU is the total differential of some system state function. When the system returns to its original state (after a cyclic change), the value of this function acquires its original value.

System state function u, defined by equalities (I, 2) or (I, 2a) is called internal energy systems .

Obviously, expression (I, 2a) can be written as follows:

\u003d U 2 - U 1 \u003d ∆U \u003d -(I, 2b)

U 2 – U 1 \u003d ∆U \u003d Q - W

This reasoning substantiates empirically the presence of a certain function of the state of the system, which has the meaning of the total measure of all movements that the system possesses.

In other words, internal energy includes the translational and rotational energy of molecules, the vibrational energy of atoms and groups of atoms in a molecule, the energy of electron motion, intranuclear and other types of energy, i.e. the totality of all types of particle energy in the system, with the exception of the potential and kinetic energy of the system itself .

Let us assume that the cyclic process was carried out in such a way that after the system returned to its initial state, the internal energy of the system did not take the initial value, but increased. In this case, the repetition of circular processes would cause the accumulation of energy in the system. It would be possible to convert this energy into work and obtain work in this way not at the expense of heat, but “out of nothing”, since in a circular process work and heat are equivalent to each other, which is shown by direct experiments.

Inability to complete the specified build cycle perpetuum mobile (perpetuum mobile) of the first kind, that gives work without spending an equivalent amount of another type of energy, is proved by the negative result of thousands of years of human experience. This result leads to the same conclusion that we obtained in a particular but more rigorous form by analyzing Joule's experiments.

Let us formulate the result obtained once more. The total energy of the system (its internal energy) as a result of a cyclic process returns to its original value, i.e., the internal energy of a system in a given state has one definite value and does not depend on what changes the system underwent before coming to this state.

In other words, the internal energy of the system is an unambiguous, continuous and finite function of the state of the system.

The change in the internal energy of the system is determined by expression (I, 2b); the expression (I, 3) is valid for a circular process. With an infinitesimal change in some properties (parameters) of the system, the internal energy of the system also changes infinitesimally. This is a property of a continuous function.

Within thermodynamics, there is no need to use a general definition of the concept of internal energy. A formal quantitative definition through expressions (I, 2) or (I, 2a) is sufficient for all further thermodynamic reasoning and conclusions.

Since the internal energy of the system is a function of its state, then, as already mentioned, the increase in internal energy with infinitesimal changes in the parameters of the system states is the total differential of the state function. Breaking the integral in equation (I, 3) into two integrals over the sections of the path from the state 1 up to the state 2 (path "a") (see Fig. I) and vice versa - from the state 2 up to the state 1 (other way "b" ), - we get:

(I, 4)

(I, 5)

We will arrive at the same result by comparing the paths "a" and "c", or "b" and "c", etc.

Rice. I. Scheme of a circular (cyclic) process.

Expression (I, 5) shows that the increase in the internal energy of the system during its transition from one state to another does not depend on the path of the process, but depends only on the initial and final states of the system.

First law of thermodynamics

The first law of thermodynamics is directly related to the law of conservation of energy. It allows you to calculate the balance of energy in the course of various processes, including chemical reactions.

From the law of conservation of energy follows:

Q = ∆U + W

The resulting expression for a closed system can be read as follows: the heat supplied to the system is spent only on changing its internal energy and doing work.

The above statement, related to equations (I, 3) and (I, 5), serves formulation of the first law of thermodynamics(combined with Equation (I, 2) which quantifies the internal energy).

The first law of thermodynamics is a quantitative formulation of the law of conservation of energy as applied to processes associated with the transformation of heat and work.

Another formulation of the first law of thermodynamics can be obtained from the expression (I, 2a). In an isolated system dQ = 0 And dW = 0, then and dU=0; therefore, for any processes occurring in an isolated system:

(I.6)

i.e. the internal energy of an isolated system is constant . This formulation of the first law of thermodynamics is a quantitative expression of the general law of conservation of energy applied to specific conditions and finite systems, according to which energy is neither created nor destroyed.

It should be noted that the first law of thermodynamics does not make it possible to find the total value of the internal energy of the system in any state, since the equations expressing the first law lead to the calculation of only the change in the energy of the system in various processes. Similarly, one cannot directly measure the change in internal energy in macroscopic processes; it is only possible to calculate this change using equation (I, 2b), taking into account the measurable quantities - heat and work of this process.

Note that heat and work (each separately) do not have the state function property expressed by equation (I, 3) or (I, 5) and inherent in internal energy. The heat and work of the process that transfers the system from state 1 to state 2 depend in the general case on the path of the process and the value δQ And δW are not differentials of the state function, but are simply infinitesimal quantities, which we will call elemental heat And elementary work.

Thus, the internal energy differential dU has other mathematical properties than elemental heat dQ and work dW. This is essential in constructing a system of thermodynamics.

State equations

Many properties of a system in equilibrium and its constituent phases are interdependent. A change in one of them causes a change in the others. Quantitative functional dependencies between the properties of a system (phase) can be reflected by equations of various types.

Of these equations, the most important is equation of state phase, connecting in integral form the pressure, temperature, density (or volume), composition and other properties of each phase of the system in equilibrium.

The equation of state is closely related to the thermodynamic equations of the system and its homogeneous parts (phases), but cannot be derived in a specific form from the basic equations of thermodynamics and must be found empirically or obtained by methods of statistical physics, based on molecular parameters (i.e., quantities characterizing the structure and properties of individual molecules). The simplest equations of state are equations for gases at low pressures: the Clapeyron-Mendeleev equation, the van der Waals equation, etc.

The presence of equations of state and other equations that relate various properties of the phase leads to the fact that for an unambiguous characterization of the state of the system, it is sufficient to know only a few, few independent properties. These properties are called independent variables or state parameters systems. The remaining properties are functions of the state parameters and are uniquely determined if the values ​​of the latter are given. In this case, for many problems it does not matter whether we know the specific equations of state of the phases under study; it is only important that the corresponding dependencies always really exist.

Thus, the state of the system is determined by independent variables (state parameters), the number of which depends on the nature of the particular system, and their choice is, in principle, arbitrary and related to considerations of expediency. To determine the state of the simplest systems - homogeneous and constant in time in mass and composition (consisting of one phase and not changing chemically) - it is enough to know two independent variables out of three (volume V, pressure P and temperature T). In more complex systems, independent variables may include concentrations, electric charge, electrostatic potential, magnetic field strength, and others.

Caloric coefficients

The internal energy of the system, being a function of the state, is a function of the independent variables (state parameters) of the system.

In the simplest systems

U = f (V, T) (I, 7)

whence the total differential U :

dU = dV + dT (1,8)

Substituting the value dU from equation (I, 8) to equation (I, 2), we find:

δQ = dV + dT + δW(I, 9)

If only expansion work takes place in the system under study and there are no electrical work, gravity, surface forces, etc., then d W = PDF. Then

δQ = + P dV + dT(I, 9a)

Denoting the coefficients at the differentials of the independent variables in equation (I, 9a) by the symbols l And C V , we get:

δQ = ldV + C V dT(1,10)

Equations (I, 9a) and (I, 10) imply:

= l = + P(I.11)

= C V =

Quantities And are not derivatives of any function. The first one is heat of isothermal expansion body. This quantity, the dimension of which coincides with the dimension of the pressure, is the sum of the external pressure and the term ; which reflects the mutual attraction of molecules. This term is small for real gases and very large (compared to the usual values ​​of external pressure) for liquids and solids.

Value C V, according to equation (I, 11), is heat capacity at constant volume. The heat absorbed by the system at a constant volume is spent entirely on increasing the internal energy (provided that all types of work, including expansion work, are absent).

The coefficients of the total differential of internal energy with variables V And T have a simple physical meaning, as shown above.

Choosing as independent variables P And T or V And P and considering the internal energy as a function of these pairs of variables, we can similarly obtain:

d Q = hdP + C P dT(I, 10a)

d Q= c dV+ l dp(I, 10b)

where the quantities h, C P , c and l are related to the derivatives of internal energy by more complex relationships than those presented in equation (I, 11). Note that C p = eat heat capacity at constant pressure, but h = – heat of isothermal increase in pressure. The latter value is essentially negative.

Odds l, h, C V , C P , c and λ are called calorie ratios. Having an independent physical meaning (especially C P,C V and l), they are also useful auxiliary quantities in thermodynamic conclusions and calculations.

Operation of various processes

Under the name of work, many energy processes are combined; a common property of these processes is the expenditure of system energy to overcome a force acting from outside. Such processes include, for example, the movement of masses in a potential field. If the motion is against the force gradient, then the system expends energy in the form of work; the amount of work is positive. When moving along a force gradient, the system receives energy in the form of work from outside; the amount of work is negative. Such is the work of lifting a known mass in a gravitational field. Elementary work in this case:

d W = – mgdH

where m- body mass; H is the height above the initial zero level. When a system expands under external pressure P, system does work , elementary work is equal in this case PdV (V 1 And V 2 - initial and final volumes of the system, respectively).

When an electric charge moves q in an electric field against the direction of potential drop j and in the area where the potential change is equal to dj, as well as with an increase in the charge of a body that has the potential j, by the value dq work is done on the system, its value is equal in the first case - qdj, and in the second case jdq.

In a similar way, the work of increasing the interface surface can be expressed S between homogeneous parts of the system (phases): d W=-s dS,
where s is the surface tension.

In general, elementary work dW is the sum of several qualitatively different elementary works:

d W = Pd V- mgdH-s dS– j d q + … (1.12)

Here P, -mg, -σ, -j are forces in a generalized sense (generalized forces) or intensity factors; V, H, S, q – generalized coordinates or capacitance factors.

In each specific case, it is necessary to determine what types of work are possible in the system under study, and, having compiled the appropriate expressions for dW, use them in equation (I, 2a). Integration of equation (I, 12) and calculation of work for a specific process are possible only in cases where the process is in equilibrium and the equation of state is known.

For very many systems, it is possible to limit the series of equation (I, 12) to one term - the expansion work.

The work of expansion in equilibrium processes is expressed by various equations that follow from the equation of state. Here are some of them:

1) The process proceeding at a constant volume (isochoric process; V = const):

W = ∫δW = ∫PdV = 0(I, 13)

2) The process proceeding at constant pressure (isobaric process; P = const):

W= = P (V 2 - V 1) \u003d PDV(I, 14)

3) A process that takes place at a constant temperature (isothermal process, T = const). The work of expansion of an ideal gas, for which PV=nRT:

W = dV = nRT log(I, 15)

Enthalpy

The equation of the first law of thermodynamics for processes where only expansion work is performed takes the form:

δQ = dU + PdV(I, 19)

If the process proceeds at constant pressure, then, by integrating, we obtain:

Q P \u003d U 2 - U 1 + P (V 2 - V 1)(I, 20)

Q P \u003d (U 2 + PV 2) - (U 1 + PV 1)(I, 21)

Because P And V– state parameters, a U is a state function, then the sum U+PV is also a state function and its change in the process does not depend on the path of the process, but only on the initial and final states. This function is called enthalpy and is denoted by the symbol H. Determination of the value H identity serves:

H U + PV(I, 22)

From equation (I, 21) it follows that the heat absorbed at constant pressure is equal to the increase in enthalpy D H and does not depend on the process path:

(I, 21a)

Second law of thermodynamics

The most common and certainly spontaneous processes are the transfer of heat from a hot body to a cold one (thermal conduction) and the transition of work into heat (friction). The centuries-old everyday, technical and scientific practice of mankind has shown the everyday reality of these processes, as well as the impossibility of the spontaneous occurrence of reverse processes, which are very tempting from a practical point of view (getting work by removing heat from the bodies surrounding the working body). This gives grounds to assert that the only result of any set of processes cannot be the transfer of heat from a less heated body to a more heated one. (postulate of Clausius).

The reverse of the indicated transition of heat from a more heated body to a less heated one is the usual non-equilibrium process of heat transfer by heat conduction. It cannot be reversed, that is, it cannot be drawn back through the same sequence of states. But this is not enough: if the process of direct heat transfer took place in the system, then in no way can such a sequence of any processes be carried out as a result of which all the bodies participating in the heat transfer would return to their original state and no changes would occur in other bodies. The heat conduction process is irreversible.

Another general position, which has the same experimental basis, states the following: the only result of any set of processes cannot be the conversion of heat into work (that is, the absorption of heat from the environment by the system and the release of work equivalent to this heat). Thus, the spontaneous process of converting work into heat (by friction) is irreversible (just like heat conduction).

The last statement can be stated differently: the heat of the coldest of the bodies participating in the process cannot serve as a source of work (Thomson's postulate).

Both positions (the postulates of Clausius and Thomson) are formulations of the second law of thermodynamics and are equivalent to each other, that is, each of them can be proved on the basis of the other.

Since the transfer of heat or its transformation into work is considered as the only result of the process, it is obviously necessary that the system participating in heat exchange returns as a result of the process or a combination of processes to its original state. In such a cyclic process, the internal energy of the system will not change.

Let us suppose that the second of the above formulations (especially in its last form) is incorrect. Then it would be possible to build a machine that works in cycles, the “working body” of which would periodically return to its original state, and this machine would give work due to heat absorbed from the outside from a body no hotter than the system itself and all other bodies surrounding the system. . Such a process would proceed without violating the first law of thermodynamics (work due to heat), but for practice it is equivalent to obtaining work from nothing, since any machine would have an almost inexhaustible source of heat in the environment. So the ship could move, taking away the warmth of ocean water and not needing fuel. Such a machine is called perpetuum mobile (perpetuum mobile) of the second kind. Based on this definition, we can formulate the second law of thermodynamics, giving Thomson's postulate a different form: a perpetuum mobile of the second kind is impossible.

It should be emphasized that both the provisions of Clausius and Thomson and the assertion that the perpetuum mobile of the second kind is impossible cannot be proved on the basis of other laws or provisions. They are conjectures that are justified by all the consequences that follow from them, but cannot be proved for all possible cases.

Let us give one more formulation of the second law of thermodynamics, which, of course, is quite accurate and concise. This formulation contains a postulate about the existence of a new state function, through which the difference between reversible and irreversible processes is expressed:

Methods for calculating entropy

Equations (II, 1) and (II, 1a), which determine the entropy, are the only initial equations for the thermodynamic calculation of the change in the entropy of the system. Replacing elemental heat in equation (II, 1a) by its expressions in terms of caloric coefficients (see equations (I, 10) and (I, 10a)), we obtain for equilibrium processes:

kJ/mol; melting temperature t sq. \u003d 5.5 ° С ( T= 278,5 TO). Therefore, the entropy change 1 mole benzene during melting (entropy of melting) is equal to:

DS sq. = 35,06J/mol

2. Heating at constant pressure (isobaric process; P = const). From equations (I, 18a) and (II, 1a) we obtain:

D.S. =(II, 6)

Let us find the change in the entropy of one mole of aluminum when heated from 25 to 600°C. The true molar heat capacity of aluminum can be expressed by the equation:

C p = 565.5 + 0.290 T. According to equation (II, 6), the change in entropy will be equal to:

DS = = 565.5 + 0.290(873 - 298) = 607.8 + 166.8 = 774.6 J/molK

Planck's postulate. Absolute Entropy Values

By equation (II, 3) it is impossible to calculate the absolute value of the entropy of the system. This possibility is provided by a new, unprovable position that does not follow from the two laws of thermodynamics, which was formulated by M. Planck (1912). According to this provision, called Planck's postulate, the entropy of an individual crystalline substance at absolute zero is zero:

Strictly speaking, Planck's postulate is valid only for individual substances, the crystals of which are ideally built (in the crystal lattice, all nodes are occupied by molecules or atoms, regularly alternating and regularly oriented). Such crystals are called ideal solids. Real crystals are not such, since their crystal lattice is not built perfectly.

The entropy of a crystal lattice built to some extent randomly is greater than the entropy of a perfectly built crystal lattice. Therefore, real crystals even at 0 K have an entropy greater than zero. However, the entropies of real well-formed crystals of individual substances at absolute zero are small.

In accordance with Planck's postulate, equation (II, 6) for an ideal rigid body will take the form:

Planck's postulate is used in the thermodynamic study of chemical processes to calculate the absolute values ​​of the entropy of chemical compounds - quantities that are of great importance in the calculation of chemical equilibria.

Entropy is widely used in technical thermodynamics (heat engineering), as one of the important parameters of the working fluid in a heat engine, for example, water vapor. The entropy values ​​of water vapor in a given state are calculated in comparison with some standard state - usually 0°C and 1 amm. These entropy values ​​are used to construct the so-called entropy state diagrams water vapor in coordinates S-T or S-H(Mollier diagram). In such diagrams, like diagrams V-P it is possible to depict various processes occurring in the working body of a heat engine and constituting the working cycles of the machine.

In conclusion, it should be noted that we do not have to delve into the field of thermodynamics. Our purpose is only to illustrate the main ideas of this science and explain the reasons why it is possible to build on its arguments.

Finally, the two laws of thermodynamics are often formulated as follows:

First law: The energy of the universe is always constant.

Second law: The entropy of the universe always increases.