Phys. chemistry - the science of the laws of chemical processes and chemistry. phenomena.

Subject of physical chemistry explanation of chemistry. phenomena based on more general laws of physics. Physical chemistry considers two main groups of questions:

1. Study of the structure and properties of matter and its constituent particles;

2. Study of the processes of interaction of substances.

Physical chemistry aims to study the connections between chemical and physical phenomena. Knowledge of such connections is necessary in order to deeply study the chemical reactions that occur in nature and are used in technology. processes, control the depth and direction of the reaction. The main goal of the discipline Physical Chemistry is the study of general connections and laws of chemistry. processes based on fundamental principles of physics. Physical chemistry uses physical. theories and methods for chemical phenomena.

It explains WHY and HOW transformations of substances occur: chemistry. reactions and phase transitions. WHY – chemical thermodynamics. HOW - chemical kinetics.

Basic concepts of physical chemistry

The main object of chemistry. thermodynamics is a thermodynamic system. Thermodynamic system – any body or set of bodies capable of exchanging energy and matter with themselves and with other bodies. Systems are divided into open, closed and isolated. Open and I - The thermodynamic system exchanges both substances and energy with the external environment. Closed and I - a system in which there is no exchange of matter with the environment, but it can exchange energy with it. Isolated and I -system volume remains constant and is deprived of the opportunity to exchange energy and matter with the environment.

The system may be homogeneous (homogeneous) or heterogeneous (heterogeneous) ). Phase - this is part of a system that, in the absence of an external field of forces, has the same composition at all its points and the same thermodynamics. St. you and is separated from other parts of the system by an interface. The phase is always uniform, i.e. homogeneous, therefore a single-phase system is called homogeneous. A system consisting of several phases is called heterogeneous.

The properties of the system are divided into two groups: extensive and intensive.

Thermodynamics uses the concepts of equilibrium and reversible processes. Equilibrium is a process passing through a continuous series of equilibrium states. Reversible thermodynamic process is a process that can be carried out in reverse without leaving any changes in the system or environment.

2. First law of thermodynamics. Internal energy, heat, work.

First law of thermodynamics directly related to the law of conservation of energy. Based on this law, it follows that in any isolated system the energy supply remains constant. From the law of conservation of energy follows another formulation of the first law of thermodynamics - the impossibility of creating a perpetual motion machine (perpetuum mobile) of the first kind, which would produce work without expending energy on it. A particularly important formulation for chemical thermodynamics

The first principle is to express it through the concept of internal energy: internal energy is a function of state, i.e. its change does not depend on the path of the process, but depends only on the initial and final state of the system. Change in internal energy of the system  U can occur due to heat exchange Q and work W with the environment. Then from the law of conservation of energy it follows that the heat Q received by the system from the outside is spent on the increase in internal energy ΔU and the work W performed by the system, i.e. Q =Δ U+W. Given at alignment is

mathematical expression of the first law of thermodynamics.

Ibeginning of thermodynamics its wording:

in any isolated system the energy supply remains constant;

different forms of energy transform into each other in strictly equivalent quantities;

perpetual motion machine (perpetuum mobile) of the first kind is impossible;

internal energy is a function of state, i.e. its change does not depend on the path of the process, but depends only on the initial and final state of the system.

analytical expression: Q = D U + W ; for an infinitesimal change in quantities d Q = dU + d W .

The first law of thermodynamics establishes the relation. m / y heat Q, work A and change in internal. energy of the system ΔU. Change internal the energy of the system is equal to the amount of heat imparted to the system minus the amount of work done by the system against external forces.

Equation (I.1) is a mathematical representation of the 1st law of thermodynamics, equation (I.2) is for an infinitesimal change in state. systems.

Int. energy is a function of state; this means that the change is internal. energy ΔU does not depend on the path of transition of the system from state 1 to state 2 and is equal to the difference in the internal values. energies U2 and U1 in these states: (I.3)

Int. The energy of the system is the sum of the potential energy of the interaction. all particles of the body in relation to each other and the kinetic energy of their movement (without taking into account the kinetic and potential energies of the system as a whole). Int. the energy of the system depends on the nature of the substance, its mass and the parameters of the state of the system. She's age. with an increase in the mass of the system, since it is an extensive property of the system. Int. energy is denoted by the letter U and expressed in joules (J). In general, for a system with a quantity of 1 mole. Int. energy, like any thermodynamic. The sacredness of the system is a function of the state. Only internal changes appear directly in the experiment. energy. That is why in calculations they always operate with its change U2 –U1 = U.

All internal changes energies are divided into two groups. The 1st group includes only the 1st form of transition of motion through chaotic collisions of molecules of two contacting bodies, i.e. by thermal conduction (and at the same time by radiation). The measure of the movement transmitted in this way is heat. Concept warmth is associated with the behavior of a huge number of particles - atoms, molecules, ions. They are in constant chaotic (thermal) motion. Heat is a form of energy transfer. The second way to exchange energy is Job. This exchange of energy is caused by an action performed by the system or an action performed on it. Usually the work is indicated by the symbol W. Work, like heat, is not a function of the state of the system, therefore the quantity corresponding to infinitesimal work is denoted by the partial derivative symbol - W.

The content of the article

PHYSICAL CHEMISTRY, a branch of chemistry that studies the chemical properties of substances based on the physical properties of their constituent atoms and molecules. Modern physical chemistry is a broad interdisciplinary field bordering on various branches of physics, biophysics and molecular biology. It has many points of contact with such branches of chemical science as organic and inorganic chemistry.

A distinctive feature of the chemical approach (as opposed to the physical and biological) is that within its framework, along with the description of macroscopic phenomena, their nature is explained based on the properties of individual molecules and the interactions between them.

New instrumental and methodological developments in the field of physical chemistry are used in other branches of chemistry and related sciences, such as pharmacology and medicine. Examples include electrochemical methods, infrared (IR) and ultraviolet (UV) spectroscopy, laser and magnetic resonance techniques, which are widely used in therapy and for the diagnosis of various diseases.

The main branches of physical chemistry are traditionally considered: 1) chemical thermodynamics; 2) kinetic theory and statistical thermodynamics; 3) questions of the structure of molecules and spectroscopy; 4) chemical kinetics.

Chemical thermodynamics.

Chemical thermodynamics is directly related to the application of thermodynamics - the science of heat and its transformations - to the problem of chemical equilibrium. The essence of the problem is formulated as follows: if there is a mixture of reagents (system) and the physical conditions in which it is located (temperature, pressure, volume) are known, then what spontaneous chemical and physical processes can bring this system to equilibrium? The first law of thermodynamics states that heat is a form of energy and that the total energy of a system (together with its surroundings) remains constant. Thus, this law is one of the forms of the law of conservation of energy. According to the second law, a spontaneous process leads to an increase in the overall entropy of the system and its environment. Entropy is a measure of the amount of energy that a system cannot expend to do useful work. The second law indicates the direction in which a reaction will go without any external influences. To change the nature of a reaction (for example, its direction), you need to expend energy in one form or another. It thus places strict limits on the amount of work that can be done by converting the heat or chemical energy released in a reversible process.

We owe important achievements in chemical thermodynamics to J. Gibbs, who laid the theoretical foundation of this science, which made it possible to combine into a single whole the results obtained by many researchers of the previous generation. Within the framework of the approach developed by Gibbs, no assumptions are made about the microscopic structure of matter, but the equilibrium properties of systems at the macro level are considered. This is why we can think that the first and second laws of thermodynamics are universal and will remain valid even as we learn much more about the properties of molecules and atoms.

Kinetic theory and statistical thermodynamics.

Statistical thermodynamics (like quantum mechanics) allows us to predict the equilibrium position for some reactions in the gas phase. Using the quantum mechanical approach, it is possible to describe the behavior of complex molecules of a number of substances in liquid and solid states. However, there are reactions whose rates cannot be calculated either within the framework of kinetic theory or using statistical thermodynamics.

The real revolution in classical statistical thermodynamics occurred in the 70s of the 20th century. New concepts such as universality (the idea that members of certain broad classes of compounds have the same properties) and the principle of similarity (estimation of unknown quantities based on known criteria) have made it possible to better understand the behavior of liquids near the critical point where the difference between the liquid and gas. Using a computer, the properties of simple (liquid argon) and complex (water and alcohol) liquids in a critical state were simulated. More recently, the properties of liquids such as liquid helium (the behavior of which is perfectly described within the framework of quantum mechanics) and free electrons in molecular liquids have been comprehensively studied using computer modeling SUPERCONDUCTIVITY). This allowed us to better understand the properties of ordinary liquids. Computer methods, combined with the latest theoretical developments, are intensively used to study the behavior of solutions, polymers, micelles (specific colloidal particles), proteins and ionic solutions. To solve problems in physical chemistry, in particular to describe some properties of systems in a critical state and study issues in high-energy physics, the mathematical method of the renormalization group is increasingly being used.

Molecular structure and spectroscopy.

Organic chemists of the 19th century. developed simple rules for determining the valence (ability to combine) of many chemical elements. For example, they found that the valence of carbon is 4 (one carbon atom can attach four hydrogen atoms to form a methane molecule CH 4), oxygen - 2, hydrogen - 1. Based on empirical concepts based on experimental data, assumptions were made about the spatial arrangement atoms in molecules (for example, the methane molecule has a tetrahedral structure, with the carbon atom located in the center of the triangular pyramid, and hydrogen at its four vertices). However, this approach did not make it possible to reveal the mechanism of formation of chemical bonds, and therefore to estimate the sizes of molecules or determine the exact distance between atoms.

Using spectroscopic methods developed in the 20th century, the structure of water molecules (H 2 O), ethane (C 2 H 6), and then much more complex molecules such as proteins was determined. The methods of microwave spectroscopy (EPR, NMR) and electron diffraction made it possible to determine the lengths of bonds, the angles between them (bond angles) and the relative positions of atoms in simple molecules, and X-ray diffraction analysis - similar parameters for larger molecules forming molecular crystals. The compilation of catalogs of molecular structures and the use of simple concepts of valency laid the foundations of structural chemistry (its pioneer was L. Pauling) and made it possible to use molecular models to explain complex phenomena at the molecular level. If the molecules did not have a specific structure or if the parameters of the C–C and C–H bonds in chromosomes were very different from those in methane or ethane molecules, then using simple geometric models, J. Watson and F. Crick would not have been able to construct at the beginning 1950s its famous double helix - a model of deoxyribonucleic acid (DNA). By studying the vibrations of atoms in molecules using IR and UV spectroscopy, it was possible to establish the nature of the forces that hold atoms in the composition of molecules, which, in turn, suggested the presence of intramolecular motion and made it possible to study the thermodynamic properties of molecules ( see above). This was the first step towards determining the rates of chemical reactions. Further, spectroscopic studies in the UV region helped to establish the mechanism of chemical bond formation at the electronic level, which made it possible to describe chemical reactions based on the concept of the transition of reagents to an excited state (often under the influence of visible or UV light). Even a whole scientific field arose - photochemistry. Nuclear magnetic resonance (NMR) spectroscopy has enabled chemists to study individual stages of complex chemical processes and identify active sites in enzyme molecules. This method also made it possible to obtain three-dimensional images of intact cells and individual organs. PHOTOCHEMISTRY.

Valence theory.

Using the empirical rules of valence developed by organic chemists, the periodic table of elements and Rutherford's planetary model of the atom, G. Lewis established that the key to understanding chemical bonding is the electronic structure of a substance. Lewis came to the conclusion that a covalent bond is formed as a result of the sharing of electrons belonging to different atoms; At the same time, he proceeded from the idea that bonding electrons are located in strictly defined electron shells. Quantum theory makes it possible to predict the structure of molecules and the nature of the covalent bonds formed in the most general case.

Our ideas about the structure of matter, formed thanks to the successes of quantum physics in the first quarter of the 20th century, can be briefly summarized as follows. The structure of an atom is determined by the balance of electrical forces of repulsion (between electrons) and attraction (between electrons and a positively charged nucleus). Almost all the mass of an atom is concentrated in the nucleus, and its size is determined by the amount of space occupied by the electrons that orbit the nuclei. Molecules are composed of relatively stable nuclei held together by rapidly moving electrons, so that all chemical properties of substances can be explained based on the idea of ​​​​the electrical interaction of the elementary particles that make up atoms and molecules. Thus, the main provisions of quantum mechanics concerning the structure of molecules and the formation of chemical bonds create the basis for an empirical description of the electronic structure of matter, the nature of chemical bonds and the reactivity of atoms and molecules.

With the advent of high-speed computers, it was possible to calculate (with low, but sufficient accuracy) the forces acting between atoms in small polyatomic molecules. Valence theory, based on computer modeling, is currently a working tool for studying structures, the nature of chemical forces and reactions in cases where conducting experiments is difficult or time-consuming. This refers to the study of free radicals present in the atmosphere and flames or formed as reaction intermediates. There is hope that someday a theory based on computer calculations will be able to answer the question: how, in a time of the order of picoseconds, chemical structures “calculate” their most stable state, while obtaining the corresponding estimates, at least to some approximation, requires a huge number of machine time.

Chemical kinetics

studies the mechanism of chemical reactions and determines their rates. At the macroscopic level, a reaction can be represented as successive transformations, during which others are formed from one substance. For example, the seemingly simple transformation

H 2 + (1/2) O 2 → H 2 O

actually consists of several successive stages:

H + O 2 → OH + O

O + H 2 → HO + H

H + O 2 → HO 2

HO 2 + H 2 → H 2 O + OH

and each of them is characterized by its own rate constant k. S. Arrhenius suggested that the absolute temperature T and reaction rate constant k related by the relation k = A exp(- E Act)/ RT, Where A– pre-exponential factor (so-called frequency factor), E act – activation energy, R– gas constant. For measuring k And T we need instruments that allow us to track events that occur over a period of about 10–13 s, on the one hand, and over decades (and even millennia) on the other (geological processes); it is also necessary to be able to measure minute concentrations of extremely unstable reagents. The task of chemical kinetics also includes predicting chemical processes occurring in complex systems (we are talking about biological, geological, atmospheric processes, combustion and chemical synthesis).

To study gas-phase reactions “in their pure form,” the molecular beam method is used; in this case, molecules with strictly defined quantum states react to form products that are also in certain quantum states. Such experiments provide information about the forces that determine the occurrence of certain reactions. For example, in a molecular beam setup, you can orient even small molecules such as CH 3 I in a given way, and measure the collision rates in two “different” reactions:

K + ICH 3 → KI + CH 3

K + CH 3 I → KI + CH 3

where the CH 3 group is oriented differently relative to the approaching potassium atom.

One of the issues that physical chemistry (as well as chemical physics) deals with is the calculation of reaction rate constants. The transition state theory, developed in the 1930s, which uses thermodynamic and structural parameters, is widely used here. This theory, combined with the methods of classical physics and quantum mechanics, makes it possible to simulate the course of a reaction as if it were occurring under experimental conditions with molecular beams. Experiments are being carried out on laser excitation of certain chemical bonds, which make it possible to verify the correctness of statistical theories of the destruction of molecules. Theories are being developed that generalize modern physical and mathematical concepts of chaotic processes (for example, turbulence). We are no longer so far from fully understanding the nature of both intra- and intermolecular interactions, revealing the mechanism of reactions occurring on surfaces with given properties, and establishing the structure of the catalytic centers of enzymes and transition metal complexes. At the microscopic level, work on the kinetics of the formation of complex structures such as snowflakes or dendrites (crystals with a tree-like structure) can be noted, which stimulated the development of computer modeling based on simple models of the theory of nonlinear dynamics; this opens up prospects for creating new approaches to describing the structure and development processes of complex systems.

The classification of sciences is based on the classification of forms of motion of matter and their relationships and differences. 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.

The chemical form of motion, i.e., the chemical process, is characterized by a change in the number and arrangement of atoms in the molecule of reacting substances. 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 - the elementary act of thermal dissociation of a molecule - occurs with an increase in the intensity (amplitude and energy) of vibrations in the molecule, especially vibrations of nuclei along the valence bond between them. Reaching a known critical value of vibration energy in the direction of a certain bond in a molecule leads to the rupture of this bond and the dissociation of the molecule into two parts.

More complex reactions involving several (usually two) molecules can be considered as the combination of two molecules upon their collision into a fragile 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 in the vibrational 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, collisions of molecules and the exchange of energies between them are necessary (transfer of the energy of movement of molecules of reaction products to molecules of starting substances through collisions). Thus, the real chemical process is closely related to the second physical form of movement - chaotic movement of molecules of macroscopic bodies, which is often called thermal movement.

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

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

The study 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.

The study of the structure of molecules examines the geometry of molecules, intramolecular motions and the forces that bind the atoms in a molecule. In experimental studies of the structure of molecules, the method of molecular spectroscopy (including radio spectroscopy) is most widely used; electrical, radiographic, magnetic and other methods are also widely used.

The study of states of aggregation examines the interactions of molecules in gases, liquids and crystals, as well as the properties of substances in various states of aggregation. 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 a part of physics.

Chemical thermodynamics . In this section, based on the laws of general thermodynamics, the laws of chemical equilibrium and the doctrine of phase equilibria, which is usually called the phase rule, are presented. Part of chemical thermodynamics is thermochemistry, which deals with the thermal effects of chemical reactions.

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

The solution to this problem requires the construction of a general theory of the interaction of dissimilar molecules, i.e., the solution to the main problem of molecular physics. To develop the 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, fumes), 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 large independent section of physical chemistry and an independent academic discipline in chemical higher educational institutions.

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

Chemical kinetics and catalysis . The rate of chemical reactions is studied, 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 influence on the reaction rate of substances not participating in the stoichiometric reaction equation (catalysis).

Photochemistry. The interaction of radiation and substances involved in chemical transformations is studied (reactions occurring under the influence of radiation, for example, photographic processes and photosynthesis, luminescence). 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 recently emerged areas and smaller sections of this science, which can be considered as parts of larger sections or as independent sections of physical chemistry. These are, for example, radiation chemistry, physical chemistry of high-molecular substances, magnetochemistry, gas electrochemistry and other branches of physical chemistry. The importance of some of them is currently growing rapidly.

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 occurrence of chemical reactions over time and the laws of chemical equilibrium.

Theoretical understanding of 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 doctrine 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 by experimental optical methods.

Method of statistical physics , which makes it possible to calculate the properties of a substance; consisting of many molecules (“macroscopic” properties), based on information about the properties of individual molecules.

Thermodynamic method , which 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.

Modern physical and chemical research in any specific field is characterized by the use of a variety of experimental and theoretical methods to study various properties of substances and 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 clarify the dependence of the direction, speed and limits of chemical transformations on external conditions and on the structure of the molecules participating in chemical reactions.

Thermodynamic system- a body or group of bodies interacting, 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 separating 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 either matter or energy with the 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.

Status Options– quantities characterizing any macroscopic property of the system under consideration.

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

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

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

1) infinitesimal difference between acting and opposing forces: F ex – F in > 0;

2) the system performs maximum work in the direct process | W| = max;

3) an infinitely slow 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 occur 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 occur reversible or irreversible.

Non-spontaneous process– a process that requires the expenditure of work from outside in an amount proportional to the change in the state of the system.

Energy– a measure of the system’s ability to do work; a general qualitative measure of the movement and interaction of matter. Energy is an integral property of matter. Distinguish potential energy, conditioned by the position of the body in the field of certain forces, and kinetic energy, caused by a change in body position in space.

Internal energy of the system U – the sum of the kinetic and potential energy of all particles that make up the system. You 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 contacting bodies, i.e., through thermal conductivity (and at the same time through radiation). Q> 0 if the system receives heat from the environment. [ Q]= J.

Job W – a form of energy transfer through the ordered movement of particles (macroscopic masses) under the influence 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 compression) and other types of work (useful work): ? W = -pdV + ?W?.

Standard state of solids and liquids– stable state of a pure substance at a given temperature under pressure p = 1 atm.

Standard state of pure gas– state of a gas that obeys the equation of state of an ideal gas at a pressure of 1 atm.

Standard values– values ​​determined for substances in the standard state (indicated by superscript 0).

1.1. First law of thermodynamics

Energy is indestructible and uncreated; it can only pass 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 a 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 internal energy of a closed system occurs due to the heat imparted to the system and/or work done on the system.

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

Open system

A change in the internal energy of an open system occurs due to the heat imparted to the system and/or 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 function of state; does this mean that the change in internal energy? U does not depend on the path of transition of the system from state 1 to state 2 and is equal to the difference in the internal energy values U 2 And U 1 in these states:

?U =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

The entire 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– molar heat capacity at constant volume, J/(mol? deg). For ideal gases:

C V = 2 / 3 R– monatomic gas;

C V = 5 / 2 R– diatomic gas.

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

H = U + pV – enthalpy– function of the system state.

?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 enthalpy of the system.

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

C r– molar heat capacity at constant pressure, J/(mol? deg).

For ideal gases: C r = 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 a reaction at a constant temperature.

Qv = ?UV Qp = ?Up 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, a change in heat capacity is specified by a change in the composition of the system:

?S p= ?(? i C p,i) cont – ?(? i C p,i) out or? C V =?(? i C V,i) cont – ?(? i C V,i) out

Integral form of Kirchhoff's law:

?Н Т2 = ?Н Т1 + ?С р (Т 2 – T 1) or? U T2 = ?U Ti + ?C V (T 2 – T 1)

1.3. 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 whose only result 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 temperature of the system as follows:

in a nonequilibrium process

in an equilibrium process

S – entropy, J/deg,

– 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 a system), the greater the more disordered or uncertain the state is. Entropy is a state function that describes the degree of disorder of a system.

S = k ln W– Boltzmann formula.

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

Absolute entropy calculation

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

?S = ?(? i S i) prod – ?(? i S i) ref

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

1.4. Thermodynamic potentials

Potential– a quantity whose loss determines the work produced by the system.

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

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

dG = dH – TdS or? G = ?Н – T?S ?G = ?(? i G i) prod – ?(? i G i) ref ?G 0 = ?(? i ?G arr 0) prod – ?(? i ?G arr 0) ref Conditions for the spontaneous occurrence of 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 is called such a thermodynamic state of a system with minimal free energy, which, with 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– concentrations, pressures of reacting substances at any time other than the equilibrium state.

Influence of external conditions on chemical equilibrium

Le Chatelier-Brown principle of shifting equilibrium

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 influence.

Effect of temperature on the equilibrium position

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

Endothermic reactions: ?Н° > 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 that can be isolated from the system and exist outside of it. The number of independent components of a system is equal to the number of components minus the number of possible chemical reactions between them.

Number of degrees of freedom– 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 influencing the equilibrium: C = K – F + n.

For a system that is influenced only by external factors temperature and pressure, can be written: C = K – F+ 2.

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

2.1. Water 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 equilibrium between three phases and C = 0; three phases can be in equilibrium only at strictly defined values ​​of temperature and pressure (for water, the triple point corresponds to the state with P = 6.1 kPa and T = 273.16 K).

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

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

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

V 2, V 1– change in the molar volume of a substance during a phase transition.

The equilibrium curve “solid - liquid” on the state diagram of water is inclined 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 solid-liquid phase transition (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 abrupt changes in its properties.

Diffusion in solutions

Diffusion– a spontaneous process of equalizing 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 that diffuses per unit time through a unit surface area is proportional to its concentration gradient:

Where j– diffusion flow; D– diffusion coefficient.

Einstein-Smoluchowski equation:

Where? – viscosity of the medium; R– 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 gases included in it:

Ptot = ? p i And pi = xi P total

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

As a rule, when a gas dissolves in a liquid, heat is released (To< 0), therefore As temperature increases, solubility decreases.

Sechenov's formula:

X = X 0 e -kС el

Where X And X 0– gas solubility in a pure solvent and an electrolyte solution with concentration WITH.

3.2. Colligative properties of non-electrolyte solutions

Colligative (collective) are 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

Vapor that is in equilibrium with a liquid is called saturated. The pressure of such steam p 0 called pressure or pressure 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 proportionality coefficient is equal to the saturated vapor pressure above 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 above 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 is satisfied 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 = p A 0 x A + p B 0 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 above the mixture will be greater than those calculated by Raoult's first law (positive deviations, ?Н TV > 0). If homogeneous particles interact with each other less than dissimilar ones, the partial vapor pressures of the components will be less than calculated (negative deviations, ?H dissolve< 0).

Crystallization temperature of dilute solutions

Raoult's second law. The decrease in the freezing temperature of a solution? T is directly proportional to the molal concentration of the solution: ? T is = T 0 – T = KS m, Where T 0 – freezing point of a pure solvent; T– freezing temperature of the solution; TO– cryoscopic constant of the solvent, deg/kg mol,

T 0 2– freezing point of the solvent; M– molecular weight of the solvent, ?Н pl – molar heat of fusion of the solvent.

Boiling point of dilute solutions

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

Increasing the boiling point of solutions of non-volatile substances? T K = T k – T k 0 proportional to the decrease in saturated vapor pressure and directly proportional to the molal concentration of the solution: ?T kip = EU m, Where E – ebullioscopic constant solvent, deg/kg mol,

Osmotic pressure of dilute solutions

Osmosis– predominantly one-way passage of solvent molecules through a semi-permeable membrane into a solution or solvent molecules from a solution with a lower concentration into a solution with a higher concentration.

The pressure that must be applied to a solution to prevent the solvent from moving into the solution through the membrane separating the solution and 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 dissolved substance 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 solution– 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?– ratio of the number of molecules n, disintegrated into ions, to the total number of molecules N:

Van Hoff's isotonic coefficient i– the ratio of the actual number of particles in an electrolyte solution to the number of particles of this solution without taking into account dissociation.

If from N molecules dissociated n, and each molecule disintegrated 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 break up into ions - 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).

Dissociation of electrolytes in solution occurs under the influence of polar solvent molecules; the presence of ions in a solution determines its electrical conductivity.

Based on 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 a certain electrolyte that disintegrates into ions in solution in accordance with the equation:

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

For a binary electrolyte:

– Ostwald’s law of dilution: the degree of dissociation of a weak electrolyte increases with dilution of the solution.

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

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

For a binary electrolyte:

– average electrolyte activity;

– average activity coefficient.

Debye-Hückel limit law for binary electrolyte: lg f = -0.51z 2 I?, Where z– charge of the ion for which the activity coefficient is calculated;

I – ionic strength of 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 transferred by electrons.

Type II conductors– solutions and melts of electrolytes with ionic conductivity.

Electricity is the ordered movement of charged particles.

Every 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; the proportionality factor is resistivity material? – resistance of a conductor having a length of 1 cm and a cross-section of 1 cm 2:

Magnitude W, the inverse of resistance is called electrical conductivity– a quantitative measure of the ability of an electrolyte solution to conduct electric current.

Electrical conductivity?(k) is the electrical conductivity of a type I conductor 1 m long with a cross-sectional area of ​​1 m2 or the electrical conductivity of 1 m3 (1 cm3) of an electrolyte solution (type II conductor) 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) ?– electrical conductivity of a solution containing 1 mole of 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 solution dilution V = 1/C), reaching a certain limiting value? 0 (? ?), called molar electrical conductivity at infinite dilution.

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

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

Where F– Faraday number; and + , and? – absolute mobility (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 solution length.

? + = 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 conductivity at infinite dilution equal to the sum of the electrolytic mobilities? ? + , ? ? ? cation and anion of a given electrolyte.

H+ and OH ions? have 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 ions? Proton exchange occurs continuously 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 (type II conductor), etc.) arises between them electric double layer (EDL). EDL is the result of an ordered distribution of oppositely charged particles at the interface.

The formation of an EDL leads to a jump in potential?, which, under equilibrium conditions between a metal (conductor of the first kind) and a solution of a metal salt (conductor of the second kind) is called galvani potential.

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

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

? > 0, if the reduction reaction of Me n+ + occurs at the electrode 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 of a conductor of the first type/conductor of the second type and measured relative to a standard hydrogen electrode.

Nernst equation, Where n– number of electrons participating in the electrode reaction; WITHМе n+ – concentration of cations; E Me n+ /Me – standard electrode potential.

Contact potential? ?– an equilibrium potential jump that occurs at the interface between two conductors of the first kind.

Diffusion potential? diff is the equilibrium potential difference that occurs at the phase boundary of a conductor of the second type/conductor of the second type.

Galvanic cell (g.e.)– an electrical circuit consisting of two or more p.e. and producing electrical energy due to the chemical reaction occurring 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 reduction process takes place is cathode.

IUPAC rules for recording galvanic cells and reactions occurring in them

1. In g. e. work is performed, therefore the emf of the element is considered a positive value.

2. The magnitude 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 from the numerical value of the cathode potential (right electrode) the value of the anode potential (left electrode) - right pole rule. Therefore, the circuit diagram of the element is written so that the left electrode is negative (oxidation occurs), and the right electrode is positive (reduction process occurs).

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

4. The boundary between two conductors of the second type is depicted with a dotted line.

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

6. Components of one phase are written separated by commas.

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

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

(-) Zn | Zn 2+ :: Cu 2+ | Cu(+)

Reactions on electrodes:

Zn 0 > Zn 2+ + 2e? Cu 2+ + 2e? > Cu 0

Total redox process:

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

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

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

EMF of the element E Zn/ Cu = ? Cu 2+ /Cu + ? Zn 2+ /Zn + ? k + ? diff.

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

Concentration chains

The only result 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 opposite in direction reversible electrode processes.

5.2. Classification of electrodes

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

Electrodes of the second kind. The metal is coated with a slightly soluble salt of that metal and is in a 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 bathed in hydrogen gas and immersed in a solution containing hydrogen ions. The hydrogen adsorbed by platinum is in equilibrium with gaseous hydrogen.

Pt, H 2 / H +

Electrochemical equilibrium at the electrode:

2H + + 2e? - N 2.

The potential of a standard hydrogen electrode (with an H + ion activity of 1 mol/l 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 calomel Hg 2 Cl 2:

Hg / Hg 2 Cl 2 , KCl

Calomel electrode is reversible with respect to chlorine anions

Silver chloride electrode– reversible with respect to chlorine anions:

Ag/AgCl, KCl

If the KCl solution is saturated, then E AgC l = 0.2224 – 0.00065(t – 25), V.

Indicator electrodes. Hydrogen ion reversible electrodes 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 previously 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 often 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, into which an auxiliary electrode (usually silver chloride) is immersed. To measure pH, a glass electrode is immersed in the test solution in pairs with a 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 alkali metal cations. The electrode process comes down to the exchange of hydrogen ions between two phases - the solution under study and glass: H solution - H st +.

Standard potential E st 0 for each electrode has its own value, which changes over time; Therefore, before each pH measurement, the glass electrode is calibrated against standard buffer solutions with an accurately 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: Ох n+ + ne? - Red.

In this case inert Me takes an indirect part in the electrode reaction, mediating 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

Superficial phenomena are processes that occur at the phase boundary and are caused by the characteristics of the composition and structure of the surface (boundary) layer.

Gs = ?s,

Where G s– surface Gibbs energy of the system, J; ? – proportionality coefficient, called surface tension, J/m 2 ; s – interfacial surface, m2.

Surface tensionO 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 of phase interface at a constant temperature.

From the Dupre model, surface tension equal to the force tending to reduce the interface and per unit length of the contour limiting the surface

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

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

1. Surfactants (surfactants)– reduce the surface tension of the solvent (? solution< ? 0) g >0 (relative to water – organic compounds of diphilic structure).

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

3. Non-surfactants (NSS)– practically do not change the surface tension of the solvent (? solution = ? 0) g = 0 (in relation to water, the substances are sucrose and a number of others).

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

For aqueous solutions of fatty acids (Shishkovsky equation):

Where b And TO– 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 any substance at the interface between two phases is called adsorption. Adsorbent is a substance on the surface of which a change in the concentration of another substance occurs - adsorbate.

Gibbs adsorption isotherm:

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

6.2. Adsorption at the solid-gas interface

Physical adsorption arises due to van der Waals interactions of the 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 through the chemical interaction of adsorbent and adsorbate molecules, usually irreversible; is localized i.e., adsorbate molecules cannot move along the surface of the adsorbent. Since chemisorption is a chemical process that requires an activation energy of the order of 40-120 kJ/mol, an increase in temperature promotes its occurrence.

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

G = Ks or G = Kr,

TO– adsorption equilibrium constant, depending on the nature of the adsorbent and adsorbate; S, p– solute concentration 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 adsorption process is reversible and equilibrium.

Langmuir adsorption isotherm:

Where Г 0 – monolayer capacity– constant equal to the limiting adsorption observed at relatively high equilibrium concentrations, mol/m2; b– constant equal to the ratio of the adsorption rate constant and the desorption rate constant.

Freundlich equation(adsorption on a non-uniform surface): Г = K F with n, Where. K F is a constant numerically equal to adsorption at an equilibrium concentration equal to unity; n– 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; WITH– equilibrium concentration of adsorbate; V– volume of adsorbate solution; m– mass of the adsorbent.

Square S0, per one molecule in the saturated adsorption layer, – landing site:

m 2 /molecule.

Adsorption layer thickness:

Where M– molecular weight of the surfactant; ? – surfactant density.

Rehbinder's rule: Polar adsorbates from low-polar solvents are better adsorbed on polar adsorbents; 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 the solid phase, in which the solid phase absorbs ions of a certain sign (cations or anions) from the solution and instead can release into the solution an equivalent number of other ions of the same sign. Forever specific, i.e., for a given adsorbent, only certain ions are capable of exchange; exchange adsorption is usually irreversible.

Paket-Peskov-Faience rule: On the surface of a crystalline solid, an ion is specifically adsorbed from an electrolyte solution, which is capable of completing 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 is a heterogeneous system 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– a collection 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 a substance – dispersity and heterogeneity.

Degree of dispersion?– the reciprocal of the average diameter or, for non-spherical particles, the reciprocal of the average equivalent diameter d(m -1):

Specific surface area– 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 of producing disperse systems

Classification according to the state of aggregation of phases

A disperse system in which both the dispersed phase and the dispersion medium are gases does not exist, since 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-disperse, 10 -7_ 10 -5 m (instant coffee);

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

Methods for obtaining colloidal systems Dispersing

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

Chemical dispersion (peptization): transferring freshly prepared sediment into a colloidal state using a peptizer.

Condensation

Physical condensation: 1) the solvent replacement method, which consists of adding a liquid miscible with the solvent, in which the substance itself is slightly soluble, to a true solution of a substance; 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) method of condensation from vapors; the starting substance is in vapor; as the temperature decreases, the steam becomes supersaturated and partially condenses, forming a dispersed phase.

Chemical condensation: any chemical reaction that results 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 substances is taken in excess and serves as a stabilizer.

7.2. Optical properties of disperse systems

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

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

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

refraction and reflection light is observed for systems in which the particles are much longer 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 dispersed phase particles are smaller, but comparable 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 thermal energy.

Rayleigh equation:

where I, I 0 – intensity of scattered and incident light; V– volume of one particle; ? – partial concentration (number of particles per unit volume); ? – wavelength; n 1, n 0 are the refractive indices of 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 a superposition of their own color and the color caused by opalescence (the phenomenon dichroism of light).

7.3. Molecular kinetic properties

It is typical for colloidal systems Brownian motion– continuous random movement of particles of microscopic and colloidal sizes. This movement is more intense the higher the temperature and the lower the mass of the particle and the viscosity of the dispersion medium.

Diffusion– a spontaneous process of equalizing the concentration of particles.

Fick's Law:

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

Osmotic pressure:

where mtot is the mass of the dissolved substance; m– mass of one particle; V– volume of the system; N A– Avogadro’s number; T– absolute temperature; ? – partial concentration; k– Boltzmann constant.

For spherical particles:

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

7.4. Micelle structure

Micelle lyophobic The system is called a heterogeneous microsystem, which consists of a dispersed phase microcrystal surrounded by solvated stabilizer ions.

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

Counterions– ions grouped near the micelle core.

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

Counterions included in the dense adsorption layer, are called “connected” and together with the nucleus make up colloidal particle or granule. A colloidal particle (granule) has a charge, the sign of which is determined by the sign of the charge of the potential-determining ions.

Counterions forming diffuse layer,– “movable” or “free”.

A colloidal particle with a surrounding diffuse layer of solvated counterions constitutes 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 an EDL at the phase boundary; a potential difference arises between the dispersed phase and the dispersion medium – thermodynamic potential f (interfacial), which is determined by the properties of a given disperse system, as well as 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 influence of an external electric field is called electrophoresis.

The surface over which 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 entire volume of the dispersion medium.

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

Sedimentation stability– the ability of a system to withstand the effects of gravity. Sedimentation is the settling of particles in a 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? – density of the dispersed phase, ? 0 – density of the dispersion medium, g – acceleration of gravity, ? – viscosity of the medium.

Aggregative stability characterizes the ability of particles of the dispersed phase to resist their adhesion to each other and thereby maintain their size.

When aggregative stability is violated, coagulation is the process of particles sticking together to form large aggregates. As a result of coagulation, the system loses its sedimentation stability, because the particles become too large and cannot participate in Brownian motion.

Causes of coagulation:

> temperature change;

> the effect of electric and electromagnetic fields;

> action of visible light;

> irradiation with elementary particles;

> mechanical impact;

> adding electrolyte, etc.

Coagulation with electrolytes is of greatest practical interest.

Types of coagulation with electrolytes

Concentration coagulation occurs under the influence indifferent electrolytes. Indifferent called an electrolyte, upon the 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 zero, coagulation occurs. The formula of the micelle in this state takes the form: (mnAg + nNO 3 ?) 0.

Neutralization coagulation occurs when added to a sol non-indifferent electrolyte. Indifferent called an electrolyte that can change the interfacial (?) and linearly associated 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 coagulum returns to the colloidal state is called peptization or disaggregation.

Coagulation rules

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

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

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

3. The greater the charge of the ion, the greater the coagulating ability of the coagulant 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 greater, the larger its crystalline radius. Ag + > Cs + > Rb + > NH 4 + > K + > Na + > Li+ – lyotropic series.

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

Protective number is 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

Subject of physical chemistry. Its meaning

Studies the relationship between chemical and physical phenomena physical chemistry. This branch of chemistry is the border between chemistry and physics. Using 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 their accompanying physical processes. Since, however, even a multilateral study is never complete and does not cover the phenomenon exhaustively, the laws and regularities of physical chemistry, as well as other natural sciences, always simplify the phenomenon and do not reflect it completely.

The rapid development and growing importance of physical chemistry are associated with its borderline position between physics and chemistry. The main general task of physical chemistry is to predict 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. He taught a course in physical chemistry to students of the Academy of Sciences and left a manuscript for this course, “Introduction to True Physical Chemistry” (1752). Lomonosov carried out many studies, the topics of which correspond to his “Plan for the Course of Physical Chemistry” (1752) and the program of experimental work “Experience in Physical Chemistry” (1754). Under his leadership, a student workshop on physical chemistry was also conducted.

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

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

The number and variety of research in the area bordering 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). L.F. Wilhelmi's research marked the beginning of the study of the rates of chemical reactions (chemical kinetics). The transfer of electricity in solutions was studied (I.V. Gittorf, F.V.G. Kohlrausch), 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 founding 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 branches of physical chemistry had been 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, based on the laws of general thermodynamics, the laws of chemical equilibrium and the doctrine of phase equilibria are presented.

The study of solutions aims to explain and predict the properties of solutions (homogeneous mixtures of several substances) based on 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 phenomena studied in surface layers is adsorption(accumulation of substance in the surface layer).

In systems where the interfaces between liquid, solid and gaseous phases are highly developed (emulsions, mists, fumes, 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 large independent branch of physical chemistry.

The given 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 is worth emphasizing once again the close relationship between the various branches of physical chemistry. When studying any phenomenon, one has to use an arsenal of ideas, theories and research methods from many branches of chemistry (and often other sciences). Only with initial acquaintance with physical chemistry is it possible to distribute the material into the indicated sections for educational purposes.

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 various processes and the laws of chemical equilibrium.

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, 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.

CHAPTER I.
FIRST LAW OF THERMODYNAMICS

Heat 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 energy transitions associated with it can be divided into two groups.

The first group includes only one form of transition of motion through chaotic collisions of molecules of two contacting bodies, i.e. by thermal 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 transition of motion, the common feature of which is the movement of macroscopic masses under the influence of any external forces of a directed nature. These are the lifting of bodies in a gravitational field, the transition of a certain amount of electricity from a higher electrostatic potential to a smaller one, the expansion of a gas under pressure, etc. The general measure of movement transmitted by such methods is Job .

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

The transfer of motion is a unique complex movement 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 should be considered as forms of energy.

The common property of heat and work is that they are significant only during the periods of time in which these processes occur. During such processes, in some bodies the movement in certain forms 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 store of heat or work in any body, but only about the heat and work of a certain process. After its completion, there is no need to talk about the presence of heat or work in bodies.

Internal energy

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

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

d Q¹d W,

hence:

d Q– d W ¹ 0

Let's 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 function of the state of the system. When the system returns to its original state (after a cyclic change), the value of this function acquires its original value.

System Status Function U, defined by equalities (I, 2) or (I, 2a) is called internal energy systems .

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

= U 2 – U 1 = ∆U = –(I, 2b)

U 2 – U 1 = ∆U = Q – W

This reasoning empirically substantiates 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 has.

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 energy of particles in a 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 original state, the internal energy of the system did not take on 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 transform 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, as shown by direct experiments.

Inability to carry out the specified construction cycle perpetual motion machine (perpetuum mobile) of the first kind, giving work without spending an equivalent amount of another type of energy, has been proven 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 again. The total energy reserve 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 specific value and does not depend on what changes the system underwent before it arrived to this state.

In other words, the internal energy of a 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); for a circular process, expression (I, 3) is valid. With an infinitesimal change in some properties (parameters) of the system, the internal energy of the system also changes infinitely small. 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. Formal quantitative determination through expressions (I, 2) or (I, 2a) is sufficient for all further thermodynamic reasoning and conclusions.

Since the internal energy of a system is a function of its state, then, as has already been said, the increase in internal energy with infinitesimal changes in the parameters of the system’s states is the total differential of the state function. Splitting the integral in equation (I, 3) into two integrals over sections of the path from the state 1 to the point 2 (path “a”) (see Fig. I) and back - from the state 2 to the point 1 (another path "b" ), – we get:

(I, 4)

(I, 5)

We will arrive at the same result by comparing 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 a 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 state 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 energy balance during various processes, including chemical reactions.

From the law of conservation of energy it 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 associated with equations (I, 3) and (I, 5) serves formulation of the first law of thermodynamics(in combination with equation (I, 2), giving a quantitative definition of 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 expression (I, 2a). In an isolated system dQ = 0 And dW = 0, then 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, applied to specific conditions and finite systems, a quantitative expression of the general law of conservation of energy, 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 full value of the internal energy of a system in any state, since the equations expressing the first law lead to the calculation of only changes in the energy of the system in various processes. Likewise, the change in internal energy in macroscopic processes cannot be directly measured; one can only calculate this change using equation (I, 2b), taking into account measurable quantities - heat and work of this process.

Note that heat and work (each separately) do not have the property of a state function 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 magnitude δQ And δW are not differentials of the state function, but are simply infinitesimal quantities, which we will call elemental heat And basic work.

Thus, the internal energy differential dU has different mathematical properties than elementary heat dQ and work dW. This is of significant importance when constructing a thermodynamic system.

Equations of state

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 the 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 pressure, temperature, density (or volume), composition and other properties of each phase of a system that is 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 experimentally 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 the 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 connecting various properties of the phase leads to the fact that for an unambiguous characterization of the state of the system, knowledge of only a few independent properties is sufficient. These properties are called independent variables or state parameters systems. The remaining properties are functions of state parameters and are determined uniquely if the values ​​of the latter are given. Moreover, for many problems it does not matter whether we know the specific equations of state of the phases under study; the only important thing is that the corresponding dependencies always actually 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 over 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 a system, being a function of state, is a function of independent variables (state parameters) of the system.

In the simplest systems

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

where does the total differential U come from? :

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 in the system under study there is only expansion work and no electrical work, gravitational force, surface forces, etc., then d W = PdV. Then

δQ = + P dV + dT(I, 9a)

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

δQ = ldV + C V dT(1,10)

From equations (I, 9a) and (I, 10) it follows:

= l = + P(I,11)

= C V =

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

Magnitude C V, in accordance with equation (I, 11), there 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).

Coefficients of the total differential of internal energy for 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 to be a function of these pairs of variables, we can obtain, similarly to the above:

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

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

where are 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 = There is heat capacity at constant pressure, A h = – heat of isothermal pressure increase. The last value is significantly negative.

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

Operation of various processes

Many energy processes are united under the name of work; a common property of these processes is the expenditure of energy by the system to overcome the force acting from the outside. Such processes include, for example, the movement of masses in a potential field. If movement occurs 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 the outside; the amount of work is negative. This is the work of raising a known mass in a gravitational field. Elementary work in this case:

d W = – mgdH

Where m- body mass; H– height above the initial zero level. When a system expands under external pressure P, the 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 opposite the direction of potential drop j and in the area where the change in potential is equal to DJ, as well as with an increase in the charge of a body having potential j, by the amount 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, we can express the work of increasing the interface surface S between homogeneous parts of the system (phases): d W= -s dS,
where s is surface tension.

In general, an elementary job 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 – forces in a generalized sense (generalized forces) or intensity factors; V, H, S, q – generalized coordinates or capacity factors.

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

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

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

1) A process occurring at constant volume (isochoric process; V = const):

W = ∫δW = ∫PdV = 0(I, 13)

2) A process occurring at constant pressure (isobaric process; P = const):

W= = P(V 2 – V 1) = PDV(I, 14)

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

W = dV = nRT ln(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 occurs at constant pressure, then, integrating, we obtain:

Q P = U 2 – U 1 + P(V 2 – V 1)(I, 20)

Q P = (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 function of state 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 indicated by the symbol H. Determining the value H is the identity:

HU+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 (obtaining work by taking away heat from 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 (Clausius's postulate).

The opposite transition of heat from a more heated body to a less heated one is the usual nonequilibrium process of heat transfer by thermal conductivity. It cannot be reversed, that is, carried in the opposite direction through the same sequence of states. But this is not enough: if the system has undergone a process of direct heat transfer, then it is in no way possible to carry out such a sequence of any processes as a result of which all the bodies involved in the transfer of heat would return to their original state and no changes would occur in other bodies. The process of thermal conduction 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 transformation of heat into work (i.e., the absorption of heat by the system from the environment and the release of work equivalent to this heat). Thus, the spontaneous process of converting work into heat (through friction) is irreversible (just like thermal conductivity).

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 provisions (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 proven on the basis of the other.

Since the transition 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 set of processes to its original state. With such a cyclic process, the internal energy of the system will not change.

Let us assume that the second of the above formulations (especially in its last form) is incorrect. Then it would be possible to build a machine operating in cycles, the “working fluid” of which would periodically return to its original state, and this machine would produce work due to heat absorbed from the outside from a body no more heated 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 every machine would have a practically inexhaustible source of heat in the environment. This way the steamship could move, taking away the heat of the ocean water and not needing fuel. This machine is called perpetuum mobile (perpetual motion machine) 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 statement about the impossibility of perpetuum mobile of the second kind, are not proven on the basis of other laws or provisions. They are assumptions that are justified by all the consequences that flow from them, but cannot be proven for all possible cases.

Let us give another formulation of the second law of thermodynamics, which is, of course, quite accurate and concise. This formulation contains the postulate of 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 entropy, are the only initial equations for the thermodynamic calculation of the change in entropy of the system. Replacing the elementary heat in equation (II, 1a) with its expressions through caloric coefficients (see equations (I, 10) and (I, 10a)), we obtain for equilibrium processes:

KJ/mol; melting temperature t pl. = 5.5°C ( T= 278,5 TO). Therefore, the entropy change is 1 mole benzene when melting (entropy of melting) is equal to:

DS pl. = 35,06J/mol

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

DS=(II, 6)

Let's find the change in 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

Using 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 whose crystals are ideally constructed (in a 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 like that, since their crystal lattice is not ideally constructed.

The entropy of a crystal lattice constructed somewhat randomly is greater than the entropy of a perfectly constructed 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 solid 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 calculating 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 so-called entropy state diagrams water vapor in coordinates S-T or S-H(Mollier diagram). In such diagrams, similar to diagrams V-P You can depict various processes occurring in the working fluid of a heat engine and making up the operating cycles of the machine.

In conclusion, it should be noted that we do not have to delve into the field of thermodynamics. Our goal 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.