Physical chemistry theory. Physical chemistry. Physical chemistry subject

Leaks 22.09.2020
Leaks

3rd ed., Rev. - M .: Higher school, 2001 - 512 p., 319 p.

The textbook is compiled in accordance with the physical chemistry program.

The first book details the following sections of the course: quantum mechanical foundations of the theory of chemical bonding, the structure of atoms and molecules, spectral methods for studying molecular structure, phenomenological and statistical thermodynamics, thermodynamics of solutions and phase equilibria.

In the second part of the section of the course in physical chemistry, electrochemistry, chemical kinetics and catalysis are presented on the basis of the concepts developed in the first part of the book - the structure of matter and statistical thermodynamics. The section "Catalysis" reflects the kinetics of heterogeneous and diffusion processes, the thermodynamics of adsorption and issues of reactivity.

For university students studying in chemical engineering specialties.

Book 1.

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Book 2.

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CONTENTS Book 1.
Foreword. 3
Introduction 6
Section one. Quantum-mechanical substantiation of the theory of molecular structure and chemical bonding
CHAPTER 1. The structure of the atom 9
§ 1.1. Quantum-mechanical features of microparticles 9
§ 1.2. Hydrogen-like atom 11
§ 1.3. Atomic orbitals of hydrogen-like atom 14
§ 1.4. Electron spin 21
§ 1.5. Multi-electron atoms 23
§ 1.6. Pauli principle 26
§ 1.7. Electronic configurations of atoms 28
CHAPTER 2. Molecules. Theoretical methods used to study the structure of molecules and chemical bonds 34
§ 2.1. Molecule. Potential surface. Equilibrium configuration 34
§ 2.2. The theory of chemical bonding and its tasks. Schrödinger equation for molecules 39
§ 2.3. A variational method for solving the Schrödinger equation 42
§ 2.4. Two main methods of the theory of molecular structure. Valence bond method and molecular orbital method 44
§ 2.5. Basic ideas of the molecular orbital method 49
§ 2.6. Approximate description of the molecular orbital in the MO LCAO method 50
§ 2.7. The U molecule in the MO LCAO method. Calculation of energy and wave function by the variational method 53
§ 2.8. Molecule H in the MO LCAO method. Covalent bond 58
Chapter 3. Diatomic molecules in the MO LCAO method 62
§ 3.1. Molecular orbitals of homonuclear diatomic molecules 62
§ 3.2. Electronic configurations and properties of homonuclear molecules formed by atoms of elements of the first and second periods 65
§ 3.3. Heteronuclear diatomic molecules 73
§ 3.4. Polar communication. Electric dipole moment of molecule 78
§ 3.5. Saturation of the covalent bond 81
§ 3.6. Donor-acceptor bond 82
§ 3.7. Ionic bond. Chemical bond polarity 84
Chapter 4. Polyatomic molecules in the MO 88 method
§ 4.1. Molecular orbitals in polyatomic molecules. Orbital symmetry. Delocalized and localized orbitals. Molecule NHO 88
§ 4.2. Description of the methane molecule. Delocalized and localized MO. Orbital hybridization 95
§ 4.3. Prediction of equilibrium configurations of molecules 99
§ 4.4. Non-Rigid Molecules 101
§ 4.5. Molecules with multiple bonds in MO LCAO 104
§ 4.6. Hückel Method 108
§ 4.7. Description of aromatic systems in the MOX 110 method
§ 4.8. Chemical bond in coordination compounds. Ligand field theory 117
§ 4.9. Ionic bond in crystal 126
Chapter 5. Intermolecular interactions 129
§ 5.1. Van der Waals forces. Other types of non-specific interactions 129
§ 5.2. Hydrogen bond 136
Section two. Spectral methods for studying the structure and energy states of molecules
Chapter 6. General information on molecular spectra. Elements of the theory of molecular spectra 141
§ 6.1. Intramolecular motion and electromagnetic spectrum. 141
§ 6.2. Molecular emission, absorption and Raman spectra. EPR and NMR Spectra 145
§ 6.3. Rotational spectrum of a diatomic molecule (rigid rotator approximation) 150
§ 6.4. Vibrational-rotational spectrum of a diatomic molecule. Harmonic Oscillator Approximation 156
§ 6.5. Molecule is an anharmonic oscillator. The structure of the vibrational spectrum 162
§ 6.6. Electronic spectra. Determination of the dissociation energy of diatomic molecules 169
§ 6.7. Rotational spectra and strict polyatomic molecules ... 171
§ 6.8. Vibrations, spectrum and structure of polyatomic molecules 175
§ 6.9. Using vibrational spectra to determine the structure of molecules 180
§ 6.10. Influence of intermolecular interaction of the medium and the state of aggregation on the vibrational spectrum 183
Section three. Chemical thermodynamics
CHAPTER 7. General concepts. The first law of thermodynamics and its application 186
§ 7.1. The subject and tasks of chemical thermodynamics 186
§ 7.2. Basic concepts and definitions of chemical thermodynamics 188
§ 7.3. The first law of thermodynamics. Non-circular processes 199
§ 7.4. Specific heat 202
§ 7.5. Influence of temperature on heat capacity. Temperature series .. 208
§ 7.6. Quantum theory of heat capacity of crystalline matter 211
§ 7.7. Quantum-statistical theory of the heat capacity of gaseous matter 215
§ 7.8. Thermal effects. Hess's Law 217
§ 7.9. Application of Hess's law to the calculation of thermal effects 220
§ 7.10. Dependence of the thermal effect on temperature. Kirchhoff Equation 227
Chapter 8. The second law of thermodynamics and its appendix 235
§ 8.1. Spontaneous and non-spontaneous processes. The second law of thermodynamics 235
§ 8.2. Entropy 236
§ 8.3. Change in entropy in non-static processes 239
§ 8.4. Change in entropy as a criterion of direction and balance in an isolated "system 240
§ 8.5. Characteristic functions. Thermodynamic potentials 241
§ 8.6. Criteria for the possibility of a spontaneous process and equilibrium in closed systems 249
§ 8.7. Change in entropy in some processes 251
§ 8.8. Gibbs energy of a mixture of ideal gases. Chemical potential 261
§ 8.9. General conditions for chemical equilibrium 265
§ 8.10. The law of the acting masses. Equilibrium constant for gas-phase reactions 266
§ 8.11. Isotherm equation of reaction 271
§ 8.12. Using the Mass Action Law to Calculate the Equilibrium Mixture Composition 273
§ 8.13. Effect of temperature on chemical equilibrium. Isobar equation of reaction 282
§ 8.14. Integral form of the temperature dependence of the change in the Gibbs energy and the equilibrium constant 284
§ 8.15. Chemical equilibrium in heterogeneous systems 286
Chapter 9. The third law of thermodynamics and the calculation of chemical equilibrium 289
§ 9.1. Thermal Nernst theorem. The third law of thermodynamics 289
§ 9.2. Calculation of the change in the standard Gibbs energy and the equilibrium constant by the Temkin - Shvartsman method 294
§ 9.3. Calculation of the change in the standard Gibbs energy and the equilibrium constant using the reduced Gibbs energy functions 297
§ 9.4. Adiabatic reactions 299
CHAPTER 10. Chemical equilibrium in real systems 303
§ 10.1. Fugacity and fugacity coefficient of gases 303
§ 10.2. Calculation of chemical equilibrium in a real gas system at high pressures 312
§ 10.3. Calculation of chemical equilibrium in systems in which several reactions occur simultaneously 314
CHAPTER 11. Introduction to Statistical Thermodynamics 320
§ 11.1. Statistical physics and statistical thermodynamics. Macroscopic and microscopic description of the state of the system 320
§ 11.2. Microscopic description of the state by the method of classical mechanics 323
§ 11.3. Microscopic description of a state by the method of quantum mechanics. Quantum Statistics 324
§ 11.4. Two kinds of averages (microcanonical and canonical averages) 325
§ 11.5. Relationship between entropy and statistical weight. The statistical nature of the second law of thermodynamics 326
§ 11.6. The system is in the thermostat. Canonical Gibbs distribution. 330
§ 11.7. The sum over the states of the system and its relation to energy. Helmholtz 335
§ 11.8. Sum over particle states 337
§ 11.9. Expression of thermodynamic functions in terms of the sum over the states of the system 340
§ 11.10. Sum over the states of a system of one-dimensional harmonic oscillators. Thermodynamic properties of a monatomic solid according to Einstein's theory 343
§ 11.11. Boltzmann's quantum statistics. Maxwell's law of molecular velocity distribution 346
§ 11.12. Fermi - Dirac and Bose - Einstein statistics 352
§ 11.13. General formulas for calculating thermodynamic functions from molecular data 353
§ 11.14 Calculation of the thermodynamic functions of an ideal gas under the assumption of rigid rotation and harmonic vibrations of molecules 357
Section four. Solutions
CHAPTER 12. General characteristics of solutions 365
§ 12.1. Classification of solutions 365
§ 12.2. Concentration of solutions 367
5 12.3. Specificity of solutions. The role of intermolecular and chemical interactions, the concept of solvation 368
§ 12.4. The main directions in the development of the theory of solutions 372
§ 12.5. Thermodynamic conditions for the formation of solutions 374
§ 12.6. Partial molar quantities 375
§ 12.7. Basic methods for determining partial molar values \u200b\u200b379
§ 12.8. Partial and relative partial molar enthalpies 381
§ 12.9. Heats of dissolution and dilution 382
§ 12.10. Thermodynamic properties of ideal liquid solutions 386
§ 12.11.3 Raoul's law 390
§ 12.12. Boiling point of ideal solution 392
§ 12.13. Freezing point of ideal solution 395
§ 12.14.0Smotic pressure of ideal solution 397
§ 12.15. Non-ideal solutions 400
§ 12.16. Extremely diluted, regular and athermal solutions 402
§ 12.17. Activity. Activity coefficient. Standard state 404
§ 12.18.0smotic factor 407
§ 12.19. Methods for determining activities 409
§ 12.20. Connection of the activity coefficient and activity with the thermodynamic properties of the solution and the excess thermodynamic functions 412
Section 5 Phase Equilibria
Chapter 13. Thermodynamic theory of phase equilibria 415
§ 13.1. Basic concepts 415
§ 13.2. Phase equilibrium conditions 418
§ 13.3. Gibbs Phase Rule 419
Chapter 14. One-Piece Systems 421
§ 14.1. Application of the Gibbs Phase Rule to One-Component Systems 421
§ 14.2. Phase transitions of the first and second kind 422
§ 14.3. Clapeyron-Clausius equation 425
§ 14.4. Saturated steam pressure 423
§ 14.5. State diagrams of one-component systems 429
§ 14.6. State diagram of carbon dioxide 431
§ 14.7. Water condition diagram 432
§ 14.8. Sulfur diagram 433
§ 14.9. Enantiotropic and monotropic phase transitions 435
Chapter 15. Two-component systems 436
§ 15.1. Physical and chemical analysis method 436
§ 15.2. Application of the Gibbs Phase Rule to Two-Component Systems 437
§ 15.3. Equilibrium gas - liquid solution in two-component systems 438
§ 15.4. Equilibrium liquid - liquid in two-component systems 442
§ 15.5. Equilibrium vapor - liquid solution in two-component systems 444
§ 15.6. Physicochemical bases of distillation of solutions 453
§ 15.7. Equilibrium crystals - liquid solution in two-component systems 457
§ 15.8. Equilibrium liquid - gas and crystals - gas (vapor) in two-component systems 476
§ 15-9. Calculations from state diagrams 476
Chapter 16. Three-piece systems 482
§ 16.1. Application of the Gibbs Phase Rule to Three-Component Systems 482
§ 16.2. Graphical representation of the composition of the 482 ternary system
§ 16.3. Equilibrium crystals - liquid solution in three-component systems 484
§ 16.4. Equilibrium liquid - liquid in three-component systems 489
§ 16.5. Distribution of the solute between two liquid phases. Extraction 491
Appendix 495
Index 497

CONTENTS Book 2.
Foreword 3
Section six. Electrochemistry
CHAPTER 17. Solutions, electrolytes 4
§ 17.1. Electrochemistry Item 4
§ 17.2. Specificity of electrolyte solutions 5
§ 17.3. Electrolytic dissociation in solution 6
§ 17.4. Average ionic activity and activity coefficient 10
§ 17.5. Basic concepts of the electrostatic theory of strong electrolytes by Debye and Hückel 13
§ 17.6. Basic concepts of the theory of association of ions 22
§ 17.7. Thermodynamic properties of ions 24
§ 17.8. Thermodynamics of ionic solvation 28
CHAPTER 18. Nonequilibrium phenomena in electrolytes. Electrical conductivity of electrolytes 30
§ 18.1. Basic concepts. Faraday's laws 30
§ 18.2. The movement of ions in an electric field. Ion transport numbers. 32
§ 18.3. Electrical conductivity of electrolytes. Specific electrical conductivity 37
§ 18.4. Electrical conductivity of electrolytes. Molar electrical conductivity 39
§ 18.5. Molar electrical conductivity of hydronium and hydroxide ions 43
§ 18.6. Electrical conductivity of non-aqueous solutions 44
§ 18.7. Electrical conductivity of solid and molten electrolytes 46
§ 18.8. Conductometry 47
CHAPTER 19. Equilibrium electrode processes 49
§ 19.1. Basic concepts 49
§ 19.2. EMF of an electrochemical system. Electrode potential 51
§ 19.3. The appearance of a potential jump at the solution-metal interface 53
§ 19.4. Diffusion potential 55
§ 19.5. The structure of the electric double layer at the solution-metal interface 56
§ 19.6. Thermodynamics of reversible electrochemical systems 60
§ 19.7. Classification of reversible electrodes 64
§ 19.8. Electrode potentials in non-aqueous solutions 74
§ 19.9. Electrochemical circuits 75
§ 19.10. Application of the theory of electrochemical systems to the study of equilibrium in solutions 82
§ 19.11. Potentiometry 85
Section seven. Kinetics of chemical reactions
CHAPTER 20. Laws of Chemical Kinetics 93
§ 20.1. General concepts and definitions 93
§ 20.2. Chemical reaction rate 95
§ 20.3. The law of mass action and the principle of independence of the course of reactions 101
CHAPTER 21. Kinetics of chemical reactions in closed systems. 105
§ 21.1. Unilateral reactions of the first order 105
§ 21.2. Unilateral second-order reactions 109
§ 21.3. Unilateral reactions of the nth order 111
§ 21.4. Methods for determining the order of reaction 112
§ 21.5. First order bilateral reactions 113
§ 21.6. Bilateral reactions of the second order 116
Section 21.T. Parallel unilateral reactions 117
§ 21.8. Unilateral sequential reactions 119
§ 21.9. Quasi-stationary concentration method 125
Chapter 22. Kinetics of reactions in open systems 127
§ 22.1. Kinetics of reactions in an ideal mixing reactor 127
§ 22.2. Kinetics of reactions in a plug-flow reactor 129
Chapter 23. Theory of the elementary act of chemical interaction 133
§ 23.1. Elementary chemical act 133
§ 23.2. Theory of active collisions 137
§ 23.3. Activated Complex Theory 141
§ 23.4. Preexponential factor in the Arrhenius equation according to the theory of transition state 154
§ 23.5. MO symmetry and activation energy of chemical reactions 159
CHAPTER 24. Kinetics of reactions in solutions, chain and photochemical reactions 166
§ 24.1. Features of the kinetics of reactions in solutions 166
§ 24.2. Influence of the environment on the reaction rate constant 170
§ 24.3. Kinetics of ionic reactions in solutions 178
§ 24.4. Chain reactions 181
§ 24.5. Photochemical reactions 189
Chapter 25. Kinetics of electrode processes 196
§ 25.1. Electrochemical reaction rate. Exchange current 196
§ 25.2. Electrode polarization 197
§ 25.3. Diffusion overvoltage 199
§ 25.4. Electrochemical overvoltage 205
§ 25.5. Other types of overvoltage 210
5 25.6. Temperature-kinetic method for determining the nature of polarization in electrochemical processes 211
§ 25.7. Overvoltage during electrolytic hydrogen evolution 213
§ 25.8. Electrolysis. Decomposition voltage 217
§ 25.9. Polarization phenomena in chemical sources of electric current 220
§ 25.10. Electrochemical corrosion of metals. Passivity of metals. Corrosion protection methods 222
Section eight. Catalysis
CHAPTER 26. Principles of catalytic action 228
§ 26.1. Basic concepts and definitions 228
§ 26.2. Features of the kinetics of catalytic reactions 232
§ 26.3. Activation energy of catalytic reactions 237
§ 26.4. Interaction of reagents with a catalyst and principles of catalytic action 241
Chapter 27. Homogeneous catalysis 245
§ 27.1. Acid-base catalysis 246
§ 27.2. Redox catalysis 255
§ 27.3. Enzymatic catalysis 260
§ 27.4. Autocatalysis, Inhibition and Batch Catalytic Reactions 266
§ 27.5. Industrial applications and prospects for the development of homogeneous catalysis 271
CHAPTER 28. Heterogeneous catalysis. 273
§ 28.1. Surface structure of heterogeneous catalysts 273
§ 28.2. Adsorption as a Stage of Heterogeneous Catalytic Reactions 277
§ 28.3. The mechanism of heterogeneous catalytic reactions 282
§ 28.4. Kinetics of heterogeneous catalytic reactions on an equally accessible surface 285
§ 28.5. Macrokinetics of heterogeneous catalytic processes 292
§ 28.6. Industrial Applications of Heterogeneous Catalysis 300
Literature 303
Appendix 305
Index 312
Table of contents 316

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

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

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

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

Isolated system - a system that does not exchange 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 parameters - quantities characterizing any macroscopic property of the system under consideration.

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

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

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

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

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

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

Spontaneous process - a process that can proceed without the cost 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. A spontaneous process can proceed reversiblyor irreversible.

Non-spontaneous process - a process for the flow of which requires the expenditure of work from the 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; general qualitative measure of the motion and interaction of matter. Energy is an inherent property of matter. Distinguish potential energy,due to the position of the body in the field of certain forces, and kinetic energy,due to a change in the position of the body 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 the system as its total energy minus the kinetic and potential energy of the system as a whole. [ U] \u003d J.

Heat Q - the form of energy transfer through the disordered movement of molecules, through chaotic collisions of molecules of two contacting bodies, that is, through heat conduction (and simultaneously through radiation). Q\u003e0 if the system receives heat from the environment. [ Q] \u003d J.

Job W - the form of energy transfer through the ordered movement of particles (macroscopic masses) under the action of any forces. W\u003e0 if the environment is doing work on the system. [W] \u003d J.

All work is divided into mechanical work of expansion (or contraction)and other types of work (useful work):? W \u003d -pdV +? W ?.

Standard state of solid and liquid substances - steady state of a pure substance at a given temperature under pressure p \u003d1 atm.

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

Standard values - values \u200b\u200bdetermined for substances in a standard state (indicated by a superscript 0).

1.1. The first law of thermodynamics

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

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

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

Isolated system

The internal energy of an isolated system remains constant.

U \u003dconst or dU \u003d0

Closed system

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

? U \u003d Q + Wor dU \u003d?Q +? W

Open system

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

?U \u003d Q + W +? U mor dU \u003d?Q +? W + i ? U i dn i

Internal energy is a function of state; does this mean a 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 values \u200b\u200bof the internal energy U 2and U 1 in these states:

? U \u003d U 2 - U 1

For some process:

? U \u003d? (V i U i) npod -? (V i U i) out

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 \u003d?Q +? W \u003d?Q - pdV dU \u003d? Q v \u003d C V dT \u003d nC V dT

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

– heat capacity at constant volume,that is, 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 \u003d 2/3 R - monoatomic gas;

C V \u003d 5/2 R - diatomic gas.

Isobaric process (R = const) dU \u003d?Q +? W \u003d? Q - pdV ? Q p \u003d dU + pdV \u003d d (U + pV) \u003d dH

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

? Н \u003d? (? I U i) prod - ? (? i U i) ref

? Q p \u003d dU + pdV \u003d dH \u003d C p dT -the thermal effect of the isobaric process is equal to the change in the enthalpy of the system.

– heat capacity at constant pressure. [FROM] \u003d J / deg.

C p - molar heat capacity at constant pressure, J / (mol? Deg).

For ideal gases: C p \u003d C V + R; C p, C V \u003d[J / (mol K)].

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

Q v \u003d? U V Q p \u003d? U p Dependence of the heat 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 set by a change in the composition of the system:

? C p\u003d? (? i C p, i) prod -? (? i C p, i) out or? C V \u003d? (? i C V, i) prod -? (? i C V, i) out

Integral form of Kirchhoff's law:

? Н Т2 \u003d? Н Т1 +? С р (Т 2 - T 1) or? U T2 \u003d? U Ti +? С V (Т 2 - T 1)

1.3. The second law of thermodynamics. Entropy

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

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

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

in a nonequilibrium process

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

S \u003d kln W Is the Boltzmann formula.

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

Calculation of absolute entropy

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

? S \u003d? (? I S i) prod - ? (? i S i) ref

The values \u200b\u200bof the absolute entropy under standard conditions are given in the reference literature.

1.4. Thermodynamic potentials

Potential - the value, the decrease of which determines the work performed by the system.

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

F \u003d U - TS - Helmholtz free energy - isochoric-isothermal potential(J) - determines the direction and limit of the spontaneous course of the process in a closed system under isochoric-isothermal conditions.

dF \u003d dU - TdSor? F \u003d? U - T? S

G \u003d H - TS \u003d U + pV - TS - Gibbs free energy - isobaric-isothermal potential(J) - determines the direction and limit of the spontaneous course of the process in a closed system in isobaric-isothermal conditions.

dG \u003d dH - TdSor? G \u003d? H - T? S ? G \u003d ? (? i G i) prod - ? (? i G i) ref ? G 0 = ? (? i? G arr 0) prod - ? (? i? G arr 0) ref Conditions for the spontaneous flow of processes in closed systems

Isobaric-isothermal (P \u003dconst, T \u003dconst):

? G< 0, dG < 0

Isochoric-isothermal (V \u003dconst, T \u003dconst):

? F< 0, dF< 0

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

Thermodynamic equilibrium conditionsin a closed system

Isobaric-isothermal (P \u003dconst, T \u003dconst):

? G \u003d 0, dG \u003d0, d 2 G\u003e0

Isochoric-isothermal (V \u003dconst, T \u003dconst):

? F \u003d0, dF \u003d 0, d 2 F\u003e0 Chemical reaction isotherm equations:

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

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

The influence of external conditions on chemical equilibrium

The Le Chatelier-Brown Equilibrium Displacement Principle

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

Effect of temperature on equilibrium position

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

Endothermic reactions:? N °\u003e0 (? U ° \u003e 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 separated from the system and exist outside it. The number of independent components of the system is equal to the number of components minus the number of possible chemical reactions between them.

Number of degrees of freedom - 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 ruleJ. Gibbs:

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

For a system that is influenced only by external factors temperature and pressure,you can write: C \u003d 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 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. Any point in the state diagram (so-called. figurative point)corresponds to a certain state of the system with certain values \u200b\u200bof the state parameters.

2.1. Water condition diagram

K \u003d1. Three phase equilibria are possible in the system: between liquid and gas (line ОА), solid and gas (line ОВ), solid and liquid (line OC). The three curves have an intersection point O called triple point of water, - meet the equilibrium between the three phases and C \u003d 0; three phases can be in equilibrium only at strictly defined values \u200b\u200bof temperature and pressure (for water, the triple point corresponds to the state with P \u003d6.1 kPa and T \u003d273.16 K).

Within each of the areas of the diagram (AOB, BOC, AOC), the system is single-phase; C \u003d 2 (the system is bivariant).

On each of the lines, the number of phases in the system is two, and, according to the phase rule, the system is monovariant: C \u003d 1 - 2 + 2 \u003d 1, i.e., 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" in the diagram of the state of water is inclined to the left, and in the diagrams of the state of other substances - to the right, since the density of water is greater than the density of ice, that is, 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 - abnormal substance).For all other substances (so-called. normal substances)? V pl\u003e 0 and, according to the Clausius-Clapeyron equation, an increase in pressure leads to an increase in the melting point.

3. Properties of solutions

3.1. Thermodynamics of solutions

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

Diffusion in solutions

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

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

where j - diffusion flow; D Is the diffusion coefficient.

Einstein-Smoluchowski equation:

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

Solubility of gases in gases

Dalton's Law:the total pressure of the gas mixture is equal to the sum of the partial pressures of all gases included in it:

P total \u003d? p iand pi \u003d xiP total

Henry-Dalton's Law:the solubility of a gas in a liquid is directly proportional to its pressure above the liquid: C i \u003d kp i,where C i - concentration of gas solution in liquid; k - coefficient of proportionality, depending on the nature of the gas.

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

Sechenov's formula:

X \u003d X 0 e -kC el

where Xand X 0 - gas solubility in pure solvent and electrolyte solution with concentration FROM.

3.2. Colligative properties of non-electrolyte solutions

Collegiate (collective)are the properties of solutions relative to the properties of the solvent, which depend mainly on the number of dissolved particles.

Saturated vapor pressure of dilute solutions

Steam in equilibrium with a liquid is called saturated.The pressure of such steam p 0called pressure or pressure of saturated vaporpure solvent.

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

p i \u003d 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 molar 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, they say. fraction in (x in) vapor pressure:

p \u003d p A 0 x A + p B 0 x B \u003d p A 0 (1 - x B) + p B 0 xB \u003d p A 0 - x B (p A 0 - p B 0)

If the molecules of this component interact with each other more strongly than with the molecules of the other component, then the true partial vapor pressures over the mixture will be higher than those calculated according to the first Raoult's law (positive deviations,? N tv\u003e 0). If homogeneous particles interact with each other weaker than dissimilar particles, the partial vapor pressures of the components will be less than the calculated (negative deviations,? H sol< 0).

Crystallization temperature of dilute solutions

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

T 0 2 - freezing point of the solvent; M Is the molecular weight of the solvent,? Н pl is the 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.

An increase in the boiling point of solutions of non-volatile substances? T K \u003d T k - T k 0proportional to the decrease in saturated vapor pressure and in direct proportion to the molar concentration of the solution: EC m,where E - ebulioscopic constantsolvent, deg / kg mol,

Osmotic pressure of dilute solutions

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

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

Van't Hoff principle:the osmotic pressure of an ideal solution is equal to the pressure that the solute would exert if it, being in a gaseous state at the same temperature, would occupy the same volume as the solution:? \u003d CRT.

Isotonic solutions - two solutions with the same osmotic pressure (? 1 \u003d? 2).

Hypertonic solution - a solution, the osmotic pressure of which is higher than that of the other (? 1\u003e? 2).

Hypotonic solution - a solution, the osmotic pressure of which is less than that of the other (? 1< ? 2).

3.3. Electrolyte solutions

Dissociation degree? Is the ratio of the number of molecules n,decayed into ions, to the total number of molecules N:

Isotonic coefficient i of Van Hoff - the ratio of the actual number of particles in the electrolyte solution to the number of particles of this solution without taking into account dissociation.

If from Nmolecules dissociated n,and each molecule decayed into? ions, then


For non-electrolytes i \u003d1.

For electrolytes 1< i? ?.

3.4. Colligative properties of electrolyte solutions:
Arrhenius' theory of electrolytic dissociation

1. Electrolytes in solutions decompose 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 (ie, the solutions are ideal).

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

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

Weak electrolytes. Dissociation constant

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

А а В b - аА x- + bВ y +

For 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, replacing concentration, - activity (effective concentration) and,related to concentration through activity coefficient f, which is a measure of the deviation of the properties of a real solution from an ideal one:

a \u003d fC; a + \u003d f + C +; a_ \u003d f_C_.

For binary electrolyte:

- average electrolyte activity;

Is the average activity coefficient.

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

I - ionic strength of solution I \u003d0.5? (С i r i 2).

4. Electrical conductivity of electrolyte solutions

Type I conductors - metals and their melts, in which electricity is carried by electrons.

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

Electricitythere is an ordered movement of charged particles.

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

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

Specific conductivity? (k) is the electrical conductivity of a type I conductor 1 m long with a cross-sectional area of \u200b\u200b1 m 2 or the electrical conductivity of 1 m 3 (1 cm 3) of an electrolyte solution (a type II conductor) with a distance between the electrodes of 1 m (1 cm) and the area of \u200b\u200belectrodes 1 m 2 (1 cm 2).

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

The molar conductivity of both strong and weak electrolytes increases with decreasing concentration (i.e., with increasing dilution of the solution V \u003d 1 / C), reaching a certain limit value? 0 (??) called molar conductivity at infinite dilution.

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

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

where F - 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 the solution length.

? + \u003d Fu +; ?? \u003d Fu ?,

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

? = ?(? + + ??)

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

With infinite dilution of the solution (V > ?, ? + > ? ? + , ?? > ? ? ?, ? \u003e 1) for both strong and weak electrolytes? ? \u003d? ? + – ? ? ? - Kohlrausch's law:molar conductivity at infinite dilution is equal to the sum of electrolytic mobilities? ? + , ? ? ? cation and anion of a given electrolyte.

Ions H + and OH? have anomalously 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? there is a continuous exchange of protons according to the equations:

H 3 O + + H 2 O\u003e H 2 O + H 3 O +

H 2 O + OH? \u003e OH? + H 2 O

5. Electrochemical processes

5.1. Electrode potentials. Galvanic cells. EMF

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

The formation of DES leads to a jump in the potential?, Which in equilibrium conditions metal (conductor of the first kind) - 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 a given Me - called electrodeor half-celland is schematically depicted as follows:

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

? \u003e 0, if the reduction reaction of Ме n + + ne? -Me 0,

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

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

nernst equation,where n - the number of electrons participating in the electrode reaction; FROM Ме n + is the concentration of cations; E Ме n + / Ме - standard electrode potential.

Contact potential? ? - equilibrium jump of potentials arising at the interface between two conductors of the first kind.

Diffusion potential? diff is the equilibrium potential difference arising at the phase boundary between a conductor of the second kind / conductor of the second kind.

Galvanic cell (g.) - an electrical circuit consisting of two or more p.e. and producing electrical energy due to a 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 takes place during the operation of the galvanic cell is called anode,the electrode on which the recovery process is taking place - cathode.

IUPAC rules for recording galvanic cells and reactions taking place in them

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

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

3. The boundary between the conductor of the first kind and the conductor of the second kind is designated by one line.

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

5. The electrolyte bridge on the border of two conductors of the second kind is indicated by two dashed lines.

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

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

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

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

Electrode reactions:

Zn 0\u003e Zn 2+ + 2e? Cu 2+ + 2e? \u003e Cu 0

Total redox process:

Cu 2+ + Zn 0\u003e Cu 0 + Zn 2+

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

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

EMF element E Zn / Cu \u003d? 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 - galvanic cells consisting of two identical metal electrodes dipped in solutions of this metal salt with different concentrations C 1\u003e C 2. In this case, the cathode will be an electrode with a higher concentration, since the standard electrode potentials of both electrodes are equal.

Concentration chains

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

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

5.2. Classification of electrodes

First-class electrodes. A metal plate immersed in a salt solution of the same metal. During the reversible operation of the element, in which the electrode is connected, the process of transition of cations from metal to solution or from solution to metal takes place on the metal plate.

Electrodes of the second kind.The metal is coated with a slightly soluble salt of this 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 electrodeis a platinum plate washed by gaseous hydrogen, immersed in a solution containing hydrogen ions. Hydrogen adsorbed by platinum is in equilibrium with hydrogen gas.

Pt, H 2 / H +

Electrochemical equilibrium at the electrode:

2H + + 2e? - H 2.

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

Electrode potential of non-standard hydrogen electrode:

Calomel electrodeconsists 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 \u003d 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.

Quinhydron electrodeis a platinum wire dipped into a vessel with a test solution, into which an excess amount of quinhydrone C 6 H 4 O 2 C 6 H 4 (OH) 2 - 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? \u003e C 6 H 4 (OH) 2

Most commonly used glass electrodein 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 a pair with a reference electrode. The glass electrode ball is pretreated for a long time with an acid solution. In this case, hydrogen ions are incorporated into the walls of the ball, replacing the alkali metal cations. The electrode process is reduced to the exchange of hydrogen ions between two phases - the test solution and glass: H rr - H st +.

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

Redox electrodes

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

Electrode reaction: Ox n + + ne? - Red.

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

6. Surface phenomena and adsorption

6.1. Surface tension and Gibbs adsorption

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

G s \u003d? S,

where G s - surface Gibbs energy of the system, J; ? - coefficient of proportionality, called surface tension, J / m 2; s - interphase surface, m 2.

Surface tensionaboutis a quantity measured by the Gibbs energy per unit area of \u200b\u200bthe surface layer. It is numerically equal to the work that must be done against the forces of intermolecular interaction to form a unit of the interface at a constant temperature.

From the Dupre model, surface tensionequal to the force tending to reduce the interface and per unit length of the contour bounding the surface

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

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

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

2. Surface Inactive Substances (SID) - slightly increase the surface tension of the solvent (? Р-р\u003e? 0) g< 0 (неорганические кислоты, основания, соли, глицерин, ?-аминокислоты и др).

3. Surface-inactive substances (PNS) - practically do not change the surface tension of the solvent (? P-p \u003d? 0) g \u003d 0 (in relation to water, substances are sucrose and a number of others).

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

For aqueous solutions of fatty acids (Shishkovsky equation):

where band TO - empirical constants, bis the same for the entire homologous series, K increases for each subsequent member of the series by 3–3.5 times.

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

Gibbs adsorption isotherm:

The excess of adsorbate in the surface layer in comparison with its initial amounts in this layer characterizes excess,or so called gibbs, adsorption(D).

6.2. Adsorption at the solid-gas interface

Physical adsorptionarises 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, ie, exothermicity (the thermal effect of physical adsorption is usually close to the heat of liquefaction of the adsorbate 10–80 kJ / mol).

Chemical adsorption (chemisorption)carried out by chemical interaction of adsorbent and adsorbate molecules, usually irreversible; is an localized,that is, 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 \u003d Ksor G \u003d Kr,

TO - constant of adsorption equilibrium, depending on the nature of the adsorbent and adsorbate; C, p - concentration of a solute 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 adsorbent surface.

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

Freundlich's equation(adsorption on an inhomogeneous surface): Г \u003d K f with n,where. K F Is a constant numerically equal to adsorption at an equilibrium concentration equal to unity; n - constant determining the curvature of the adsorption isotherm (n= 0,1–0,6).

Molecular adsorption from solutions:


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

Area S 0,per molecule in the saturated adsorption layer, - landing site:

m 2 / molecule.

Adsorption layer thickness:

where M - molecular weight of surfactant; ? - surfactant density.

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

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


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Fick's law:

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{!LANG-1539362506c0ba21e073fee3bd48d419!} {!LANG-090bbc5ec56af1309dce45b5f35c5646!}


{!LANG-34945f1906adc1a408fae3c2d675c0e3!} {!LANG-99d5da2d4b8b19c079d3a6b41ef32fca!}{!LANG-a6e91406dc2235d62c0bf3659356d1b0!} {!LANG-2c8dbb2a01c874e5f3a84eab6ef840e2!}

{!LANG-e2d1456356c42ccaf4043c0044128fea!} {!LANG-9ecd05b8b7ba22937273a74f4aea8394!}{!LANG-895b4fa16700d5c5723d896a6fc886bc!}

{!LANG-0655c1f5ec0f93959d005bb1fb27b578!} {!LANG-239b00fcd976501e947b0070ec1a6b87!}{!LANG-c2dafd8f87005d67d49a599df58bc8b9!}


{!LANG-f0ad2eac8bf00fb8baf34cb76c97bfc6!} {!LANG-ec51fe285659368af6702e936913208c!}{!LANG-024dddde335501b144d8e003050e6287!} {!LANG-44663bb8e6af64b14b300f56fcf724b0!}{!LANG-807252d8ea87315506370406dc3b2253!}


{!LANG-01e38dfd4167bafd2614c8ec26a2a38b!} {!LANG-4879b767d0451cfc865ba5b0817d3f22!}

{!LANG-6fb68ce745d5d4cc37f3e71a613b1f8c!} {!LANG-f8be99379b3bcba0ae2c3b537dd77162!}{!LANG-e680419de42d01d5c4f7263b8916926a!} {!LANG-febce118b5334ae76dcb6c7e635ac180!}

{!LANG-fd8d1b6c43fc38a8993a116761970132!}

{!LANG-f731da6863ab8eeb5b8793c7a3d2b75b!}{!LANG-6d6fd8197be1cd0ccbcff428378f89bb!}

{!LANG-4f9e33050fcf7c379c202a1e79ca59c4!} {!LANG-a188bc8d4c5b436504c118a1749b6588!}

{!LANG-e6b1ccbc5656f848f8a87bce9aa8b321!}{!LANG-965e619234eda8b51e59c935ed8b5108!}

{!LANG-96b05dc3e08fc2b61b6b30015d05285b!} {!LANG-81185896d6259da9421bde180b5c6b55!}{!LANG-db8cac9db33cc49b8f1734b325e17a9b!} {!LANG-02c7f91365f7d5ada409ff1fcf991da3!}{!LANG-9ecb0cab0cac98dec005dceff2e320df!}

{!LANG-cb771aaf5eb5f667165bc8f2a64fcd54!}{!LANG-a931c24269a87b963322792d12761ad8!}

{!LANG-7effae545acff28077a124927b5b2ba6!}

{!LANG-6909bfbd91957111253efd08b7c475c1!}{!LANG-49b3b427e38296146b8791081d0ca8c7!}

{!LANG-0533dc2cf9c64f38379fab01455b5079!} {!LANG-b90383d160fbe33942cab9bdff87a32b!}{!LANG-8be5447c7547b0857569457937f932c0!}

{!LANG-58c9d80b635b751bbd4742d38ee56db8!}

{!LANG-1e17962922d42e112cc1c208bdb15b55!}

{!LANG-01177c902c75e41fef92b5c7984e185c!}

{!LANG-95b688a25b38155d7768dd68981d50c7!}

{!LANG-30ce81d78438df82b1332092d822a9e3!}

{!LANG-8fcd142647f09e1753ddaa8e54d17c1f!}

{!LANG-a29275a8be8658774696a3b0cf1ae95c!}

{!LANG-19e152248bb76821973983546bfec0a9!}

{!LANG-ec7c7645985a30ccb8db3be1d35d6ccb!}

{!LANG-3a396732afcaffb40c57ed8f85f30914!}{!LANG-7fda7ef1fec5c0fca2e1c1f0f58a76b6!} {!LANG-579a8df9041d12cfdbe251483f549a0b!}{!LANG-a9d86424205bfa125ec94de7878ffc72!} {!LANG-717526b12333ddc0cb18338a7b5e2cb2!}{!LANG-3a90ef70ec0eb47e3520a4f8c82edc9d!}<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:


{!LANG-7f801c818d26e959555b1332b0338477!} {!LANG-f9d79a4709b34d475b74596e72e4f237!}{!LANG-c87bbad6abf33556f6b4516974889f6b!}

{!LANG-b466265cff1f488897d389ba3559de62!}{!LANG-337536ba3df3e0faa0d555f692328e1f!} {!LANG-6014f847cf71824b4a758a52311e1588!}{!LANG-a64fc0a9bed818b0ee6730d6df2e439b!} {!LANG-86ec28033a3c6ad420c4db8e80ff2c63!}{!LANG-c020fadc7168ff27089fa4fb7edd496e!}


{!LANG-1cc610bbb49e599396791545a3a387ef!} {!LANG-99abffd9aa414afa4170493f32088db9!}

{!LANG-4adbd3e0dbed782ef819dbb50b0ff12f!}

{!LANG-cc2348ae7f7026fbbe73d39c6f6728ce!} {!LANG-929fc94f29380f93d5afcf785b9e55d9!}

{!LANG-a749bbd79965ed7d9a692e89fc6aabcb!} V{!LANG-3bd8ceb8cce8976325f9fddbebae424b!} V{!LANG-9491f2672ee3bb306902d2729bb80c4d!}

{!LANG-f70348189248a8974a66e0f3d8fabbab!} {!LANG-d5730489a0a3cefd77dd7c9b4034dc10!}

{!LANG-0f4c717ae4e21c2faa5be50274ab8cbf!}

{!LANG-4d786de0dee35bb5c1fb3d3d53f938c7!}

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

{!LANG-acf3165514d10ee245b485bc9bfc0b91!} {!LANG-f94ba701bbfce0ea0969d109bf42ad34!}

{!LANG-4362fc00825d4b284d232fdac88f27b6!}{!LANG-99b45371a710655742d02307b01f258b!}

{!LANG-9d35a5b2a32bcb6f051e2cf8670ce45d!}{!LANG-f02b1cee7e9f921a9202fa1fc9605478!}

{!LANG-3fb3b0e88ba201e918e51f28bf2e82f0!}

{!LANG-16ea7cd8ec08c2d6f5bb0051f8f29f1e!}

{!LANG-1e19a52f5b4a00cdd29a1b467dcbf7db!}

{!LANG-0be82a77b077d60fbd81e94f82ed8b90!}

{!LANG-76acb741c881e1bb1cfbbbf13a1d169c!}

{!LANG-e7e4ef550d398650713a178c343b0cdd!}

{!LANG-faccac57ad3cd0b0f1ce5b62f3e99619!}

{!LANG-9633da4005fde0b1f0a943404b24cd71!}

{!LANG-ea51a4ae7cb24178442f13fcc5450653!}

{!LANG-b17894c0958745a6cd6d4f8e8c09f97d!}

{!LANG-166edd1ac152fee3b30244cee64242aa!}

{!LANG-a1d56bdd612f51d6da7716e68233db24!} {!LANG-68f47003aae073a64d6068e64ebcf8c4!}{!LANG-06164dcc661a9e9454faedc027c9d386!}

{!LANG-1236a4a2d46aaed2682e24368edbe5db!}

{!LANG-6538e77403ea980a029e3f7b6b4eb9ec!}

{!LANG-65f3cbdabf5cf3679ec85849c25065ae!}

{!LANG-dd9a20fbcc3c4fdea334a4757ac66840!}

{!LANG-0ef85d41946063f2411cc2b80017394c!}

{!LANG-1ac3fba6f402372348dbe0eeaca2bf56!}

{!LANG-e3bf64ebd2cf8b7f647fbb70bca7ec26!}

{!LANG-6ac0e37f7bf461f43eb20575e76b85a9!}

{!LANG-538d20dd784906bcd29dde4564947cfa!}

{!LANG-6a9e4ce6cb6c305358c5f062c8f47d95!}

{!LANG-d1317170036d0261ebb3d5b35cd48a4b!}

{!LANG-31fe5a15a2768270d977cc08d6664df4!} {!LANG-2f4473ea51d814e1e7a32068d4f700c3!}{!LANG-83029679d26469ffbf68255368b2f321!}

{!LANG-5d1a39946c34882d48dd3ca3a36f11da!} {!LANG-15c2d7f4e690a049537e3f3f26d8a2b2!} ({!LANG-156cdc0dc3257e9efb6c89f64bc66338!}{!LANG-42f6ba33d126471f67a1d7f1da463492!} {!LANG-309114888e3e04051ae10354e06d7df4!}{!LANG-6297fa2d2dd208d356d3af0cb63982e8!}

{!LANG-8e6d02067be82a3e234d116b4d649fed!}

{!LANG-d41363d791564114bb0185443ab991da!}{!LANG-0294f8fbac4abee53f56634f8e210bb4!}

{!LANG-7ec4ccfaefde46f0b08b5cd2d8c9da17!}

{!LANG-9d858ae78624cb8c178cc11dce494962!}

{!LANG-bc4e50bd80b3d1dbc537775ef9071da8!}
{!LANG-3bc714376f1db0b2c41c43ed00ff9099!}

{!LANG-701312292a343b96886b88d31f917a54!}

{!LANG-07ef4c0f0599b14d7ede20ed1e87a773!} {!LANG-8ba95c27faec3e007398c91a21ef81af!}{!LANG-4e5e2a69515c6c692d40cdc93ffdcf92!}

{!LANG-60659ceab9fd0731ded6794cdfc76605!} {!LANG-b9a70eccc520b17b29f427903cd1d40c!}{!LANG-9b7e9a309294ebe2932853a53c219505!} {!LANG-0407f93d642c4349aaf560037338096f!}{!LANG-6ccaa785623a9ac55a1040d1052c708a!} {!LANG-ca8c759bfa170b3caa01d60edf24c4a2!}1 {!LANG-c05f554f7f53a63de5aee73468bd73b8!}

{!LANG-dc4e86951c6ade0bb7c0a78a81ba6d81!} {!LANG-384013d573aa6077fbded337e48e5844!}{!LANG-d98f1a5aef4ae356d7954191ae7af6f9!} {!LANG-f91f21955ca1707b57fc7edbe70b4187!}{!LANG-e153b78cbcf003cccdf7fedc827b92f4!} {!LANG-5de524e1169c5a4c46765a186f07c4ef!}{!LANG-7099db7060e6f6150b2276fef144f7e8!}

{!LANG-64f4fee7d7c146330f3346d9ab6bf537!}{!LANG-e134338fef3067ea2754d5e59e2bd83e!} {!LANG-384013d573aa6077fbded337e48e5844!}{!LANG-87c16473b52ce7bdd4073c6be304396a!}

{!LANG-50e78dd87b907715bf98ba0c2b52ff2b!}

{!LANG-6d2510a01dfa0bec5a116b7bf23cbf4f!} {!LANG-ef8cd6101ad63c37e1936c9ed50fd88d!}{!LANG-a73cf0e92cc84db363afd69f786181dd!} {!LANG-0fb5d27e864eb8adee09aa0d41504915!}{!LANG-466a41d578b9f9ba929ca304dbe83fc6!}

{!LANG-57db616566e23ad9ecd8482091c8041b!}

{!LANG-a80abd9f3dcc7fd7056084983b40780d!}

{!LANG-87999fc865c7b09b0759144023577f0c!}

{!LANG-d42d193b2e50eab6e0b7d28c5979afbe!}

{!LANG-c5f1e9f310a9f69ff53c3ef6e707f37f!}

{!LANG-aece174b24502d1d13b418b5f46bfc90!} {!LANG-78fe2553bbd8b095b1efc477dd5b919d!}{!LANG-e31443f3ec01bf0d9c9d5a42cd252cf9!} {!LANG-864d9ee1a8e8cf7c24d9a6156d20a608!}

{!LANG-380f72211db76800bcf282aa5ce14f73!} {!LANG-d8d308fe85689b380885ff0d55f8181c!} .

{!LANG-764604c38bab0e1366b0a559141e18cf!} {!LANG-acd801bc508d98b850db18771f2b174e!}{!LANG-b6e3fbdff6508b8ceab23d95d978d821!}

{!LANG-8bfbf04149bf7b39dfeb277551b84d97!} {!LANG-470776c240de30701c0280a02fca8f38!} {!LANG-edb0c80be875745e2827a4d7c62fa915!} {!LANG-b8db593fd692d0c4802131f710020e46!}

{!LANG-99a0845f3ff8e12cac0a24646524be98!}

{!LANG-e65f249f84625ce85b245875cf260774!} {!LANG-6d666bad6c5a8413ffb87e6c0bbeb1f4!} , {!LANG-5dad3ab06f5f21068c6e57115baf7fd2!}

{!LANG-e65f249f84625ce85b245875cf260774!} {!LANG-f0644d7ba2a51fb02517a61323f48e9a!} , {!LANG-ee03e06c1cb901e0a81e03eee60655ee!}

{!LANG-f66016f807406bffa55a94743922140e!} {!LANG-4a69c173209fdc102b2bfc0ce6510385!} . {!LANG-dd8c5cfcae894c406b039fccc90d06b4!}

{!LANG-5358e16e427cbb69f626eed5e6cd2364!} {!LANG-2a33470649c7220fdcc0b0716fb7db55!} .

{!LANG-a4fa4f2dcfcf35162d5725e6f5feb2bb!} {!LANG-ebd67ebb9140fde3718be191a3cf1ad5!}

{!LANG-af9c4fd24984a3ef253447427c76e321!} {!LANG-09be7f2e68247a9597b30af7f12426eb!} .

{!LANG-a9394620fb22f67ebbd393afe2737599!}

{!LANG-91542bad6f7aa038b1a0f95086de1e73!} {!LANG-9e0c6b9b9e00d302020a48f3a95484b1!}{!LANG-955a98aed047d48d30588fa8e7469d06!} {!LANG-12a82454b652ab4b00887c05cd9651d4!}{!LANG-152bd35f27a7052da9652049e063a3a8!}

{!LANG-664725eba157308585d368e19bbc76c5!}

{!LANG-54f4b697980e5c1d3e9ef955779663a6!}{!LANG-09068781c31bad8f277eb73dd3653272!}

{!LANG-a5273ef29229a160ebd29743cb9e55b2!}{!LANG-4f3b6bc5242365d7cd57d0eb791cc300!}

{!LANG-d835bf34a76de54d3858fc59ff3ccb9f!} {!LANG-484091ad169117a6c062d8f225144219!}

{!LANG-b4744a60968b45f0614d9b7d46dab6a1!} {!LANG-ea8cb0d6d34480962fa094ed4b88a365!}

{!LANG-0e51005711bc838823b16421707b16d3!} {!LANG-9e8c964b1bf1bbdd70bfaca674ebce0e!}{!LANG-b30043595ca9cbd8fcbc85f8cd10add5!}

{!LANG-250c0a03530fe322dd99d4b4863e8121!} {!LANG-ed73b3ddeec6fc6d1f15e281a5a9aeb9!}{!LANG-7ed12194f6264288c69cf3afbae42b9d!} {!LANG-70bd92d77174a792c5e641ccd8647a14!}{!LANG-9bd2606b870db6302d6cc08c0ce36fb0!} {!LANG-f3c185c905fbc118dffe13024539ec0d!}{!LANG-dce967a7f47d1336ca2d4b878de6d99a!} {!LANG-1d0ea6d3722d533d32a38a1174ac484d!}{!LANG-d03bf898cbb8ef9232ba2304babb3ac0!}

{!LANG-a8db3dab3d0e06b8a5fad206245d8877!}

{!LANG-327652d8d8c91b550d4eaa4e6dfe0c80!}

{!LANG-184ebb7a6f8b2967cee5b3ca8324ef47!} {!LANG-4ea705eab914b3e71ac211985fb3b6b2!} .

{!LANG-f2f7729330e17084bb58d9d9e6b4f3a8!} {!LANG-74c54fda1f3367cf9e9e2c1e4ad141e3!} .

{!LANG-940c9884b9178d4c3ec4cc2f4c3985b7!}

{!LANG-26792eb55e77671fd1ee55eb4bd2804b!}

{!LANG-447bc8595395b45c0ef6c6e145466533!}

{!LANG-ee0c8acd408a1f5f1d8ea81ae62a8ef4!}

{!LANG-1275595027db882cf2f0944574d53f01!}

{!LANG-a1de087bc34eee0f511ce05b8f78ca64!}

{!LANG-ef412819a2fbbed17e03202641a0dc3b!}

{!LANG-15587d0f27554118a227b10939379865!}

{!LANG-d365de974a0b2cbf8c9eb38835c84028!} {!LANG-ae05b51616e1b5ff4fbba7682e4a6a84!} {!LANG-657c96b509aa9e4d9e59eae16a01a45f!} {!LANG-e224bb03e75558deed16e423d3709f07!} .

{!LANG-7cd127a514c7aad9f59aa80c955d1265!}

{!LANG-44fa92e2a77a150ab129f4487c218399!}

{!LANG-c9e0da8254bd54d7381039b8dc612556!} Q{!LANG-d7a7563363de7a857dcbba936d1a56e3!} W{!LANG-b6d9e1f1efc1fa6b96ecaaff059a06b4!}

{!LANG-073a6f19ca3e074bfdd2d103b2e50e4d!}

{!LANG-c845e29aac2c6f4130001bc462cc578a!}

{!LANG-393cd5bf70313812e56cca5860680eee!} {!LANG-ee64d86e0f8e9a783d1914be67742fd1!} k {!LANG-b331ddb7f63f4a58686cc036db437234!} k{!LANG-ab54c08e09f34f8c27804bc5f282583b!}

{!LANG-47c1d30e22db2dd129464e1502c450de!} k {!LANG-9231a2c90cd425b95bdb81ee7708d31f!}

{!LANG-f5f20a0a22f2024a7700b85b07f1bd89!} k{!LANG-27e7b4dbf63b85ddd1e17ae62693885c!} k{!LANG-be484d527817a7094b1b69f2bf4b855f!}

{!LANG-1f2d66150ad73a5a3eebead4a4c7c224!}

{!LANG-f3d7a07a4f4ff6a74ccc3dec557c8466!} k):

≠

{!LANG-eff792aaea753e29aec35a5050ec7a5e!} W and Q:

Q   W,

{!LANG-8c485be6b205af3ab60618f366212268!}

Q – W  0

{!LANG-84ee9a6ed333a72e5b212dff46c86c37!} Q – W{!LANG-679a8d3e023f238a34a82ec03bf17fa0!} {!LANG-1cff59187b1bf5b57f6baacd82adfe30!}:

{!LANG-1cff59187b1bf5b57f6baacd82adfe30!}   Q – W {!LANG-4a5438bbe7ce49b593980da6bbf902de!}

{!LANG-fe582c252b71832b004528d1ff5007c3!}


–
{!LANG-70b081133ef6be1cd4395b12f7929112!}

{!LANG-ea060d7c20f17a2c8782befddfb55eeb!}

=
–
{!LANG-64d59bb2b7d5003eef36330308ae76fb!}

{!LANG-8a7bc638725f7a65331a696a2af60a0e!} {!LANG-1cff59187b1bf5b57f6baacd82adfe30!} {!LANG-231a65105dad2d8bf40a5d2f79cc4b70!}

{!LANG-af6562db52e26f033b1414302737dd98!}U , {!LANG-142f7d4118b6750b15e4238ce88c07de!}{!LANG-32f8e0bb6944a6efe8b1351b72b8facc!}{!LANG-952ff082276ad93b64f30c5be46ddb20!}{!LANG-32f8e0bb6944a6efe8b1351b72b8facc!}{!LANG-39f65ad343799811bbfcc1246ea8b1f4!}{!LANG-55de95ee504d4b6222ac08662b1851bd!} {!LANG-71181ae1dc121fea68098c83a814feaa!} .

{!LANG-4ae9c091443fe98465338a22637c9d81!}

= U 2 – U 1 = ∆ U = – {!LANG-a9df8a09ea1482d97dc43297532bd191!}

U 2 – U 1 {!LANG-2c72a398b1d715942ab2dde903d98924!}

{!LANG-87ee977ae55c0e33930e9dae2f4bb836!}

{!LANG-edfec50bdc0b776c451f38692c6b5fef!}

{!LANG-db3ecbbef844b6e8b9588a3c088d4beb!}

{!LANG-8941bd1f6b0fa1fa210ad14db9b6328b!} {!LANG-617d9e02062461d6752344d21ef4487e!}{!LANG-e04adb08d32a0d8abd108977432c1165!}

{!LANG-26e3caa5acd4e6cf959aa655e2963cd8!}

{!LANG-2a42d25cb7ca609105acb7318f7a3cfd!} {!LANG-f97d58880e3751f66c83439c619872de!}

{!LANG-976cd590a90c09e0fb4b087db785ff41!}

{!LANG-d74609770fccf86dbafbcb2b7da22696!}

{!LANG-63676540dd8e8b0153a3b4362a607630!} 1 {!LANG-271276a71fa8a723cb2b48496c122d21!} 2 {!LANG-7c2250a5628ff25e931ba684da763a0b!} 2

{!LANG-650b8faf954f7178f20a287c59132aad!} {!LANG-564f98c30b51b8ac46474c62037256d1!} {!LANG-1bd57c68fcfc6c559730aeaa73785fae!}{!LANG-6a386af5179870bf4cd3647d1c4826c2!} {!LANG-564f98c30b51b8ac46474c62037256d1!} {!LANG-1bd57c68fcfc6c559730aeaa73785fae!}{!LANG-d293dbfb6decbb49a27794880d9e0f22!} {!LANG-564f98c30b51b8ac46474c62037256d1!} {!LANG-1bd57c68fcfc6c559730aeaa73785fae!}{!LANG-dc73c6ec65351a08dd32485a8ec391e7!} {!LANG-b3229d7da212f12a9ae1435920db0c3f!}{!LANG-cf95b93383bbcc88c7e646ed84e5a3ca!} {!LANG-564f98c30b51b8ac46474c62037256d1!} {!LANG-1bd57c68fcfc6c559730aeaa73785fae!} ...

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