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3rd ed., rev. - M.: high school, 2001 - 512 p., 319 p.
The textbook is compiled in accordance with the program in physical chemistry.
The following sections of the course are detailed in the first book: 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 of physical chemistry, electrochemistry, chemical kinetics and catalysis are presented on the basis of the ideas developed in the first part of the book - the structure of matter and statistical thermodynamics. The `Catalysis` section reflects the kinetics of heterogeneous and diffusion processes, adsorption thermodynamics and questions of reactivity.
For university students enrolled in chemical engineering specialties.
Book 1.
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Book 2.
Format: djvu
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TABLE OF CONTENTS Book 1.
Preface. 3
Introduction 6
Section one. Quantum-mechanical substantiation of the theory of molecular structure and chemical bond
Chapter 1. The structure of the atom 9
§ 1.1. Quantum mechanical features of microparticles 9
§ 1.2. Hydrogen atom 11
§ 1.3. Atomic orbitals of a hydrogen-like atom 14
§ 1.4. Electron spin 21
§ 1.5. Multielectron atoms 23
§ 1.6. Pauli Principle 26
§ 1.7. Electronic configurations of atoms 28
Chapter 2. Molecules. Theoretical methods used in the study of the structure of molecules and chemical bonding 34
§ 2.1. Molecule. potential surface. Equilibrium configuration 34
§ 2.2. Theory of chemical bond and its problems. Schrödinger equation for molecules 39
§ 2.3. Variational method for solving the Schrödinger equation 42
§ 2.4. Two main methods of the theory of the structure of molecules. 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 50 method
§ 2.7. The II 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 connection. Electric dipole moment of a molecule 78
§ 3.5. Saturation of a covalent bond 81
§ 3.6. Donor-acceptor bond 82
§ 3.7. Ionic bond. The degree of polarity of the chemical bond 84
Chapter 4. Polyatomic molecules in the MO method 88
§ 4.1. Molecular orbitals in polyatomic molecules. Orbital symmetry. Delocalized and localized orbitals. HgO 88 molecule
§ 4.2. Description of the methane molecule. Delocalized and localized MOs. Hybridization of orbitals 95
§ 4.3. On the prediction of equilibrium configurations of molecules 99
§ 4.4. Nonrigid Molecules 101
§ 4.5. Molecules with multiple bonds in the MO LCAO method 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 bonding in a crystal 126
Chapter 5. Intermolecular interaction 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 about molecular spectra. Elements of the theory of molecular spectra 141
§ 6.1. Intramolecular motion and electromagnetic spectrum. 141
§ 6.2. Molecular spectra of emission, absorption and Raman scattering. 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. The molecule is an anharmonic oscillator. 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. Use of vibrational spectra to determine the structure of molecules 180
§ 6.10. Influence of the intermolecular interaction of the medium and 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. Subject and tasks of chemical thermodynamics 186
§ 7.2. Basic concepts and definitions of chemical thermodynamics 188
§ 7.3. First law of thermodynamics. Non-circular processes 199
§ 7.4. Heat capacity 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 a gaseous substance 215
§ 7.8. thermal effects. Hess Law 217
§ 7.9. Application of Hess' law to the calculation of thermal effects 220
§ 7.10. Dependence of thermal effect on temperature. Kirchhoff equation 227
Chapter 8. The second law of thermodynamics and its application 235
§ 8.1. Spontaneous and non-spontaneous processes. The Second Law of Thermodynamics 235
§ 8.2. Entropy 236
§ 8.3. Entropy change in non-static processes 239
§ 8.4. Entropy change as a criterion of directionality and equilibrium 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. Entropy change in some processes 251
§ 8.8. Gibbs energy of a mixture of ideal gases. Chemical potential 261
§ 8.9. General conditions of chemical equilibrium 265
§ 8.10. The law of active masses. Equilibrium constant for gas phase reactions 266
§ 8.11. Reaction isotherm equation 271
§ 8.12. Using the law of mass action to calculate the composition of an equilibrium mixture 273
§ 8.13. Effect of temperature on chemical equilibrium. Reaction isobar equation 282
§ 8.14. Integral form of dependence of Gibbs energy and equilibrium constant on temperature 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. Third law of thermodynamics 289
§ 9.2. Calculation of the change in standard Gibbs energy and equilibrium constant by the method of Temkin - Schwartzman 294
§ 9.3. Calculation of the change in the standard Gibbs energy and the equilibrium constant using the functions of the reduced Gibbs energy 297
§ 9.4. Adiabatic reactions 299
Chapter 10. Chemical equilibrium in real systems 303
§ 10.1. Fugacity and coefficient of fugacity 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 the state by the method of quantum mechanics. Quantum statistics 324
§ 11.4. Two types of averages (microcanonical and canonical averages) 325
§ 11.5. Relationship between entropy and statistical weight. Statistical nature of the second law of thermodynamics 326
§ 11.6. Thermostat system. Canonical Gibbs distribution. 330
§ 11.7. The sum over the states of the system and its connection with 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. The 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 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 solutions 365
§ 12.1. Classification of mortars 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 values 375
§ 12.7. Basic Methods for Determining Partial Molar Values 379
§ 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 Raoult law 390
§ 12.12. Boiling point of an ideal solution 392
§ 12.13. Freezing point of an ideal solution 395
§ 12.14.0 smotic pressure of an ideal solution 397
§ 12.15 Non-ideal solutions 400
§ 12.16. Extremely dilute, regular and athermal solutions 402
§ 12.17. Activity. Activity coefficient. Standard state 404
§ 12.18.0smotic coefficient 407
§ 12.19. Methods for determining activities 409
§ 12.20. Relationship of the activity and activity coefficient with the thermodynamic properties of the solution and excess thermodynamic functions 412
Section Five. 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 Single Component 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. Equation of Clapeyron - Clausius 425
§ 14.4. Saturated steam pressure 423
§ 14.5. State diagrams of one-component systems 429
§ 14.6. Carbon dioxide state diagram 431
§ 14.7. Water Status Diagram 432
§ 14.8. Sulfur state chart 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. Physical and chemical bases of solution distillation 453
§ 15.7. Equilibrium crystals - liquid solution in two-component systems 457
§ 15.8. Equilibrium liquid - gas and crystals - gas (steam) in two-component systems 476
§ 15-9. State Diagram Calculations 476
Chapter 16. Three-component systems 482
§ 16.1. Application of the Gibbs phase rule to three-component systems 482
§ 16.2. Graphical representation of the composition of a three-component system 482
§ 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 a solute between two liquid phases. Extraction 491
Appendix 495
Index 497
TABLE OF CONTENTS Book 2.
Preface 3
Section six. Electrochemistry
Chapter 17. Solutions, electrolytes 4
§ 17.1. Electrochemistry subject 4
§ 17.2. Specificity of electrolyte solutions 5
§ 17.3. Electrolytic dissociation in solution 6
§ 17.4. Average ionic activity and activity factor 10
§ 17.5. Basic concepts of the electrostatic theory of strong electrolytes Debye and Hückel 13
§ 17.6. Basic concepts of ion association theory 22
§ 17.7. Thermodynamic properties of ions 24
§ 17.8. Thermodynamics of ionic solvation 28
Chapter 18. Non-equilibrium phenomena in electrolytes. Electrical conductivity of electrolytes 30
§ 18.1. Basic concepts. Faraday's laws 30
§ 18.2. Movement of ions in an electric field. Ion transport numbers. 32
§ 18.3. Electrical conductivity of electrolytes. 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 is not 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. Occurrence of a potential jump at the solution-metal interface 53
§ 19.4. Diffusion potential 55
§ 19.5. The structure of the electrical 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 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 reactions 101
Chapter 21. Kinetics of chemical reactions in closed systems. 105
§ 21.1. Unilateral first order reactions 105
§ 21.2. Unilateral Second Order Reactions 109
§ 21.3. One-way reactions of the nth order 111
§ 21.4. Methods for determining the order of the reaction 112
§ 21.5. Bilateral reactions of the first order 113
§ 21.6. Bilateral reactions of the second order 116
§ 21.T. Parallel one-way reactions 117
§ 21.8. Unilateral sequential reactions 119
§ 21.9. Method of quasi-stationary concentrations 125
Chapter 22. Kinetics of reactions in open systems 127
§ 22.1. Reaction kinetics in a perfectly mixed reactor 127
§ 22.2. Reaction kinetics in a plug flow reactor 129
Chapter 23. The theory of the elementary act of chemical interaction 133
§ 23.1. Elementary chemical act 133
§ 23.2. Theory of active collisions 137
§ 23.3. Theory of the activated complex 141
§ 23.4. Preexponential factor in the Arrhenius equation according to the transition state theory 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 medium 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. The rate of an electrochemical reaction. 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 periodic catalytic reactions 266
§ 27.5. Application in industry 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. 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. Application of heterogeneous catalysis in industry 300
Literature 303
Application 305
Index 312
Contents 316
Thermodynamic system- a body or a group of bodies that are in interaction, mentally or actually isolated from the environment.
homogeneous system- a system within which there are no surfaces separating parts of the system (phases) that differ in properties.
heterogeneous system- a system within which there are surfaces that separate parts of the system that differ in properties.
Phase- a set of homogeneous parts of a heterogeneous system that are identical in physical and chemical properties separated from other parts of the system by visible interfaces.
isolated system A system that does not exchange matter or energy with its environment.
closed system- a system that exchanges energy with the environment, but does not exchange matter.
open system- a system that exchanges both matter and energy with the environment.
State Options are quantities characterizing some macroscopic property of the system under consideration.
Thermodynamic process– any change in the thermodynamic state of the system (changes in at least one state parameter).
Reversible process- a process that allows the system to return to its original state without leaving any changes in the environment.
equilibrium process- a process in which the system passes through a continuous series of states that are infinitely close to the state of equilibrium. Characteristics equilibrium process:
1) an infinitesimal difference between acting and opposing forces: Fex-Fin > 0;
2) performance by the system in the direct process of maximum work | W| = max;
3) an infinitely slow flow of the process associated with an infinitely small difference in the acting forces and an infinitely large number of intermediate states t > ?.
Spontaneous process- a process that can proceed without the expenditure of work from the outside, and as a result, work can be obtained in an amount proportional to the change in the state of the system that has occurred. A spontaneous process can take place reversible or irreversibly.
Non-spontaneous process A process that requires external work in an amount proportional to the change in the state of the system.
Energy is a measure of the system's ability to do work; a general qualitative measure of the motion and interaction of matter. Energy is an inherent property of matter. Distinguish potential energy due to the position of the body in the field of some forces, and kinetic energy caused by a change in the position of the body in space.
Internal energy of the system U is the sum of the kinetic and potential energies of all particles that make up the system. One can also define the internal energy of a system as its total energy minus the kinetic and potential energy of the system as a whole. [ U]= J.
Heat Q - a form of energy transfer through the disordered movement of molecules, through chaotic collisions of molecules of two contiguous bodies, i.e. through heat conduction (and at the same time through radiation). Q > 0 if the system receives heat from the environment. [ Q]= J.
Work W - a form of energy transfer by the ordered movement of particles (macroscopic masses) under the action of any forces. W > 0 if the environment does work on the system. [W] = J.
All work is divided into mechanical work of expansion (or contraction) and other types of work (useful work): ? W = -pdV + ?W?.
Standard State of Solids and Liquids is the stable state of a pure substance at a given temperature under pressure p = 1 atm.
Standard state pure gas- the state of the gas, obeying the equation of state of an ideal gas at a pressure of 1 atm.
Standard values– quantities defined for substances in the standard state (denoted by superscript 0).
1.1. First law of thermodynamics
Energy is indestructible and uncreated; it can only change from one form to another in equivalent proportions.
The first law of thermodynamics is a postulate - it cannot be proven logically or derived from any more general provisions.
The first law of thermodynamics establishes the relationship between heat Q, work W and change in the internal energy of the system? U.
isolated system
The internal energy of an isolated system remains constant.
U= const or dU= 0closed system
The change in the internal energy of a closed system occurs due to the heat imparted to the system and/or the work done on the system.
?U=Q+W or dU=? Q+? Wopen system
The change in the internal energy of an open system occurs due to the heat imparted to the system and/or the work done on the system, as well as due to a change in the mass of the system.
?U = Q + W + ?U m or dU=? Q+? W+ i?U i dn iInternal energy is a state function; this means that the change in internal energy? U does not depend on the path of the system transition from state 1 to state 2 and is equal to the difference between the values of internal energy U 2 And U 1 in these states:
?U \u003d U 2 - U 1For some process:
?U = ?(v i U i) npod - ?(v i U i) ref1.2. 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 dTAll the amount of heat received by the system goes to change the internal energy.
– heat capacity at constant volume, i.e., the amount of heat required to raise the temperature of the system by one degree at a constant volume. [ C V] = J / deg.
C V is the molar heat capacity at constant volume, J/(mol? deg). For ideal gases:
C V = 2 / 3 R is a monatomic gas;
C V = 5 / 2 R is a diatomic gas.
isobaric process (R = const) dU=? Q+? W = ?Q – pdV ?Q p = dU + pdV = d(U + pV) = dHH \u003d U + pV - enthalpy is the system state function.
?Н = ?(? i U i) prod - ?(? i U i) ref?Q p = dU + pdV =dH = C p dT – the thermal effect of an isobaric process is equal to the change in the enthalpy of the system.
– heat capacity at constant pressure. [FROM] = J/deg.
C p is the molar heat capacity at constant pressure, J/(mol? deg).
For ideal gases: C p = C V + R; C p, C V =[J/(mol K)].
Thermal effect (heat) of a chemical reaction- the amount of heat released or absorbed during the reaction at a constant temperature.
Qv = ?UV Qp = ?Up The dependence of the thermal effect of the reaction on temperature. Kirchhoff's lawThe temperature coefficient of the thermal effect of a chemical reaction is equal to the change in the heat capacity of the system during the reaction.
Kirchhoff's law:
For a chemical process, the change in heat capacity is given by the change in the composition of the system:
?C p= ?(? i C p,i) prod – ?(? i C p,i) ref or? C V =?(? i C V,i) prod – ?(? i C V,i) refIntegral form of Kirchhoff's law:
?H T2 \u003d ?H T1 + ?C p (T 2 - T 1) or? U T2 \u003d? U Ti +? C V (T 2 - T 1)1.3. The second law of thermodynamics. Entropy
1) Heat cannot spontaneously transfer from a less heated body to a more heated one.
2) A process is impossible, the only result of which is the conversion of heat into work.
3) There is some system state function called entropy the change of which is related to the absorbed heat and the temperature of the system as follows:
in a non-equilibrium process
in an equilibrium process
S is entropy, J / deg,
is the reduced heat.
Statistical interpretation of entropyEach state of the system is assigned thermodynamic probability(defined as the number of microstates that make up a given macrostate of the system), the greater, the more disordered or indeterminate this state is. Entropy is a state function that describes the degree of disorder in a system.
S=k ln W is the Boltzmann formula.
The system tends to spontaneously transition to a state with the maximum thermodynamic probability.
Absolute Entropy Calculation
The change in entropy during a chemical process is determined only by the type and state of the initial substances and reaction products and does not depend on the reaction path:
?S = ?(? i S i) prod - ?(?iSi) refThe absolute entropy values under standard conditions are given in the reference literature.
1.4. Thermodynamic potentials
Potential is the value whose decrease determines the work done by the system.
Only those processes that lead to a decrease in the free energy of the system can proceed spontaneously; the system comes to a state of equilibrium when the free energy reaches its minimum value.
F = U – TS – Helmholtz free energy – isochoric-isothermal potential(J) - determines the direction and limit of the spontaneous flow of the process in a closed system under isochoric-isothermal conditions.
dF = dU – TdS or? F = ?U - T?SG = H – TS = U + pV – TS – Gibbs free energy – isobaric-isothermal potential(J) - determines the direction and limit of the spontaneous flow of the process in a closed system under isobaric-isothermal conditions.
dG = dH – TdS or? G = ?H - T?S ?G= ?(? i G i) prod - ?(? i G i) ref ?G0 = ?(? i ?G arr 0) prod - ?(? i ?G arr 0) ref Conditions for spontaneous processes in closed systemsIsobaric-isothermal (P = const, T = const):
?G< 0, dG < 0Isochoric-isothermal (V = const, T = const):
?F< 0, dF< 0Thermodynamic equilibrium such a thermodynamic state of a system with a minimum free energy is called, which, under constant external conditions, does not change in time, and this invariability is not due to any external process.
Thermodynamic equilibrium conditionsin a closed systemIsobaric-isothermal (P = const, T = const):
?G = 0, dG= 0, d 2 G > 0Isochoric-isothermal (V = const, T = const):
?F=0, dF = 0, d 2 F >0 Chemical reaction isotherm equations:For reaction v 1 A 1 + v 2 A 2+ … = v? 1 B 1 + v? 2 B 2 + …
Here C i ,p i- concentration, pressure of reacting substances at any moment of time, different from the state of equilibrium.
Influence of external conditions on chemical equilibriumLe Chatelier-Brown equilibrium shift principle
If an external influence is exerted on a system that is in a state of true equilibrium, then a spontaneous process arises in the system that compensates for this impact.
Effect of Temperature on the Equilibrium Position
Exothermic reactions: ?H°< 0 (?U° < 0). Повышение температуры уменьшает величину константы равновесия, т. е. смещает равновесие влево.
Endothermic reactions: ?H° > 0 (?U°> 0). An increase in temperature increases the value of the equilibrium constant (shifts the equilibrium to the right).
2. Phase equilibria
Component- chemically homogeneous component a system that can be isolated from the system and exist outside of it. The number of independent components of the system is equal to the number of components minus the number of possible chemical reactions between them.
Number of degrees of freedom is the number of system state parameters that can be simultaneously arbitrarily changed within certain limits without changing the number and nature of phases in the system.
Phase Rule J. Gibbs:
The number of degrees of freedom of an equilibrium thermodynamic system C is equal to the number of independent components of the system K minus the number of phases Ф plus the number of external factors affecting the equilibrium: C \u003d K - F + n.
For a system that is affected by external factors only temperature and pressure, can be written: C \u003d K - F+ 2.
Continuity principle- with a continuous change in the parameters of the state, all the properties of individual phases also change continuously; the properties of the system as a whole change continuously until the number or nature of the phases in the system changes, which leads to an abrupt change in the properties of the system.
According to conformity principle, on the system state diagram, each phase corresponds to a part of the plane - the field of the phase. The lines of intersection of the planes correspond to the equilibrium between the two phases. Any point on the state diagram (the so-called. figurative point) corresponds to a certain state of the system with certain values of the state parameters.
2.1. Water Status Diagram
K = 1. Three phase equilibria are possible in the system: between liquid and gas (line OA), solid and gas (line OB), solid and liquid (line OC). The three curves have an intersection point O called triple point of water,– correspond to the equilibrium between the three phases and С = 0; three phases can be in equilibrium only at strictly defined values of temperature and pressure (for water, the triple point corresponds to a state with P = 6.1 kPa and T = 273.16 K).
Inside each of the areas of the diagram (AOB, BOC, AOC) the system is single-phase; C = 2 (the system is bivariant).
On each of the lines, the number of phases in the system is two, and, according to the phase rule, the system is monovariant: C \u003d 1 - 2 + 2 \u003d 1, i.e., there is only one pressure value for each temperature value.
The effect of pressure on the phase transition temperature is described by the Clausius-Clapeyron equation:
V2, V1 is the change in the molar volume of a substance during a phase transition.
The equilibrium curve "solid matter - liquid" on the state diagram of water is tilted to the left, and on the state diagrams of other substances - to the right, since the density of water is greater than the density of ice, i.e. melting is accompanied by a decrease in volume (AV< 0). In this case, an increase in pressure will lower the temperature of the phase transition "solid - liquid" (water - anomalous substance). For all other substances (so-called. normal substances) ?V pl> 0 and, according to the Clausius-Clapeyron equation, an increase in pressure leads to an increase in the melting temperature.
3. Properties of solutions
3.1. Thermodynamics of solutions
Solution- a homogeneous system consisting of two or more components, the composition of which can continuously change within certain limits without an abrupt change in its properties.
Diffusion in solutions
Diffusion- a spontaneous process of leveling the concentration of a substance in a solution due to the thermal movement of its molecules or atoms.
Fick's law: the amount of a substance diffusing per unit time through a unit surface area is proportional to its concentration gradient:
where j is the diffusion flux; D is the diffusion coefficient.
Einstein-Smoluchowski equation:
where? is the viscosity of the medium; R is the radius of diffusing particles.
Solubility of gases in gasesDalton's law: total pressure gas mixture equal to the sum of the partial pressures of all the gases included in it:
R total = ? pi And pi = xi P totalHenry Dalton's law: The solubility of a gas in a liquid is directly proportional to its pressure over the liquid: C i = kp i , where C i is the concentration of the gas solution in the liquid; k is the coefficient of proportionality, depending on the nature of the gas.
As a rule, when a gas dissolves in a liquid, heat is released (to< 0), so with increasing temperature, the solubility decreases.
Sechenov's formula:
X \u003d X 0 e -kC elwhere X And X 0 is the solubility of a gas in a pure solvent and an electrolyte solution with concentration FROM.
3.2. Colligative properties of non-electrolyte solutions
colligative (collective) called the properties of solutions relative to the properties of the solvent, depending mainly on the number of dissolved particles.
Saturated vapor pressure of dilute solutionsA vapor in equilibrium with a liquid is called saturated. The pressure of this steam p 0 called pressure or elasticity of saturated steam pure solvent.
Raoult's first law. The partial pressure of the saturated vapor of a solution component is directly proportional to its mole fraction in the solution, and the coefficient of proportionality is equal to the saturated vapor pressure over the pure component:
p i = p i 0 x iFor a binary solution consisting of components A and B: the relative decrease in the vapor pressure of the solvent over the solution is equal to the mole fraction of the solute and does not depend on the nature of the solute:
Solutions for which Raoult's law holds are called ideal solutions.
Vapor pressure of ideal and real solutions
If the components of a binary (consisting of two components) solution are volatile, then the vapor above the solution will contain both components. General Composition, mol. fractions in (x in) steam pressure:
p = pA0 x A + pB0 x B = p A 0 (1 – x B) + p B 0 x B = p A 0 – x B (p A 0 – p B 0)
If the molecules of a given component interact with each other more strongly than with the molecules of another component, then the true partial vapor pressures over the mixture will be greater than those calculated using Raoult's first law (positive deviations, ?Н TV > 0). If homogeneous particles interact with each other weaker than heterogeneous particles, the partial vapor pressures of the components will be less than the calculated (negative deviations, ?H solution< 0).
Crystallization temperature of dilute solutionsRaoult's second law. The decrease in the freezing point of the solution? T deputy is directly proportional to the molar concentration of the solution:? T deputy \u003d T 0 - T \u003d KS m, where T 0 - freezing point of pure solvent; T is the freezing point of the solution; TO is the cryoscopic constant of the solvent, deg/kg mol,
T 0 2 is the freezing temperature of the solvent; M is the molecular weight of the solvent, ?Nm is the molar heat of fusion of the solvent.
Boiling point of dilute solutionsBoiling temperature is the temperature at which the saturated vapor pressure becomes equal to the external pressure.
An increase in the boiling point of solutions of non-volatile substances? T K \u003d T k - T k 0 proportional to the decrease in saturated vapor pressure and directly proportional to the molar concentration of the solution: EU m , where E - ebullioscopic constant solvent, deg/kg mol,
Osmotic pressure of dilute solutions
Osmosis- predominantly one-sided passage of solvent molecules through a semipermeable membrane into a solution or solvent molecules from a solution with a lower concentration to a solution with a higher concentration.
The pressure that must be applied to the solution to prevent the solvent from moving into the solution through the membrane separating the solution from the pure solvent is numerically equal to osmotic pressure?(Pa).
Van't Hoff principle: The osmotic pressure of an ideal solution is equal to the pressure that the solute would exert if it, being in a gaseous state at the same temperature, occupied the same volume that the solution occupies: = CRT.
Isotonic solutions– two solutions with the same osmotic pressure (?1 = ?2).
Hypertonic saline- a solution whose osmotic pressure is greater than that of another (? 1 > ? 2).
Hypotonic solution- a solution whose osmotic pressure is less than that of another (? 1< ? 2).
3.3. Electrolyte solutions
Degree of dissociation? is the ratio of the number of molecules n, decayed into ions, to the total number of molecules N:
Isotonic ratio i Van Hoff is the ratio of the actual number of particles in the electrolyte solution to the number of particles in this solution without dissociation.
If from N molecules dissociated n, and each molecule broke up into ions, then
For non-electrolytes i = 1.
For electrolytes 1< i? ?.
3.4. Colligative properties of electrolyte solutions:
Arrhenius theory of electrolytic dissociation
1. Electrolytes in solutions decompose into ions - they dissociate.
2. Dissociation is a reversible equilibrium process.
3. The forces of interaction of ions with solvent molecules and with each other are small (i.e., solutions are ideal).
The dissociation of electrolytes in solution occurs under the action of polar solvent molecules; the presence of ions in a solution determines its electrical conductivity.
According to the degree of dissociation, electrolytes are divided into three groups: strong(? ? 0,7), medium strength(0,3 < ? < 0,7) и weak(? ? 0,3).
Weak electrolytes. Dissociation constantFor some electrolyte that decomposes into ions in solution in accordance with the equation:
A a B b - aA x- + bB y+
For binary electrolyte:
- Ostwald dilution law: the degree of dissociation of a weak electrolyte increases with dilution of the solution.
Solute activity– empirical value that replaces the concentration, – activity (effective concentration) but, related to concentration via activity coefficient f, which is a measure of the deviation of the properties of a real solution from an ideal one:
a = fC; a + = f+ C + ; a_ = f_C_.For binary electrolyte:
is the average activity of the electrolyte;
is the average activity coefficient.
Debye-Hückel limit law for binary electrolyte: lg f = -0.51z2I?, where z is the charge of the ion for which the activity coefficient is calculated;
I is the ionic strength of the solution I = 0.5? (C i r i 2).
4. Electrical conductivity of electrolyte solutions
Conductors of the first kind- metals and their melts, in which electricity is carried by electrons.
Conductors of the II kind– solutions and melts of electrolytes with ionic type of conductivity.
Electricity is the orderly movement of charged particles.
Any conductor through which current flows represents a certain resistance R, which, according to Ohm's law, is directly proportional to the length of the conductor l and inversely proportional to the cross-sectional area S; proportionality factor is resistivity material? - resistance of a conductor having a length of 1 cm and a cross section of 1 cm 2:
Value W, the opposite of resistance is called electrical conductivity- a quantitative measure of the ability of an electrolyte solution to conduct an electric current.
Electrical conductivity? (k) - electrical conductivity of a conductor of the first kind 1 m long with a cross-sectional area of \u200b\u200b1 m 2 or the electrical conductivity of 1 m 3 (1 cm 3) of an electrolyte solution (conductor of the second kind) with a distance between the electrodes of 1 m (1 cm) and an electrode area of 1 m 2 (1 cm 2).
Molar electrical conductivity of the solution) ? is the electrical conductivity of a solution containing 1 mol of a solute and placed between electrodes located at a distance of 1 cm from each other.
The molar electrical conductivity of both strong and weak electrolytes increases with decreasing concentration (i.e., with increasing dilution of the solution V = 1 / C) reaching some limit value? 0 (? ?), called molar electrical conductivity at infinite dilution.
For a binary electrolyte with singly charged ions at a constant temperature and a field strength of 1 V m -1:
? = ?F(u + + and?),where F is the Faraday number; and + , and? - absolute mobilities (m 2 V -1 s -1) cation and anion - the speed of movement of these ions under standard conditions, with a potential difference of 1 V per 1 m of the length of the solution.
? + = Fu + ; ?? = Fu?,where? + , ?? – mobility cation and anion, Ohm m 2 mol -1 (Ohm cm 2 mol -1).
? = ?(? + + ??)For strong electrolytes? ?1 and ? = ? + + ??
With infinite dilution of the solution (V > ?, ? + > ? ? + , ?? > ? ? ?, ? > 1) for both strong and weak electrolytes? ? = ? ? + – ? ? ? - Kohlrausch's law: is the molar electrical conductivity at infinite dilution equal to the sum of the electrolytic mobilities? ? + , ? ? ? cation and anion of a given electrolyte.
Ions H + and OH? have an abnormally high mobility, which is associated with a special mechanism of charge transfer by these ions - relay mechanism. Between hydronium ions H 3 O + and water molecules, as well as between water molecules and OH? protons are continuously exchanged according to the equations:
H 3 O + + H 2 O > H 2 O + H 3 O +
H 2 O + OH? >OH? + H 2 O
5. Electrochemical processes
5.1. Electrode potentials. Galvanic elements. EMF
When two chemically or physically dissimilar materials come into contact (metal 1 (conductor of the first kind) - metal 2 (conductor of the first kind), metal (conductor of the first kind) - metal salt solution (conductor of the second kind), electrolyte solution 1 (conductor of the second kind) - electrolyte solution 2 (conductor of the second kind), etc.) between them arises electric double layer (DES). DES is the result of an ordered distribution of oppositely charged particles at the interface.
The formation of a DEL leads to a potential jump?, which, under conditions of equilibrium, a metal (conductor of the first kind) - a solution of a metal salt (conductor of the second kind) is called galvanic potential.
System: metal (Me) - an aqueous solution of a salt of a given Me - is called electrode or half element and is shown schematically as follows:
The electrode (p / e) is written so that all substances in solution are placed to the left, and the electrode material is placed to the right of the vertical line.
? > 0, if the reduction reaction occurs on the electrode Me n+ + ne? - Me 0 ,
? < 0, если на электроде протекает реакция окисления Ме 0 - Ме n+ + ne?.
Electrode potential E Me n+ / Me is the equilibrium potential difference that occurs at the phase boundary conductor of the first kind / conductor of the second kind and measured relative to a standard hydrogen electrode.
Nernst Equation, where n is the number of electrons involved in the electrode reaction; FROM Me n+ is the concentration of cations; E Me n+ /Me is the standard electrode potential.
contact potential? ?- equilibrium potential jump that occurs at the interface between two conductors of the first kind.
Diffusion potential? dif is the equilibrium potential difference that occurs at the phase boundary conductor of the second kind / conductor of the second kind.
Galvanic cell (g.e.)- an electrical circuit consisting of two or more p.e. and producing electrical energy due to the chemical reaction taking place in it, and the stages of oxidation and reduction of the chemical reaction are spatially separated.
The electrode on which the oxidation process occurs during the operation of a galvanic cell is called anode, the electrode on which the recovery process is taking place, - cathode.
IUPAC rules for recording galvanic cells and the reactions occurring in them1. In g. e. work is done, so the EMF of the element is considered a positive value.
2. The value of the EMF of the galvanic circuit E is determined by the algebraic sum of potential jumps at the interfaces of all phases, but since oxidation occurs at the anode, the EMF is calculated by subtracting the value of the anode (left electrode) potential from the numerical value of the cathode (right electrode) potential - right pole rule. Therefore, the element circuit is written so that the left electrode is negative (oxidation occurs), and the right electrode is positive (reduction process occurs).
3. The interface between the conductor of the first kind and the conductor of the second kind is indicated by one line.
4. The boundary between two conductors of the second kind is depicted by a dotted line.
5. An electrolyte bridge at the boundary of two conductors of the II kind is indicated by two dotted lines.
6. The components of one phase are written separated by commas.
7. The equation of the electrode reaction is written so that the substances in the oxidized form (Ox) are located on the left, and in the reduced form (Red) on the right.
Daniel-Jacobi galvanic cell consists of zinc and copper plates immersed in the corresponding solutions of ZnSO 4 and CuSO 4 , which are separated by a salt bridge with a KCl solution: an electrolytic bridge provides electrical conductivity between the solutions, but prevents their mutual diffusion.
(-) Zn | Zn2+ :: Cu2+ | Cu(+)Reactions on the electrodes:
Zn0 > Zn2+ + 2e? Cu 2+ + 2е? > Cu 0Total redox process:
Cu 2+ + Zn 0 > Cu 0 + Zn 2+The work of the current of a galvanic cell (and, consequently, the potential difference) will be maximum during its reversible operation, when the processes on the electrodes proceed infinitely slowly and the current strength in the circuit is infinitely small.
The maximum potential difference that occurs during the reversible operation of a galvanic cell is electromotive force (EMF) of a galvanic cell E.
element emf E Zn/Cu = ? Cu2+ /Cu+? Zn2+ /Zn + ? to +? diff.
Excluding? diff and? to: E Zn/Cu = ? Cu2+ /Cu+? Zn2+ /Zn = E Cu 2+ /Cu + E Zn 2+ /Zn - galvanic cells consisting of two identical metal electrodes immersed in salt solutions of this metal with different concentrations С 1 > С 2 . In this case, the cathode will be an electrode with a higher concentration, since the standard electrode potentials of both electrodes are equal.
concentration chains
The only result of the work of the concentration element is the transfer of metal ions from a more concentrated solution to a less concentrated one.
The work of an electric current in a concentration galvanic cell is the work of a diffusion process, which is carried out reversibly as a result of its spatial division into two reversible electrode processes opposite in direction.
5.2. Electrode classification
Electrodes of the first kind. A metal plate immersed in a salt solution of the same metal. During the reversible operation of the element in which the electrode is included, the process of transition of cations from metal to solution or from solution to metal takes place on a metal plate.
Electrodes of the second kind. The metal is covered with a sparingly soluble salt of this metal and is in solution containing another soluble salt with the same anion. Electrodes of this type are reversible with respect to the anion.
Reference electrodes– electrodes with precisely known and reproducible potential values.
Hydrogen electrode is a platinum plate washed with hydrogen gas, immersed in a solution containing hydrogen ions. The hydrogen adsorbed by platinum is in equilibrium with gaseous hydrogen.
Pt, N 2 / N +Electrochemical equilibrium on the electrode:
2H++ 2e? - H 2 .The potential of a standard hydrogen electrode (with an activity of H + 1 mol/l ions and a hydrogen pressure of 101.3 kPa) is assumed to be zero.
Electrode potential of non-standard hydrogen electrode:
Calomel electrode consists of a mercury electrode placed in a KCl solution of a certain concentration and saturated with Hg 2 Cl 2 calomel:
Hg / Hg 2 Cl 2 , KClCalomel electrode is reversible with respect to chloride anions
Silver chloride electrode– reversible with respect to chlorine anions:
Ag/AgCl, KCl
If the KCl solution is saturated, then E AgC l \u003d 0.2224 - 0.00065 (t - 25), V.
indicator electrodes. Electrodes that are reversible with respect to the hydrogen ion are used in practice to determine the activity of these ions in solution.
Quinhydrone electrode is a platinum wire lowered into a vessel with the test solution, into which an excess amount of quinhydrone C 6 H 4 O 2 C 6 H 4 (OH) 2 is first placed - a compound of quinone C 6 H 4 O 2 and hydroquinone C 6 H 4 (OH ) 2 capable of interconversion in an equilibrium redox process in which hydrogen ions participate:
C 6 H 4 O 2 + 2H + + 2e? > C 6 H 4 (OH) 2Most commonly used glass electrode in the form of a tube ending in a thin-walled glass ball. The ball is filled with a buffer solution with a certain pH value, in which an auxiliary electrode (usually silver chloride) is immersed. To measure pH, the glass electrode is immersed in the test solution in tandem with the reference electrode. The glass electrode ball is pre-treated for a long time with an acid solution. In this case, hydrogen ions are introduced into the walls of the ball, replacing the alkali metal cations. The electrode process is reduced to the exchange of hydrogen ions between two phases - the test solution and glass: H solution - H st + .
standard capacity E st 0 for each electrode has its own value, which changes over time; therefore, the glass electrode is calibrated before each pH measurement against standard buffer solutions with exactly known pH.
Redox electrodesAn electrode consisting of an inert conductor of the 1st kind, placed in an electrolyte solution containing one element in various oxidation states, is called redox or redox electrode.
Electrode reaction: Oh n+ + ne? - red.
IN this case inert Me takes an indirect part in the electrode reaction, being an intermediary in the transfer of electrons from the reduced form of Me (Red) to the oxidized form (Ox) or vice versa.
6. Surface phenomena and adsorption
6.1. Surface Tension and Gibbs Adsorption
Surface phenomena called the processes occurring at the interface and due to the peculiarities of the composition and structure of the surface (boundary) layer.
Gs = ?s,where Gs is the surface Gibbs energy of the system, J; ? - coefficient of proportionality, called surface tension, J / m 2; s is the interfacial surface, m2.
Surface tensionabout is a quantity measured by the Gibbs energy per unit area of the surface layer. It is numerically equal to the work that must be done against the forces of intermolecular interaction to form a unit interface at a constant temperature.
From the Dupre model, surface tension equal to the force tending to reduce the interface and related to the unit length of the contour that bounds the surface
The ability of solutes to change the surface tension of a solvent is called surface activity g:
Classification of substances according to the effect on the surface tension of the solvent1. Surfactants (surfactants)– lower the surface tension of the solvent (? solution< ? 0) g >0 (in relation to water - organic compounds of amphiphilic structure).
2. Surface Inactive Substances (SIDs)– slightly increase the surface tension of the solvent (? solution > ? 0) g< 0 (неорганические кислоты, основания, соли, глицерин, ?-аминокислоты и др).
3. Surface-inactive substances (NSV)- practically do not change the surface tension of the solvent (? rr = ? 0) g = 0 (in relation to water, substances are sucrose and a number of others).
Duclos-Traube rule: in any homologous series at low concentrations, elongation of the carbon chain by one CH 2 group increases the surface activity by 3–3.5 times:
For aqueous solutions of fatty acids (Shishkovsky equation):
where b And TO are empirical constants, b the same for the entire homologous series, K increases for each subsequent member of the series by 3–3.5 times.
The process of spontaneous change in the concentration of a substance at the interface between two phases is called adsorption. Adsorbent a substance is called, on the surface of which there is a change in the concentration of another substance - adsorbate.
Gibbs adsorption isotherm:
The excess of the adsorbate in the surface layer compared to its initial amount in this layer characterizes excess or the so-called Gibbs, adsorption(G).
6.2. Adsorption at the solid-gas interface
physical adsorption arises due to van der Waals interactions of 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 by chemical interaction of adsorbent and adsorbate molecules, usually irreversible; is an localized i.e., the adsorbate molecules cannot move over the surface of the adsorbent. Since chemisorption is a chemical process requiring an activation energy of the order of 40-120 kJ/mol, an increase in temperature contributes to its occurrence.
Henry's equation(monomolecular adsorption on a homogeneous surface at low pressures or low concentrations):
G = Ks or G \u003d Kr,TO is the adsorption equilibrium constant, which depends on the nature of the adsorbent and adsorbate; C, r is the concentration of the dissolved substance or gas pressure.
Langmuir's theory of monomolecular adsorption
1. Adsorption is localized and is caused by forces close to chemical ones.
2. Adsorption occurs on a homogeneous surface of the adsorbent.
3. Only one layer of adsorbed molecules can form on the surface.
4. The process of adsorption is reversible and equilibrium.
Langmuir adsorption isotherm:
where Г 0 – monolayer capacity is a constant equal to the limiting adsorption observed at relatively high equilibrium concentrations, mol/m 2 ; b is a constant equal to the ratio of the adsorption rate constant and the desorption rate constant.
Freundlich equation(adsorption on an inhomogeneous surface): Г = K F with n , where. K F is a constant numerically equal to adsorption at an equilibrium concentration equal to unity; n is the constant that determines the curvature of the adsorption isotherm (n= 0,1–0,6).
Molecular adsorption from solutions:
where C 0 is the initial concentration of the adsorbate; FROM is the equilibrium concentration of the adsorbate; V is the volume of the adsorbate solution; m is the mass of the adsorbent.
Area S 0 , per molecule in a saturated adsorption layer, landing area:
m 2 /molecule.
Adsorption layer thickness:
where M is the molecular weight of the surfactant; ? is the surfactant density.
Rebinder's rule: on polar adsorbents, polar adsorbates from low-polarity solvents are better adsorbed; on polar adsorbents, non-polar adsorbates from polar solvents.
The orientation of surfactant molecules on the surface of the adsorbent is shown schematically in the figure:
6.3. Adsorption from electrolyte solutions
Exchange adsorption- the process of ion exchange between a solution and a solid phase, in which the solid phase absorbs ions of any sign (cations or anions) from the solution and instead of them can release an equivalent number of other ions of the same sign into the solution. Forever specific i.e., for a given adsorbent, only certain ions are capable of exchange; exchange adsorption is usually irreversible.
Package-Peskov-Faience Rule: on the surface of a crystalline solid, an ion is specifically adsorbed from an electrolyte solution, which is able to complete its crystal lattice or can form a poorly soluble compound with one of the ions that make up the crystal.
7. Colloidal (dispersed) systems
Colloidal (dispersed) system a heterogeneous system is called, in which one of the phases is represented by small particles uniformly distributed in the volume of another homogeneous phase. These are ultramicroheterogeneous systems consisting of particles dispersed phase- aggregates of crushed particles, the size of which lies within 10 -9 -10 -5 m, and continuous dispersion medium, in which these particles are distributed.
signs colloidal state of matter - dispersion and heterogeneity.
The degree of dispersion? is the reciprocal of the mean diameter or, for non-spherical particles, the reciprocal of the mean equivalent diameter d(m -1):
Specific surface area- attitude total area surface of the dispersed phase S DF to its total volume or to its mass:
7.1. Classification and methods for obtaining dispersed 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 the gases are infinitely soluble in each other.
Classification of systems according to the particle size of the dispersed phase:
1) highly dispersed, 10 -9_ 10 -7 m (ruby glass);
2) medium dispersed, 10 -7_ 10 -5 m (instant coffee);
3) coarse, > 10 -5 m (raindrops).
Methods for obtaining colloidal systems dispersionPhysical dispersion: mechanical grinding using colloid mills; electrical spraying of substances; ultrasonic dispersion and other methods. To prevent the formed particles from sticking together, the dispersion is carried out in the presence of stabilizer– electrolyte or substance adsorbed at the interface (surfactants).
Chemical dispersion (peptization): conversion of a freshly prepared precipitate into a colloidal state using a peptizer.
CondensationPhysical Condensation: 1) the method of replacing the solvent, which consists in the fact that a liquid that mixes with the solvent is added to the true solution of the substance, in which the substance itself is poorly soluble; due to a decrease in the solubility of the substance in the new solvent, the solution becomes supersaturated, and part of the substance condenses, forming particles of the dispersed phase; 2) vapor condensation method; the original substance is in a pair; as the temperature decreases, the vapor becomes supersaturated and partially condenses, forming a dispersed phase.
Chemical condensation: any chemical reaction resulting in the formation of a poorly soluble compound; in order to obtain a colloidal solution, the reaction must be carried out in a dilute solution at a low particle growth rate, one of the starting materials is taken in excess and is a stabilizer.
7.2. Optical properties of dispersed systems
When light falls on a disperse system, the following phenomena can be observed:
light passage particles of the dispersed phase (observed for transparent systems in which the particles are much smaller than the wavelength of the incident light (r<< ?);
light refraction particles of the dispersed phase (if these particles are transparent);
light reflection particles of the dispersed phase (if the particles are opaque);
refraction and reflection light is observed for systems in which the particles are much larger than the wavelength of the incident light (r >> ?). Visually, this phenomenon is expressed in the turbidity of these systems;
light scattering observed for systems in which the particles of the dispersed phase are smaller, but commensurate with the wavelength of the incident light (r ? 0.1 ?);
adsorption(absorption) of light by the dispersed phase with the conversion of light energy into heat.
Rayleigh equation:
where I, I 0 are the intensity of the scattered and incident light; V is the volume of one particle; ? – partial concentration (number of particles per unit volume); ? is the wavelength; n 1 , n 0 are the refractive indices of the particles and the medium, respectively.
The phenomenon of different colors of a colloidal solution in transmitted and scattered (reflected) light is called opalescence. In the case of colored solutions, there is an overlay of their own color and the color caused by opalescence (phenomenon dichroism of light).
7.3. Molecular kinetic properties
Colloidal systems are characterized Brownian motion- continuous random movement of particles of microscopic and colloidal sizes. This movement is the more intense, the higher the temperature and the lower the mass of the particle and the viscosity of the dispersion medium.
Diffusion is a spontaneous process of particle concentration equalization.
Fick's law:
Due to the large size of colloidal particles, diffusion in colloidal systems is slower than in true solutions.
Osmotic pressure:
where mtot is the mass of the dissolved substance; m is the mass of one particle; V is the volume of the system; N A is the Avogadro number; T is the absolute temperature; ? – partial concentration; k is the Boltzmann constant.
For spherical particles:
where? m is the mass of the dispersed phase per unit volume of the solution; ? is the density of the dispersion medium; r is the particle radius.
7.4. The structure of a micelle
Lyophobic micelle system is called a heterogeneous microsystem, which consists of a microcrystal of the dispersed phase, surrounded by solvated stabilizer ions.
Potential-determining called ions adsorbed on the surface of a particle of the solid phase (unit) and give it a charge. The aggregate, together with potential-determining ions, is micelle core.
Counterions are ions grouping near the micelle core.
The location of counterions in a dispersion medium is determined by two opposite factors: thermal motion (diffusion) and electrostatic attraction.
The counterions that make up the dense adsorption layer, are called "connected" and together with the core make up colloidal particle or granule. A colloidal particle (granule) has a charge, the sign of which is due to the sign of the charge of potential-determining ions.
The counterions that form diffuse layer,- "mobile", or "free".
A colloidal particle with a surrounding diffuse layer of solvated counterions is micelle. Unlike a colloidal particle, a micelle is electrically neutral and does not have strictly defined dimensions.
In a micelle with an ionic stabilizer, there is a DES at the phase boundary, a potential difference arises between the dispersed phase and the dispersion medium - thermodynamic potential f (interphase), which is determined by the properties of a given disperse system, as well as by the charge and concentration of potential-determining ions adsorbed on the solid phase.
The movement of charged colloidal particles in a stationary liquid to one of the electrodes under the action of an external electric field is called electrophoresis.
The surface on which the movement occurs is called sliding surface. The magnitude of the potential jump at the boundary of phases that are in motion relative to each other during electrophoresis and in Brownian motion, i.e., on the sliding surface, is called electrokinetic or?-potential (zeta potential).
7.5. Stability and coagulation
Stability of dispersed systems characterizes the ability of the dispersed phase to maintain a state of uniform distribution of particles throughout the volume of the dispersion medium.
There are two types of relative stability of disperse systems: sedimentation and aggregation.
Sedimentation resistance- the ability of the system to resist the action of gravity. Sedimentation is the settling of particles in solution under the influence of gravity.
Condition sedimentation equilibrium: the particle moves at a constant speed, i.e. evenly, the force of friction balances the force of gravity:
6??rU = 4/3?r 3 (? - ? 0)g,where? is the density of the dispersed phase, ? 0 is the density of the dispersion medium, g is the acceleration of gravity, ? is the viscosity of the medium.
Aggregative stability characterizes the ability of the particles of the dispersed phase to resist their sticking together and thereby maintain their size.
In violation of aggregative stability occurs coagulation is the process of sticking together of particles with the formation of large aggregates. As a result of coagulation, the system loses its sedimentation stability, since the particles become too large and cannot participate in Brownian motion.
Reasons for coagulation:
> temperature change;
> action of electric and electromagnetic fields;
> action of visible light;
> exposure to elementary particles;
> mechanical impact;
> adding electrolyte, etc.
Of greatest practical interest is coagulation with electrolytes.
Types of coagulation with electrolytesconcentration coagulation occurs under the influence indifferent electrolytes. indifferent is called an electrolyte, upon introduction of which the interfacial potential<р не изменяется. Данный электролит не содержит таких ионов, которые были бы способны к специфической адсорбции на частицах по правилу Па-нета-Фаянса, т. е. не способны достраивать кристаллическую решетку агрегата:
The state in which the diffuse layer disappears and the colloidal particle becomes electrically neutral is called isoelectric– electrokinetic potential (?) is equal to zero, coagulation occurs. The micelle formula in this state takes the form: (mnAg + nNO 3 ?) 0 .
Neutralization coagulation occurs when added to the sol non-indifferent electrolyte. Non-indifferent an electrolyte is called that is capable of changing the interfacial (?) and linearly related electrokinetic (?) potentials, i.e. this electrolyte contains ions that can be specifically adsorbed on the surface of the aggregate, complete its crystal lattice, or chemically interact with potential-determining ions.
The reversible process in which the coagulate again goes into a colloidal state is called peptization or disaggregation.
coagulation rules1. All strong electrolytes added to the sol in sufficient quantities cause it to coagulate. The minimum electrolyte concentration that causes coagulation of the sol in a certain short period of time is called coagulation threshold:
where C el is the concentration of electrolyte-coagulant; V el is the volume of added electrolyte; V sol (usually 10 ml) is the volume of the sol.
2. The ion whose charge coincides in sign with the charge of the counterions of the micelle of the lyophobic sol has a coagulating effect (the charge of the coagulating ion is opposite to the charge of the colloidal particle). This ion is called coagulant ion.
3. The coagulating ability of an ion - coagulant is the greater, the greater the charge of the ion:
Significance rule:
? 1: ? 2: ? 3 = 1/1 6: 1/2 6: 1/3 6 = 729: 11: 1The coagulating ability of an ion with the same charge is the greater, the larger its crystal radius. Ag + > Cs + > Rb + > NH 4 + > K + > Na + > Li+ - lyotropic series.
Colloidal protection is called increasing the aggregative stability of the sol by introducing into it an IUD (high molecular weight compound) or a surfactant (surfactant).
guard number called minimal amount milligrams of dry matter, which is necessary to protect 10 ml of the sol when an electrolyte is added to it in an amount equal to the coagulation threshold.
Ministry of Education Russian Federation Tomsk Polytechnic University __________________________________________________________________________ N. A. Kolpakova, V. A. Kolpakov, S. V. Romanenko PHYSICAL CHEMISTRY Textbook Part I Tomsk 2004 UDC 541.1 Physical chemistry. Textbook / N.A. Kolpakova, V.A. Kolpakov, S.V. Romanenko. - Tomsk: Ed. TPU, 2004. - Part 1. - 168 p. IN study guide the following sections of "Physical Chemistry" are considered: the basic laws of thermodynamics, chemical and phase equilibrium, thermodynamics of nonelectrolyte solutions. The manual was prepared at the Department of Physical and Analytical Chemistry of TPU and is intended for students of correspondence courses in chemical specialties. Published by order of the Editorial and Publishing Council of Tomsk Polytechnic University Reviewers: Kurina L.N. – Prof. Department of Physical Chemistry, TSU, Doctor of Chem. sciences; Buinovsky A.S. - Head. cafe Chemistry TPU STU, doctor of chem. Sciences. © Tomsk Polytechnic University, 2004 © Authors, 2004 CHAPTER 1 . INTRODUCTION TO PHYSICAL CHEMISTRY 1.1. BRIEF HISTORICAL OUTLINE OF THE DEVELOPMENT OF PHYSICAL CHEMISTRY The name and definition of the content of physical chemistry was first given by M.V. Lomonosov (1752): “Physical chemistry is a science that, on the basis of the positions and experiments of physical scientists, must explain the reason for what happens through chemical operations in complex bodies” . The teaching of physical chemistry in Russia as an independent science was introduced by prof. N. N. Beketov in 1860 at Kharkov University. The most important theoretical and experimental studies Lomonosov led him to discoveries that have not lost their significance even now. Lomonosov came close to the correct definition of the principle of conservation of matter and motion, the kinetic nature of heat, and also noted the impossibility of a spontaneous transfer of heat from a colder body to a warmer one, which is currently one of the formulations of the second law of thermodynamics. Over the next century, research was carried out, on the basis of which many important discoveries and generalizations were made. K. V. Scheele in Sweden (1773) and Fontana in France (1777) discovered the adsorption of gases; T. E. Lovits in Russia (1785) discovered adsorption from solutions. A. L. Lavoisier and P. S. Laplace in France (1779–1784) studied the heat capacities of substances and the heat effects of reactions. At the beginning of the XIX century. G. Davy in England and L. J. Tenard in France discovered catalytic reactions, and J. J. Berzelius in Sweden (1835) further developed the idea of catalysis. The foundations of electrochemistry were laid by research on galvanic cells, electrolysis, and current transfer in electrolytes. Galvani and A. Volta in Italy created in 1799 a galvanic cell. VV Petrov in Russia (1802) discovered the phenomenon of an electric arc. T. Grotgus in Russia in 1805 laid the foundations for the theory of electrolysis. In 1800, G. Davy advanced the electrochemical theory of the interaction of substances: he widely used electrolysis for chemical research. M. Faraday, a student of Davy, in 1833-1834 formulated the quantitative laws of electrolysis. B. S. Jacobi in Russia, solving the problems of the practical use of the electrolysis process, discovered in 1836 galvanoplasty. In the first half of the XIX century. thanks to the works of D. Dalton in England (1801–1803), J. L. Gay-Lussac in France (1802) and A. Avogadro in Italy (1811), who discovered the most important laws of the gaseous state, atomistic ideas were widely developed. The works of G. I. Hess (1802–1856) on thermochemistry belong to the same period. K. Guldberg and P. Waage in Norway (1864–1867), J. W. Gibbs in the USA (1873–1878) developed the thermodynamic theory of chemical equilibrium, and A. L. Le Chatelier in France (1884) discovered general principle equilibrium shifts when external conditions change. In the works of the Dutch chemist J. H. van't Hoff, the thermodynamic theory of chemical equilibrium was developed. He also developed the quantitative theory of dilute solutions (1885–1889). The transfer of electricity in solutions was studied in Germany by I. V. Gittorf and F. V. G. Kohlrausch. The Swedish scientist S. A. Arrhenius developed in 1883–1887. theory of electrolytic dissociation. A. M. Butlerov, who created the theory of the structure of organic compounds, left a deep mark on the development of physical chemistry. The great Russian chemist D. I. Mendeleev (1834–1907) discovered the existence of a critical temperature (1860), derived the general equation of state for gases (1874) and developed the chemical theory of solutions (1887). D. P. Konovalov (1889), a student of Mendeleev, is one of the founders of the theory of solutions. At the end of the XIX century. a number of major discoveries were made in the field of the doctrine of the structure of matter, which proved the complexity of the structure of the atom and played a huge role in the development of physical chemistry. These include the discoveries of the electron by J. B. Perrin (1895) and J. Thomson (1897), the quantum nature of light by R. Planck (1900), the existence of light pressure by P. N. Lebedev (1899), the study (since 1898 of ) phenomena of radioactivity by P. Curie and M. Sklodowska-Curie. By the beginning of the XX century. physical chemistry was defined as the science that studies the structure of matter, chemical thermodynamics, including thermochemistry and the theory of equilibrium, solutions, chemical kinetics and electrochemistry. New theoretical methods were applied, and studies of the structure of atoms, molecules, and crystals came to the fore. The doctrine of the structure of matter, especially the structure of atoms and molecules, developed most rapidly in the 20th century. A major achievement in this area was the nuclear theory of the atom, proposed by E. Rutherford (1911) and developed in the first quantitative theory of the hydrogen atom, developed by the Danish physicist N. Bohr (1913). The study of the nature of the chemical bond and the structure of molecules developed in parallel with the study of the structure of the atom. By the early 1920s, W. Kossel and G. N. Lewis had developed the fundamentals of the electronic theory of chemical bonding. VG Geitler and F. London (1927) developed the quantum-mechanical theory of chemical bonding. Based on the largest discoveries of physics in the field of atomic structure and using the theoretical methods of quantum mechanics and statistical physics, as well as new experimental methods, 4 such as x-ray analysis, spectroscopy, mass spectroscopy, magnetic methods, the method of labeled atoms, and others, physicists and physical chemists have made great strides in studying the structure of molecules and crystals and in understanding the nature of chemical bonds. The theory of the rates of chemical reactions, i.e., chemical kinetics, has been greatly developed, and is now associated specifically with studies of the structure of molecules and the strength of bonds between atoms in a molecule. New branches of physical chemistry have arisen and are successfully developing: magnetochemistry, radiation chemistry, physical chemistry of high polymers, physical chemistry of silicates, gas electrochemistry, etc. Like other sciences, physical chemistry and its individual branches arose or began to develop especially successfully in periods when one or another practical need necessitated the rapid development of some branch of industry, and for this development a solid theoretical foundation was required. Here it is necessary to note the major studies of N. S. Kurnakov on physicochemical analysis, the work in the field of electrochemistry by A. N. Frumkin, the creation of the theory of chain reactions by N. N. Semenov, and the development of the theory of heterogeneous catalysis by A. A. Balandin. Physical chemistry plays a leading role in solving numerous problems facing chemical science and practice. Currently, physical chemistry is independent discipline with its research methods and is the theoretical basis of applied chemical engineering disciplines. 1.2. SUBJECT AND OBJECTIVES OF PHYSICAL CHEMISTRY Physical chemistry is the science of regularities of chemical processes and physical phenomena. The main task of physical chemistry is the study and explanation of the main regularities that determine the direction of chemical processes, their speed, the influence of the medium, impurities, radiation, and the conditions for obtaining the maximum yield of a useful product. The study of physical chemistry makes it possible to understand the laws of chemistry, as well as to predict and control chemical phenomena. Modern physical chemistry makes it possible to solve the problems of efficient production control, intensification and automation of production processes. She serves theoretical basis chemical technology. Such important production processes in chemical technology as the synthesis and oxidation of ammonia, the contact production of sulfuric acid, the production of ethanol from natural gas, oil cracking, and many others are based on the results of physicochemical studies of the reactions underlying these processes. 5 processes. Without physical chemistry, it is impossible to solve the problem of creating substances with desired properties, develop new current sources, and many other issues of efficient production. Therefore, knowledge of physical chemistry for future process engineers opens up great opportunities for solving various problems encountered in the practical activities of an engineer at factories and research institutes. The name of the science - "physical chemistry" - reflects both the history of its emergence at the junction of two sciences - physics and chemistry, as well as the fact that it widely uses the theoretical laws and experimental methods of physics in the study of chemical phenomena. 1.3. CLASSIFICATION OF METHODS OF PHYSICAL CHEMISTRY Several theoretical methods are used in physical chemistry. The quantum chemical method uses the properties of elementary particles to describe chemical transformations. Using the laws of quantum mechanics, the properties and reactivity of molecules are described, as well as the nature of the chemical bond based on the properties of the elementary particles that make up the molecules. The thermodynamic (phenomenological) method is based on several laws (postulates), which are a generalization of experimental data. It makes it possible, on their basis, to find out the energy properties of the system, to predict the course of the chemical process and its result by the moment of equilibrium. The quantum-statistical method explains the properties of substances on the basis of the properties of the molecules that make up these substances. The kinetic method allows you to establish the mechanism and create a theory of chemical processes by studying the change in the rate of chemical reactions from various factors. Physical chemistry is characterized by the widespread use of mathematics, which not only makes it possible to most accurately express theoretical laws, but is also a necessary tool for establishing them. 6 CHAPTER 2 . BASIC LAWS OF THERMODYNAMICS The word "thermodynamics" comes from the Greek therme - heat and dynamis - force. Thermodynamics is the science of the transformation of various types of energy from one into another. Chemical thermodynamics studies the transformation of various types of energy occurring during the course of chemical reactions. 2.1. BASIC CONCEPTS OF CHEMICAL THERMODYNAMICS A system is a separate body or a group of bodies interacting and separated from the environment by a real or imaginary shell (boundary). An open system is a system that exchanges substances (mass) and energy (for example, heat) with the external environment. An isolated system (or closed system) is a system that does not exchange heat and work with the environment. The energy and volume of an isolated system are constant in time. An example of such a system is, for example, a thermos. If the boundary does not pass heat, then the process occurring in the system is called adiabatic. When a system exchanges heat and work with the environment, changes occur both in the system and in the environment. Thermodynamic systems can be homogeneous or heterogeneous. If there are no interfaces inside the system separating parts of the system that differ in composition or structure, then this system is called homogeneous. Accordingly, a heterogeneous system is a system consisting of various parts that differ in structure or chemical composition . These parts are called phases. Thus, a phase is a part of a heterogeneous system limited by the interface and characterized by the same physical and chemical properties at all points. Each system consists of one or more substances. Individual chemicals that can be isolated from the system and exist outside of it on their own as a separate phase are called constituent substances of the system. For example, in a glass there is water in which a platinum plate is lowered. Above the glass is a mixture of gases: oxygen, hydrogen and nitrogen. This system is three-phase, it contains five constituent substances. 7 The thermodynamic state of a system is a set of values of independent variables (system parameters) that determine its properties. Any property of a system can be called a thermodynamic state parameter if it is considered as one of the independent variables that determine the state of the system. Thermodynamics considers matter as a continuous medium and uses for research such thermodynamic parameters that are the result of the action of a large number of particles (macroparameters). For example, the macroparameters of a chemical reaction that proceeds even under “normal conditions” are temperature, pressure, volume, concentration, strength of gravitational, magnetic, electric and electromagnetic fields, etc. “Normal conditions” is a temperature of 20– 25 °C, atmospheric pressure, i.e. about 101 kPa, acceleration of gravity - on average about 9.8 m/s2, magnetic field strength - on average about 40 A/m, electric field strength - on average about 130 V/m, visible light illumination - about 500 lux on average. To characterize the thermodynamic state of a system, it is necessary to know not all properties, but only the smallest number of them, the so-called independent parameters of the system. As a rule, when describing a chemical process occurring on the Earth, we do not indicate the characteristics of the field, since they are constant and therefore do not affect the composition and yield of the reaction products. If the chemical process is carried out under conditions of strong magnetic or electric fields, or under intense irradiation with ultraviolet, X-rays, or even visible light, then the field parameters will have a significant effect on the composition and yield of the reaction products. In this case, the field parameters must be specified. Thermodynamic parameters are divided into extensive and intensive. Quantities proportional to the mass (or amount of substance) of the considered working fluid or thermodynamic system are called extensive, they are volume, internal energy, enthalpy, etc. Intensive quantities do not depend on the mass of the thermodynamic system. These are, for example, temperature and pressure. Pressure is a physical quantity equal to the ratio of a force uniformly distributed over the surface of a body to the surface area located perpendicular to the force: p \u003d S The unit of pressure in SI - pascal (Pa) is the pressure caused by a force of 1 N, uniformly distributed on a surface of 1 m2 located perpendicular to the direction of force: 1 N/m2 = 1 Pa. In practice, multiple and sub-multiple units of pressure are used: kilopascal 8 (103 Pa = 1 kPa); megapascal (106 Pa = 1 MPa); hectapascal (102 Pa = 1 hPa), as well as an off-system unit - bar (1 bar = 105 Pa). According to the conclusions of the molecular-kinetic theory, the pressure of a gas is the result of impacts of randomly continuously moving molecules against the vessel wall. The simplest relationships between the parameters and the behavior of molecules were obtained for an ideal gas. An ideal gas is a gas consisting of elastic molecules, between which there are no interaction forces, which have a negligibly small volume in comparison with the volume occupied by the gas. Any real gas at a relatively low pressure (close to atmospheric pressure) behaves practically like an ideal one (strictly at p → 0). The equation of state of an ideal gas - the Mendeleev - Clapeyron equation has the form: pV = nRT, where p is the gas pressure, Pa; V - volume, m3; n is the amount of gas, mol; R is the universal gas constant equal to 8.314 J/(mol K); T is the absolute temperature, K. The temperature characterizes the thermal state of the system. Experimentally, the concepts of a warmer and colder body can be established, but the temperature cannot be measured directly. It is determined from the numerical values of other physical parameters that depend on temperature, which is the basis for constructing empirical temperature scales. Various physical quantities can serve as such parameters (thermometric parameters). Among them are the volume of a body at constant pressure, pressure at a constant volume, electrical conductivity, thermoelectromotive force, geometric parameters of bodies, brightness of the glow, etc. A device for measuring temperature is called a thermometer. To build any empirical temperature scale, three assumptions are used: 1) the size of a degree is set by choosing the numerical value of ∆T between two reference temperature points - temperature standards; 2) the position of the temperature zero in empirical scales is arbitrary; 3) it is assumed that the thermometric function is linear in a given temperature range. The phase transitions of pure substances are used as reference points. For example, for the empirical Celsius scale, the melting and boiling points of water at atmospheric pressure (0 and 100 degrees, respectively) are taken as reference points. The interval between these temperatures is divided into one hundred equal parts (degrees Celsius - °C). Although an objective temperature scale can be constructed using any theoretically defined thermometric function, thermodynamics uses the ideal gas equation of state as such a function. The gas thermometer makes it possible to carry out the most accurate (close to the absolute temperature scale - the Kelvin scale) temperature measurements. However, determining the temperature on the scale of a gas thermometer is a rather difficult job, which is carried out only to establish the absolute temperatures of a few reference points of phase transitions, taken as reference ones. Intermediate temperatures are usually determined by empirical thermometric methods. The International Practical Temperature Scale (IPTS), adopted in 1954, is the most accurate approximation to the absolute temperature scale at the present stage. In contrast to the empirical scales, the MPST uses one experimental temperature reference point. The temperature of the triple point of water (when ice, water and water vapor are in equilibrium at the same time) was used as such a point. The temperature of the triple point of water is taken in the IPTS as 273.16 K (exactly). At atmospheric pressure, ice melts 0.01° lower. The reference point on the Celsius scale - 0 °C - corresponds to 273.15 K. The numerical value of temperatures for all other reference points (except for the triple point of water) is continuously refined as the accuracy of working with a gas thermometer increases. In 1968, twelve reference points were recommended as reference temperature points, spanning the range from the triple point of hydrogen to the melting point of gold. Currently, Celsius temperature (t) is expressed as a relationship with absolute temperature (T), which is: T = 273.15 + t. The properties of a system that can be unambiguously expressed as functions of temperature, pressure, and concentration of the substances that make up the system are called thermodynamic functions. For example, heat capacity, internal energy, entropy, etc. If the change in the thermodynamic function depends only on the initial and final state of the system and does not depend on the path of the process, then such a function is called the state function of the system. A thermodynamic process is any change in a system associated with a change in at least one of the thermodynamic parameters. A circular process or cycle is a process in which a thermodynamic system, having left some initial state and undergoing a series of changes, returns to the same state; in this process, the change in any state parameter is equal to zero. 10
The beginning of physical chemistry was laid in the middle of the 18th century. The term "Physical chemistry", in the modern understanding of the methodology of science and questions of the theory of knowledge, belongs to M. V. Lomonosov, who for the first time read the "Course of True Physical Chemistry" to students of St. Petersburg University. In the preamble to these lectures, he gives the following definition: "Physical chemistry is a science that must, on the basis of the provisions and experiments of physical scientists, explain the reason for what happens through chemical operations in complex bodies." The scientist in the works of his corpuscular-kinetic theory of heat deals with issues that fully meet the above tasks and methods. This is precisely the nature of the experimental actions that serve to confirm individual hypotheses and provisions of this concept. M. V. Lomonosov followed these principles in many areas of his research: in the development and practical implementation of the “science of glass” founded by him, in various experiments devoted to confirming the law of conservation of matter and force (motion); - in works and experiments related to the doctrine of solutions - he developed an extensive program of research on this physical and chemical phenomenon, which is in the process of development to the present day.
This was followed by a break of more than a hundred years, and one of the first physicochemical studies in Russia in the late 1850s was started by D. I. Mendeleev.
The next course in physical chemistry was taught by N. N. Beketov at Kharkov University in 1865.
The first department of physical chemistry in Russia was opened in 1914 at the Faculty of Physics and Mathematics of St. Petersburg University, in the fall, a student of D.P. Konovalov, M.S. Vrevsky, began to read the compulsory course and practical classes in physical chemistry.
The first scientific journal intended to publish articles on physical chemistry was founded in 1887 by W. Ostwald and J. van't Hoff.
The subject of physical chemistry
Physical chemistry is the main theoretical foundation of modern chemistry, using the theoretical methods of such important sections of physics as quantum mechanics, statistical physics and thermodynamics, nonlinear dynamics, field theory, etc. It includes the doctrine of the structure of matter, including: the structure of molecules, chemical thermodynamics, chemical kinetics and catalysis. As separate sections in physical chemistry, electrochemistry, photochemistry, physical chemistry of surface phenomena (including adsorption), radiation chemistry, the theory of metal corrosion, physical chemistry of macromolecular compounds (see polymer physics), etc. are also distinguished. Very closely adjacent to physical chemistry and are sometimes considered as its independent sections of colloid chemistry, physico-chemical analysis and quantum chemistry. Most sections of physical chemistry have fairly clear boundaries in terms of objects and research methods, methodological features and the apparatus used.
The difference between physical chemistry and chemical physics
The molecularity of an elementary reaction is the number of particles that, according to the experimentally established reaction mechanism, participate in an elementary act of chemical interaction. Monomolecular reactions- reactions in which a chemical transformation of one molecule occurs (isomerization, dissociation, etc.): H 2 S → H 2 + S Bimolecular reactions- reactions, the elementary act of which is carried out when two particles (identical or different) collide: CH 3 Br + KOH → CH 3 OH + KBr Trimolecular reactions- reactions, the elementary act of which is carried out when three particles collide: O 2 + NO + NO → 2NO 2 Reactions with a molecularity greater than three are unknown. For elementary reactions carried out at close concentrations of the starting substances, the values of molecularity and order of the reaction are the same. There is no clearly defined relationship between the concepts of molecularity and reaction order, since the reaction order characterizes the kinetic equation of the reaction, and molecularity characterizes the reaction mechanism. The main areas of chemical thermodynamics are:
Chemical thermodynamics is closely related to such branches of chemistry as
Physico-chemical analysisThe theory of physicochemical analysis is based on the principles of correspondence and continuity formulated by N. S. Kurnakov. The principle of continuity states that if new phases are not formed in the system or existing ones do not disappear, then with a continuous change in the parameters of the system, the properties of individual phases and the properties of the system as a whole change continuously. The correspondence principle states that each complex of phases corresponds to a certain geometric image on the composition-property diagram. Theory of reactivity of chemical compoundsHigh energy chemistry (HVE) studies the chemical reactions and transformations that occur in matter under the influence of nonthermal energy. The mechanisms and kinetics of such reactions and transformations are characterized by essentially nonequilibrium concentrations of fast, excited or ionized particles with an energy greater than the energy of their thermal motion and, in some cases, chemical bonding. Carriers of non-thermal energy acting on matter: accelerated electrons and ions, fast and slow neutrons, alpha and beta particles, positrons, muons, pions, atoms and molecules at supersonic speeds, electromagnetic radiation quanta, as well as pulsed electrical, magnetic and acoustic fields. The processes of high-energy chemistry are distinguished by time stages into physical, occurring in a time of femtoseconds or less, during which non-thermal energy is distributed unevenly in the medium and a “hot spot” is formed, physical-chemical, during which disequilibrium and inhomogeneity in the “hot spot” are manifested and, finally, chemical, in which the transformations of matter obey the laws of general chemistry. As a result, such ions and excited states of atoms and molecules are formed at room temperatures that cannot arise due to equilibrium processes. The external manifestation of CHE is the formation of ions and excited states of atoms and molecules at room temperatures, at which these particles cannot arise due to equilibrium processes. NE Ablesimov formulated a relaxation principle for controlling the properties of non-equilibrium physical and chemical systems. In the case when the relaxation times are much longer than the duration of the physical impact, it is possible to control the release of chemical forms, phases and, as a consequence, the properties of substances (materials), using information about the relaxation mechanisms in nonequilibrium condensed systems at the physicochemical stage of relaxation processes (including number and during operation). The main sections of the HVE
and others. laser chemistryThe ionizing ability is possessed by electromagnetic radiation (X-rays, γ-radiation, synchrotron radiation) and streams of accelerated particles (electrons, protons, neutrons, helions, heavy ions; fission fragments of heavy nuclei, etc.), the energy of which exceeds the ionization potential of atoms or molecules ( in most cases, lying in the range of 10-15 eV). Within the framework of radiation chemistry, some chemical processes are considered that are impossible using traditional chemical approaches. Ionizing radiation can greatly reduce the temperature of chemical reactions without the use of catalysts and initiators. History of radiation chemistry Radiation chemistry arose after the discovery of x-rays by W. Roentgen in 1895 and radioactivity by A. Becquerel in 1896, who were the first to observe radiation effects in photographic plates. The first works on radiation chemistry were carried out in 1899-1903 by the spouses M.Curie and P.Curie. In later years largest number research was devoted to the radiolysis of water and aqueous solutions. nuclear chemistryMain directions of nuclear chemistry:
ElectrochemistryElectrochemistry is a branch of chemical science that considers systems and interphase boundaries when an electric current flows through them, processes in conductors, on electrodes (from metals or semiconductors, including graphite) and in ionic conductors (electrolytes) are studied. Electrochemistry investigates processes |
PHYSICAL CHEMISTRY
§ 1. The subject of physical chemistry. Its meaning
The relationship of chemical and physical phenomena studies physical chemistry. This branch of chemistry is the boundary between chemistry and physics. Using the theoretical and experimental methods of both sciences, as well as its own methods, physical chemistry is engaged in a multifaceted study of chemical reactions and the physical processes accompanying them. Since, however, even a multifaceted study is never complete and does not cover the phenomenon in an exhaustive way, the laws and laws of physical chemistry, like those of other natural sciences, always simplify the phenomenon and do not fully reflect it.
The rapid development and growing importance of physical chemistry are associated with its boundary position between physics and chemistry. The main general task of physical chemistry is the prediction of the time course of the process and the final result (equilibrium state) in various conditions based on data on the structure and properties of the substances that make up the system under study.
§ 2. Brief outline of the history of the development of physical chemistry
The term "physical chemistry" and the definition of this science were first given by M.V. Lomonosov, who in 1752-1754. read a course in physical chemistry to the students of the Academy of Sciences and left the manuscript of this course "Introduction to True Physical Chemistry" (1752). Lomonosov carried out many studies, the topics of which correspond to the "Plan for the course of physical chemistry" (1752) compiled by him and the program of experimental work "Experience in Physical Chemistry" (1754). Under his leadership, a student workshop in physical chemistry was also held.
Lomonosov gave the following definition of physical chemistry: "Physical chemistry is a science that explains, on the basis of the provisions and experiments of physics, what happens in mixed bodies during chemical operations." This definition is close to modern.
For the development of physical chemistry, the discovery of two laws of thermodynamics in the middle of the 19th century (S. Carnot, Yu.R. Mayer, G. Helmholtz, D.P. Joule, R. Clausius, W. Thomson) was of great importance.
The number and variety of research, lying in the field that borders between physics and chemistry, constantly increased in the 19th century. The thermodynamic theory of chemical equilibrium was developed (K.M. Guldberg, P. Waage, D.W. Gibbs). The studies of L.F. Wilhelmi laid the foundation for the study of the rates of chemical reactions (chemical kinetics). The transfer of electricity in solutions was studied (I.V. Gittorf, F.V.G. Kolrausch), the laws of equilibrium of solutions with steam were studied (D.P. Konovalov) and the theory of solutions was developed (D.I. Mendeleev).
The recognition of physical chemistry as an independent science and academic discipline was expressed in the establishment at the University of Leipzig (Germany) in 1887 of the first department of physical chemistry headed by W. Ostwald and in the foundation of the first scientific journal on physical chemistry there. At the end of the 19th century, the University of Leipzig was the center for the development of physical chemistry, and the leading physical chemists were W. Ostwald, J. H. Van't Hoff, S. Arrhenius and W. Nernst. By this time, three main sections of physical chemistry were defined - chemical thermodynamics, chemical kinetics and electrochemistry.
The most important areas of science, the development of which is a necessary condition for technical progress, include the study of chemical processes; physical chemistry plays a leading role in the development of this problem.
§ 3. Sections of physical chemistry. Research methods
Chemical thermodynamics. In this section, on the basis of the laws of general thermodynamics, the laws of chemical equilibrium and the doctrine of phase equilibria are expounded.
The doctrine of solutions aims to explain and predict the properties of solutions (homogeneous mixtures of several substances) on the basis of the properties of the substances that make up the solution.
The doctrine of surface phenomena. Various properties of surface layers of solids and liquids (interfaces between phases) are studied; one of the main studied phenomena in the surface layers is adsorption(accumulation of matter in the surface layer).
In systems where the interfaces between liquid, solid, and gaseous phases are highly developed (emulsions, mists, smokes, etc.), the properties of the surface layers become of primary importance and determine many of the unique properties of the entire system as a whole. Such dispersed (microheterogeneous) systems are being studied colloid chemistry, which is a major independent branch of physical chemistry.
The above list of the main sections of physical chemistry does not cover some areas and smaller sections of this science, which can be considered as parts of larger sections or as independent sections of physical chemistry. It should be emphasized once again the close interrelationship between the various branches of physical chemistry. In the study of any phenomenon, one has to use an arsenal of ideas, theories and methods for studying many branches of chemistry (and often other sciences). Only with an initial acquaintance with physical chemistry is it possible for educational purposes to distribute the material into the indicated sections.
Methods of physical and chemical research. The basic methods of physical chemistry are naturally the methods of physics and chemistry. This is, first of all, an experimental method - the study of the dependence of the properties of substances on external conditions, the experimental study of the laws of the flow of various processes and the laws of chemical equilibrium.
The theoretical understanding of experimental data and the creation of a coherent system of knowledge is based on the methods of theoretical physics.
The thermodynamic method, which is one of them, makes it possible to quantitatively relate various properties of a substance (“macroscopic” properties) and calculate some of these properties based on the experimental values of other properties.
CHAPTER I
THE FIRST LAW OF THERMODYNAMICS
§ 1. Energy. The law of conservation and transformation of energy
An integral property (attribute) of matter is movement; it is indestructible, like matter itself. The motion of matter manifests itself in different forms, which can pass one into another. The measure of motion of matter is energy. Quantitatively, energy is expressed in a certain way through the parameters characteristic of each specific form of movement, and in units specific to this form.
In the SI system of units, the unit of energy (heat and work) is the joule ( J), equal to the work of force in 1 H on the way to 1 m. 1 J = 1 Nm.
The widespread unit of energy (heat) calorie is currently an off-system unit that is allowed for use. The currently used calorie, by definition, equates to a certain number of joules: 1 feces equals 4.1868 joules. This unit is used in heat engineering and can be called thermal calorie. In chemical thermodynamics, a slightly different unit is used, equated to 4.1840 joules and called thermochemical calorie. The expediency of its application is connected with the convenience of using the extensive experimental thermochemical material collected in reference books and expressed in these units.
When one form of motion is transformed into another, the energies of the disappeared and appeared motion, expressed in different units, are equivalent to each other, i.e., the energy of the disappeared motion is in a constant quantitative relation to the energy of the motion that has arisen (the law of equivalent transformations of energy). This ratio does not depend on the energies of the two forms of motion and on the specific conditions under which the transition from one form of motion to another took place. So, when the energy of an electric current is converted into the energy of chaotic molecular motion, one joule of electrical energy always turns into 0.239 feces energy of molecular motion.
Thus, energy as a measure of the motion of matter always manifests itself in a qualitatively original form, corresponding to a given form of motion, and is expressed in the appropriate units of measurement. On the other hand, it quantitatively reflects the unity of all forms of movement, their mutual convertibility and the indestructibility of movement.
The above law of equivalent transformations of energy is a physical experimental law. The law of equivalent energy transformations can be expressed differently, namely in the form the law of conservation and transformation of energy: energy is neither created nor destroyed; in all processes and phenomena, the total energy of all parts of an isolated material system participating in this process does not increase or decrease, remaining constant.
The law of conservation and transformation of energy is universal in the sense that it is applicable to phenomena occurring in arbitrarily large bodies, representing an aggregate of a huge number of molecules, and to phenomena occurring with the participation of one or a few molecules.
For various forms of mechanical motion, the law of conservation of energy has long been expressed in a qualitative form (Descartes - 1640) and a quantitative form (Leibniz - 1697).
For the mutual transformations of heat and work (see below), the law of conservation of energy was proved as a natural science law by the studies of Yu. R. Mayer, G. Helmholtz and D.P. Joule, carried out in the forties of the XIX century.
Using the law of equivalent transformations, it is possible to express the energies of various forms of motion in units characteristic of one type of energy (one form of motion), and then perform operations of addition, subtraction, etc.
§ 2. Subject, method and limits of thermodynamics
Thermodynamics is one of the main branches of theoretical physics. Thermodynamics studies the laws of mutual transformations of various types of energy associated with the transfer of energy between bodies in the form of heat and work. Focusing its attention on heat and work as forms of energy transfer in a variety of processes, thermodynamics involves numerous energy connections and dependencies between various properties of a substance in its circle of consideration and gives very widely applicable generalizations called the laws of thermodynamics.
When establishing the basic thermodynamic laws, energy transformations (often very complex) occurring inside the body are usually not detailed. The types of energy inherent in the body in its given state are also not differentiated; the totality of all these types of energy is considered as a single internal energy of the system .
The subject matter of thermodynamics outlined above defines the method and boundaries of this science. The distinction between heat and work, taken as a starting point by thermodynamics, and the opposition of heat to work makes sense only for bodies consisting of many molecules, since for one molecule or for a set of a small number of molecules, the concepts of heat and work lose their meaning. Therefore, thermodynamics considers only bodies consisting of a large number of molecules, the so-called macroscopic systems moreover, thermodynamics in its classical form does not take into account the behavior and properties of individual molecules.
The thermodynamic method is also characterized by the fact that the object of study is a body or a group of bodies isolated from the material world into thermodynamic system (hereinafter referred to simply system).
The system has certain boundaries separating it from the outside world (environment).
The system is homogeneous , if each of its parameters has the same value in all parts of the system or continuously changes from point to point.
The system is heterogeneous , if it consists of several macroscopic (consisting in turn of many molecules) parts, separated from one another by visible interfaces. On these surfaces, some parameters change abruptly. Such, for example, is the system "solid salt - saturated aqueous salt solution - saturated water vapor." Here, at the boundaries of salt - solution and solution - vapor, the composition and density change abruptly.
Homogeneous parts of the system, separated from other parts by visible interfaces, are called phases . In this case, the set of individual homogeneous parts of the system that have the same physical and thermodynamic properties is considered to be one phase (for example, a set of crystals of one substance or a set of liquid droplets suspended in a gas and forming fog). Each phase of the system is characterized by its own equation of state.
A system that cannot exchange matter and energy with the environment (in the form of heat or work) is called isolated .
A system that can exchange matter and energy with the environment (in the form of heat or work) is called open.
A system that cannot exchange matter with the environment, but can exchange energy (in the form of heat or work) is called closed .
Thermodynamics studies the relationship between such measurable properties of a material system as a whole and its macroscopic parts (phases), such as temperature, pressure, mass, density and chemical composition of the phases included in the system, and some other properties, as well as the relationship between changes in these properties.
The set of properties studied by thermodynamics (the so-called thermodynamic parameters of the system) defines thermodynamic state of the system. A change in any thermodynamic properties (even if only one) leads to a change in the thermodynamic state of the system.
All processes occurring in nature can be divided into spontaneous (natural) and non-spontaneous.
Spontaneous processes These are processes that do not require external energy input. For example, the transfer of heat from a body with a higher temperature to a body with a lower temperature, the dissolution of salt in water, etc., proceed by themselves.
Non-spontaneous processes require energy from the outside for their flow, for example, the separation of air into nitrogen and oxygen.
In thermodynamics, mainly such states of a system are considered in which its parameters (temperature, pressure, electrostatic potential, etc.) do not change spontaneously in time and have the same value at all points in the volume of individual phases. Such states are called balanced.
One of the basic postulates of thermodynamics is the statement that the course of any spontaneous process ultimately brings the isolated system to an equilibrium state, when its properties will no longer change, i.e., equilibrium will be established in the system.
States characterized by uneven and time-varying distributions of temperature, pressure, and composition within phases are nonequilibrium. They are considered by the thermodynamics of non-equilibrium (irreversible) processes, in which, in addition to the basic thermodynamic laws, additional assumptions are used.
Thermodynamics, built on the basis of the basic laws of thermodynamics, which are considered as a generalization of experience, is often called classical or phenomenological thermodynamics. Thermodynamics provides the theoretical foundations for the theory of heat engines; this section is called technical thermodynamics. The study of chemical processes from a thermodynamic point of view is engaged in chemical thermodynamics, which is one of the main branches of physical chemistry.
§ 3. 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 transitions of energy connected with it can be divided into two groups.
The first group includes only one form of motion transition by chaotic collisions of molecules of two adjoining bodies, i.e. by conduction (and at the same time by radiation). The measure of the movement transmitted in this way is heat .
The second group includes various forms of movement transition, a common feature of which is the movement of macroscopic masses under the action of any external forces that have a directed character. Such are the rise of bodies in a gravitational field, the transition of a certain amount of electricity from a larger electrostatic potential to a smaller one, the expansion of a gas under pressure, etc. The general measure of the movement transmitted by such means is Job .
Heat and work characterize qualitatively and quantitatively two different forms of transmission of motion from one part of the material world to another.
The transmission of motion is a kind of complex motion of matter, the two main forms of which we distinguish. Heat and work are measures of these two complex forms of motion of matter, and they should be considered as types of energy.
The common property of heat and work is that they matter only during the time intervals in which these processes take place. In the course of such processes, in some bodies the movement in one form or another decreases and the corresponding energy decreases, while in other bodies the movement in the same or other forms increases and the corresponding types of energy increase.
We are not talking about the stock of heat or work in any body, but only about the heat and work of a known process. After its completion, there is no need to talk about the presence of heat or work in the bodies.
§ 4. Equivalence of heat and work
A constant equivalent ratio between heat and work during their mutual transitions was established in the classical experiments of D.P. Joule (1842-1867). A typical Joule experiment is as follows.
Joule device for determining the mechanical equivalent of heat.
Weights falling from a known height rotate a stirrer immersed in water in a calorimeter (a weight and a calorimeter with water constitute a thermodynamic system.) The rotation of the stirrer blades in water causes the water in the calorimeter to heat up; the corresponding rise in temperature is quantified.
After the specified process is completed, the system must be brought to its original state. This can be done through mental experience. The weights rise to their original height, while external work is expended, which increases the energy of the system. In addition, the calorimeter is taken away (transferred to environment) heat by cooling it to its original temperature. These operations return the system to its original state, i.e., all measurable properties of the system acquire the same values that they had in the initial state. The process during which the properties of the system changed, and at the end of which it returned to its original state, is called circular (cyclic) process or cycle .
The only result of the described cycle is the removal of work from the environment surrounding the system, and the transfer to this environment of the heat taken from the calorimeter.
Comparison of these two quantities, measured in the corresponding units, shows a constant relationship between them, independent of the size of the load, the size of the calorimeter, and the specific amounts of heat and work in different experiments.
It is advisable to write the heat and work in a cyclic process as the sum (integral) of infinitely small (elementary) heats Q and infinitesimal (elementary) jobs W, and the initial and final limits of integration coincide (cycle).
Then the equivalence of heat and work in a cyclic process can be written as follows:
(I, 1)
In equation (I, 1), the sign 
denotes integration over a cycle. Coefficient constancy k
reflects the equivalence of heat and work ( k is the mechanical equivalent of heat). Equation (I, 1) expresses the law of conservation of energy for a particular, very important case of the transformation of work into heat.
In the studies of Joule, Rowland (1880), Miculescu (1892), and others, the methods of friction in metals, impact, direct conversion of the work of an electric current into heat, stretching of solids, etc. were used. k always constant within the experimental error.
In what follows, it is always assumed that work and heat, with the help of the coefficient k expressed in the same units (no matter what) and the coefficient k goes down.
§ 5. Internal energy
For a non-circular process, the equality (I, 1) is not observed, since the system does not return to its original state. Instead, the equalities for a non-circular process can be written (omitting the coefficient k):
≠
Since the limits of integration are generally arbitrary, then for elementary quantities W And Q:
Q W,
Consequently:
Q – W 0
Denote the difference Q – W for any elementary thermodynamic process through dU:
dU Q – W (I, 2)
or for the final process:
–
(I, 2a)
Returning to the circular process, we obtain (from Equation I, 1):
=
–
= 0 (I, 3)
Thus, the value dU is the total differential of some system state function. When the system returns to its original state (after a cyclic change), the value of this function acquires its original value.
System state functionU , defined by the equalities (I, 2) or (I, 2a) is calledinternal 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 substantiates empirically the presence of a certain function of the state of the system, which has the meaning of the total measure of all movements that the system possesses.
In other words, internal energy includes the translational and rotational energy of molecules, the vibrational energy of atoms and groups of atoms in a molecule, the energy of electron motion, intranuclear and other types of energy, i.e. the totality of all types of particle energy in the system, with the exception of the potential and kinetic energy of the system itself .
Let us assume that the cyclic process was carried out in such a way that after the system returned to its initial state, the internal energy of the system did not take the initial value, but increased. In this case, the repetition of circular processes would cause the accumulation of energy in the system. It would be possible to convert this energy into work and obtain work in this way not at the expense of heat, but “out of nothing”, since in a circular process work and heat are equivalent to each other, which is shown by direct experiments.
Inability to complete the specified build cycle perpetuum mobile (perpetuum mobile) of the first kind, that gives work without spending an equivalent amount of another type of energy, is proved by the negative result of thousands of years of human experience. This result leads to the same conclusion that we obtained in a particular but more rigorous form by analyzing Joule's experiments.
Let us formulate the result obtained once more. The total energy of the system (its internal energy) as a result of a cyclic process returns to its original value, i.e., the internal energy of a system in a given state has one definite value and does not depend on what changes the system underwent before coming to this state.
In other words, the internal energy of the system is a single-valued, continuous and finite function of the state of the system.
The change in the internal energy of the system is determined by expression (I, 2b); the expression (I, 3) is valid for a circular process. With an infinitesimal change in some properties (parameters) of the system, the internal energy of the system also changes infinitesimally. This is a property of a continuous function.
Within thermodynamics, there is no need to use a general definition of the concept of internal energy. A formal quantitative definition through expressions (I, 2) or (I, 2a) is sufficient for all further thermodynamic reasoning and conclusions.
Since the internal energy of the system is a function of its state, then, as already mentioned, the increase in internal energy with infinitesimal changes in the parameters of the system states is the total differential of the state function. Breaking the integral in equation (I, 3) into two integrals over the sections of the path from the state 1 up to the state 2 (path "a") (see Fig. I) and vice versa - from the state 2
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