Molecular Physical Chemistry for Engineering Applications

Authors
	From the Same Authors
Preface
	Macroscopic and Microscopic in Matter Sciences
	The Document Subdivision
Contents
Notations (Symbols)
	Latin Symbols
	Greek Symbols
	Indices
	Exponents
	Prefixes
	Binary Operators
	Other Operators
	Abbreviations
Constants and Units of Measure
	Universal Physical Constants
	Six Fundamental Quantities of the S.I.
	Other Quantities (of measure)
Part I: Molecular Structure of Matter
	The Atom and the Molecule
	Chapter 1: Molecular Physics
		1.1 Structure of Matter and Molecular Physics
			Quantum Physics
			Statistical Physics
			Molecular Kinetics
		1.2 Statistical Physics of Particles
			Microstate: An Elementary Configuration of Particles
			Microstates and Macrostates
			Thermodynamic Probability
			Mathematical and Thermodynamic Probabilities
			Combinatorial Analysis Calculation
			Stirling´s Approximations
			Energy Conservation for a Set of Particles
			Discernibility of Particles and Limitation of their Number
		1.3 Distribution of Particles on Energy Levels
			System´s Discrete Energy Values
			Distribution on Non-degenerate Energy Levels
			Degeneracy of Energy Levels
			Distribution on Degenerate Energy Levels
			Highly Degenerated Systems
		1.4 Boltzmann´s Relationship Between Entropy and Probability
			Parallelism of Thermodynamic Probability with Entropy
			Entropy of Mixing
			Thermodynamic Interpretation of Boltzmann Equation
		1.5 Distribution of Particles on Energetic Levels
			Equilibrium and Evolution in Statistical Mechanics
			Maximization of Thermodynamic Probability
			Partition Functions
			Partition Function and Thermodynamic Properties
			Maxwell-Boltzmann Distribution of Energies
		1.6 Factors Influencing the Equilibrium Distribution
			Boltzmann Factor of the Energy Level
			Energy Level Multiplicity and System Size Effects
			Influence of Temperature on Distribution
		1.7 Deviations from Equilibrium Distribution
			Non-equilibrium States
			Simplest Change of State
			Relative Stability of a Non-Equilibrium State
			Role of the Non-Equilibrium Extent
			Relative Probability of a Non-Equilibrium State
			Fluctuation Errors
		1.8 Statistics of Thermodynamic Properties
			Internal Energy
			Entropy
			Free Energy
			Caloric Capacity
			Properties Depending on Pressure
		1.9 Five Worked Examples
	Chapter 2: Statistical Thermodynamics of Ideal Gas
		2.1 Components of the Partition Function
			Composition of the Sum-Over-States
			Molecule Displacement and Motion
			Simplifications of Composition Laws
			Sum-Over-States with Single Term and Integrals
			Perfect Gas and Ideal Gas
		2.2 Nuclear Partition Function
			Atom and Molecular Partition Functions
			Nuclear Partition Function of Polyatomic Molecules
			Nuclear Contribution to Thermodynamic Functions
			Practical Functions and Spectroscopic Functions
		2.3 Electronic Partition Functions
			Electronic Contribution to the Thermodynamic Functions
			Electronic Sum-Over-States for Monoatomic Molecules
			Spectral Term for Atoms
			Electronic Sum-Over-States of Polyatomic Molecules
		2.4 Translational Motion
			Physical Space and Phase Space
			Translational Distribution Function
			Translational Sum-Over-States
			Translational Partition Function
			Thermodynamic Translational Functions
		2.5 Thermodynamics of Monoatomic Ideal Gas
		2.6 Rotational and Vibrational Motions
			Rigid Rotor Geometry
			Sum-Over-States of Molecule Rotation
			Effect of Temperature on Rotational Sum-Over-States
			The Harmonic Oscillator as a Vibrator
			Vibrational Sum-Over-States
		2.7 Thermodynamics of Diatomic Ideal Gas
			Contribution of Rotation to Thermodynamic Functions
			Experimental Determination of the Rotational Contribution
			Spectral Features of Rotation
			Vibrational Einstein Functions
			Characteristic Vibrational Temperatures
			Total Thermodynamic Functions of Diatomic Molecule
			Temperature Dependence on Heat Capacity
		2.8 Thermodynamics of the Polyatomic Ideal Gas
			Thermodynamics of Rotation for Polyatomic Molecules
			Moment of Inertia for a Polyatomic Molecule
			Vibrational Sum-Over-States for Polyatomic Molecules
			Vibrational Thermodynamics for Polyatomic Molecules
		2.9 Equipartition of Energy Over the Degrees of Freedom
			Degrees of Freedom for Energy Equipartition
		2.10 Five Worked Examples
	Chapter 3: Distribution of Molecular Properties in Gases
		3.1 Elements of the General Theory of Distribution
			Distribution for the Reduced Size Sample
			Distribution Functions
			Differential Distribution Function
			Integral Distribution Function
			Link between Differential and Integral Distribution Functions
			Normalization of Distributions
			Concomitant Distribution of Several Quantities
		3.2 Molecular Velocities Distributions
			Concomitant Distribution of Position and Momentum Coordinates
			Concomitant Distribution of the Three Velocities Projections
			Velocity Projection Distribution after a Given Direction
			Particles Velocity Distribution
			Velocity Distribution Function Form
		3.3 Features of Velocity and Its Projections
			The Most Probable Value
			Mean Values
			Arithmetic Mean Value
			Quadratic Mean Value of Velocity Projections
			Velocity Quadratic Mean Value
			Factors Influencing Velocities Distribution
		3.4 Molecular Energies Distribution
			Translational Energy Distribution
			Degrees of Freedom for Molecules Energy Distribution
			Mean Energies
		3.5 Wall Collision of Gaseous Molecules
			Molecular Number Density
			Wall Collisions Frequency
			Molecule-Wall Collisions in Physics and Chemistry
		3.6 Intermolecular Collisions within Gases
			Identical Type Molecules Collisions
			Different Type Molecules Collisions
			Density of Intermolecular Collisions in Pure Gases
			Density of Intermolecular Collisions in Multicomposant Gases
			Macroscopic Factors Effect on Collisions
		3.7 Molecular Diameters
			Molecular Diameter Evaluation Methods
			Molecular Diameter Dependence on Temperature
		3.8 Mean Free Path
			Free Path Dependence on Temperature
			Free Path in Knudsen Regime
			Free Path in Intermediate Pressures Domain
		3.9 Triple Collisions
			Relative Frequency of Double and Triple Collisions
		3.10 Eleven Worked Examples
Part II: Molecular Models in Thermodynamics
	Phenomenological and Molecular Thermodynamics
	Chapter 4: Models in Thermodynamics of Real Gases
		4.1 Equation of State (ES) and PVT Dependencies
			Graphical PVT Dependencies
			Analytical Formulations of ES
		4.2 Van der Waals (VdW) ES
			Deduction of VdW ES
			Internal Pressure
			Covolume
			Values of VdW Equation´s Constants
			VdW Equation´s Constants Incremental Calculation
		4.3 Diversity of the ESs
			Material Constants
			Examples of ESs for Gases
			ESs with Numerous Material Constants
			Applications of ESs
			Virial ES
		4.4 Features of Thermal ES
			Attraction and Repulsion in ES
			Cubic ESs
			Completely or Incompletely Defined ES
				Functional Parameters
			Restrictions for the ES
			Modified ES
			ES Modification
		4.5 Pressure Dependence on Volume
			Boyle Curve
			Boyle Temperature
			Boyle Features of VdW Gas
			Boyle Temperature of VdW Gas
		4.6 Pressure Dependence on Temperature
			Joule-Thomson Curve
			Real Gas Isochores
		4.7 Real Gas Molecular Models
			Intermolecular Potential
			Spherical Potentials
			Mie Potential
			Lennard Jones Potential
		4.8 ES for Real Gases Mixtures
			The Complete ES
			Fugacity of Compounds in a Gas Mixture
			Material Constants for Mixtures
			Combination Rules of Components Constants
			Combination Rules of Components Pairs
			Properties of Components in a Mixture
			Combination of ESs
		4.9 Interactions among Components in a Mixture
			Interaction Formulae
		4.10 Four-Worked Examples
	Chapter 5: Liquid-Vapor Equilibrium Models - Critical Point, Corresponding States, and Reduced Properties
		5.1 Phase Equilibrium of Pure Substances
			Vapors in Molecular Physics
			Mono-Component System: Phase Diagrams
			Mono-Component System: The State Diagrams
			Triple Points
			Singularity of Vaporization among Phase Transitions
			Variation of Properties on the Vaporization Curve
			Single-Phase Fluid
		5.2 Pure Substances´ Critical Point
			Critical Point in Molecular Thermodynamics
			Critical Exponents
			Peri-critical Domain and Critical Exponents
			Experimental Determination of Critical Quantities
			Critical Quantities Examples
			Critical Quantities Values
			Dependence of the Critical Point on the Nature of the Substance
		5.3 ES and the Critical Point
			From ES to Critical Point
			VdW ES Critical Quantities
			Critical Quantities for Other ES
				Redlich and Kwong
			Critical Quantities of ESs with more than Two Constants
				Clausius
				Martin
			From Critical Point to ES
		5.4 ES and Liquid-Vapor Equilibrium
			Liquid-Vapor Equilibrium in the Pressure/Volume Graph
			Stable, Metastable, and Unstable Monophasic States
			Calculation of PVT Equilibrium Features for VdW Fluid
		5.5 Stability of the Liquid-Vapor Equilibrium
			Binodal Curve
			Spinodal Curve
			Spinodal and Binodal Curves within the Peri-critical Domain
		5.6 Corresponding States
			Reduced Properties
			Reduction Method through Critical Quantities
			Principle of Corresponding States (PCS)
			Reduced ES
			Heat Capacities from Reduced ES
			Ideality Deviation Calculation through Reduced ES
		5.7 Physicochemical Similarity
			Hougen-Watson Diagram
			Extended PCS
			Physicochemical Similarity Criteria
			Material Constants Calculation from ES
		5.8 Critical Point of Mixtures
			Pseudocritical Properties
		5.9 Six Worked Examples
	Chapter 6: Thermodynamic Models of Condensed Phases
		6.1 State of Aggregation
			Condensed States of Aggregation
			Liquid State Particularities
			Thermodynamic Physical Quantities in Liquids
			Non-thermodynamic Macroscopic Physical Quantities
		6.2 Molecular Structure of the States of Aggregation
			Diagrams of Interference
			Continuous and Discontinuous Spatial Distributions
			Molecular Order in Liquids
			Coordination Number at Different Temperatures
			Coordination Number at Liquids and Solids
			Void Fraction Deduction
		6.3 Liquid Models
			ES of a Liquid as an Extremely Compressed Gas
			Internal Pressure
			``Gaseous´´ Type Liquid Models
			Mayer Model for Correlation Functions
			Bogoliubov Model of Molecular Dynamics
			``Solid´´ Type Liquid Models
			Devonshire Cell Model
			Eyring Free Volume Model
			Thermodynamic-Statistical Calculation of Free Volume
			Calculation of Free Volume from Speed of Sound
			Frenkel Model of Empty Cells
			Significant Structure Theory: Gas and Solid
		6.4 Equilibrium Structural Models for Solids
			Types of Solids
			Crystal Quantity Models
			Einstein Vibrations
			Thermodynamic Functions of Einstein Vibration
			Dulong-Petit Law
			Einstein Model at Low Temperatures
		6.5 Debye Vibrations
			Debye Vibrational Sum-Over-States
			Debye and Einstein Phononic Heat Capacities
			Debye Thermodynamic Quantities at Low Temperatures
			Debye Temperature Measurement
		6.6 Other Contributions to Sum-Over-States
			Conductivity Electrons
			Sum-Over-States Magnetic Component
			Sum-Over-States of Combinations´ Crystals
		6.7 Lattice Energy from Molecular Interactions
			Lattice Energy Determination Methods
			Lattice Energy from the Born-Landé Potential
			Lattice Geometry and Madelung Constant
			Lattice Energy from Mie Potential
		6.8 Hess´s Law Lattice Energies
			Born-Haber Cycle Steps
			Born-Haber Lattice Energy for Aluminum Oxide
			Born-Haber Cycle for Other Ionic Crystals
			Atomic, Molecular or Metallic Lattice Crystals
		6.9 Real Crystal Lattice Defects
			Punctiform Defect Generation
				Schottky Defect
				Frenkel Defect
			Thermodynamics of Schottky Defect Formation
			Thermodynamics of Frenkel Defect Formation
			Defect Ratio Dependence on Temperature
		6.10 Seven Worked Examples
Part III: Transport Phenomena and Their Mechanism
	Disequilibrium and Evolution
		Transfer
	Transport
	Chapter 7: General Laws of Transport in Gases
		7.1 Physical Kinetics
			Equilibrium and Disequilibrium-Kinetics and Thermodynamics
			Nuclear, Chemical, and Physical Kinetics
			Transfer and Stationarity
			Transfer: Location and Mechanism
		7.2 Transport Phenomenology
			Viscous Flow
			Heat Conduction
			Stationary Heat Transport and the Isolated System Transport
			Mass Transport
			Diffusivity
			Interdiffusion
			Transport Phenomena Similarity
			General Law of Transport
		7.3 Transport in Perfect Gases
			Free Path and Transport in Gases
			General Equation of Transport in Perfect Gases
			Viscosity of Gases
			Gas Viscosity Dependence on Different Factors
			Thermal Conductivity in Gases
			Diffusion
			Molecular Diameter Dependence on Temperature
			Collision Integrals Calculation
			Dimensionless Transport Criteria
			Prandtl Criterion
			Schmidt Criterion
		7.4 Transport in Mixtures of Perfect Gases
			Interdiffusion in Binary Gas Mixtures
			Interdiffusion and Self-diffusion
			Diffusion in Mixtures with More than Two Components
		7.5 Pressure Effect on Transport in Gases
			Transport Regimes Applicability
			Pressure Effect on Transport Regime
		7.6 Knudsen Transport Field
			Knudsen Viscosity Field
			Law of Cosines
			Mechanical Accommodation Coefficients
			Thermal Conductivity and Diffusion at Low Pressures
			Diffusion
			Effusion
		7.7 Pure Real Gases at Moderate Pressures
			Knudsen and ``Normal´´ Simultaneous Transport
			Corresponding States for Transport Phenomena
			The Reference State
			Corresponding States Intermolecular Potential
			Transport in Mixtures of Real Gases
		7.8 Transport in Pure Gases at High Pressure
			Kinematic Viscosity Minimum Value
			Transport Coefficients Dependence on Temperature
			Reduction to Critical Features
			Transport in Gas Mixtures
		7.9 Seven Worked Examples
	Chapter 8: Transport in Liquids and Solids
		8.1 Transport and State of Aggregation
			Thermal Conduction
			Diffusion
			Rheology
			Liquids Viscosity
		8.2 Variation of Viscosity with State Quantities
			Variation of Viscosity with Temperature
			Voids Theories to Explain the Temperature Effect on Viscosity
			Mobility of Voids
			Frequency of Jumps between Voids
			Variation of Liquid Viscosity with Pressure
			Calculation of Viscosity Dependence on Pressure
		8.3 Viscosity Variation with the Nature of the Liquid
			Comparison of Liquid Viscosities
			Systems of Increments
			Orthochor Function
			Rheochor Function
			Viscosity of Liquid Mixtures
			Intrinsic Viscosity
		8.4 The Flow Process
			Flowing Regimes
				Reynolds Criterion
			Laminar Flow within a Circular Section Tube
			Fanning and Hagen-Poiseuille Relations
			Turbulent Flow
			Energy Consumption in Different Flow Regimes
		8.5 Rheology of Liquids
			Non-Newtonian Liquids
			Types of Non-Newtonian Rheology Liquids
			Viscoelastic Behavior
			Time as State Variable in Rheology
			Structural Explanations of Viscoelasticity
			Maxwell Viscoelastic Model
		8.6 Heat Conduction
			Mass and Heat Transfer in Condensed States of Aggregation
			Thermal Conductivity of Liquids
			Models of Energy Transfer into Liquids
			Heat Conduction in Solids
		8.7 Diffusion
			Diffusion in Solids
			Diffusion in Liquids
			Diffusivity/Viscosity Correlation for Liquids
			Crystalline Lattice Defects
			Defect Classification According to their Dimension Number
				Three-Dimensional Defects
				Two-Dimensional Defects
				One-Dimensional Defects
				Zero-Dimensional Defects
			Punctiform Defects in Simple Lattices
			Punctiform Defects in Nonequivalent Node Lattices
			Diffusion in Solids
			Diffusion Mechanisms in Solids
		8.8 Nine Worked Examples
Mathematical Annex
	A.1 Basic Notions
		The Factorial Double
		The Integration by Parts
		The Recurrence
	A.2 Gamma Functions
		The Parity of the Gamma Function Index
			When n Is Even
			When n Is Uneven
	A.3 The Integration of the Exponential/Polynomial Product
	A.4 Decompositions According to Series of Integer Powers
		The Definitions of Taylor´s and MacLaurin´s Series
		Usual Decompositions in a MacLaurin Series
	A.5 The Rapid Solution of Algebraical Equations
		The Iterative Method
		The Secant Method
Complementary Readings
Index