This textbook introduces the molecular side of physical chemistry. It offers students and practitioners a new approach to the subject by presenting numerous applications and solved problems that illustrate the concepts introduced for varied and complex technical situations. The book offers a balance between theory, tools, and practical applications. The text aims to be a practical manual for solving engineering problems in industries where processes depend on the chemical composition and physical properties of matter.
The book is organized into three main topics: (I) the molecular structure of matter, (II) molecular models in thermodynamics, and (III) transport phenomena and mechanisms. Part I presents methods of analysis of the molecular behavior in a given system, while the following parts use these methods to study the equilibrium states of a material system and to analyze the processes that can take place when the system is in a state of non-equilibrium, in particular the transport phenomena.
Molecular Physical Chemistry for Engineering Applications is designed for upper-level undergraduate and graduate courses in physical chemistry for engineers, applied physical chemistry, transport phenomena, colloidal chemistry, and transport/transfer processes. The book will also be a valuable reference guide for engineers, technicians, and scientists working in industry.
- Offers modeling techniques and tools for solving exercises and practical cases;
- Provides solutions and conclusions so students can follow results more closely;
- Step-by-step problem solving enables students to understand how to approach complex issues.
Author(s): Florin Emilian Daneș, Silvia Daneș, Valeria Petrescu, Eleonora-Mihaela Ungureanu
Publisher: Springer
Year: 2021
Language: English
Pages: 413
City: Cham
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
