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Thermodynamics and Chemical Equilibrium

Physical chemistry encompasses a wide variety of ideas that are intimately linked. For the most part, we cannot understand one without having some understanding of many others. We overcome this problem by looking at the same idea from a series of slightly different and increasingly sophisticated perspectives. This book focuses on the theories of physical chemistry that describe and make predictions about chemical equilibrium.

Physical and Theoretical Chemistry Textbook Maps Chemistry

Author: Paul Ellgen
Publisher: Oklahoma School of Science Mathematics
Source: LibreTexts
License: CC BY-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 362 sections

01: Introduction - Background and a Look Ahead
1.01: The Role of the Ideal Gas
1.02: Chemical Kinetics
1.03: Classical Thermodynamics
1.04: Statistical Thermodynamics
1.05: Heat Transfer in Practical Devices
1.06: The Concept of Equilibrium
1.07: Chemical Equilibrium and Predicting Chemical Change
1.08: Equilibrium and Classical Thermodynamics
1.09: A Few Ideas from the Philosophy of Science
1.10: A Few Ideas from Formal Logic
1.11: Problems
02: Gas Laws
2.01: Boyle's Law
2.02: Charles' Law
2.03: Avogadro's Hypothesis
2.04: Finding Avogadro's Number
2.05: The Kelvin Temperature Scale
2.06: Deriving the Ideal Gas Law from Boyle's and Charles' Laws
2.07: The Ideal Gas Constant and Boltzmann's Constant
2.08: Real Gases Versus Ideal Gases
2.09: Temperature and the Ideal Gas Thermometer
2.10: Deriving Boyle's Law from Newtonian Mechanics
2.11: The Barometric Formula
2.12: Van der Waals' Equation
2.13: Virial Equations
2.14: Gas Mixtures - Dalton's Law of Partial Pressures
2.15: Gas Mixtures - Amagat's Law of Partial Volums
2.16: Problems
03: Distributions Probability and Expected Values
3.01: The Distribution Function as a Summary of Experimental Results
3.02: Outcomes Events and Probability
3.03: Some Important Properties of Events
3.04: Applying the Laws of Probability
3.05: Bar Graphs and Histograms
3.06: Continuous Distribution Functions - the Envelope Function is the Derivative of the Area
3.07: A Heuristic View of the Probability Density Function
3.08: A Heuristic View of the Cumulative Distribution Function
3.09: Random Variables Expected Values and Population Sets
3.10: Statistics - the Mean and the Variance of a Distribution
3.11: The Variance of the Average- The Central Limit Theorem
3.12: The Normal Distribution
3.13: The Expected Value of a Function of Several Variables and the Central Limit Theorem
3.14: Where Does the N - 1 Come from
3.15: Problems
04: The Distribution of Gas Velocities
4.01: Distribution Functions for Gas-velocity Components
4.02: Probability Density Functions for Velocity Components in Spherical Coordinates
4.03: Maxwell's Derivation of the Gas-velocity Probability-density Function
4.04: The Probability-density Function for Gas Velocities in One Dimension
4.05: Combining the One-dimensional Probability Density Functions
4.06: Boyle's Law from the Maxwell-Boltzmann Probability Density
4.07: Experimental Test of the Maxwell-Boltzmann Probability Density
4.08: Statistics for Molecular Speeds
4.09: Pressure Variations for Macroscopic Samples
4.10: Collisions between Gas Molecules Relative Velocity Coordinates
4.11: The Probability Density Function for the Relative Velocity
4.12: The Frequency of Collisions between Unlike Gas Molecules
4.13: The Rate of Collisions between Unlike Gas Molecules
4.14: Collisions between like Gas Molecules
4.15: The Geometry of A Collision between Spherical Molecules
4.16: The Energy of A Collision between Gas Molecules
4.17: Problems
05: Chemical Kinetics Reaction Mechanisms and Chemical Equilibrium
5.01: Chemical Kinetics
5.02: Reaction Rates and Rate Laws
5.03: Simultaneous Processes
5.04: The Effect of Temperature on Reaction Rates
5.05: Other Factors that Affect Reaction Rates
5.06: Mechanisms and Elementary Processes
5.07: Rate Laws for Elementary Processes
5.08: Experimental Determination of Rate Laws
5.09: First-order Rate Processes
5.10: Rate Laws by the Study of Initial Rates
5.11: Rate Laws from Experiments in a Continuous Stirred Tank Reactor
5.12: Predicting Rate Laws from Proposed Mechanisms
5.13: The Michaelis-Menten Mechanism for Enzyme-catalyzed Reactions
5.14: The Lindemann-Hinshelwood Mechanism for First-order Decay
5.15: Why Unimolecular Reactions are First Order
5.16: The Mechanism of the Base Hydrolysis of Co(NH)X
5.17: Chemical Equilibrium as the Equality of Rates for Opposing Reactions
5.18: The Principle of Microscopic Reversibility
5.19: Microscopic Reversibility and the Second Law
5.20: Problems
06: Equilibrium States and Reversible Processes
6.01: The Thermodynamic Perspective
6.02: Thermodynamic Systems and Variables
6.03: Equilibrium and Reversibility - Phase Equilibria
6.04: Distribution Equilibria
6.05: Equilibria in Chemical Reactions
6.06: Le Chatelier's Principle
6.07: The Number of Variables Required to Specify Some Familiar Systems
6.08: Gibbs' Phase Rule
6.09: Reversible vs. Irreversible Processes
6.10: Duhem's Theorem - Specifying Reversible Change in A Closed System
6.11: Reversible Motion of A Mass in A Constant Gravitational Field
6.12: Equilibria and Reversible Processes
6.13: The Laws of Thermodynamics
6.14: Thermodynamic Criteria for Change
6.15: State Functions in Systems Undergoing Spontaneous Change
6.16: Problems
07: State Functions and The First Law
7.01: Changes in a State Function are Independent of Path
7.02: The Total Differential
7.03: Line Integrals
7.04: Exact Differentials and State Functions
7.05: Determining Whether an Expression is an Exact Differential
7.06: The Chain Rule and the Divide-through Rule
7.07: Measuring Pressure-Volume Work
7.08: Measuring Work- Non-Pressure-Volume Work
7.09: Measuring Heat
7.10: The First Law of Thermodynamics
7.11: Other Statements of the First Law
7.12: Notation for Changes in Thermodynamic Quantities - E vs. E
7.13: Heat Capacities for Gases- Cv Cp
7.14: Heat Capacities of Solids- the Law of Dulong and Petit
7.15: Defining Enthalpy H
7.16: Heat Transfer in Reversible Processes
7.17: Free Expansion of a Gas
7.18: Reversible vs. Irreversible Pressure-Volume Work
7.19: Isothermal Expansions of An Ideal Gas
7.20: Adiabatic Expansions of An Ideal Gas
7.21: Problems
08: Enthalpy and Thermochemical Cycles
8.01: Enthalpy
8.02: Using Thermochemical Cycles to Find Enthalpy Changes
8.03: How Enthalpy Depends on Pressure
8.04: Standard States and Enthalpies of Formation
8.05: The Ideal Gas Standard State
8.06: Standard Enthalpies of Reaction
8.07: Standard State Heat Capacities
8.08: How The Enthalpy Change for a Reaction Depends on Temperature
8.09: Calorimetry
8.10: Problems
09: The Second Law - Entropy and Spontaneous Change
9.01: The Second Law of Thermodynamics
9.02: The Carnot Cycle for an Ideal Gas and the Entropy Concept
9.03: The Carnot Cycle for Any Reversible System
9.04: The Entropy Change around Any Cycle for Any Reversible System
9.05: The Tiling Theorem and the Paths of Cyclic Process in Other Spaces
9.06: Entropy Changes for A Reversible Process
9.07: Entropy Changes for A Spontaneous Process in An Isolated System
9.08: The Entropy of the Universe
9.09: The Significance of The Machine-based Statement of The Second Law
9.10: A Slightly Philosophical Digression on Energy and Entropy
9.11: A Third Statement of the Second Law
9.12: Entropy and Predicting Change
9.13: Defining the Helmholtz and Gibbs Free Energies
9.14: The Fundamental Equation and Other Criteria for Reversible Change
9.15: Entropy and Spontaneous Change
9.16: Internal Entropy and the Second Law
9.17: Notation and Terminology- Conventions for Spontaneous Processes
9.18: The Heat Exchanged by A Spontaneous Process at Constant Entropy
9.19: The Energy Change for A Spontaneous Process at Constant S and V
9.20: The Enthalpy Change for A Spontaneous Process at Constant S and P
9.21: The Entropy Change for A Spontaneous Process at Constant E and V
9.22: The Entropy Change for A Spontaneous Process at Constant H and P
9.23: The Reversible Work is the Minimum Work at Constant T
9.24: The Free Energy Changes for A Spontaneous Process at Constant T
9.25: Summary- Thermodynamic Functions as Criteria for Change
9.26: Problems
10: Some Mathematical Consequences of the Fundamental Equation
10.01: Thermodynamic Relationships from dE dH dA and dG
10.02: dE TdS - PdV and Internal consistency
10.03: Expressing Thermodynamic Functions with Other Independent Variables
10.04: Expressing Thermodynamic Functions with Independent Variables V and T
10.05: Expressing Thermodynamic Functions with Independent Variables P and T
10.06: The Transformation of Thermodynamic Variables in General
10.07: Reversibility and Thermodynamic Variables in Gerneral
10.08: Using the Pair (V P) or the Pair (T S) as Independent Variables
10.09: The Relationship Between Cv and Cp for Any Substance
10.10: The Dependence of Cv on Volume and of Cp on Pressure
10.11: The Gibbs-Helmholtz Equation
10.12: The Second Law and the Properties of Ideal Gases
10.13: The second-dependence of the Energy and Enthalpy of A Real Gas
10.14: The Joule-Thomson Effect
10.15: Problems
11: The Third Law Absolute Entropy and the Gibbs Free Energy of Formation
11.01: Heat Capacity as a Function of Temperature
11.02: Enthalpy as a function of Temperature
11.03: The Third Law
11.04: Genesis of the Third Law - the Nernst Heat Theorem
11.05: Absolute Entropy
11.06: The Standard State for Third-law Entropies
11.07: The Fugacity of a Gas
11.08: A General Strategy for Expressing the Thermodynamic Properties of a Substance
11.09: The Standard Entropy and the Gibbs Free Energy of Formation
11.10: The Nature of Hypothetical States
11.11: The Fugacity and Gibbs Free Energy of A Substance in Any System
11.12: Evaluating Entropy Changes Using Thermochemical Cycles
11.13: Absolute Zero is Unattainable
11.14: Problems
12: Applications of the Thermodynamic Criteria for Change
12.01: Mechanical Processes
12.02: The Direction of Spontaneous Heat Transfer
12.03: Phase Changes - the Fusion of Ice
12.04: Measuring the Entropy Change for Any Reversible Process
12.05: Another Perspective on the Principle of Le Chatelier
12.06: Phase Equilibria - Temperature Dependence of the Boiling Point
12.07: Phase Equilibria - Temperature Dependence of the Melting Point
12.08: The Clapeyron Equation
12.09: The Clausius-Clapeyron Equation
12.10: Problems
13: Equilibria in Reactions of Ideal Gases
13.01: The Gibbs Free Energy of an Ideal Gas
13.02: The Gibbs Free Energy Change for A Reaction of Ideal Gases
13.03: The Thermodynamics of Mixing Ideal Gases
13.04: The Gibbs Free Energy Change for Reaction at Constant Partial Pressures
13.05: rG is the rate at which the Gibbs Free Energy Changes with The Extent of Reaction
13.06: The Standard Gibbs Free Energy Change and Equilibrium in Ideal Gas Reactions
13.07: The Gibbs Free Energy of Formation and Equilibrium in Ideal Gas Reactions
13.08: Equilibrium When A Component is Also Present as A Condensed Phase
13.09: Equilibrium When An Ideal Gas Component is Also Present as A solute
13.10: Problems
14: Chemical Potential - Extending the Scope of the Fundamental Equation
14.01: Dependence of the Internal Energy on the Composition of the System
14.02: Dependence of Other Thermodynamic Functions on the Composition
14.03: Partial Molar Quantities
14.04: Chemical Potentials and Stoichiometry
14.05: jdnj 0 and Primitive Vs. Gibbsian Equilibrium
14.06: The Change Criteria in A System Composed of Subsystems
14.07: At Constant P and T r is the Change in Gibbs Free Energy
14.08: Gibbs-Duhem Equation
14.09: The Dependence of Chemical Potential on Other Variables
14.10: Chemical Activity
14.11: Back to the Fugacity- the Fugacity of A Component of A Gas Mixture
14.12: Relating Fugacity and Chemical Activity
14.13: Relating the Differentials of Chemical Potential and Activity
14.14: Dependence of Activity on Temperature- Relative Partial Molar Enthalpies
14.15: Problems
15: Chemical Potential Fugacity Activity and Equilibrium
15.01: The Chemical Potential and Fugacity of a Gas
15.02: The Chemical Potential and Activity of a Gas
15.03: The Pressure-dependence of the Fugacity and Activity of a Condensed Phase
15.04: Standard States for the Fugacity and Activity of a Pure Solid
15.05: The Chemical Potential Fugacity and Activity of a Pure Solid
15.06: Chemical Potential Fugacity and Equilibrium
15.07: Chemical Potential Activity and Equilibrium
15.08: The Rate of Gibbs Free Energy Change with Extent of Reaction
15.09: Problems
16: The Chemical Activity of the Components of a Solution
16.01: Solutions Whose Components are in Equilibrium with Their Own Gases
16.02: Raoult's Law and Ideal Solutions
16.03: Expressing the Activity Coefficient as a Deviation from Raoult's Law
16.04: Henry's Law and the Fugacity and Activity of A Solution Component
16.05: Expressing the Activity Coefficient as A Deviation from Henry's Law
16.06: Henry's Law and the Hypothetical One-molal Standard State
16.07: Finding the Activity of a Solute from the Activity of the Solvent
16.08: When the Solute Obeys Henry's Law the Solvent Obeys Raoult's Law
16.09: Properties of Ideal Solutions
16.10: Colligative Properties - Boiling-point Elevation
16.11: Colligative Properties - Freezing-point Depression
16.12: Colligative Properties - Osmotic Pressure
16.13: Colligative Properties - Solubility of a Solute in an Ideal Solution
16.14: Colligative Properties - Solubility of a Gas
16.15: Solvent Activity Coefficients from Freezing-point Depression Measurements
16.16: Electrolytic Solutions
16.17: Activities of Electrolytes - The Mean Activity Coefficient
16.18: Activities of Electrolytes - The Debye-Huckel Theory
16.19: Finding Solute Activity Using the Hypothetical One-molal Standard State
16.20: Problems
17: Electrochemistry
17.01: Oxidation-reduction Reactions
17.02: Electrochemical Cells
17.03: Defining Oxidation States
17.04: Balancing Oxidation-reduction Reactions
17.05: Electrical Potential
17.06: Electrochemical Cells as Circuit Elements
17.07: The Direction of Electron Flow and its Implications
17.08: Electrolysis and the Faraday
17.09: Electrochemistry and Conductivity
17.10: The Standard Hydrogen Electrode (S.H.E)
17.11: Half-reactions and Half-cells
17.12: Standard Electrode Potentials
17.13: Predicting the Direction of Spontaneous Change
17.14: Cell Potentials and the Gibbs Free Energy
17.15: The Nernst Equation
17.16: The Nernst Equation for Half-cells
17.17: Combining two Half-cell Equations to Obtain a new Half-cell Equation
17.18: The Nernst Equation and the Criterion for Equilibrium
17.19: Problems
18: Quantum Mechanics and Molecular Energy Levels
18.01: Energy Distributions and Energy Levels
18.02: Quantized Energy - De Broglie's Hypothesis and the Schroedinger Equation
18.03: The Schrodinger Equation for A Particle in A Box
18.04: The Schrodinger Equation for a Molecule
18.05: Solutions to Schroedinger Equations for Harmonic Oscillators and Rigid Rotors
18.06: Wave Functions Quantum States Energy Levels and Degeneracies
18.07: Particle Spins and Statistics- Bose-Einstein and Fermi-Dirac Statistics
19: The Distribution of Outcomes for Multiple Trials
19.01: Distribution of Results for Multiple Trials with Two Possible Outcomes
19.02: Distribution of Results for Multiple Trials with Three Possible Outcomes
19.03: Distribution of Results for Multiple Trials with Many Possible Outcomes
19.04: Stirling's Approximation
19.05: Problems
20: Boltzmann Statistics
20.01: The Independent-Molecule Approximation
20.02: The Probability of An Energy Level at Constant N V and T
20.03: The Population Sets of a System at Equilibrium at Constant N V and T
20.04: How can Infinitely Many Probabilities Sum to Unity
20.05: The Total Probability Sum at Constant N V and T
20.06: The Most Probable Population Set at Constant N V and T
20.07: The Microstates of a Given Population Set
20.08: The Probabilities of Microstates that Have the Same Energy
20.09: The Probabilities of the Population Sets of an Isolated System
20.10: Entropy and Equilibrium in an Isolated System
20.11: Thermodynamic Probability and Equilibrium in an Isomerization Reaction
20.12: The Degeneracy of an Isolated System and Its Entropy
20.13: The Degeneracy of an Isolated System and its Entropy
20.14: Effective Equivalence of the Isothermal and Constant-energy Conditions
20.15: Problems
21: The Boltzmann Distribution Function
21.01: Finding the Boltzmann Equation
21.02: Lagrange's Method of Undetermined Multipliers
21.03: Deriving the Boltzmann Equation I
21.04: Deriving the Boltzmann Equation II
21.05: Partition Functions and Equilibrium - Isomeric Molecules
21.06: Finding and the Thermodynamic Functions for Distinguishable Molecules
21.07: The Microscopic Model for Reversible Change
21.08: The Third Law of Thermodynamics
21.09: The Partition Function for a System of N Molecules
21.10: Problems
22: Some Basic Applications of Statistical Thermodynamics
22.01: Interpreting the Partition Function
22.02: Conditions under which Integrals Approximate Partition Functions
22.03: Probability Density Functions from the Energies of Classical-mechanical Models
22.04: Partition Functions and Average Energies at High Temperatures
22.05: Energy Levels for a Three-dimensional Harmonic Oscillator
22.06: Energy and Heat Capacity of the Einstein Crystal
22.07: Applications of Other Entropy Relationships
22.08: Problems
23: The Ensemble Treatment
23.01: Ensembles of N-molecule Systems
23.02: The Ensemble Entropy and the Value of
23.03: The Thermodynamic Functions of the N-molecule System
24: Indistinguishable Molecules - Statistical Thermodynamics of Ideal Gases
24.01: The Partition Function for N Distinguishable Non-interacting Molecules
24.02: The Partition Function for N Indistinguishable Non-interacting Molecules
24.03: Occupancy Probabilities for Translational Energy Levels
24.04: The Separable-modes molecular Model
24.05: The Partition Function for A Gas of Indistinguishable Non-interacting Separable-modes Molecules
24.06: The Translational Partition Function of An Ideal Gas
24.07: The Electronic Partition Function of an Ideal Gas
24.08: The Vibrational Partition Function of A Diatomic Ideal Gas
24.09: The Rotational Partition Function of A Diatomic Ideal Gas
24.10: The Gibbs Free Energy for One Mole of An Ideal Gas
24.11: The Standard Gibbs Free Energy for H(g) I(g) and HI(g)
24.12: The Gibbs Free Energy Change for Forming HI(g) from H(g) and I(g)
24.13: The Reference State for Molecular Partition Functions
24.14: Problems
25: Bose-Einstein and Fermi-Dirac Statistics
25.01: Quantum Statistics
25.02: Fermi-Dirac Statistics and the Fermi-Dirac Distribution Function
25.03: Bose-Einstein Statistics and the Bose-Einstein Distribution Function
26: Appendices
26.01: Appendix A. Standard Atomic Weights 1999
26.02: Appendix B.
26.03: Appendix B. Fundamental Constants
26.04: Appendix C.
26.05: Units and Conversion Factors
26.06: Appendix D.
26.07: Appendix D. Some Important Definite Integrals