Modules
- Page ID
- 352480
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1.1: Activity
- 1.1.1: Acid Dissociation Constants- Weak Acids- Debye-Huckel Limiting Law
- 1.1.2: Acquisitive Convention
- 1.1.3: Activity- Solutions and Liquid Mixtures
- 1.1.4: Activity of Aqueous Solutions
- 1.1.5: Activity of Solvents
- 1.1.6: Activity of Solvents- Classic Analysis
- 1.1.7: Activity of Water - Foods
- 1.1.8: Activity of Water - One Solute
- 1.1.9: Activity of Water - Two Solutes
- 1.1.10: Activity Coefficient- Two Neutral Solutes- Solute + Trace Solute i
- 1.1.11: Activity Coefficients
- 1.1.12: Activity Coefficients- Salt Solutions- Ion-Ion Interactions
- 1.1.13: Activity of Water - Salt Solutions
- 1.2: Affinity for Spontaneous Chemical Reaction
- 1.2.1: Affinity for Spontaneous Chemical Reaction
- 1.2.2: Affinity for Spontaneous Reaction- Chemical Potentials
- 1.2.3: Affinity for Spontaneous Chemical Reaction- Phase Equilibria
- 1.2.4: Affinity for Spontaneous Reaction- General Differential
- 1.2.5: Affinity for Spontaneous Reaction- Dependence on Temperature
- 1.2.6: Affinity for Spontaneous Reaction - Dependence on Pressure
- 1.2.7: Affinity for Spontaneous Reaction - Stability
- 1.2.8: Affinity for Spontaneous Chemical Reaction - Law of Mass Action
- 1.2.9: Affinity for Spontaneous Chemical Reaction - Isochoric Condition and Controversy
- 1.3: Calorimeter
- 1.3.1: Calorimeter- Isobaric
- 1.3.2: Calorimetry- Isobaric- General Operation
- 1.3.3: Calorimetry- Solutions- Isobaric
- 1.3.4: Calorimetry- Solutions- Adiabatic
- 1.3.5: Calorimetry- Solutions - Heat Flow
- 1.3.6: Calorimetry - Titration Microcalorimetry
- 1.3.7: Calorimeter- Titration Microcalorimetry- Enzyme-Substrate Interaction
- 1.3.8: Calorimetry- Titration Microcalorimetry- Micelle Deaggregation
- 1.3.9: Calorimetry- Scanning
- 1.3.10: Calorimetry- Solutions- Flow Microcalorimetry
- 1.4: Chemical Equilibria
- 1.4.1: Chemical Equilibria- Solutions
- 1.4.2: Chemical Equilibria- Solutions- Derived Thermodynamic Parameters
- 1.4.3: Chemical Equilibria- Solutions- Simple Solutes
- 1.4.4: Chemical Equilibria- Solutions- Ion Association
- 1.4.5: Chemical Equilibria- Solutions- Sparingly Soluble Salt
- 1.4.6: Chemical Equilibria- Cratic and Unitary Quantities
- 1.4.7: Chemical Equilibria- Composition- Temperature and Pressure Dependence
- 1.4.8: Chemical Equilibrium Constants- Dependence on Temperature at Fixed Pressure
- 1.4.9: Chemical Equilibria- Dependence on Pressure at Fixed Temperature
- 1.5: Chemical Potentials
- 1.5.1: Chemical Potentials, Composition and the Gas Constant
- 1.5.2: Chemical Potentials- Gases
- 1.5.3: Chemical Potentials- Solutions- General Properties
- 1.5.4: Chemical Potentials- Solutions- Composition
- 1.5.5: Chemical Potentials- Solutions- Partial Molar Properties
- 1.5.6: Chemical Potentials- Liquid Mixtures- Raoult's Law
- 1.5.7: Chemical Potentials- Solutions- Raoult's Law
- 1.5.8: Chemical Potentials- Solutions- Osmotic Coefficient
- 1.5.9: Chemical Potentials; Excess; Aqueous Solution
- 1.5.10: Chemical Potentials- Solutions- Henry's Law
- 1.5.11: Chemical Potentials- Solutes
- 1.5.12: Chemical Potentials- Solute; Molality Scale
- 1.5.13: Chemical Potentials- Solutes- Mole Fraction Scale
- 1.5.14: Chemical Potentials; Solute; Concentration Scale
- 1.5.15: Chemical Potentials- Solute- Concentration and Molality Scales
- 1.5.16: Chemical Potentials- Solute- Molality and Mole Fraction Scales
- 1.5.17: Chemical Potentials- Solutions- Salts
- 1.5.18: Chemical Potentials- Solutions- 1-1 Salts
- 1.5.19: Chemical Potentials- Solutions- Salt Hydrates in Aqueous Solution
- 1.5.20: Chemical Potentials- Salt Solutions- Ion-Ion Interactions
- 1.5.21: Chemical Potentials- Salt Solutions- Debye-Huckel Equation
- 1.7: Compressions
- 1.7.1: Compressions and Expansions- Liquids
- 1.7.2: Compressibilities (Isothermal) and Chemical Potentials- Liquids
- 1.7.3: Compressions- Isentropic- Solutions- General Comments
- 1.7.4: Compressibilities- Isentropic- Related Properties
- 1.7.5: Compressions- Isentropic- Solutions- Partial and Apparent Molar
- 1.7.6: Compressions- Isentropic- Neutral Solutes
- 1.7.7: Compressions- Isentropic- Salt Solutions
- 1.7.8: Compresssions- Isentropic- Aqueous Solution
- 1.7.9: Compressions- Isentropic and Isothermal- Solutions- Approximate Limiting Estimates
- 1.7.10: Compressions- Desnoyers - Philip Equation
- 1.7.11: Compression- Isentropic- Apparent Molar Volume
- 1.7.12: Compressions- Isentropic- Binary Liquid Mixtures
- 1.7.13: Compressions- Isothermal- Equilibrium and Frozen
- 1.7.14: Compressions- Ratio- Isentropic and Isothermal
- 1.7.15: Compression- Isentropic and Isothermal- Solutions- Limiting Estimates
- 1.7.16: Compressions- Isentropic and Isothermal- Apparent Molar Volume
- 1.7.17: Compressions- Isothermal- Solutes- Partial Molar Compressions
- 1.7.18: Compressions- Isothermal- Apparent Molar Compression
- 1.7.19: Compressions- Isothermal- Solutions- Apparent Molar- Determination
- 1.7.20: Compressions- Isothermal- Salt Solutions
- 1.7.21: Compressions- Isothermal- Binary Aqueous Mixtures
- 1.7.22: Compressions- Isothermal- Liquid Mixtures Binary- Compressibilities
- 1.8: Enthalpy
- 1.8.1: Enthalpies and Gibbs Energies
- 1.8.2: Enthalpy
- 1.8.3: Enthalpy- Thermodynamic Potential
- 1.8.4: Enthalpy- Solutions- Partial Molar Enthalpies
- 1.8.5: Enthalpies- Solutions- Equilibrium and Frozen Partial Molar Enthalpies
- 1.8.6: Enthalpies- Neutral Solutes
- 1.8.7: Enthalpies- Solutions- Dilution- Simple Solutes
- 1.8.8: Enthalpies- Solutions- Simple Solutes- Interaction Parameters
- 1.8.9: Enthalpies- Salt Solutions- Apparent Molar- Partial Molar and Relative Enthalpies
- 1.8.10: Enthalpy of Solutions- Salts
- 1.8.11: Enthalpies- Salt Solutions- Dilution
- 1.8.12: Enthalpies- Born-Bjerrum Equation- Salt Solutions
- 1.8.13: Enthalpies- Liquid Mixtures
- 1.10: Gibbs Energies
- 1.10.1: Gibbs Energy
- 1.10.2: Gibbs Energy- Thermodynamic Potential
- 1.10.3: Gibbs Energies- Solutions- Solvent and Solute
- 1.10.4: Gibbs Energies- Equilibrium and Spontaneous Change
- 1.10.5: Gibbs Energies- Raoult's Law
- 1.10.6: Gibbs Energies- Solutions- Pairwise Solute Interaction Parameters
- 1.10.7: Gibbs Energies- Solutions- Parameters Phi and ln(gamma)
- 1.10.8: Gibbs Energies- Solutions- Solute-Solute Interactions
- 1.10.9: Gibbs Energies- Solutes- Cospheres
- 1.10.10: Gibbs Energies- Solutions- Cosphere-Cosphere Interactions
- 1.10.11: Gibbs Energies- Solutions- Solute-Solute Interactions- Pairwise
- 1.10.12: Gibbs Energies- Solutions- Two Neutral Solutes
- 1.10.13: Gibbs Energies- Solutions- Hydrates in Aqueous Solution
- 1.10.14: Gibbs Energies- Salt Hydrates
- 1.10.15: Gibbs Energies- Salt Solutions- Electric Neutrality
- 1.10.16: Gibbs Energies- Salt Solutions- Born Equation
- 1.10.17: Gibbs Energies- Salt Solutions- Lattice Models
- 1.10.18: Gibbs Energies- Salt Solutions- Debye-Huckel Equation
- 1.10.19: Gibbs Energies- Salt Solutions- Debye-Huckel Limiting Law
- 1.10.20: Gibbs Energies- Salt Solutions- DHLL- Derived Parameters
- 1.10.21: Gibbs Energies- Salt Solutions- DHLL- Empirical Modifications
- 1.10.22: Gibbs Energies- Salt Solutions- Solvent
- 1.10.23: Gibbs Energies- Salt Solutions- Excess Gibbs Energies
- 1.10.24: Gibbs Energies- Salt Solutions- Pitzer's Equations
- 1.10.25: Gibbs Energies- Salt Solutions- Cosphere - Cosphere Interactions
- 1.10.26: Gibbs Energies- Binary Liquid Mixtures
- 1.10.27: Gibbs Energies- Binary Liquid Mixtures- General Properties
- 1.10.28: Gibbs Energies- Liquid Mixtures- Thermodynamic Patterns
- 1.10.29: Gibbs Energies- Binary Liquid Mixtures- Excess Thermodynamic Variables
- 1.10.30: Gibbs Energies- General Equations
- 1.10.31: Gibbs Energies- Liquid Mixtures- Ideal
- 1.10.32: Gibbs Energies- Liquid Mixtures- Typically Aqueous (TA)
- 1.10.33: Gibbs Energies- Liquid Mixtures- Typically Non-Aqueous Positive; TNAP
- 1.10.34: Gibbs Energies- Liquid Mixtures- Typically Non-Aqueous Negative; TNAN
- 1.10.35: Gibbs Energies- Liquid Mixtures- Immiscibility
- 1.10.36: Gibbs Energies- Salt Solutions- Aqueous Mixtures
- 1.12: Expansions
- 1.12.1: Heat Capacities- Isobaric- Solutions
- 1.12.2: Heat Capacity- Isobaric- Partial Molar- Solution
- 1.12.3: Heat Capacities- Isobaric and Isochoric
- 1.12.4: Heat Capacities- Isobaric- Equilibrium and Frozen
- 1.12.5: Heat Capacity- Isobaric- Solutions- Excess
- 1.12.6: Heat Capacities- Isobaric- Dependence on Temperature
- 1.12.7: Expansions- Isobaric and Isentropic
- 1.12.8: Expansions- Solutions- Isobaric- Partial and Apparent Molar
- 1.12.9: Expansions- Apparent Molar Isobaric- Composition Dependence
- 1.12.10: Expansions- Solutions Apparent Molar Isobaric Expansions- Determination
- 1.12.11: Expansions- Isobaric- Apparent Molar- Neutral Solutes
- 1.12.12: Expansions- Isobaric- Salt Solutions- Apparent Molar
- 1.12.13: Expansions- Isobaric- Binary Liquid Mixtures
- 1.12.14: Expansibilities- Isobaric- Binary Liquid Mixtures
- 1.12.15: Expansions- Isentropic- Solutions
- 1.12.16: Expansions- Solutions- Apparent Molar Isentropic and Isobaric
- 1.12.17: Expansions- Isentropic- Solutions- Apparent and Partial Molar
- 1.12.18: Expansions- Solutions- Isentropic Dependence of Apparent Molar Volume of Solute on Temperature and Pressure
- 1.12.19: Expansions- Solutions- Isentropic Dependence of Partial Molar Volume on Temperature
- 1.12.20: Expansions- Isentropic- Liquid Mixtures
- 1.12.21: Expansions- Solutions- Partial Molar Isobaric and Isentropic
- 1.12.22: Expansions and Compressions- Solutions- Isentropic Dependence of Volume on Temperature and Pressure
- 1.12.23: Expansions- The Difference
- 1.12.24: Expansions- Equations
- 1.13: Equilibrium
- 1.13.1: Equilibrium and Frozen Properties
- 1.13.2: Equilibrium- Isochoric and Isobaric Paramenters
- 1.13.3: Equilibirium- Solid-Liquid
- 1.13.4: Equilibrium- Liquid-Solid- Schroeder - van Laar Equation
- 1.13.5: Equilibrium - Eutectics
- 1.13.6: Equilibrium - Depression of Freezing Point of a Solvent by a Solute
- 1.13.7: Equilibrium - Liquid-Solids - Hildebrand Rules
- 1.14: Excess and Extra Thermodynamics
- 1.14.10: Extrathermodynamics - Solvent Effects in Chemical Kinetics
- 1.14.1: "Excess" Thermodynamic Properties
- 1.14.2: Excess Thermodynamic Properties - Liquid Mixtures
- 1.14.3: Excess Thermodynamic Properties- Aqueous Solutions
- 1.14.4: Extensive and Intensive Variables
- 1.14.5: Extent of Reaction
- 1.14.6: Extent of Reaction - General
- 1.14.7: Extrathermodynamics - Background
- 1.14.8: Extrathermodynamics - Equilbrium - Acid Strength
- 1.14.9: Extrathermodynamics - Solvent Polarity
- 1.21: Thermodynamics
- 1.21.1: Thermodynamics and Mathematics
- 1.21.2: Thermodynamic Energy
- 1.21.3: Thermodynamic Energy: Potential Function
- 1.21.4: Thermodynamic Potentials
- 1.21.5: Thermodynamic Stability: Chemical Equilibria
- 1.21.6: Thermodynamic Stability: Thermal, Diffusional and Hydrostatic
- 1.21.7: Thermodynamics and Kinetics
- 1.21.8: Third Law of Thermodynamics
- 1.22: Volume
- 1.22.10: Volume: Aqueous Binary Liquid Mixtures
- 1.22.11: Volumes: Liquid Mixtures: Binary: Method of Tangents
- 1.22.12: Volume of Reaction: Dependence on Pressure
- 1.22.1: Volume: Partial Molar: General Analysis
- 1.22.2: Volume: Components
- 1.22.3: Volume: Partial and Apparent Molar
- 1.22.4: Volume: Partial Molar: Frozen and Equilibrium
- 1.22.5: Volumes: Solutions: Apparent and Partial Molar Volumes: Determination
- 1.22.6: Volumes: Apparent Molar and Excess Volumes
- 1.22.7: Volumes: Neutral Solutes: Limiting Partial Molar Volumes
- 1.22.8: Volume: Salt Solutions: Born-Drude-Nernst Equation
- 1.22.9: Volume: Liquid Mixtures
- 1.24: Misc
- 1.14.1: Adiabatic
- 1.14.2: Adsorption- Langmuir Adsorption Isotherm- One Adsorbate
- 1.14.3: Absorption Isotherms - Two Absorbates
- 1.14.4: Apparent Molar Properties- Solutions- Background
- 1.14.5: Apparent Molar Properties- Solutions- General
- 1.14.6: Axioms
- 1.14.7: Boundary
- 1.14.8: Calculus
- 1.14.9: Clausius - Clapeyron Equation
- 1.14.10: Gibbs - Helmholtz Equation
- 1.14.11: Guggenheim-Scatchard Equation / Redlich-Kister Equation
- 1.14.12: Legendre Transformations
- 1.14.13: Closed System
- 1.14.14: Cohesive Energy Density
- 1.14.15: Degree of Dissociation
- 1.14.16: Energy and First Law of Thermodynamics
- 1.14.17: Energy and Entropy
- 1.14.18: Electrochemical Units
- 1.14.19: Electrical Units
- 1.14.20: Electric Conductivities of Salt Solutions- Dependence on Composition
- 1.14.21: Donnan Membrane Equilibria
- 1.14.22: Descriptions of Systems
- 1.14.23: Enzyme-Substrate Interaction
- 1.14.24: Equation of State- General Thermodynamics
- 1.14.25: Equation of State- Perfect Gas
- 1.14.26: Equation of State - Real Gases, van der Waals, and Other Equations
- 1.14.27: Euler's Theorem
- 1.14.28: First Law of Thermodynamics
- 1.14.29: Functions of State
- 1.14.30: Heat, Work, and Energy
- 1.14.31: Helmholtz Energy
- 1.14.32: Hildebrand Solubility Parameter
- 1.14.33: Infinite Dilution
- 1.14.34: Internal Pressure
- 1.14.35: Internal Pressure: Liquid Mixtures: Excess Property
- 1.14.36: Irreversible Thermodynamics
- 1.14.37: Irreversible Thermodynamics: Onsager Phenomenological Equations
- 1.14.38: Joule-Thomson Coefficient
- 1.14.39: Kinetic Salt Effects
- 1.14.40: Laws of Thermodynamics
- 1.14.41: Lewisian Variables
- 1.14.42: L'Hospital's Rule
- 1.14.43: Master Equation
- 1.14.44: Maxwell Equations
- 1.14.45: Moderation
- 1.14.46: Molality and Mole Fraction
- 1.14.47: Newton-Laplace Equation
- 1.14.48: Open System
- 1.14.49: Osmotic Coefficient
- 1.14.50: Osmotic Pressure
- 1.14.51: Partial Molar Properties: General
- 1.14.52: Partial Molar Properties: Definitions
- 1.14.53: Phase Rule
- 1.14.54: Poynting Relation
- 1.14.55: Process
- 1.14.56: Properties: Equilibrium and Frozen
- 1.14.57: Reversible Change
- 1.14.58: Reversible Chemical Reactions
- 1.14.59: Salting-In and Salting-Out
- 1.14.60: Second Law of Thermodynamics
- 1.14.61: Solubility Products
- 1.14.62: Solubilities of Gases in Liquids
- 1.14.63: Solubilities of Solids in Liquids
- 1.14.64: Solutions: Solute and Solvent
- 1.14.65: Spontaneous Change: Isothermal and Isobaric
- 1.14.66: Spontaneous Chemical Reaction
- 1.14.67: Standard States: Reference States: Processes
- 1.14.68: Surroundings and System
- 1.14.69: Temperature of Maximum Density: Aqueous Solutions
- 1.14.70: Solutions: Neutral Solutes: Inter-Solute Distances
- 1.14.71: Time and Thermodynamics (Timenote)
- 1.14.72: Variables: Independent and Dependent
- 1.14.73: Variables: Gibbsian and Non-Gibbsian
- 1.14.74: Vaporization
- 1.14.75: Viscosities: Salt Solutions
- 1.14.76: Work