Chapter 1: Introduction...1 Chapter 2: Energy, Entropy and Fundamental Thermodynamic Concepts...24

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1 Table of Contents Part I: The Geochemical Toolbox Chapter 1: Introduction...1 Geochemistry...1 This Book...2 The Philosophy of Science...4 Building Scientific Understanding...4 The Scientist as Skeptic...5 Elements, Atoms, and Chemical Bonds...6 The Periodic Table...6 Electrons and Orbits...7 Some Chemical Properties of the Elements...13 Chemical Bonding...16 A Brief Look at the Earth...18 Structure of the Earth...18 Plate Tectonics and the Hydrologic Cycle...19 Earth Materials...21 References and Suggestions for Further Reading...23 Chapter 2: Energy, Entropy and Fundamental Thermodynamic Concepts...24 The Thermodynamic Perspective...24 Thermodynamic Systems and Equilibrium...24 Fundamental Thermodynamic Variables...26 Equations of State...28 Ideal Gas Law...28 Equations of State for Real Gases...29 Critical phenomena...31 Equation of State for Other Substances...32 Temperature, Absolute Zero, and The Zeroth Law Of Thermodynamics...33 Energy and The First Law of Thermodynamics...34 Energy...34 Work...34 Path independence, Exact differentials, State functions, and the First Law...35 The Second Law and Entropy...37 Statement...37 Statistical Mechanics: A Microscopic Perspective of Entropy...38 Integrating Factors and Exact Differentials...44 Enthalpy...45 Heat Capacity...46 Constant Volume Heat Capacity...47 Constant Pressure Heat Capacity...47 Energy Associated with Volume Occupied and the Relationshp between C v and C p...47 Heat Capacity of Solids: A Problem in Quantum Physics...50 Relationship of Entropy to Other State Variables...57 Additive Nature of Silicate Heat Capacities...57 The Third Law and Absolute Entropy...58 Statement of the Third Law...58 Absolute Entropy...58 Calculating Enthalpy and Entropy Changes...59 Adiabatic Changes...59 Isobaric and Isothermal Changes in Enthalpy...59 Enthalpies of Formation, Vaporization and Fusion...60 Entropies of Reaction...61 i November 25, 1997

2 Free Energy...62 Helmholtz Free Energy...63 Gibbs Free Energy...64 Criteria for Equilibrium and Spontaneity...64 Temperature and Pressure Dependence of the Gibbs Free Energy...65 The Maxwell Relations...67 References and Suggestions for Further Reading...67 Problems...68 Chapter 3: Solutions and Thermodynamics of Multicomponent Systems...70 Introduction...70 Phase Equilibria...70 Some Definitions...70 The Gibbs Phase Rule...73 The Clapeyron Equation...75 Solutions...77 Raoult's Law...77 Henry's Law...77 The Chemical Potential...78 Partial Molar Quantities...78 Definition of Chemical Potential and Relationship to Gibbs Free Energy...79 Properties of the Chemical Potential...80 The Gibbs-Duhem Relation...80 Derivation of the Phase Rule...81 Ideal Solutions...82 Real solutions...84 Chemical Potential in Real Solutions...84 Fugacities...85 Activities and Activity Coefficients...86 Excess Functions...88 Electrolyte Solutions...90 The Nature of Water and Water-Electrolyte Interaction...90 Some Definitions and Conventions...92 Activities in Electrolytes...94 Solid Solutions and Their Activities Ideal Solutions in Crystalline Solids Equilibrium Constants Derivation and Definition K D Values, Apparent Equilibrium Constants and the Solubility Product HenryÕs Law and Gas Solubilities Temperature Dependence of Equilibrium Constant Pressure Dependence of Equilibrium Constant Practical Approach to Electrolyte Equilibrium Chosing Components and Species Mass Balance Electrical Neutrality Equilibrium Constant Expressions Oxidation and Reduction Redox in Aqueous Solutions Redox in Magmatic Systems References and Suggestions for Further Reading Problems Chapter 4: Applications of Thermodynamics to the Earth Introduction i i November 25, 1997

3 Activities in Non-Ideal Solid Solutions Mathematical Models of Real Solutions Exsolution Phenomena Thermodynamics and Phase Diagrams The Thermodynamics of Melting Thermodynamics of Phase Diagrams for Binary Systems Geothermometry and Geobarometry Theoretical considerations Practical Thermobarometers Thermodynamic Models of Magmas Structure of Silicate Melts Magma Solution Models Reprise: Thermodynamics of Electrolyte Solutions Mean Ionic Quantities Activities in High Ionic Strength Solutions References and Suggestions For Further Reading Problems Chapter 5: Kinetics: The Pace of Things Introduction Reaction Kinetics Elementary and Overall Reactions Reaction Mechanisms Reaction Rates Rates of Complex Reactions Steady-State and Equilibrium Relationships between Kinetics and Thermodynamics Principle of Detailed Balancing Enthalpy and Activation Energy Aspects of Transition State Theory Diffusion Diffusion Flux and Fick's Law Diffusion in Multicomponent Systems and The Diffusion Coefficient Diffusion in Solds and the Temperature Dependence of the Diffusion Coefficient Diffusion in Liquids Surfaces, Interfaces, and Inferface Processes The Surface Free Energy The Kelvin Effect Nucleation and Crystal Growth Adsorption Catalysis Kinetics of Dissolution and Leaching Diagenesis Compostional Gradients in Accumulating Sediment References and Suggestions for Further Reading Problems Chapter 6: Aquatic Chemistry Introduction Acid-Base Reactions Proton Accounting, Charge Balance, and Conservation Equations The Carbonate System Conservative and Non-Conservative Ions Total Alkalinity and Carbonate Alkalinity Buffer Intensity i i i November 25, 1997

4 Complexation Stability Constants Water-Related Complexes Other Complexes Complexation in Fresh Waters Dissolution and Precipitation Reactions Dissolution of Carbonates by Ground and Surface Waters Solubility of Mg Solubility of SiO Solubility of Al(OH) 3 and Other Hydroxides Solubility of Silicates and Related Minerals Clays and Their Properties Clay Mineralogy Ion-Exchange Properties of Clays Mineral Surfaces and Their Interaction With Solutions Adsorption Development of Surface Charge and the Electric Double Layer References and Suggestions for Further Reading Problems Chapter 7: Trace Elements in Igneous Processes Introduction What is a Trace Element? Goldschmidt's Classification of the Elements The Geochemical Periodic Table The Volatile Elements The Semi-Volatiles The Alkali and Alkaline Earth Elements The Rare Earth Elements and Y The HFS Elements The First Series Transition Metals The Noble Metals Other Elements Distribution of Trace Elements Between Co-existing Phases The Partition Coefficient Factors Governing the Value of Parition Coefficients Temperature and Pressure Dependence of the Partition Coefficient Ionic Size and Charge Compositional Dependency Mineral-Liquid Partition Coefficients for Mafic and Ultramafic Systems Crystal-Field Effects Crystal Field Influences on Transition Metal Partitioning Trace Element Distribution During Partial Melting Equilibrium or Batch Melting Fractional Melting Zone Refining Multiphase Solids Continuous Melting Constraints on Melting Models Trace Element Distribution during Crystallization Equilibrium Crystallization Fractional Crystallization In Situ Crystallization Crystallization in Open System Magma Chambers i v November 25, 1997

5 Summary of Trace Element Variations during Melting and Crystallization References and Suggestions for Further Reading Problems Chapter 8: Radiogenic Isotope Geochemistry Introduction Physics of the Nucleus and the Structure of Nuclei Nuclear Structure and Energetics The Decay of Excited and Unstable Nuclei Basics of Radiogenic Isotope Geochemistry Geochronology Decay Systems and Their Applications Rb-Sr Sm-Nd Lu-Hf Re-Os La-Ce U-Th-Pb U and Th Decay Series Isotopes Isotopes of He and Other Rare Gases Cosmogenic and Fossil Isotopes C Cl in hydrology Be in Subduction Zone Studies Cosmic-Ray Exposure Ages of Meteorites Fossil Nuclides References and Suggestions for Further Reading Problems Chapter 9: Stable Isotope Geochemistry Introduction Scope of Stable Isotope Geochemistry Notation Theoretical Considerations Equilibrium Isotope Fractionations Kinetic Isotope Fractionations Isotope Geothermometry Isotope Fractionation in the Hydrologic System Isotope Fractionation in Biological Systems Carbon Isotope Fractionation During Photosynthesis Nitrogen Isotope Fractionation in Biological Processes Oxygen and Hydrogen Isotope Fractionation by Plants Biological Fractionation of Sulfur Isotopes Isotopes and Diet: You Are What You Eat Paleoclimatology The Marine Quaternary δ 18 O Record and Milankovitch Cycles The Record in Glacial Ice Soils and Paleosols Hydrothermal Systems and Ore Deposits Water-Rock Ratios Sulfur Isotopes and Ore Deposits Stable Isotopes in the Mantle and Magmatic Systems Stable Isotopic Composition of the Mantle v November 25, 1997

6 Stable Isotopes in Crystallizing Magmas Combined Fractional Crystallization and Assimilation Isotopes of Boron and Lithium References and Suggestions for Further Reading Problems Part II: Understanding the Earth Chapter 10: The Big Picture: Cosmochemistry Introduction In the Beginning...Nucleosynthesis Astronomical Background The Polygenetic Hypothesis of Burbidge, Burbidge, Fowler and Hoyle Cosmological Nucleosynthesis Nucleosynthesis in Stellar Interiors Explosive Nucleosynthesis Nucleosynthesis in Interstellar Space Summary Meteorites: Essential Clues to the Beginning Chondrites: The Most Primitive Objects Differentiated Meteorites Meteorite Mineralogy Relationships among Meteorites and Meteorite Parent-Bodies Time and the Isotopic composition of the Solar System Meteorite Ages Cosmic Ray Exposure Ages and the Origin of Meteorites Isotopic Anomalies in Meteorites Formation of the Solar System Astronomical Observations and Theoretical Models of Star Formation Formation of Chondritic Meteorites and Processes in the Solar Nebula Formation of the Planets The Moon: Its Chemistry and History The Giant Impact Hypothesis Geology and History of the Moon References and Suggestions for Further Reading Problems Chapter 11: Geochemistry of the Solid Earth I: The Mantle and Core Introduction Composition of the EarthÕs Mantle Cosmochemical Constraints on the EarthÕs Composition Upper Mantle Composition Phase Transitions in the Mantle The Transition Zone Composition of the Lower Mantle The Primitive Mantle Magma Ocean and Mantle Differentiation The Core and Core Formation Mantle Geochemical Reservoirs Evidence from Oceanic Basalts Evolution of the Depleted Upper Mantle Geochemical Evolution of Mantle Plume Reservoirs The Subcontinental Lithosphere References and Suggestions for Further Reading vi November 25, 1997

7 Problems Chapter 12: Geochemistry of the Solid Earth II: The Crust Introduction The Oceanic Crust Processes in Subduction Zones and Island Arc Geochemistry Major Element Composition Trace Element Composition Isotopic Composition and Sediment Subduction Magma Genesis in Subduction Zones CrustÑMantle Interaction: Assimilation Geochemistry of Two-Component Mixtures AssimilationÐFractional Crystallization Composition of the Continental Crust The Upper Crust The Middle and Lower Crust The Total Continental Crust Growth of the Continental Crust The Pace of Crustal Growth Mechanisms of Crustal Growth Crustal Growth in the Archean References and Suggestions for Further Reading Problems Chapter 13: Reactions at the EarthÕs Surface: Weathering, Soils, and Stream Chemistry Introduction Redox in Natural Waters Biogeochemical Reodox Reactions Redox Buffers and Transition Metal Chemistry Weathering, Soils, and Biogeochemical Cycling Soil Profiles Chemical Cycling in Soils Biogeochemical Cycling Weathering Rates and Reactions The Watershed Approach Thermodynamic and Kinetic Assessment of Stream Compositions Factors Controlling Weathering Rates The Composition of Rivers Continental Saline Waters References and Suggestions for Further Reading Problems Chapter 14: Organic Geochemistry Introduction A Brief Biological Background Organic Compounds and Their Nomenclature Hydrocarbons Functional Groups Biologically Important Organic Compounds The Chemistry of Life: Important Biochemical Processes Photosynthesis Respiration Organic Matter in Soils and Natural Waters Dissolved Organic Substances vii November 25, 1997

8 Organic Matter in Soils Chemical Properties of Organic Molecules Acid-Base Properties Complexation Adsorption Phenomena Sedimentary Organic Matter and Coal and Oil Formation Formation and Diagenesis of Organic-Rich Sediments Kerogen and Bitumen Thermal Evolution of Organic Matter and Petroleum Generation Compositional Evolution of Coal Isotopic Composition of Hydrocarbons References and Suggestions for Further Reading Problems Chapter 15: The Oceans as a Chemical System Introduction Some Background Oceanographic Concepts Salinity, Chlorinity, Density, and Temperature Circulation of the Ocean and the Structure of Ocean Water Composition of Seawater Conservative Elements Dissolved Gases Nutrient Elements Particle-Reactive Elements Sources and Sinks of Dissolved Matter in Seawater Residence Time The Riverine Source Ridge Hydrothermal Systems The Atmospheric Source Sedimentary Sinks and Sources References and Suggestions for Further Reading Problems vi i i November 25, 1997

AN INTRODUCTION TO COSMOCHEMISTRY

AN INTRODUCTION TO COSMOCHEMISTRY CHARLES R. COWLEY Professor of Astronomy, University of Michigan CAMBRIDGE UNIVERSITY PRESS Foreword V a % e x i 1 Overview 1 1.1 The Scope of Cosmochemistry 1 1.2 Cosmochemistry