Chemistry in Quantitative Language: Fundamentals of General Chemistry Calculations

Description

Problem-solving is one of the most challenging aspects students encounter in general chemistry courses, leading to frustration and failure. Consequently, many students become less motivated to take additional chemistry courses after the first year. This book tackles this issue head on and provides innovative, intuitive, and systematic strategies to tackle any type of calculations encountered in chemistry. The material begins with the basic theories, equations, and concepts of the underlying chemistry, followed by worked examples with carefully explained step-by-step solutions to showcase the ways in which the problems can be presented. The second edition contains additional problems at the end of each chapter with varying degrees of difficulty, and many of the original examples have been revised. Cover Chemistry in Quantitative Language: Fundamentals of General Chemistry Calculations Copyright Preface Acknowledgement Contents 1: Atomic Structure and Isotopes 1.1 Atomic Theory 1.1.1 The law of conservation of mass 1.1.2 The law of definite proportion 1.1.3 The law of multiple proportions 1.1.4 The law of reciprocal proportions 1.2 The Structure of the Atom 1.2.1 Atomic number (Z) 1.2.2 Mass number (A) 1.2.3 Ions 1.3 Isotopes 1.4 Relative Atomic Mass 1.4.1 Calculating atomic masses 1.5 Problems 2: Formula and Molecular Mass 2.1 Formula Mass 2.2 Molecular Mass 2.3 Molar Mass 2.4 Problems 3: The Mole and Avogadro’s Number 3.1 The Mole and Avogadro’s Number (NA) 3.2 The Mole and Molar Mass 3.3 Calculating the Number of Moles 3.4 Problems 4: Formulas of Compounds and Percent Composition 4.1 Percent Composition 4.2 Types of Chemical Formula 4.2.1 Empirical formula 4.2.2 Steps for determining empirical formula 4.3 Empirical Formula from Combustion Analysis 4.4 Molecular Formula 4.4.1 Determination of molecular formula 4.5 Problems 5: Chemical Formulas and Nomenclature 5.1 General Background 5.1.1 Elements 5.1.2 Some basic definitions 5.2 Chemical Formula 5.3 Oxidation Numbers 5.3.1 Rules for assigning ONs 5.3.2 ONs in formulas 5.4 Writing the Formulas of Compounds 5.5 Nomenclature of Inorganic Compounds 5.6 Problems 6: Chemical Equations 6.1 Writing Chemical Equations 6.1.1 General rules for writing chemical equations 6.2 Balancing Chemical Equations 6.2.1 Guidelines for balancing a chemical equation 6.3 Types of Chemical Reactions 6.3.1 Combination or synthesis 6.3.2 Decomposition 6.3.3 Displacement 6.3.4 Double decomposition or metathesis 6.3.5 Neutralization 6.4 Problems 7: Stoichiometry 7.1 Reaction Stoichiometry 7.2 Information From a Balanced Equation 7.3 Types of Stoichiometric Problems 7.3.1 Solving stoichiometric problems 7.3.2 Mole-to-mole stoichiometric problems 7.3.3 Mass-to-mole stoichiometry problems 7.3.4 Mass-to-mass stoichiometry problems 7.3.5 Mass-to-volume stoichiometry problems 7.3.6 Volume-to-volume stoichiometry problems 7.4 Limiting Reagents 7.4.1 Limiting reagent calculations 7.5 Reaction Yields: Theoretical, Actual, and Percent Yields 7.6 Problems 8: Structure of the Atom 8.1 Electronic Structure of the Atom 8.2 Electromagnetic Radiation 8.3 The Nature of Matter and Quantum Theory 8.3.1 Photoelectric effect 8.4 The Hydrogen Atom 8.4.1 The Bohr model 8.4.2 Emission and absorption spectra 8.5 The Quantum-Mechanical Description of the Hydrogen Atom 8.5.1 The wave nature of the electron 8.5.2 The Heisenberg uncertainty principle 8.6 Quantum Mechanics and Atomic Orbitals 8.6.1 Orbitals and quantum numbers 8.6.1.1 Principal quantum number (n) 8.6.1.2 Angular-momentum (or azimuthal) quantum number () 8.6.1.3 Magnetic (or orbital) quantum number (ml) 8.6.1.4 Spin quantum number (ms) 8.7 Electronic Configuration of Multielectron Atoms 8.7.1 Aufbau principle 8.7.1.1 Shorthand notation for electron configuration 8.7.2 Pauli exclusion principle 8.7.3 Hund’s principle (or rule) 8.7.4 Summary of building-up principles 8.7.5 Orbital diagrams 8.8 Problems 9: Chemical Bonding 1: Basic Concepts 9.1 Introduction: Types of Chemical Bonds 9.1.1 Types of chemical bonds 9.2 Lewis Dot Symbols 9.2.1 Octet rule 9.2.2 Duet rule 9.3 Ionic Bonding: Formation of Ionic Compounds 9.3.1 Lattice energies and the strength of the ionic bond 9.3.2 Calculating lattice energies of ionic solids 9.3.3 Lewis structure of ionic compounds 9.4 Covalent Bonding: Lewis Structures for Molecules 9.5 Covalent Bonding: Writing Lewis Structures 9.5.1 Rules for writing Lewis structures 9.6 Resonance and Formal Charge 9.6.1 Resonance 9.6.2 Rules for writing resonance structures 9.6.3 Formal charge 9.6.4 Rules for assigning formal charge to an atom in a molecule 9.6.5 Using formal charge to determine molecular structure 9.7 Exceptions to the Octet Rule 9.8 Polar Covalent Bonds: Bond Polarity and Electronegativity 9.8.1 Determining polarity of a molecule 9.8.2 Dipole moment and percent ionic character 9.8.3 Dipole moment (μ) 9.8.4 Percent ionic character of a covalent polar bond 9.9 Problems 10: Chemical Bonding 2: Modern Theories of Chemical Bonding 10.1 VSPER Theory: Molecular Geometry and the Shapes of Molecules 10.1.1 VSEPR theory 10.1.2 Assumptions of the VSEPR theory 10.2 VSEPR Theory: Predicting Electron Group Geometry and Molecular Shape with the VSEPR Model 10.2.1 Electron group geometries 10.2.2 VSEPR theory: the AXE system 10.3 VSEPR Theory: Predicting Molecular Shape and Polarity 10.3.1 Steps for predicting molecular polarity 10.4 Valence Bond Theory 10.4.1 Postulates of valence bond theory 10.5 Valence Bond Theory: Types of Overlap 10.5.1 Sigma (σ) bond 10.5.2 Pi (π) bond 10.5.3 The strength of sigma and pi bonds 10.6 Hybridization 10.6.1 Characteristics of hybrid orbitals 10.6.2 Types of hybrid orbitals 10.6.2.1 sp3 hybridization—tetrahedral structure 10.6.2.2 sp2 hybridization—trigonal planar structure 10.6.2.3 sp hybridization 10.6.3 Hybridization and multiple bonds 10.6.3.1 Ethene, C2H4 10.6.3.2 Ethyne (acetylene), C2H2 10.6.4 Hybridization of elements involving d-orbitals 10.6.4.1 sp3d hybridization 10.6.4.2 sp3d2 hybridization 10.6.5 Predicting the hybrid orbitals used by an atom in bonding 10.7 Limitations of Valence Bond Theory 10.8 Molecular Orbital Theory 10.8.1 Linear combination of atomic orbitals (LCAO) 10.8.2 Molecular orbitals for simple diatomic molecules (H2 and He2) 10.8.3 Bonding in Li2 molecules 10.8.4 Molecular orbital energy-level diagram for homonuclear diatomic molecules 10.8.5 Molecular orbitals for heteronuclear diatomic molecules 10.8.6 MO electronic configuration and properties of the molecule 10.9 Problems 11: Gas Laws 11.1 Standard Temperature and Pressure 11.2 Boyle’s Law: Volume vs Pressure 11.3 Charles’s Law: Volume vs Temperature 11.4 The Combined Gas Law 11.5 Gay-Lussac’s Law and Reactions Involving Gases 11.6 Avogadro’s Law 11.7 The Ideal Gas Law 11.8 Density and Molecular Mass of a Gas 11.9 Molar Volume of an Ideal Gas 11.10 Dalton’s Law of Partial Pressure 11.11 Partial Pressure and Mole Fraction 11.12 Real Gases and Deviation from the Gas Laws 11.13 Graham’s Law of Diffusion 11.14 Problems 12: Liquids and Solids 12.1 The Liquid State 12.1.1 Properties of liquids 12.2 Vapor Pressure and the Clausius–Clapeyron Equatio 12.3 The Solid State 12.3.1 Types of solids 12.3.2 Crystal lattices 12.3.3 Unit cells 12.4 The Crystal System 12.4.1 Close-packed structure 12.4.2 Cubic unit cells 12.4.2.1 Guidelines for determining the number of atoms in a unit cell 12.4.2.2 Simple or primitive cubic unit cell 12.4.2.3 Body-centered cubic unit cell 12.4.2.4 Face-centered cubic unit cell 12.4.3 Coordination number 12.5 Calculations Involving Unit Cell Dimensions 12.6 Ionic Crystal Structure 12.6.1 The sodium chloride (NaCl), or “rock-salt” structur 12.6.2 The cesium chloride (CsCl) structure 12.6.3 The zinc blende (ZnS) structure 12.7 The Radius Ratio Rule for Ionic Compounds 12.8 Determination of Crystal Structure by X-Ray Diffraction 12.9 Problems 13: Solution Chemistry 13.1 Solution and Solubility 13.1.1 Some definitions 13.2 Concentration of Solutions 13.2.1 Percent by mass 13.2.2 Parts per million (ppm) and parts per billion (ppb) 13.2.3 Percent by volume 13.2.4 Molarity 13.2.5 Normality 13.2.6 Mole fraction 13.2.7 Molality 13.2.8 Dilute solutions 13.3 Solving Solubility Problems 13.3.1 Solubility in grams per 100 g of solvent 13.3.2 Solubility in moles per liter of solvent 13.4 Effect of Temperature on Solubility 13.5 Solubility Curves 13.6 Effect of Pressure on Solubility 13.7 Problems 14: Volumetric Analysis 14.1 Introduction 14.2 Applications of Titration 14.2.1 Acid-base titrations 14.2.2 A molar solution 14.2.3 Standard solutions 14.2.4 Standardization 14.3 Calculations Involving Acid-Base Titration 14.3.1 Calculation involving mass and percentage of substance titrated 14.3.2 Calculations involving molarity, mass concentration, solubility, and percentage purity from a standardizing titration 14.4 Back Titrations 14.5 Kjeldahl Nitrogen Determination 14.6 Problems 15: Ideal Solutions and Colligative Properties 15.1 Colligative Properties 15.2 Vapor Pressure and Raoult’s Law 15.2.1 Vapor pressure 15.2.2 Raoult’s law 15.2.3 Ideal solutions with two or more volatile components 15.3 Elevation of Boiling Point 15.4 Depression of Freezing Point 15.5 Osmosis and Osmotic Pressure 15.6 Problems 16: Chemical Kinetics 16.1 Rates of Reaction 16.2 Measurement of Reaction Rates 16.2.1 Instantaneous rate 16.3 Reaction Rates and Stoichiometry 16.4 Collision Theory of Reaction Rates 16.4.1 Factors affecting reaction rates 16.5 Rate Laws and the Order of Reactions 16.6 Experimental Determination of Rate Law Using Initial Rates 16.6.1 Alternate method 16.6.2 Determining the value of x 16.6.3 Determining the value of y 16.6.4 Determining the value of z 16.7 The Integrated Rate Equation 16.7.1 First-order reactions 16.7.2 Graphing first-order data 16.7.3 Second-order reactions 16.8 Half-Life of a Reaction 16.9 Reaction Rates and Temperature: The Arrhenius Equation 16.10 Problems 17: Chemical Equilibrium 17.1 Reversible and Irreversible Reactions 17.2 The Equilibrium Constant 17.2.1 Equilibrium constant in terms of pressure 17.2.2 Relationship between Kp and Kc 17.3 The Reaction Quotient 17.4 Predicting the Direction of Reaction 17.5 Position of Equilibrium 17.6 Homogeneous vs Heterogeneous Equilibria 17.7 Calculating Equilibrium Constants 17.7.1 Calculating Kc or Kp from known equilibrium a 17.7.2 Calculating K from initial concentration and one equilibrium concentration 17.8 Calculating Equilibrium Concentrations from K 17.8.1 A faster method for solving equilibrium problems 17.8.2 When to use the approximation method 17.9 Qualitative Treatment of Equilibrium: Le Chatelier’s Principle 17.9.1 Factors affecting a chemical reaction at eq 17.9.1.1 Changes in concentration 17.9.1.2 Changes in pressure 17.9.1.3 Changes in temperature 17.9.2 Addition of a catalyst 17.10 Problems 18: Ionic Equilibria and pH 18.1 The Ionization of Water 18.2 Definition of Acidity and Basicity 18.2.1 Ionic product of water 18.3 The pH of a Solution 18.4 The pOH of a Solution 18.5 The Acid Ionization Constant, Ka 18.5.1 Definition of pKa 18.6 Calculating pH and Equilibrium Concentrations in Solutions of Weak Acid 18.6.1 When to use the approximation method 18.7 Percent Dissociation of Weak Acids 18.8 The Base Dissociation Constant, Kb 18.9 Relationship Between Ka and Kb 18.10 Salt Hydrolysis: Acid–Basis Properties of Salts 18.10.1 The hydrolysis constant, Kh 18.10.2 Relationship between Kh and Kw 18.11 The Common Ion Effect 18.12 Buffers and pH of Buffer Solutions 18.12.1 How does a buffer work? 18.12.2 Buffer capacity and pH 18.12.3 The Henderson–Hasselbalch equation 18.13 Polyprotic Acids and Bases 18.14 More Acid–Base Titration 18.14.1 Acid–base indicators 18.14.2 Perception of color change of indicators 18.15 pH Titration Curves 18.15.1 Titration of strong acid against a strong base 18.15.2 Titration of weak acid against a strong base 18.16 Problems 18.16.1 pH, pOH, and percent ionization 18.16.2 Salt hydrolysis 18.16.3 Common ion effect 18.16.4 Buffers 18.16.5 Titration 19: Solubility and Complex-Ion Equilibria 19.1 Solubility Equilibria 19.2 The Solubility Product Principle 19.3 Determining Ksp from Molar Solubility 19.4 Calculating Molar Solubility from Ksp 19.5 Ksp and Precipitation 19.6 Complex-Ion Equilibria 19.6.1 Formation of complex ions 19.7 Problems 20: Thermochemistry 20.1 Introduction 20.2 Calorimetry and Heat Capacity 20.3 Enthalpy 20.3.1 Calculating H of reaction 20.4 Hess’s Law of Heat Summation 20.4.1 Hints for using Hess’s law 20.5 Lattice Energy and the Born–Haber Cycle 20.6 Bond Energies and Enthalpy 20.7 Problems 21: Chemical Thermodynamics 21.1 Definition of Terms 21.2 The First Law of Thermodynamics 21.3 Expansion Work 21.4 Entropy 21.5 The Second Law of Thermodynamics 21.6 Calculation of Entropy Changes in Chemical Reactions 21.7 Free Energy 21.8 The Standard Free Energy Change 21.8.1 Calculating the standard free energy change 21.9 Enthalpy and Entropy Changes During a Phase Change 21.10 Free Energy and the Equilibrium Constant 21.11 Variation of G0 and Equilibrium Constant with Temperature 21.11.1 Relationship between G0 and K at different temperatures 21.12 Problems 22: Oxidation and Reduction Reactions 22.1 Introduction 22.2 Oxidation and Reduction in Terms of Electron Transfer 22.3 Oxidation Numbers (ON) 22.3.1 Rules for assigning oxidation numbers 22.3.2 Oxidation numbers in formulas 22.3.3 Oxidation number and nomenclature 22.4 Oxidation and Reduction in Terms of Oxidation Number 22.5 Disproportionation Reactions 22.6 Oxidizing and Reducing Agents 22.6.1 Identifying oxidizing and reducing agents 22.7 Half-Cell Reactions 22.8 Balancing Redox Equations 22.8.1 The oxidation-number method 22.8.2 The half-reaction method 22.9 Oxidation-Reduction Titration 22.9.1 Calculations involving redox titration 22.9.1.1 The conversion factor method 22.9.1.2 The formula method 22.10 Problems 23: Fundamentals of Electrochemistry 23.1 Galvanic Cells 23.2 The Cell Potential 23.3 Standard Electrode Potential 23.3.1 Standard reduction potential 23.4 The Electrochemical Series (ECS) 23.5 Applications of Electrode Potentia 23.6 Cell Diagrams 23.7 Calculating E0cell from Electrode Potential 23.8 Relationship of the Standard Electrode Potential, the Gibbs Free Energy, and the Equilibrium Constant 23.8.1 Conditions for spontaneous change in redox reactions 23.9 Dependence of Cell Potential on Concentration (the Nernst Equation) 23.10 Electrolysis 23.11 Faraday’s Laws of Electrolysis 23.11.1 First law of electrolysis 23.11.2 The Faraday constant 23.11.3 Second law of electrolysis 23.12 Problems 24: Radioactivity and Nuclear Reactions 24.1 Definitions 24.2 Radioactive Decay and Nuclear Equations 24.2.1 Alpha emission 42α 24.2.2 Beta emission ( 0−1β) 24.2.3 Gamma radiation (γ ) 24.2.4 Positron emission (01e) 24.2.5 Electron capture ( 0−1e) 24.3 Nuclear Transmutations 24.4 Rates of Radioactive Decay and Half-Life 24.4.1 Half-life 24.5 Energy of Nuclear Reactions 24.5.1 Mass defect 24.5.2 Binding energy 24.6 Problems Appendix A A.1 Essential mathematics A.1.1 Significant figures A.1.2 Rounding-off A.2 Significant figures and mathematical operations A.2.1 Multiplication and division A.2.2 Addition and subtraction A.3 Scientific notation and exponents A.3.1 Addition and subtraction A.3.2 Multiplication and division A.3.3 Powers and roots A.4 Logarithms A.4.1 Common logarithm A.4.2 Antilogarithms A.4.3 Natural logarithms A.4.4 Calculations involving logarithms A.5 Algebraic equations A.5.1 Linear equations A.5.2 Straight-line graphs and linear equations A.5.3 Quadratic equations A.5.3.1 Solution of quadratic equations A.5.3.2 Extraction of the square root A.5.3.3 The factor method A.5.3.4 Quadratic formula Appendix A: Sample Problems Appendix A: Solutions to Problems Appendix B B.1 Systems of measurement B.1.1 Measurements in chemistry B.2 Measurement of mass, length, and time B.2.1 Measurement of mass B.2.2 Measuring length B.2.3 Measuring time B.3 Temperature B.4 Derived units B.5 Density and specific gravity B.5.1 Density B.5.2 Specific gravity B.6 Dimensional analysis and conversion factors B.7 Problems Appendix B: Solutions to Problems Solutions Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Index