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F i ft h E d i t i o n Chemistry The Science in Context Thomas R Gilbert NORTHEASTERN UNIVERSITY Rein V Kirss NORTHEASTERN UNIVERSITY Natalie Foster LEHIGH UNIVERSITY Stacey Lowery Bretz MIAMI UNIVERSITY Geoffrey Davies NORTHEASTERN UNIVERSITY n W W Norton & Company New York • London W W Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D Herter Norton first published lectures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union The firm soon expanded its program beyond the Institute, publishing books by celebrated academics from America and abroad By midcentury, the two major pillars of Norton’s publishing program—trade books and college texts—were firmly established In the 1950s, the Norton family transferred control of the company to its employees, and today—with a staff of four hundred and a comparable number of trade, college, and professional titles published each year—W W Norton & Company stands as the largest and oldest publishing house owned wholly by its employees Copyright © 2018, 2015, 2012, 2009, 2004 by W W Norton & Company, Inc All rights reserved Printed in Canada Editor: Erik Fahlgren Developmental Editor: Andrew Sobel Associate Managing Editor, College: Carla L Talmadge Assistant Editor: Arielle Holstein Production Manager: Eric Pier-Hocking Managing Editor, College: Marian Johnson Managing Editor, College Digital Media: Kim Yi Media Editor: Christopher Rapp Associate Media Editor: Julia Sammaritano Media Project Editor: Marcus Van Harpen Media Editorial Assistants: Victoria Reuter, Doris Chiu Digital Production: Lizz Thabet Marketing Manager, Chemistry: Stacy Loyal Associate Design Director: Hope Miller Goodell Photo Editor: Aga Millhouse Permissions Manager: Megan Schindel Composition: Graphic World Illustrations: Imagineering—Toronto, ON Manufacturing: Transcontinental Permission to use copyrighted material is included at the back of the book Library of Congress Cataloging-in-Publication Data Names: Gilbert, Thomas R | Kirss, Rein V | Foster, Natalie | Bretz, Stacey Lowery, 1967- | Davies, Geoffrey, 1942Title: Chemistry The science in context Description: Fifth edition / Thomas R Gilbert, Northeastern University, Rein V Kirss, Northeastern University, Natalie Foster, Lehigh University, Stacey Lowery Bretz, Miami University, Geoffrey Davies, Northeastern University | New York : W.W Norton & Company, Inc., [2018] | Includes index Identifiers: LCCN 2016048998 | ISBN 9780393264845 (hardcover) Subjects: LCSH: Chemistry Textbooks Classification: LCC QD33.2 G55 2018 | DDC 540 dc23 LC record available at https://lccn.loc.gov/2016048998 W W Norton & Company, Inc., 500 Fifth Avenue, New York, NY 10110 wwnorton.com W W Norton & Company Ltd., 15 Carlisle Street, London W1D 3BS 1234567890 Brief Contents 1 Particles of Matter: Measurement and the Tools of Science 2 Atoms, Ions, and Molecules: Matter Starts Here 44 3 Stoichiometry: Mass, Formulas, and Reactions 82 4 Reactions in Solution: Aqueous Chemistry in Nature 142 5 Thermochemistry: Energy Changes in Reactions 208 6 Properties of Gases: The Air We Breathe 272 7 A Quantum Model of Atoms: Waves, Particles, and Periodic Properties 330 8 Chemical Bonds: What Makes a Gas a Greenhouse Gas? 386 9 Molecular Geometry: Shape Determines Function 436 10 Intermolecular Forces: The Uniqueness of Water 496 11 Solutions: Properties and Behavior 536 12 Solids: Crystals, Alloys, and Polymers 588 13 Chemical Kinetics: Reactions in the Atmosphere 634 14 Chemical Equilibrium: How Much Product Does a Reaction Really Make? 694 15 Acid–Base Equilibria: Proton Transfer in Biological Systems 738 16 Additional Aqueous Equilibria: Chemistry and the Oceans 784 17 Thermodynamics: Spontaneous and Nonspontaneous Reactions and Processes 832 18 Electrochemistry: The Quest for Clean Energy 878 19 Nuclear Chemistry: Applications to Energy and Medicine 922 20 Organic and Biological Molecules: The Compounds of Life 960 21 The Main Group Elements: Life and the Periodic Table 1016 22 Transition Metals: Biological and Medical Applications 1052 iii Contents List of Applications xv List of ChemTours xvii About the Authors xviii Preface xix Particles of Matter: Measurement and the Tools of Science 1.1 How and Why 1.2 Macroscopic and Particulate Views of Matter Classes of Matter 5 • A Particulate View 1.3 Mixtures and How to Separate Them 1.4 A Framework for Solving Problems 11 1.5 Properties of Matter 12 1.6 States of Matter 14 1.7 The Scientific Method: Starting Off with a Bang 16 1.8 SI Units 18 1.9 Unit Conversions and Dimensional Analysis 20 1.10 Evaluating and Expressing Experimental Results 22 Just how small are these atoms? (Chapter 1) Significant Figures 23 • Significant Figures in Calculations 23 • Precision and Accuracy 27 1.11 Testing a Theory: The Big Bang Revisited 32 Temperature Scales 32 • An Echo of the Big Bang 34 Summary 37 • Particulate Preview Wrap-Up 37 • Problem-Solving Summary 38 • Visual Problems 38 • Questions and Problems 40 Atoms, Ions, and Molecules: Matter Starts Here 44 2.1 Atoms in Baby Teeth 46 2.2 The Rutherford Model 47 Electrons 47 • Radioactivity 49 • Protons and Neutrons 50 2.3 Isotopes 52 2.4 Average Atomic Mass 54 2.5 The Periodic Table of the Elements 55 Navigating the Modern Periodic Table 56 2.6 Trends in Compound Formation 59 What can baby teeth tell us about nuclear fallout? (Chapter 2) Molecular Compounds 60 • Ionic Compounds 60 v vi Contents 2.7 Naming Compounds and Writing Formulas 62 Molecular Compounds 62 • Ionic Compounds 63 • Compounds of Transition Metals 64 • Polyatomic Ions 65 • Acids 66 2.8 Organic Compounds: A First Look 67 Hydrocarbons 67 • Heteroatoms and Functional Groups 68 2.9 Nucleosynthesis: The Origin of the Elements 70 Primordial Nucleosynthesis 70 • Stellar Nucleosynthesis 72 Summary 74 • Particulate Preview Wrap-Up 74 • Problem-Solving Summary 75 • Visual Problems 75 • Questions and Problems 77 Stoichiometry: Mass, Formulas, and Reactions 82 3.1 Air, Life, and Molecules 84 Chemical Reactions and Earth’s Early Atmosphere 85 3.2 The Mole 87 Molar Mass 89 • Molecular Masses and Formula Masses 91 • Moles and Chemical Equations 95 How much medicine can be isolated from the bark of a yew tree? (Chapter 3) 3.3 Writing Balanced Chemical Equations 96 3.4 Combustion Reactions 101 3.5 Stoichiometric Calculations and the Carbon Cycle 104 3.6 Determining Empirical Formulas from Percent Composition 108 3.7 Comparing Empirical and Molecular Formulas 113 Molecular Mass and Mass Spectrometry 116 3.8 Combustion Analysis 117 3.9 Limiting Reactants and Percent Yield 122 Calculations Involving Limiting Reactants 122 • Actual Yields versus Theoretical Yields 126 Summary 129 • Particulate Preview Wrap-Up 130 • Problem-Solving Summary 130 • Visual Problems 131 • Questions and Problems 134 Reactions in Solution: Aqueous Chemistry in Nature 142 4.1 Ions and Molecules in Oceans and Cells 144 4.2 Quantifying Particles in Solution 146 Concentration Units 147 4.3 Dilutions 154 Determining Concentration 156 How antacid tablets relieve indigestion? (Chapter 4) 4.4 Electrolytes and Nonelectrolytes 158 4.5 Acid–Base Reactions: Proton Transfer 159 4.6 Titrations 166 4.7 Precipitation Reactions 169 Making Insoluble Salts 170 • Using Precipitation in Analysis 174 • Saturated Solutions and Supersaturation 177 4.8 Ion Exchange 178 4.9 Oxidation–Reduction Reactions: Electron Transfer 180 Oxidation Numbers 181 • Considering Changes in Oxidation Number in Redox Reactions 183 • Considering Electron Transfer in Redox Reactions 184 • Balancing Redox Reactions by Using Half-Reactions 185 • The Activity Series for Metals 188 • Redox in Nature 190 Summary 194 • Particulate Preview Wrap-Up 195 • Problem-Solving Summary 195 • Visual Problems 197 • Questions and Problems 198 Contents vii Thermochemistry: Energy Changes in Reactions 208 5.1 Sunlight Unwinding 210 5.2 Forms of Energy 211 Work, Potential Energy, and Kinetic Energy 211 • Kinetic Energy and Potential Energy at the Molecular Level 214 5.3 Systems, Surroundings, and Energy Transfer 217 Isolated, Closed, and Open Systems 218 • Exothermic and Endothermic Processes 219 • P–V Work and Energy Units 222 5.4 Enthalpy and Enthalpy Changes 225 5.5 Heating Curves, Molar Heat Capacity, and Specific Heat 227 Hot Soup on a Cold Day 227 • Cold Drinks on a Hot Day 232 What reaction powers hydrogen-fueled vehicles? (Chapter 5) 5.6 Calorimetry: Measuring Heat Capacity and Enthalpies of Reaction 235 Determining Molar Heat Capacity and Specific Heat 235 • Enthalpies of Reaction 238 • Determining Calorimeter Constants 241 5.7 Hess’s Law 243 5.8 Standard Enthalpies of Formation and Reaction 246 5.9 Fuels, Fuel Values, and Food Values 252 Alkanes 252 • Fuel Value 255 • Food Value 257 Summary 260 • Particulate Preview Wrap-Up 261 • Problem-Solving Summary 261 • Visual Problems 262 • Questions and Problems 264 Properties of Gases: The Air We Breathe 272 6.1 Air: An Invisible Necessity 274 6.2 Atmospheric Pressure and Collisions 275 6.3 The Gas Laws 280 Boyle’s Law: Relating Pressure and Volume 280 • Charles’s Law: Relating Volume and Temperature 283 • Avogadro’s Law: Relating Volume and Quantity of Gas 285 • Amontons’s Law: Relating Pressure and Temperature 287 6.4 The Ideal Gas Law 288 6.5 Gases in Chemical Reactions 293 6.6 Gas Density 295 6.7 Dalton’s Law and Mixtures of Gases 299 6.8 The Kinetic Molecular Theory of Gases 304 Explaining Boyle’s, Dalton’s, and Avogadro’s Laws 304 • Explaining Amontons’s and Charles’s Laws 305 • Molecular Speeds and Kinetic Energy 306 • Graham’s Law: Effusion and Diffusion 309 6.9 Real Gases 311 Deviations from Ideality 311 • The van der Waals Equation for Real Gases 313 Summary 315 • Particulate Preview Wrap-Up 316 • Problem-Solving Summary 317 • Visual Problems 318 • Questions and Problems 321 A Quantum Model of Atoms: Waves, Particles, and Periodic Properties 330 7.1 Rainbows of Light 332 7.2 Waves of Energy 335 7.3 Particles of Energy and Quantum Theory 337 Quantum Theory 337 • The Photoelectric Effect 339 • Wave–Particle Duality 340 How is emergency oxygen generated on airplanes? (Chapter 6) viii Contents 7.4 The Hydrogen Spectrum and the Bohr Model 341 The Hydrogen Emission Spectrum 341 • The Bohr Model of Hydrogen 343 7.5 Electron Waves 345 De Broglie Wavelengths 346 • The Heisenberg Uncertainty Principle 348 7.6 Quantum Numbers and Electron Spin 350 7.7 The Sizes and Shapes of Atomic Orbitals 355 s Orbitals 355 • p and d Orbitals 357 7.8 The Periodic Table and Filling the Orbitals of Multielectron Atoms 358 7.9 Electron Configurations of Ions 366 Why does a metal rod first glow red when being heated? (Chapter 7) Ions of the Main Group Elements 366 • Transition Metal Cations 368 7.10 The Sizes of Atoms and Ions 369 Trends in Atom and Ion Sizes 369 7.11 Ionization Energies 372 7.12 Electron Affinities 375 Summary 377 • Particulate Preview Wrap-Up 377 • Problem-Solving Summary 377 • Visual Problems 378 • Questions and Problems 380 Chemical Bonds: What Makes a Gas a Greenhouse Gas? 386 8.1 Types of Chemical Bonds and the Greenhouse Effect 388 Forming Bonds from Atoms 389 8.2 Lewis Structures 391 Lewis Symbols 391 • Lewis Structures 392 • Steps to Follow When Drawing Lewis Structures 392 • Lewis Structures of Molecules with Double and Triple Bonds 394 • Lewis Structures of Ionic Compounds 397 8.3 Polar Covalent Bonds 398 Why is CO2 considered a greenhouse gas? (Chapter 8) Polarity and Type of Bond 400 Vibrating Bonds and Greenhouse Gases 401 8.4 Resonance 403 8.5 Formal Charge: Choosing among Lewis Structures 407 Calculating Formal Charge of an Atom in a Resonance Structure 408 8.6 Exceptions to the Octet Rule 411 Odd-Electron Molecules 411 • Atoms with More than an Octet 413 • Atoms with Less than an Octet 416 • The Limits of Bonding Models 418 8.7 The Lengths and Strengths of Covalent Bonds 419 Bond Length 419 • Bond Energies 420 Summary 424 • Particulate Preview Wrap-Up 424 • Problem-Solving Summary 424 • Visual Problems 425 • Questions and Problems 427 Molecular Geometry: Shape Determines Function 436 9.1 Biological Activity and Molecular Shape 438 9.2 Valence-Shell Electron-Pair Repulsion (VSEPR) Theory 439 Central Atoms with No Lone Pairs 440 • Central Atoms with Lone Pairs 444 9.3 Polar Bonds and Polar Molecules 450 How some insects communicate chemically? (Chapter 9) 9.4 Valence Bond Theory 453 Bonds from Orbital Overlap 453 • Hybridization 454 • Tetrahedral Geometry: sp3 Hybrid Orbitals 455 • Trigonal Planar Geometry: sp2 Hybrid Orbitals 456 • Linear Geometry: sp Hybrid Orbitals 458 • Octahedral and Trigonal Bipyramidal Geometries: sp3d2 and sp3d Hybrid Orbitals 461 Contents ix 9.5 Shape and Interactions with Large Molecules 463 Drawing Larger Molecules 465 • Molecules with More than One Functional Group 467 9.6 Chirality and Molecular Recognition 468 9.7 Molecular Orbital Theory 470 Molecular Orbitals of Hydrogen and Helium 472 • Molecular Orbitals of Homonuclear Diatomic Molecules 474 • Molecular Orbitals of Heteronuclear Diatomic Molecules 478 • Molecular Orbitals of N21 and Spectra of Auroras 480 • Metallic Bonds and Conduction Bands 480 • Semiconductors 482 Summary 485 • Particulate Preview Wrap-Up 486 • Problem-Solving Summary 486 • Visual Problems 487 • Questions and Problems 488 10 Intermolecular Forces: The Uniqueness of Water 496 10.1 Intramolecular Forces versus Intermolecular Forces 498 10.2 Dispersion Forces 499 The Importance of Shape 501 10.3 Interactions among Polar Molecules 502 Ion–Dipole Interactions 502 • Dipole–Dipole Interactions 503 • Hydrogen Bonds 504 10.4 Polarity and Solubility 510 Combinations of Intermolecular Forces 513 10.5 Solubility of Gases in Water 514 10.6 Vapor Pressure of Pure Liquids 517 Why does ice float on top of liquid water? (Chapter 10) Vapor Pressure and Temperature 518 • Volatility and the Clausius–Clapeyron Equation 519 10.7 Phase Diagrams: Intermolecular Forces at Work 520 Phases and Phase Transformations 520 10.8 Some Remarkable Properties of Water 523 Surface Tension, Capillary Action, and Viscosity 524 • Water and Aquatic Life 526 Summary 528 • Particulate Preview Wrap-Up 528 • Problem-Solving Summary 528 • Visual Problems 529 • Questions and Problems 530 11 Solutions: Properties and Behavior 536 11.1 Interactions between Ions 538 11.2 Energy Changes during Formation and Dissolution of Ionic Compounds 542 Calculating Lattice Energies by Using the Born–Haber Cycle 545 • Enthalpies of Hydration 548 11.3 Vapor Pressure of Solutions 550 Raoult’s Law 551 11.4 Mixtures of Volatile Solutes 553 Vapor Pressures of Mixtures of Volatile Solutes 553 11.5 Colligative Properties of Solutions 558 Molality 558 • Boiling Point Elevation 561 • Freezing Point Depression 562 • The van ’t Hoff Factor 564 • Osmosis and Osmotic Pressure 568 • Reverse Osmosis 573 11.6 Measuring the Molar Mass of a Solute by Using Colligative Properties 575 Summary 580 • Particulate Preview Wrap-Up 580 • Problem-Solving Summary 580 • Visual Problems 582 • Questions and Problems 584 How is blood different from a pure liquid? (Chapter 11) 9 Oxidation–Reduction Reactions: Electron Transfer 193 b Balance O by adding water as needed Oxidation: H 2O(/) Fe(OH)2(s) S Fe(OH)3(s) Reduction: O2(g) S OH2(aq) H 2O(/) c Balance H by adding H1(aq) as needed H 2O(/) Fe(OH)2(s) S Fe(OH)3(s) H1(aq) Balance the charges H1(aq) O2(g) S OH2(aq) H 2O(/) H 2O(/) Fe(OH)2(s) S Fe(OH)3(s) H1(aq) 1 e2 e H1(aq) O2(g) S OH2(aq) H 2O(/) Balance the numbers of electrons lost and gained [H 2O(/) Fe(OH)2(s) S Fe(OH)3(s) H1(aq) 1 e2] [4 e2 H1(aq) O2(g) S OH2(aq) H 2O(/)] Add the two equations H2O 1/2 Fe 1OH2 1s2 S Fe 1OH2 1s2 H1 1aq2 e2 e2 H1 1aq2 O2 1g2 S OH2 1aq2 H2O 1,2 This gives us the balanced equation: H 2O(/) Fe(OH)2(s) O2(g) S Fe(OH)3(s) OH2(aq) H1(aq) which can be simplified: H 2O(/) to ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ H 2O(/) Fe(OH)2(s) O2(g) S Fe(OH)3(s) OH2(aq) H1(aq) H 2O(/) Fe(OH)2(s) O2(g) S Fe(OH)3(s) Think About It This reaction occurs in neutral and basic soils as H 2O and O2 combine to form the OH2 ions needed in the conversion of Fe(OH)2(s) to Fe(OH)3(s) d Practice Exercise The hydroperoxide ion, HO22(aq), reacts with permanganate ion, MnO42(aq), to produce MnO2(s) and oxygen gas Balance the equation for the oxidation of hydroperoxide ion to O2(g) by permanganate ion in a basic solution (Answers to Practice Exercises are in the back of the book.) Reactions in aqueous solutions are an integral part of our daily lives On a large scale, in oceans, rivers, and rain, they shape our physical world Many reactions that produce the substances that are part of modern life—from paint pigments to drugs—are run in water, and many analytical procedures rely on reactions in water to determine the content of aqueous solutions that we drink, swim in, and use in countless consumer products like car batteries and shampoos On a small scale, reactions in the water within the cells of our bodies and in all living organisms make the chemical processes that are essential to life possible On Earth, there may be water without life, but there is no life without water SAMPLE EXERCISE 4.22 Integrating Concepts: Shelf-Stability of Drugs Commercial pharmaceutical agents undergo extensive analysis to establish how long they may be stored without degradation and loss of potency A candidate drug has the following percent composition from combustion analysis: C, 62.50%; H, 4.20% The drug is a diprotic acid A standard tablet containing 325 mg of the drug is dissolved in 100.00 mL of water and titrated to the 194 c h a p t e r Reactions in Solution equivalence point with 16.45 mL of 0.2056 M NaOH(aq) After storage at 50°C under high humidity for one month, a second tablet, when dissolved in 50.00 mL of water, requires 10.10 mL of 0.1755 M NaOH(aq) to be completely neutralized a What is the empirical formula of the drug? b What is its molar mass? c What is its molecular formula? d What is the percent of active drug substance remaining in the tablet after storage? Collect and Organize We are given the percent composition of the drug and information from titration experiments From these data we can find the empirical formula, the molar mass, and the amount of active drug in the stored tablet Analyze The percent composition data from the combustion analysis not add to 100% We may assume that the amount missing is due to oxygen in the molecule The drug is a diprotic acid, so neutralizing mole of the drug requires moles of NaOH The titration of the drug requires about 20 mL of 0.2 M NaOH, which is about 0.004 mol OH2 That means the pure sample is about 0.002 moles of the drug; if about 0.3 grams contains 0.002 moles, the drug must have a molar mass of about 150 g If any of the drug decomposes upon storage, we should have less than 325 mg in the second sample Solve a The percent oxygen in the drug molecule is 100.00% (62.50% 4.20%) 33.30% Calculating the moles of C, H, and O in exactly 100 g of the drug: 62.50 g C 5.20 mol C 12.01 g/mol 4.20 g H 4.17 mol H 1.008 g/mol 33.30 g O 2.08 mol O 16.00 g/mol Reducing these quantities to ratios of small whole numbers: 5.20 mol C 2.50 mol C 2.08 4.17 mol H 2.00 mol H 2.08 2.08 mol O 1.00 mol O 2.08 requires multiplying by 2, which gives us mol C:4 mol H:2 mol O and the empirical formula: C5H4O2 b To find the molar mass of the drug from the titration data, we first find the number of moles of drug in the sample: mol drug 0.2056 mol NaOH L NaOH mol NaOH 5 0.001691 mol drug 0.01645 L NaOH If 0.325 g of drug is 0.001691 mol of drug, then the mass of mole is 0.325 g 192.2 g/mol } drug 0.001691 mol c The mass of mole of empirical formula units (C5H4O2) is (5 12.01 g/mol) (4 1.008 g/mol) (2 16.00 g/mol) 5 96.08 g/mol The number of moles of formula units per mole of molecules is g mol 52 g 96.08 mol 192.16 So the molecular formula of the drug is (C5H4O2)2 C10H8O4 d The stored tablet contains mol drug 0.1755 mol NaOH L NaOH mol NaOH 5 0.0008863 mol drug 8.863 1024 mol 0.01010 L NaOH Comparing this value with the original amount: 8.863 1024 mol 100% 52.41% 1.691 1023 mol of the active drug is left in the tablet Think About It The molar mass we calculated is close to our estimated value, so it seems reasonable If only half the active agent is present in the tablet after storage under these conditions, the manufacturer may have to reformulate the drug or package it differently to protect it from its surroundings Summary LO1 The concentration of solute in a solution can be expressed many different ways: as mass of solute per mass of solution (such as grams of solute per kilogram of solution), parts per million (1 ppm μg solute/g solution mg solute/kg solution), or parts per billion (1 ppb μg solute/kg solution) Solute concentration can also be expressed as mass of solute per volume of solvent and as moles of solute per liter of solution, or molarity (M) One set of units can be converted into another by using dimensional analysis (Sections 4.1 and 4.2) Problem-Solving Summary 195 LO2 Two common techniques to make solutions of desired concentration are determining the mass of solute to be dissolved in an appropriate amount of solvent to produce the quantity of solution needed and the dilution of a stock solution (Sections 4.2 and 4.3) proton donors and Brønsted–Lowry bases are proton acceptors; they may also be strong or weak electrolytes (Sections 4.4 and 4.5) LO6 Solubility rules define substances that dissolve readily in water and those that have very limited solubility We can use them to determine combinations of ions in solution that result in precipitate formation, and we can quantify the amount of precipitate formed and the concentration of ions left in solution after reaction We can remove ions from solution by precipitation and by ion exchange (Sections 4.7 and 4.8) LO3 We can determine the concentration of a solution by spectrophotometry and the application of Beer’s law, which relates the absorbance of a solution (A) to concentration (c), path length (b) and molar absorptivity (e) by the equation A εbc We can also use titrations based on acid–base neutralizations or precipitation reactions (Sections 4.3, 4.5, 4.6, and 4.7) LO4 There are three different ways to write chemical equations Molecular equations may be the easiest to balance; overall ionic equations show all the species present in solution; net ionic equations eliminate spectator ions and show only the species that are involved in the reaction (Sections 4.5, 4.6, and 4.7) LO5 Measuring the conductivity of a solution enables us to identify solutes as strong electrolytes, weak electrolytes, or nonelectrolytes In aqueous solution, Brønsted–Lowry acids are LO7 In a redox reaction, substances either gain electrons (and thereby undergo reduction) or lose electrons (undergo oxidation) A reaction is a redox reaction if the oxidation numbers (O.N.), or oxidation states, of the atoms in the reactants change during the reaction An activity series allows us to predict whether a particular metal ion will oxidize a different metal In balancing equations for redox reactions, we must consider the number of electrons transferred as well as the number of atoms involved (Section 4.9) Particul ate Preview Wr ap-Up The balanced equation when the contents of the two beakers are mixed is NH4Cl(aq) AgNO3(aq) S NH4NO3(aq) AgCl(s) Therefore ammonium nitrate remains as dissociated ions dissolved in water, while silver chloride precipitates as a solid AgNO3(aq) is the limiting reagent, and all the nitrate ions (0.01 moles) remain in solution because they are spectator ions The starting materials are drawn showing four cations and four anions for each reactant, so they form the products drawn here Problem-Solving Summary Type of Problem Concepts and Equations Comparing concentrations in aqueous solutions Use conversion factors to express concentrations in different units Calculating molarity from solute mass and solution volume or from solute mass, solution mass, and density Convert the solute mass into grams and then into moles Convert the solution mass into volume by dividing by the density of the solvent Divide moles of solute by liters of solution: Molarity moles of solute liter of solution Sample Exercises 4.1 4.2, 4.3 196 c h a p t e r Reactions in Solution Type of Problem Calculating the mass of solute or volume of stock solution to prepare a solution Concepts and Equations a Multiply the known concentration (in mol/L) by the target volume (in L) to obtain the moles of solute needed Then multiply moles of solute by solute molar mass, }, to get mass of solute needed: Sample Exercises 4.4, 4.5 Mass of solute (g) (V M) } (4.2) b Given three of the four variables, use Vinitial Minitial Vdiluted Mdiluted (4.3) to solve for the fourth Applying Beer’s law Substitute for A, b, and c in Equation 4.4 and solve for ε for a solution of known concentration: ε5 4.6 A bc Use A, b, and ε to find c for a solution of unknown concentration: c5 A εb 4.7, 4.11 Writing neutralization reaction equations Balance the molecular equation by balancing the moles of H1 ions donated by the acid and accepted by the base Next, create the overall ionic equation by writing strong electrolytes in their ionic form Finally, create the net ionic equation by eliminating spectator ions from the overall ionic equation Comparing electrolytes, acids, and bases Use the definitions of a strong electrolyte, a weak electrolyte, a nonelectrolyte, an acid, and a base to classify compounds into one or more categories Calculating molarity from titration data Use the volume and concentration of titrant used to neutralize a sample along with a balanced chemical equation to calculate the number of moles in a sample of known volume and determine its molarity Predicting precipitation reactions Write all the ions present in the solutions being mixed If any cation/anion pair forms an insoluble compound, that compound will precipitate 4.12 Calculating the mass of a precipitate Find the limiting reactant Use the stoichiometry of the net ionic equation to calculate the moles of precipitate, and then convert moles into mass of precipitate by using the precipitate’s molar mass 4.13, 4.15 Calculating a solute concentration from a precipitate mass Convert precipitate mass into moles by dividing by its molar mass Convert moles of precipitate into moles of solute Calculate molarity of the solute in the sample by dividing the moles of solute by the volume of sample in liters 4.14 Determining oxidation numbers (O.N.) O.N of a monatomic ion is equal to the ion’s charge O.N of a pure element is To assign O.N in a molecule containing more than one type of atom, assign O.N 11 to H, 22 to O, and then calculate O.N for any remaining atoms such that all the O.N sum to For polyatomic ions, the sum of the O.N values must equal the charge on the ion 4.16 Identifying oxidizing and reducing agents and number of electrons transferred The oxidizing agent contains an atom whose O.N decreases during the reaction; the reducing agent contains an atom whose O.N increases; the change in O.N determines the number of electrons transferred 4.17 Balancing redox reactions with half-reactions Multiply one or both half-reactions by the appropriate coefficient(s) to balance the loss and gain of electrons Combine the two half-reactions and simplify 4.18 Using the activity series Any metal in Table 4.6 will be oxidized by a cation listed below it in the activity series 4.19 Balancing redox reactions that involve acidic or basic conditions Follow the steps described on pp 190–193 4.8 4.9, 4.10 4.20, 4.21 Visual Problems 197 Visual Problems (Answers to boldface end-of-chapter questions and problems are in the back of the book.) 4.1 In Figure P4.1, which shows a solution containing three binary acids, one of the three is a weak acid and the other two are strong acids Which color sphere represents the anion of the dissociated weak acid? – + + – – – + – – – + + + – + – – – + + – + + – + + FIGURE P4.1 4.2 Solutions of sodium chloride and silver iodide are mixed together and vigorously shaken Which colored spheres in Figure P4.2 represent the following ions? (a) Na1; (b) Cl2; (c) I2 4.5 Which of the drawings in Figure P4.5 depicts a strong electrolyte? A weak electrolyte? A strong acid? A weak acid? A nonelectrolyte? Each drawing may fit more than one category − − 2+ – + + + + – + +– +– +– +– +– +– +– +– +– +– FIGURE P4.2 4.3 Which of the highlighted elements in Figure P4.3 forms an acid with the following generic formula? (a) HX; (b) H XO4; (c) HXO3; (d) H3XO4 − − − − + (b) + − + 2+ − 2+ − – + – FIGURE P4.4 (a) – – 10 11 12 13 14 15 16 17 18 + − + + + − − + − − (c) (d) FIGURE P4.5 4.6 Which of the three half-reactions shown in Figure P4.6 depicts an oxidation? Which depicts a reduction? − (a) 10 11 12 13 14 15 16 17 18 + (b) − (c) Legend: − bromide ion; FIGURE P4.6 FIGURE P4.3 4.4 In which of the highlighted groups of elements in Figure P4.4 will you find an element that forms the following? (a) insoluble halides; (b) insoluble hydroxides; (c) hydroxides that are soluble; (d) binary compounds with hydrogen that are strong acids − + hydronium ion; − iodate ion 198 c h a p t e r Reactions in Solution 4.7 Which ions in Figure P4.7 will remain in solution? + − − − 2+ + + − A B C − 2+ − − + Cu(s) + HNO3(aq) − Legend: − bromide ions; 2+ lead(II) ions D Sodium chloride E Glucose Zn(s) F FIGURE P4.7 4.8 Use representations [A] through [I] in Figure P4.8 to answer questions a–f a Which solutes form aqueous solutions that conduct electricity? b Solutions of which solutes will produce a precipitate when mixed? c Which solutes are nonelectrolytes? d Which, if any, depict(s) precipitation reaction(s)? e Which, if any, depict(s) redox reaction(s)? f Which, if any, depict(s) acid–base reaction(s)? Ethanol G CuSO4(aq) H Acetic acid Lead(II) nitrate Cu(s) I Perchloric acid MnCl2(aq) + NaOH(aq) FIGURE P4.8 Questions and Problems Quantifying Particles in Solution Concept Review 4.9 How you decide which component in a solution is the solvent? 4.10 Can a solid ever be a solvent? Explain 4.11 What is the molarity of a solution that contains 1.00 mmol of solute per milliliter of solution? *4.12 A beaker contains 100 g of 1.00 M NaCl If you transfer 50 g of the solution to another beaker, what is the molarity of the solution remaining in the first beaker? Problems 4.13 Calculate the molarity of each of the following solutions: a 0.56 mol of BaCl in 100.0 mL of solution b 0.200 mol of Na 2CO3 in 200.0 mL of solution c 0.325 mol of C6H12O6 in 250.0 mL of solution d 1.48 mol of KNO3 in 250.0 mL of solution 4.14 Calculate the molarity of each of the following solutions: a 0.150 mol of urea (CH4N2O) in 250.0 mL of solution b 1.46 mol of NaC2H3O2 in 1.000 L of solution c 1.94 mol of methanol (CH3OH) in 5.000 L of solution d 0.045 mol of sucrose (C12H 22O11) in 50.0 mL of solution 4.15 Calculate the molarity of each of the following ions: a 0.33 g Na1 in 100.0 mL of solution b 0.38 g Cl2 in 100.0 mL of solution c 0.46 g SO422 in 50.0 mL of solution d 0.40 g Ca 21 in 50.0 mL of solution 4.16 Calculate the molarity of each of the following solutions: a 64.7 g LiCl in 250.0 mL of solution b 29.3 g NiSO4 in 200.0 mL of solution c 50.0 g KCN in 500.0 mL of solution d 0.155 g AgNO3 in 100.0 mL of solution 4.17 How many grams of solute are needed to prepare each of the following solutions? a 1.000 L of 0.200 M NaCl b 250.0 mL of 0.125 M CuSO4 c 500.0 mL of 0.400 M CH3OH 4.18 How many grams of solute are needed to prepare each of the following solutions? a 500.0 mL of 0.250 M KBr b 25.0 mL of 0.200 M NaNO3 c 100.0 mL of 0.375 M CH3OH 4.19 River Water The Mackenzie River in northern Canada contains, on average, 0.820 mM Ca 21, 0.430 mM Mg21, 0.300 mM Na1, 0.0200 M K1, 0.250 mM Cl2, 0.380 mM SO422, and 1.82 mM HCO32 What, on average, is the total mass of these ions in 2.75 L of Mackenzie River water? 4.20 Toxicity of Metal Ions Zinc, copper, lead, and mercury ions are toxic to Atlantic salmon at concentrations of 6.42 1022 mM, 7.16 1023 mM, 0.965 mM, and Questions and Problems 199 5.00 3 1022 mM, respectively What are the corresponding concentrations in milligrams per liter? 4.21 Calculate the number of moles of solute contained in the following volumes of aqueous solutions of four pesticides: a 0.400 L of 0.024 M lindane b 1.65 L of 0.473 mM dieldrin c 25.8 L of 3.4 mM DDT d 154 L of 27.4 mM aldrin 4.22 Hemoglobin in Blood A typical adult body contains 6.0 L of blood The hemoglobin content of blood is about 15.5 g/100.0 mL of blood The approximate molar mass of hemoglobin is 64,500 g/mol How many moles of hemoglobin are present in a typical adult? 4.23 DDT Affects Neurons The pesticide DDT (C14H9Cl 5) kills insects such as malaria-carrying mosquitoes by opening sodium ion channels in neurons, causing them to fire spontaneously, which leads to spasms and eventual death However, its toxicity in wildlife and humans led to the banning of its use in the United States in 1972 Analysis of DDT concentrations in groundwater samples between 1969 and 1971 in Pennsylvania yielded the following results: Location Orchard Residential Residential after a storm Sample Size Mass of DDT 250.0 mL 0.030 mg 1.750 L 0.035 mg 50.0 mL 0.57 mg Express these concentrations in ppm and in millimoles per liter 4.24 Pesticides in the Environment Pesticide concentrations in the Rhine River between Germany and France between 1969 and 1975 averaged 0.55 mg/L of hexachlorobenzene (C 6Cl 6), 0.06 mg/L of dieldrin (C12H8Cl 6O), and 1.02 mg/L of hexachlorocyclohexane (C 6H6Cl 6) Express these concentrations in ppb and in millimoles per liter *4.28 For which of the following compounds is it possible to make a 1.0 M solution at 20°C? a CuSO4, solubility 32.0 g/100 mL b Ba(OH)2, solubility 3.9 g/100 mL c FeCl 2, solubility 68.5 g/100 mL d Ca(OH)2, solubility 0.173 g/100 mL Dilutions Problems 4.29 Calculate the final concentrations of the following aqueous solutions after each has been diluted to a final volume of 25.0 mL: a 3.00 mL of 0.175 M K1 b 2.50 mL of 10.6 mM LiCl c 15.00 mL of 7.24 1022 mM Zn 21 4.30 Dilution of Adult-Strength Cough Syrup A standard dose of an over-the-counter cough suppressant for adults is 20.0 mL A portion this size contains 35 mg of the active pharmaceutical ingredient (API) Your pediatrician says you may give this medication to your 6-year-old child, but the child may take only 10.0 mL at a time and receive a maximum of 4.00 mg of the API What is the concentration in mg/mL of the adult-strength medication, and how many millimeters of it would you need to dilute to make 100.0 mL of child-strength cough syrup? 4.31 The concentration of Na1 in seawater, 0.481 M, is higher than in the cytosol, the fluid inside human cells (12 mM) How much water must be added to 1.50 mL of seawater to make the Na1 concentration equal to that found in the cytosol? Assume the volumes are additive 4.32 The concentration of chloride ion in blood, 116 mM, is less than that in the ocean, 0.559 M Describe how you would prepare 2.50 mL of a solution of 116 mM chloride ion from seawater 4.33 Water is allowed to evaporate from 100.0 mL of 0.24 M Na 2SO4 until the solution volume is 60.0 mL What is the molar concentration of the evaporated solution? *4.34 Mixing Fertilizer The label on a bottle of “organic” liquid fertilizer concentrate states that it contains g of phosphate per 100.0 mL and that 16 fluid ounces should be diluted with water to make 32 gallons of fertilizer to be applied to growing plants What is the phosphate concentration in grams per liter in the diluted fertilizer? (1 gallon 128 fluid ounces.) 4.25 Nitrogen trifluoride, NF 3, is used in the production of flat panel displays It is also a potent greenhouse gas The average concentration of NF in the atmosphere increased from 0.02 parts per trillion (ppt) in 1978 to 0.454 ppt in 2008 What is the concentration of NF in mg per kg of air? *4.26 Gases Found in Air Sulfur hexafluoride, SF6, is used in electrical transformers Like NF 3, it has a potential impact on climate Between 1978 and 2012, the concentration of SF6 increased from 0.51 parts per trillion (ppt) to 7.48 ppt How many more molecules of SF6 were found in one liter of air in 2012 than in 1978? (1 mole of gas 22.4 L of gas.) 4.35 If the absorbance of a solution of copper ion decreases by 45% upon dilution, how much water was added to 15.0 mL of a 1.00 M solution of Cu 21? 4.36 By what percentage does the absorbance decrease if 12.25 mL of water is added to a 16.75 mL sample of 0.500 M Cr31? *4.27 The concentration of copper(II) sulfate in one brand of soluble plant fertilizer is 0.07% by mass If a 20 g sample of this fertilizer is dissolved in 2.0 L of solution, what is the molarity of Cu 21? *4.37 The reaction of SnCl 2(aq) with Pt41(aq) in aqueous HCl yields a yellow-orange solution of a 1:1 Pt–Sn compound with a molar absorptivity (ε) of 1.3 104 M 21 cm21 What is the absorbance in a cell with a path length of 1.00 cm of a 200 c h a p t e r Reactions in Solution solution prepared by adding 100 mL of an aqueous solution of 5.2 mg (NH4)2PtCl6 to 100 mL of an aqueous solution of 2.2 mg SnCl 2? *4.38 The reaction of SnCl 2(aq) with RhCl 3(aq) in aqueous HCl yields a red solution of a 1:1 Rh–Sn compound If a solution prepared by adding 150 mL of a 0.272 mM aqueous solution of SnCl to 50 mL of an aqueous solution of 8.5 mg RhCl has an absorbance of 0.85, as measured in a 1.00 cm cell, what is the molar absorptivity of the red compound? Electrolytes and Nonelectrolytes Concept Review 4.39 A solution of table salt is a good conductor of electricity, but a solution containing an equal molar concentration of table sugar is not Why? 4.40 Corrosion at Sea Metallic fixtures on the bottom of a ship corrode more quickly in seawater than in freshwater Why? 4.41 Explain why liquid methanol, CH3OH, cannot conduct electricity, whereas molten NaOH can 4.42 Fuel Cells The electrolyte in an electricity-generating device called a fuel cell consists of a mixture of Li 2CO3 and K 2CO3 heated to 650°C At this temperature the ionic solids melt Explain how this mixture of molten carbonates can conduct electricity 4.43 Rank the following solutions on the basis of their ability to conduct electricity, starting with the most conductive: (a) 1.0 M NaCl; (b) 1.2 M KCl; (c) 1.0 M Na 2SO4; (d) 0.75 M LiCl 4.44 Rank the conductivities of M aqueous solutions of each of the following solutes, starting with the most conductive: (a) acetic acid; (b) methanol; (c) sucrose (table sugar); (d) hydrochloric acid Problems 4.45 Calculate the molarity of Na1 ions in a 0.025 M aqueous solution of: (a) NaBr; (b) Na 2SO4; (c) Na 3PO4 4.46 Calculate the molarity of each ion in a 0.025 M aqueous solution of: (a) KCl; (b) CuSO4; (c) CaCl 4.47 Which of the following solutions has the greatest number of particles (atoms or ions) of solute per liter? (a) M NaCl; (b) M CaCl 2; (c) M ethanol; (d) M acetic acid 4.48 Which of the following solutions contains the most solute particles per liter? (a) M KBr; (b) M Mg(NO3)2; (c) M ethanol; (d) M acetic acid Acid–Base Reactions: Proton Transfer Concept Review 4.49 What name is given to a proton donor? 4.50 What is the difference between a strong acid and a weak acid? 4.51 Identify each compound as either a weak acid or a strong acid in aqueous solution: (a) HNO3; (b) HNO2; (c) CH3CH 2CH 2COOH; (d) H 2SO4 4.52 Why is HSO42(aq) a weaker acid than H 2SO4(aq)? 4.53 What name is given to a proton acceptor? 4.54 What is the difference between a strong base and a weak base? 4.55 Identify each compound as either a weak base or a strong base in aqueous solution: (a) Ca(OH)2; (b) NH3; (c) CH3CH 2NH 2; (d) NaOH 4.56 Write the net ionic equation for the neutralization of a strong acid by a strong base Problems 4.57 For each of the following acid–base reactions, identify the acid and the base, and then write the overall ionic and net ionic equations a H 2SO4(aq) Ca(OH)2(aq) S CaSO4(s) H 2O(/) b PbCO3(s) H 2SO4(aq) S PbSO4(s) CO2(g) H 2O(/) c Ca(OH)2(s) CH3COOH(aq) S Ca(CH3COO)2(aq) H 2O(aq) 4.58 Complete and balance each of the following neutralization reactions, name the products, and write the overall ionic and net ionic equations a HBr(aq) KOH(aq) S b H3PO4(aq) Ba(OH)2(aq) S c Al(OH)3(s) HCl(aq) S d CH3COOH(aq) Sr(OH)2(aq) S 4.59 Write a balanced molecular equation and a net ionic equation for the following reactions: a Solid magnesium hydroxide reacts with a solution of sulfuric acid b Solid magnesium carbonate reacts with a solution of hydrochloric acid c Ammonia gas reacts with hydrogen chloride gas d Gaseous sulfur trioxide is dissolved in water and reacts with a solution of sodium hydroxide 4.60 Write a balanced molecular equation and a net ionic equation for the following reactions: a Solid aluminum hydroxide reacts with a solution of hydrobromic acid b A solution of sulfuric acid reacts with solid sodium carbonate c A solution of calcium hydroxide reacts with a solution of nitric acid d Solid potassium oxide is dissolved in water and reacts with a solution of sulfuric acid 4.61 Toxicity of Lead Pigments The use of lead(II) carbonate and lead(II) hydroxide as white pigments in paint was discontinued because children have been known to eat paint chips The pigments dissolve in stomach acid, and lead ions enter the nervous system and interfere with neurotransmissions in the brain, causing neurological disorders Using net ionic equations, show why lead(II) carbonate and lead(II) hydroxide dissolve in acidic solutions 4.62 Lawn Care Many homeowners treat their lawns with CaCO3(s) to reduce the acidity of the soil Write a net ionic equation for the reaction of CaCO3(s) with a strong acid Questions and Problems 201 Titrations Problems 4.63 How many milliliters of 0.250 M NaOH are required to neutralize the following solutions? a 60.0 mL of 0.0750 M HCl b 35.0 mL of 0.226 M HNO3 c 75.0 mL of 0.190 M H 2SO4 4.64 How many milliliters of 0.250 M HNO3 are needed to neutralize the following solutions? a 25.0 mL of 0.395 M KOH b 78.6 mL of 0.0100 M Al(OH)3 c 65.9 mL of 0.475 M NaOH *4.65 The solubility of slaked lime, Ca(OH)2, in water at 20°C is 0.185 g/100.0 mL What volume of 0.00100 M HCl is needed to neutralize 10.0 mL of a saturated Ca(OH)2 solution? *4.66 The solubility of magnesium hydroxide, Mg(OH)2, in water is 9.0 1024 g/100.0 mL What volume of 0.00100 M HNO3 is required to neutralize 1.00 L of saturated Mg(OH)2 solution? 4.67 A 10.0 mL dose of the antacid in Figure P4.67 contains 830 mg of magnesium hydroxide What volume of 0.10 M stomach acid (HCl) could one dose neutralize? 4.70 What are common solubility units? 4.71 An aqueous solution containing Ca 21, Cl2, CO322, and NO32 is allowed to evaporate Which compound will precipitate first? 4.72 A precipitate may appear when two completely clear aqueous solutions are mixed What circumstances are responsible for this event? 4.73 Is a saturated solution always a concentrated solution? Explain 4.74 Behavior of Honey Honey is a concentrated solution of sugar molecules in water Clear, viscous honey becomes cloudy after being stored for long periods Explain how this transition illustrates supersaturation Problems 4.75 According to the solubility rules in Table 4.4 and Table 4.5, which of the following compounds have limited solubility in water? (a) barium sulfate; (b) barium hydroxide; (c) lanthanum nitrate; (d) sodium acetate; (e) lead hydroxide; (f) calcium phosphate 4.76 Ocean Vents The black “smoke” that flows out of deep ocean hydrothermal vents (Figure P4.76) is made of insoluble metal sulfides suspended in seawater Of the following cations that are present in the water flowing up through these vents, which ones could contribute to the formation of the black smoke? Na1, Li1, Mn 21, Fe21, Ca 21, Mg21, Zn 21, Pb21, Cu 21 FIGURE P4.67 *4.68 Exercise Physiology The ache, or “burn,” you feel in your muscles during strenuous exercise is related to the accumulation of lactic acid, which has the structure shown in Figure P4.68 Only the hydrogen atom in the 2COOH group is acidic, that is, can be released as an H1 ion in aqueous solutions To determine the concentration of a solution of lactic acid, a chemist titrates a 20.00 mL sample of it with 0.1010 M NaOH and finds that 12.77 mL of titrant is required to reach the equivalence point What is the concentration of the lactic acid solution in moles per liter? O H H C H C H H C O H O FIGURE P4.68 Precipitation Reactions Concept Review 4.69 What is the difference between a saturated solution and a supersaturated solution? FIGURE P4.76 4.77 Complete and balance the molecular equations for the precipitation reactions, if any, between the following pairs of reactants, and write the overall and net ionic equations a Pb(NO3)2(aq) Na 2SO4(aq) S b NiCl 2(aq) NH4NO3(aq) S c FeCl 2(aq) Na 2S(aq) S d MgSO4(aq) BaCl 2(aq) S *4.78 Wastewater Treatment Show with appropriate net ionic equations how Cr31 and Cd 21 can be removed from wastewater by treatment with solutions of sodium hydroxide 4.79 Calculate the mass of MgCO3 precipitated by mixing 10.0 mL of a 0.200 M Na 2CO3 solution with 5.00 mL of 0.0500 M Mg(NO3)2 solution 4.80 Toxic chromate can be precipitated from an aqueous solution by bubbling SO2 through the solution How 202 c h a p t e r Reactions in Solution many grams of SO2 are required to treat 3.0 108 L of 0.050 mM CrO42? CrO422(aq) SO2(g) H1(aq) S Cr2(SO4)3(s) H 2O(/) 4.81 Iron(II) can be precipitated from a slightly basic aqueous solution by bubbling oxygen through the solution, which converts soluble Fe(OH)1 to insoluble Fe(OH)3 How many grams of O2 are consumed to precipitate all of the iron in 75 mL of 0.090 M iron(II)? Fe(OH)1(aq) OH2(aq) O2(g) H 2O(/) S Fe(OH)3(s) 4.82 Given the following equation, how many grams of PbCO3 will dissolve when 1.00 L of 1.00 M H1 is added to 5.00 g of PbCO3? PbCO3(s) H1(aq) S Pb21(aq) H 2O(/) CO2(g) *4.83 Treating Drinking Water Phosphate can be removed from drinking-water supplies by treating the water with Ca(OH)2 How much Ca(OH)2 is required to remove 90% of the PO432 from 4.5 106 L of drinking water containing 25 mg/L of PO432? Ca(OH)2(aq) PO432(aq) S Ca 5OH(PO4)3(s) OH2(aq) 4.84 Toxic cyanide ions can be removed from wastewater by adding hypochlorite CN2(aq) OCl2(aq) H 2O(/) S N2(g) HCO32(aq) Cl2(aq) a If 1.50 103 L of 0.125 M OCl2 are required to remove the CN2 in 3.4 106 L of wastewater, what is the CN2 concentration in the water in mg/L? * b How many milliliters of 0.575 M AgNO3 would you need to add to a 50.00 mL aliquot of the final solution (consider the volumes simply additive) to precipitate the chloride ions formed in the reaction? 4.85 For each of the following aqueous mixtures, determine which ionic concentrations decrease and which remain the same a Sodium chloride and silver nitrate are dissolved in 100 mL of water b Equimolar amounts of sodium hydroxide and hydrochloric acid react c Ammonium sulfate and potassium bromide are dissolved in 100 mL of water 4.86 For each of the following aqueous mixtures, determine which ionic concentrations decrease and which remain the same a Sodium chloride and iron(II) chloride are dissolved in 100 mL of water b Equimolar amounts of sodium carbonate and sulfuric acid react c Potassium sulfate and barium nitrate are dissolved in 100 mL of water Ion Exchange Concept Review 4.87 Explain how a mixture of anion and cation exchangers can be used to deionize water 4.88 Describe the process by which the ion exchanger in a home water softener is regenerated for further use 4.89 (a) Use the solubility rules to write the balanced net ionic equation for each of the following “molecular” reactions If there is no net reaction, write “NR.” (b) Which of these three reactions give clear visual evidence of the ion exchange process? NaCl(aq) AgNO3(aq) S AgCl(s) NaNO3(aq) NaCl(aq) KNO3(aq) S NaNO3(aq) KCl(aq) MgCl 2(aq) KOH(aq) S Mg(OH)2(s) KCl(aq) 4.90 (a) Use the solubility rules to write the balanced net ionic equation for each of the following “molecular” reactions If there is no net reaction, write “NR.” (b) Which of these three reactions give clear visual evidence of the ion exchange process? BaCl 2(aq) Na 2CO3(aq) S BaCO3(s) NaCl(aq) NaCl(aq) KOH(aq) S NaOH(aq) KCl(aq) Na 3PO4(aq) CaCl 2(aq) S Ca 3(PO4)2(s) NaCl(aq) Oxidation–Reduction Reactions: Electron Transfer Concept Review 4.91 How are the gains or losses of electrons related to changes in oxidation numbers? 4.92 What is the sum of the oxidation numbers of the atoms in a molecule? 4.93 What is the sum of the oxidation numbers of all the atoms in each of the following polyatomic ions? (a) OH2; (b) NH41; (c) SO422; (d) PO432 4.94 Gold does not dissolve in concentrated H 2SO4 but readily dissolves in H 2SeO4 (selenic acid) Which acid is the stronger oxidizing agent? 4.95 Silver dissolves in sulfuric acid to form silver sulfate and H 2, but gold does not dissolve in sulfuric acid to form gold sulfate Which of the two metals is the better reducing agent? 4.96 What is meant by a half-reaction? 4.97 What are the half-reactions that take place in the electrolysis of molten NaCl? 4.98 Electron gain is associated with half-reactions, and electron loss is associated with half-reactions Problems 4.99 Give the oxidation number of boron in each of the following: (a) HBO2 (metaboric acid); (b) H3BO3 (boric acid); (c) Na 2B4O7 (sodium borate) 4.100 Give the oxidation number of nitrogen in each of the following: (a) elemental nitrogen (N2); (b) hydrazine (N2H4); (c) ammonium ion (NH41) Questions and Problems 203 101 Balance the following half-reactions by adding the appropriate number of electrons Identify the oxidation half-reactions and the reduction half-reactions a Br2(/) S Br2(aq) b Pb(s) Cl2(aq) S PbCl 2(s) c O3(g) H1(aq) S O2(g) H 2O(/) d H 2SO3(aq) H1(aq) S HS2O42(aq) H 2O(/) 4.102 Balance the following half-reactions by adding the appropriate number of electrons Which are oxidation half-reactions and which are reduction half-reactions? a Fe21(aq) S Fe31(aq) b AgI(s) S Ag(s) I2(aq) c VO21(aq) H1(aq) S VO21(aq) H 2O(/) d I 2(s) H 2O(/) S IO32(aq) 12 H1(aq) 103 Balance the following net ionic reactions, and identify which elements are oxidized and which are reduced: a MnO2(s) HCl(aq) S Mn 21(aq) Cl 2(g) b I 2(s) S2O322(aq) S S4O622(aq) I2(aq) c MnO42(aq) Fe21(aq) S Mn 21(aq) Fe31(aq) 4.104 Balance the following net ionic reactions, and identify which elements are oxidized and which are reduced: a MnO42(aq) S22(aq) S MnO2(s) S(s) b IO32(aq) I2(aq) S I 2(s) c Mn 21(aq) BiO32(aq) S MnO42(aq) Bi31(aq) 105 Earth’s Crust The following chemical reactions have helped to shape Earth’s crust Determine the oxidation numbers of all the elements in the reactants and products, and identify which elements are oxidized and which are reduced a SiO2(s) Fe3O4(s) S Fe2SiO4(s) O2(g) b SiO2(s) Fe(s) O2(g) S Fe2SiO4(s) c FeO(s) O2(g) H 2O(/) S Fe(OH)3(s) 4.106 Determine the oxidation numbers of each of the elements in the following reactions, and identify which of them are oxidized or reduced, if any a SiO2(s) H 2O(/) S H4SiO4(aq) b MnCO3(s) O2(g) S MnO2(s) CO2(g) c NO2(g) H 2O(/) S NO32(aq) NO(g) H1(aq) 4.107 Combine the half-reaction for the reduction of O2 O2(aq) H1(aq) e2 S H 2O(/) with the following oxidation half-reactions (which are based on common iron minerals) to develop complete redox reactions: a FeCO3(s) H 2O(/) S Fe2O3(s) CO2(g) H1(aq) e2 b FeCO3(s) H 2O(/) S Fe3O4(s) CO2(g) H1(aq) e2 c Fe3O4(s) H 2O(/) S Fe2O3(s) H1(aq) e2 4.108 Uranium is found in Earth’s crust as UO2 and an assortment of compounds containing UO2n1 cations Add the following pairs of reduction and oxidation equations to develop overall equations for converting soluble uranium polyatomic ions into insoluble UO2 a H1(aq) UO2(CO3)342(aq) e2 S UO2(s) CO2(g) H 2O(/) Fe21(aq) H 2O(/) S Fe(OH)3(s) H1(aq) e2 b H1(aq) UO2(CO3)342(aq) e2 S UO2(s) CO2(g) H 2O(/) HS2(aq) H 2O(/) S SO422(aq) H1(aq) e2 c e2 UO2(HPO4)222(aq) S UO2(s) HPO422(aq) OH2(aq) S H 2O(/) HO22(aq) e2 109 Nitrogen in the hydrosphere is found primarily as ammonium ions and nitrate ions Complete and balance the following chemical equation describing the oxidation of ammonium ions to nitrate ions in acid solution: NH41(aq) O2(g) S NO32(aq) 4.110 When Soil Smells Bad In sediments and waterlogged soil, dissolved O2 concentrations are so low that the microorganisms living there must rely on other sources of oxygen for respiration Some bacteria can extract the oxygen from sulfate ions, reducing the sulfur in them to hydrogen sulfide gas and giving the sediments or soil a distinctive rotten-egg odor a What is the change in oxidation state of sulfur as a result of this reaction? b Write the balanced net ionic equation for the reaction, under acidic conditions, that releases O2 from sulfate and forms hydrogen sulfide gas 111 Chromium is more toxic and more soluble in natural waters as HCrO42 than as chromium(III) ion In the presence of H 2S, the following reaction takes place in neutral solution: HCrO42(aq) H 2S(aq) S Cr2O3(s) SO422 a Assign oxidation numbers to the reactants and products b Balance the equation c How many electrons are transferred for each atom of chromium that reacts? 4.112 The water-soluble uranyl cation, UO21, can be removed by reaction with methane gas: UO21(aq) CH4(g) S UO2(s) HCO32(aq) a Assign oxidation numbers to the reactants and products b Balance the equation in acidic solution c How many electrons are transferred for each atom of uranium that reacts? 113 The solubilities of Fe and Mn in freshwater streams are affected by changes in their oxidation states Complete and balance the following redox equation in which soluble Mn 21 becomes solid MnO2: Fe(OH)21(aq) Mn 21(aq) S MnO2(s) Fe21(aq) 204 c h a p t e r Reactions in Solution 4.114 Bactericide and Virucide The water-soluble gas ClO2 is known as an oxidative biocide It destroys bacteria by oxidizing their cell walls and destroys viruses by attacking their viral envelopes ClO2 may be prepared for use as a decontaminating agent from several different starting materials in slightly acidic solutions Complete and balance the following chemical equations for the synthesis of ClO2 a ClO32(aq) SO2(g) S ClO2(g) SO422(aq) b ClO32(aq) Cl2(aq) S ClO2(g) Cl 2(g) c ClO32(aq) Cl 2(g) S ClO2(g) O2(g) 4.115 Refer to Table 4.6 to determine which of the following metals will reduce aqueous Fe21 to iron metal: lead, copper, zinc, or aluminum 4.116 Which ions will oxidize aluminum? Li1; Ca 21; Ag1; Sn 21 4.117 Through appropriate experiments, we could expand the activity series in Table 4.6 to include additional metals If aluminum is oxidized by V31 but aluminum does not reduce Sc 31, where would you place vanadium and scandium in the activity series? Which metal would you test to firmly establish scandium’s position? 4.118 If iron is oxidized by Cd 21 but iron does not reduce Ga 31, where would you place cadmium and gallium in the activity series? Which metal would you test to firmly establish gallium’s position? 4.119 Dichromate ion oxidizes Fe21 ion in aqueous, acidic solution, producing Fe31 and Cr31 by the unbalanced chemical equation: Cr2O722(aq) Fe21(aq) S Fe31 Cr31 a Balance the equation b If 15.2 mL of 0.135 M Cr2O722 is required to completely react with 100.0 mL of Fe21, what is the concentration of the Fe21 solution? *4.120 Ozone, O3, reacts with iodide ion (I2) in basic solution to form O2 and I by the unbalanced chemical equation: O3(aq) I2(aq) S O2(g) I 2(aq) a Balance the equation b A saturated solution of ozone in 125 mL of water at 0°C is treated with 10 mL of 2.0 M KI After the reaction is complete, the solution is titrated with 0.100 M H1 If 54.7 mL of acid is needed, what is the concentration of O3 in a saturated solution? Additional Problems 4.121 A puddle of coastal seawater, caught in a depression formed by some coastal rocks at high tide, begins to evaporate on a hot summer day as the tide goes out If the volume of the puddle decreases to 23% of its initial volume, what is the concentration of Na1 after evaporation if initially it was 0.449 M? 4.122 Antifreeze Ethylene glycol is the common name for the liquid used to keep the coolant in automobile cooling systems from freezing It is 38.7% carbon, 9.7% hydrogen, and 51.6% oxygen by mass Its molar mass is 62.07 g/mol, and its density is 1.106 g/mL at 20°C a What is the empirical formula of ethylene glycol? b What is the molecular formula of ethylene glycol? c In a solution prepared by mixing equal volumes of water and ethylene glycol, which ingredient is the solute and which is the solvent? 4.123 According to the label on a bottle of concentrated hydrochloric acid, the contents are 36.0% HCl by mass and have a density of 1.18 g/mL a What is the molarity of concentrated HCl? b What volume of it would you need to prepare 0.250 L of 2.00 M HCl? c What mass of sodium hydrogen carbonate would be needed to neutralize the spill if a bottle containing 1.75 L of concentrated HCl dropped on a lab floor and broke open? 4.124 Synthesis and Toxicity of Chlorine Chlorine was first prepared in 1774 by heating a mixture of NaCl and MnO2 in sulfuric acid: NaCl(aq) H 2SO4(aq) MnO2(s) S Na 2SO4(aq) MnCl 2(aq) H 2O(/) Cl 2(g) a Assign oxidation numbers to the elements in each compound, and balance the redox reaction in acid solution b Write a net ionic equation describing the reaction for formation of chlorine c If chlorine gas is inhaled, it causes pulmonary edema (fluid in the lungs) because it reacts with water in the alveolar sacs of the lungs to produce the strong acid HCl and the weaker acid HOCl Balance the equation for the conversion of Cl to HCl and HOCl *4.125 When a solution of dithionate ions (S2O422) is added to a solution of chromate ions (CrO422), the products of the reaction under basic conditions include soluble sulfite ions and solid chromium(III) hydroxide This reaction is used to remove chromium(VI) from wastewater generated by factories that make chrome-plated metals a Write the net ionic equation for this redox reaction b Which element is oxidized and which is reduced? c Identify the oxidizing and reducing agents in this reaction d How many grams of sodium dithionate would be needed to remove the chromium(VI) in 100.0 L of wastewater that contains 0.00148 M chromate ion? 4.126 An Iron Battery A prototype battery based on iron compounds with large, positive oxidation numbers was developed in 1999 In the following reactions, assign oxidation numbers to the elements in each compound, and balance the redox reactions in basic solution a FeO422(aq) H 2O(/) S FeOOH(s) O2(g) OH2(aq) b FeO422(aq) H 2O(/) S Fe2O3(s) O2(g) OH2(aq) 4.127 Polishing Silver Silver tarnish is the result of silver metal reacting with sulfur compounds, such as H 2S, in the air The tarnish on silverware (Ag2S) can be removed by soaking in a solution of NaHCO3 (baking soda) in a basin lined with aluminum foil Questions and Problems 205 a Write a balanced equation for the tarnishing of Ag to Ag2S, and assign oxidation numbers to the reactants and products How many electrons are transferred per mole of silver? b Write a balanced equation for the reaction of Ag2S with Al metal, NaHCO3, and water to produce Al(OH)3, H 2S, H 2, and Ag metal 4.128 Many nonmetal oxides react with water to form acidic solutions Give the formula and name for the acids produced from the following reactions: a P4O10 H 2O S b SeO2 H 2O S c B2O3 H 2O S 4.129 Write overall and net ionic equations for the reactions that occur when a a sample of acetic acid is titrated with a solution of KOH b a solution of sodium carbonate is mixed with a solution of calcium chloride c calcium oxide dissolves in water *4.130 Fluoride Ion in Drinking Water Sodium fluoride is added to drinking water in many municipalities to protect teeth against cavities The target of the fluoridation is hydroxyapatite, Ca10(PO4)6(OH)2, a compound in tooth enamel There is concern, however, that fluoride ions in water may contribute to skeletal fluorosis, an arthritis-like disease a Write a net ionic equation for the reaction between hydroxyapatite and sodium fluoride that produces fluorapatite, Ca10(PO4)6F b The EPA currently restricts the concentration of F 2 in drinking water to mg/L Express this concentration of F 2 in molarity c One study of skeletal fluorosis suggests that drinking water with a fluoride concentration of mg/L for 20 years raises the fluoride content in bone to 6 mg/g, a level at which a patient may experience stiff joints and other symptoms How much fluoride (in milligrams) is present in a 100 mg sample of bone with this fluoride concentration? *4.131 Rocket Fuel in Drinking Water Near Las Vegas, NV, improper disposal of perchlorates used to manufacture rocket fuel has contaminated a stream that flows into Lake Mead, the largest artificial lake in the United States and a major supply of drinking and irrigation water for the American Southwest The EPA has proposed an advisory range for perchlorate concentrations in drinking water of to 18 μg/L The perchlorate concentration in the stream averages 700.0 μg/L, and the stream flows at an average rate of 161 million gallons per day (1 gal 3.785 L) a What are the formulas of sodium perchlorate and ammonium perchlorate? b How many kilograms of perchlorate flow from the Las Vegas stream into Lake Mead each day? c What volume of perchlorate-free lake water would have to mix with the stream water each day to dilute the stream’s perchlorate concentration from 700.0 to 4 μg/L? d Since 2003, Maryland, Massachusetts, and New Mexico have limited perchlorate concentrations in drinking water to 0.1 μg/L Five replicate samples were analyzed for perchlorates by laboratories in each state, and the following data (μg/L) were collected: MD MA NM 1.1 0.90 1.2 1.1 0.95 1.2 1.4 0.92 1.3 1.3 0.90 1.4 0.9 0.93 1.1 Which of the labs produced the most precise analytical results? *4.132 Acidic Mine Drainage Water draining from abandoned mines on Iron Mountain in California is extremely acidic and leaches iron, zinc, and other metals from the underlying rock (Figure P4.132) One liter of drainage contains as much as 80.0 g of dissolved iron and g of zinc a Calculate the molarity of iron and of zinc in the drainage b One source of the dissolved iron is the reaction between water containing H 2SO4 and solid Fe(OH)3 Complete the following chemical equation, and write a net ionic equation for the process Fe(OH)3(s) H 2SO4(aq) S c Sources of zinc include the mineral smithsonite, ZnCO3 Write a balanced net ionic equation for the reaction between smithsonite and H 2SO4 that produces Zn 21(aq) d One member of a class of minerals called ferrites is found to contain a mixture of zinc(II), iron(II), and iron(III) oxides The generic formula for the mineral is ZnxFe12xO ∙ Fe2O3 If acidic mine waste flowing through a deposit of this mineral contains 80 g of Fe and g of Zn as a result of dissolution of the mineral, what is the value of x in the formula of the mineral in the deposit? FIGURE P4.132 H Ethanol CH3 CH2 OH (a) H H C C O H H Acetic acid CH3 COOH (b) FIGURE P4.133 a Write a balanced chemical equation describing the fermentation of natural sugars to ethanol and carbon dioxide You may use the empirical formula given in the above paragraph b Write a balanced chemical equation describing the acid fermentation of ethanol to acetic acid c What are the oxidation states of carbon in the reactants and products of the two fermentation reactions? d If a sample of apple juice contains 1.00 102 g of natural sugar, what is the maximum quantity of acetic acid that could be produced by the two fermentation reactions? *4.134 A food chemist determines the concentration of acetic acid in a sample of apple cider vinegar (see Problem 4.133) by acid–base titration The density of the sample is 1.01 g/mL The titrant is 1.002 M NaOH The average volume of titrant required to titrate 25.00 mL aliquots of the vinegar is 20.78 mL What is the concentration of acetic acid in the vinegar? Express your answer the way a food chemist probably would: as percent by mass *4.135 One way to follow the progress of a titration and detect its equivalence point is by monitoring the conductivity of the titration reaction mixture For example, consider the way the conductivity of a sample of sulfuric acid changes as it is titrated with a standard solution of barium hydroxide before and then after the equivalence point a Write the overall ionic equation for the titration reaction b Which of the four graphs in Figure P4.135 comes closest to representing the changes in conductivity during the titration? (The zero point on the y-axis of these graphs represents the conductivity of pure water; the break points on the x-axis represent the equivalence point.) (c) Conductivity (b) Ba(OH)2 (mL) Conductivity H Ba(OH)2 (mL) FIGURE P4.135 (d) Ba(OH)2 (mL) *4.136 Which of the graphs in Figure P4.136 best represents the changes in conductivity that occur before and after the equivalence point in each of the following titrations: a sample, AgNO3(aq); titrant, KCl(aq) b sample, HCl(aq); titrant, LiOH(aq) c sample, CH3COOH(aq); titrant, NaOH(aq) (a) Conductivity O Titrant (mL) (c) 0 (b) Titrant (mL) Conductivity C O (a) Ba(OH)2 (mL) Conductivity H C H Conductivity H H Conductivity *4.133 Making Apple Cider Vinegar Some people who prefer natural foods make their own apple cider vinegar They start with freshly squeezed apple juice that contains about 6% natural sugars These sugars, which all have nearly the same empirical formula, CH 2O, are fermented with yeast in a chemical reaction that produces equal numbers of moles of ethanol (Figure P4.133a) and carbon dioxide The product of this fermentation, called hard cider, undergoes an acid fermentation step in which ethanol and dissolved oxygen gas react to form acetic acid (Figure P4.133b) and water This acetic acid is the principal solute in vinegar Conductivity 206 c h a p t e r Reactions in Solution Titrant (mL) FIGURE P4.136 (d) Titrant (mL) 4.137 When electrodes connected to a lightbulb are inserted into an aqueous solution of acetic acid, the bulb glows dimly Will the bulb become brighter, remain the same, or turn off after one equivalent of aqueous NaOH is added to the solution? Write a balanced net ionic equation that supports your answer *4.138 When electrodes connected to a lightbulb are inserted into a beaker containing silver carbonate and water, will the bulb not glow, glow dimly, or glow brightly? What you think will happen after addition of one equivalent of Questions and Problems 207 aqueous HCl? Write a balanced net ionic equation that supports your answer 4.139 Superoxide Dismutases Oxygen in the form of superoxide ions, O22, is quite hazardous to human health Superoxide dismutases represent a class of enzymes that convert superoxide ions to hydrogen peroxide and oxygen by the unbalanced chemical equation: O22(aq) H (aq) S H 2O2(aq) O2(aq) a Identify the oxidation and reduction half-reactions b Balance the equation 4.140 Nitrogen-Fixing Bacteria Bacteria found among the roots of legumes perform an important biological function, converting nitrogen to ammonia in a process known as nitrogen fixation The electrons required for this redox reaction are supplied by transition metal–containing enzymes called nitrogenases The unbalanced chemical equation for this process is N2(g) H1(aq) M 21(aq) S NH3(aq) H 2(g) M31(aq) where M represents a transition metal such as iron Nitrification is a multistep process in which the nitrogen in organic and inorganic compounds is biochemically oxidized Bacteria and fungi are responsible for a part of the nitrification process described by the reaction: NH41(aq) M31(aq) S NO22(aq) M 21(aq) a What are the oxidation numbers of nitrogen in the reactants and products of each reaction? b Which compounds or ions are being reduced in each reaction? c Balance the equations in acidic solution 4.141 Rocks in Caves The stalactites and stalagmites in most caves are made of limestone (calcium carbonate; see Figure 4.14) However, in the Lower Kane Cave in Wyoming they are made of gypsum (calcium sulfate) The presence of CaSO4 is explained by the following sequence of reactions: H 2S(aq) O2(g) S H 2SO4(aq) H 2SO4(aq) CaCO3(s) S CaSO4(s) H 2O(/) CO2(g) a Which (if either) of these reactions is a redox reaction? How many electrons are transferred? b Write a net ionic equation for the reaction of H 2SO4 with CaCO3 c How would the net ionic equation be different if the reaction were written as follows? H 2SO4(aq) CaCO3(s) S CaSO4(s) H 2CO3(aq) 4.142 Balance this net ionic reaction and answer the questions that follow: BrO32(aq) Br2(aq) S Br2(aq) a Is BrO32(aq) reduced? b What is the product of BrO32(aq) reduction in this reaction? c Is Br2(aq) oxidized? d What is the product of Br2(aq) oxidation in this reaction? 4.143 Which of the following reactions of calcium compounds is/ are redox reactions? a CaCO3(s) S CaO(s) CO2(g) b CaO(s) SO2(g) S CaSO3(s) c CaCl 2(s) S Ca(s) Cl 2(g) d Ca(s) N2(g) S Ca 3N2(s) 4.144 Preparation of Fluorine Gas HF is prepared by reacting CaF with H 2SO4: CaF 2(s) H 2SO4(/) S HF(g) CaSO4(s) HF can in turn be electrolyzed when dissolved in molten KF to produce fluorine gas: HF(/) S F 2(g) H 2(g) Fluorine is extremely reactive, so it is typically sold as a 5% mixture by volume in an inert gas such as helium How much CaF is required to produce 500.0 L of 5% F in helium? Assume the density of F gas is 1.70 g/L *4.145 A piece of Zn metal is placed in a solution containing Cu 21 ions At the surface of the Zn metal, Cu 21 ions react with Zn atoms, forming Cu atoms and Zn 21 ions Is this reaction an example of ion exchange? Explain why or why not TUV If your instructor uses Smartwork5, log in at digital.wwnorton.com/chem5 ... within Smartwork5 Clickers in Action: Increasing Student Participation in General Chemistry by Margaret Asirvatham, University of Colorado, Boulder An instructor-oriented resource providing information... pond when the temperature drops in the winter and the water freezes This process is reversed when warmer temperatures return in the spring and the ice melts The heat of the sun may vaporize liquid... Thomas Sorensen, and David Winters for checking the accuracy of the myriad facts that form the framework of our science Thomas R Gilbert Rein V Kirss Natalie Foster Stacey Lowery Bretz Geoffrey