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`[“The Experiment” by Sempé. Copyright C. Charillon, Paris.]
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`[“The Experiment” by Sempé. Copyright C. Charillon, Paris.]
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`

`Exploring
`Chemical Analysis
`
`Fourth Edition
`
`Daniel C. Harris
`Michelson Laboratory
`China Lake, California
`
`W. H. Freeman and Company
`New York
`
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`

`Publisher: Clancy Marshall
`Senior Acquisitions Editor: Jessica Fiorillo
`Executive Marketing Manager: Mark Santee
`Media Editor: Samantha Calamari
`Supplements Editor: Kathryn Treadway
`Senior Project Editor: Georgia Lee Hadler
`Manuscript Editor: Jodi Simpson
`Design Manager: Diana Blume
`Illustration Coordinator: Susan Timmins
`Illustrations: Network Graphics
`Photo Editor: Ted Szczepanski
`Production Coordinator: Susan Wein
`Composition: Aptara, Inc.
`Printing and Binding: RR Donnelly
`
`Library of Congress Control Number: 2008922928
`
`© 2009 by W. H. Freeman and Company
`All rights reserved.
`
`ISBN-13: 978-1-4292-0147-6
`ISBN-10: 1-4292-0147-9
`
`Printed in the United States of America
`First printing
`
`W. H. Freeman and Company
`41 Madison Avenue
`New York, NY 10010
`Houndmills, Basingstoke RG21 6XS, England
`
`www.whfreeman.com
`
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`

`Contents
`
`Preface
`
`CHAPTER 0 The Analytical Process
`Cocaine Use? Ask the River
`0-1 The Analytical Chemist’s Job
`Box 0-1 Constructing a Representative Sample
`0-2 General Steps in a Chemical Analysis
`0-3 Charles David Keeling and the
`Measurement of Atmospheric CO2
`
`CHAPTER 1 Chemical Measurements
`Biochemical Measurements with a
`Nanoelectrode
`1-1 SI Units and Prefixes
`Box 1-1 Exocytosis of Neurotransmitters
`1-2 Conversion Between Units
`1-3 Chemical Concentrations
`1-4 Preparing Solutions
`1-5 The Equilibrium Constant
`
`CHAPTER 2 Tools of the Trade
`A Quartz-Crystal Sensor with
`an Imprinted Layer for Yeast Cells
`2-1 Safety, Waste Disposal, and Green
`Chemistry
`2-2 Your Lab Notebook
`Box 2-1 Dan’s Lab Notebook Entry
`2-3 The Analytical Balance
`2-4 Burets
`2-5 Volumetric Flasks
`2-6 Pipets and Syringes
`2-7 Filtration
`2-8 Drying
`2-9 Calibration of Volumetric Glassware
`2-10 Methods of Sample Preparation
`Reference Procedure: Calibrating a 50-mL Buret
`
`CHAPTER 3 Math Toolkit
`Experimental Error
`3-1 Significant Figures
`
`xi
`
`0
`1
`8
`9
`
`10
`
`18
`19
`22
`23
`25
`29
`33
`
`40
`
`41
`42
`43
`43
`46
`48
`50
`52
`53
`54
`54
`57
`
`60
`61
`
`3-2 Significant Figures in Arithmetic
`3-3 Types of Error
`Box 3-1 What Are Standard Reference Materials?
`Box 3-2 Case Study: Systematic Error in Ozone
`Measurement
`3-4 Propagation of Uncertainty
`3-5 Introducing Spreadsheets
`3-6 Graphing in Excel
`
`62
`65
`66
`
`67
`69
`74
`77
`
`CHAPTER 4 Statistics
`Is My Red Blood Cell Count High Today? 82
`4-1 The Gaussian Distribution
`83
`4-2 Student’s t
`86
`Box 4-1 Analytical Chemistry and the Law
`88
`4-3 A Spreadsheet for the t Test
`90
`4-4 Grubbs Test for an Outlier
`92
`4-5 Finding the “Best” Straight Line
`93
`4-6 Constructing a Calibration Curve
`96
`4-7 A Spreadsheet for Least Squares
`98
`
`CHAPTER 5 Quality Assurance and Calibration
`Methods
`The Need for Quality Assurance
`5-1 Basics of Quality Assurance
`Box 5-1 Control Charts
`5-2 Validation of an Analytical Procedure
`5-3 Standard Addition
`5-4 Internal Standards
`
`CHAPTER 6 Good Titrations
`The Earliest Known Buret
`6-1 Principles of Volumetric Analysis
`6-2 Titration Calculations
`6-3 Chemistry in a Fishtank
`Box 6-1 Studying a Marine Ecosystem
`6-4 Solubility Product
`Box 6-2 The Logic of Approximations
`6-5 Titration of a Mixture
`6-6 Titrations Involving Silver Ion
`Demonstration 6-1 Fajans Titration
`
`106
`107
`111
`112
`115
`119
`
`126
`127
`130
`132
`134
`136
`138
`140
`142
`144
`
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`vi
`
`Contents
`
`150
`151
`153
`154
`156
`160
`164
`
`CHAPTER 7 Gravimetric and Combustion
`Analysis
`The Geologic Time Scale and
`Gravimetric Analysis
`7-1 Examples of Gravimetric Analysis
`7-2 Precipitation
`Box 7-1 Shorthand for Organic Structures
`Demonstration 7-1 Colloids and Dialysis
`7-3 Examples of Gravimetric Calculations
`7-4 Combustion Analysis
`CHAPTER 8 Introducing Acids and Bases
`Acid Rain
`8-1 What Are Acids and Bases?
`8-2 Relation Between [H⫹], [OH⫺], and pH
`8-3 Strengths of Acids and Bases
`Demonstration 8-1 HCl Fountain
`8-4 pH of Strong Acids and Bases
`8-5 Tools for Dealing with Weak Acids
`and Bases
`8-6 Weak-Acid Equilibrium
`Box 8-1 Quadratic Equations
`Demonstration 8-2 Conductivity of Weak
`Electrolytes
`8-7 Weak-Base Equilibrium
`Box 8-2 Five Will Get You Ten: Crack Cocaine
`CHAPTER 9 Buffers
`Measuring pH Inside Single Cells
`9-1 What You Mix Is What You Get
`9-2 The Henderson-Hasselbalch Equation
`9-3 A Buffer in Action
`Box 9-1 Strong Plus Weak Reacts Completely
`Demonstration 9-1 How Buffers Work
`9-4 Preparing Buffers
`9-5 Buffer Capacity
`9-6 How Acid-Base Indicators Work
`Demonstration 9-2 Indicators and Carbonic Acid
`Box 9-2 The Secret of Carbonless Copy Paper
`CHAPTER 10 Acid-Base Titrations
`Kjeldahl Nitrogen Analysis: Chemistry
`212
`Behind the Headline
`213
`10-1 Titration of Strong Base with Strong Acid
`216
`10-2 Titration of Weak Acid with Strong Base
`220
`10-3 Titration of Weak Base with Strong Acid
`222
`10-4 Finding the End Point
`227
`10-5 Practical Notes
`228
`10-6 Kjeldahl Nitrogen Analysis
`230
`10-7 Putting Your Spreadsheet to Work
`Reference Procedure: Preparing standard acid and base 236
`
`170
`171
`172
`174
`176
`179
`
`181
`182
`184
`
`185
`186
`188
`
`194
`195
`196
`198
`199
`200
`201
`203
`206
`208
`209
`
`CHAPTER 11 Polyprotic Acids and Bases
`Acid Dissolves Buildings and Teeth
`11-1 Amino Acids Are Polyprotic
`11-2 Finding the pH in Diprotic Systems
`Box 11-1 Carbon Dioxide in the Air and Ocean
`11-3 Which Is the Principal Species?
`11-4 Titrations in Polyprotic Systems
`Box 11-2 What is Isoelectric Focusing?
`
`238
`239
`242
`244
`249
`252
`257
`
`CHAPTER 12 A Deeper Look at Chemical
`Equilibrium
`Chemical Equilibrium in the Environment 264
`12-1 The Effect of Ionic Strength on
`Solubility of Salts
`Demonstration 12-1 Effect of Ionic Strength on
`Ion Dissociation
`12-2 Activity Coefficients
`12-3 Charge and Mass Balances
`12-4 Systematic Treatment of Equilibrium
`12-5 Fractional Composition Equations
`Box 12-1 Aluminum Mobilization from Minerals
`by Acid Rain
`
`267
`267
`274
`276
`279
`
`280
`
`265
`
`CHAPTER 13 EDTA Titrations
`Nature’s Ion Channels
`13-1 Metal-Chelate Complexes
`Box 13-1 Chelation Therapy and Thalassemia
`13-2 EDTA
`Box 13-2 Notation for Formation Constants
`13-3 Metal Ion Indicators
`Demonstration 13-1 Metal Ion Indicator
`Color Changes
`13-4 EDTA Titration Techniques
`Box 13-3 What Is Hard Water?
`13-5 The pH-Dependent Metal-EDTA
`Equilibrium
`13-6 EDTA Titration Curves
`
`CHAPTER 14 Electrode Potentials
`Remediation of Underground Pollution
`with Emulsified Iron Nanoparticles
`14-1 Redox Chemistry and Electricity
`14-2 Galvanic Cells
`Demonstration 14-1 Electrochemical Writing
`Demonstration 14-2 The Human Salt Bridge
`14-3 Standard Potentials
`14-4 The Nernst Equation
`14-5 E⬚ and the Equilibrium Constant
`Box 14-1 Why Biochemists Use E⬚⬘
`14-6 Reference Electrodes
`
`286
`287
`289
`290
`291
`293
`
`294
`295
`297
`
`298
`301
`
`308
`309
`312
`313
`314
`316
`319
`324
`326
`327
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`CHAPTER 15 Electrode Measurements
`Measuring Carbonate in Seawater
`with an Ion-Selective Electrode
`15-1 The Silver Indicator Electrode
`Demonstration 15-1 Potentiometry with an
`Oscillating Reaction
`15-2 What Is a Junction Potential?
`15-3 How Ion-Selective Electrodes Work
`15-4 pH Measurement with a Glass Electrode
`Box 15-1 Systematic Error in Rainwater pH
`Measurement: The Effect of Junction
`Potential
`15-5 Ion-Selective Electrodes
`Box 15-2 Ammonium Ion-Selective Microelectrode
`
`CHAPTER 16 Redox Titrations
`High-Temperature Superconductors
`16-1 Theory of Redox Titrations
`Box 16-1 Environmental Carbon Analysis and
`Oxygen Demand
`Demonstration 16-1 Potentiometric Titration of
`Fe2⫹ with MnO4
`⫺
`16-2 Redox Indicators
`16-3 Titrations Involving Iodine
`Box 16-2 Disinfecting Drinking Water with Iodine
`
`CHAPTER 17 Instrumental Methods in
`Electrochemistry
`A Biosensor for Personal Glucose
`Monitoring
`17-1 Electrogravimetric and Coulometric
`Analysis
`17-2 Amperometry
`17-3 Voltammetry
`17-4 Polarography
`
`CHAPTER 18 Let There Be Light
`The Ozone Hole
`18-1 Properties of Light
`18-2 Absorption of Light
`Box 18-1 Discovering Beer’s Law
`Demonstration 18-1 Absorption Spectra
`18-3 Practical Matters
`18-4 Using Beer’s Law
`Box 18-2 Designing a Colorimetric Reagent to
`Detect Phosphate
`
`CHAPTER 19 Spectrophotometry: Instruments
`and Applications
`Flu Virus Identification with an RNA
`Array and Fluorescent Markers
`
`334
`335
`
`338
`339
`341
`343
`
`345
`347
`350
`
`356
`357
`
`358
`
`362
`363
`364
`367
`
`372
`
`373
`376
`381
`383
`
`392
`393
`396
`398
`401
`402
`404
`
`405
`
`414
`
`Contents
`
`19-1 The Spectrophotometer
`19-2 Analysis of a Mixture
`19-3 Spectrophotometric Titrations
`19-4 What Happens When a Molecule
`Absorbs Light?
`Demonstration 19-1 In Which Your Class
`Really Shines
`19-5 Luminescence in Analytical Chemistry
`Box 19-1 Immunoassays in Environmental Analysis
`
`CHAPTER 20 Atomic Spectroscopy
`Historical Record of Mercury in the
`Snow Pack
`20-1 What Is Atomic Spectroscopy?
`20-2 Atomization: Flames, Furnaces,
`and Plasmas
`20-3 How Temperature Affects Atomic
`Spectroscopy
`20-4 Instrumentation
`20-5 Interference
`20-6 Inductively Coupled Plasma–Mass
`Spectrometry
`
`CHAPTER 21 Principles of Chromatography
`and Mass Spectrometry
`Katia and Dante
`21-1 What Is Chromatography?
`21-2 How We Describe a Chromatogram
`21-3 Why Do Bands Spread?
`Box 21-1 Polarity
`21-4 Mass Spectrometry
`Box 21-2 Volatile Flavor Components of Candy
`21-5 Information in a Mass Spectrum
`
`vii
`
`415
`421
`424
`
`425
`
`428
`430
`434
`
`440
`441
`
`442
`
`447
`448
`451
`
`453
`
`458
`459
`461
`465
`468
`469
`472
`473
`
`CHAPTER 22 Gas and Liquid Chromatography
`480
`Protein Electrospray
`481
`22-1 Gas Chromatography
`491
`22-2 Classical Liquid Chromatography
`22-3 High-Performance Liquid Chromatography 492
`Box 22-1 A “Green” Idea: Superheated Water as
`Solvent for HPLC
`22-4 Sample Preparation for Chromatography
`
`499
`501
`
`CHAPTER 23 Chromatographic Methods and
`Capillary Electrophoresis
`Capillary Electrophoresis in Medicine
`23-1 Ion-Exchange Chromatography
`Box 23-1 Applications of Ion Exchange
`23-2 Ion Chromatography
`23-3 Molecular Exclusion Chromatography
`23-4 Affinity Chromatography
`
`510
`511
`513
`515
`516
`518
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`viii
`
`Contents
`
`23-5 What Is Capillary Electrophoresis?
`23-6 How Capillary Electrophoresis Works
`23-7 Types of Capillary Electrophoresis
`Box 23-2 What Is a Micelle?
`23-8 Lab on a Chip: Probing Brain Chemistry
`
`Appendix A: Solubility Products
`Appendix B: Acid Dissociation Constants
`Appendix C: Standard Reduction Potentials
`Appendix D: Oxidation Numbers and Balancing
`Redox Equations
`
`Glossary
`Solutions to “Ask Yourself” Questions
`Answers to Problems
`Index
`
`519
`521
`523
`525
`527
`
`533
`535
`543
`
`547
`550
`567
`588
`597
`
`Experiments
`(See Web site www.whfreeman.com/exploringchem4e)
`1. Calibration of Volumetric Glassware
`2. Gravimetric Determination of Calcium as CaC2O4 ⴢ H2O
`3. Gravimetric Determination of Iron as Fe2O3
`4. Penny Statistics
`5. Statistical Evaluation of Acid-Base Indicators
`6. Preparing Standard Acid and Base
`7. Using a pH Electrode for an Acid-Base Titration
`8. Analysis of a Mixture of Carbonate and Bicarbonate
`9. Analysis of an Acid-Base Titration Curve: The Gran Plot
`10. Fitting a Titration Curve with Excel SOLVER®
`11. Kjeldahl Nitrogen Analysis
`12. EDTA Titration of Ca2⫹ and Mg2⫹ in Natural Waters
`13. Synthesis and Analysis of Ammonium Decavanadate
`14.
`Iodimetric Titration of Vitamin C
`
`15. Preparation and Iodometric Analysis of High-Temperature
`Superconductor
`16. Potentiometric Halide Titration with Ag⫹
`17. Measuring Ammonia in an Aquarium with an Ion-Selective
`Electrode
`18. Electrogravimetric Analysis of Copper
`19. Measuring Vitamin C in Fruit Juice by Voltammetry with
`Standard Addition
`20. Polarographic Measurement of an Equilibrium Constant
`21. Coulometric Titration of Cyclohexene with Bromine
`22. Spectrophotometric Determination of Iron in Vitamin Tablets
`23. Microscale Spectrophotometric Measurement of Iron in
`Foods by Standard Addition
`24. Spectrophotometric Determination of Nitrite in Aquarium
`Water
`25. Spectrophotometric Measurement of an Equilibrium
`Constant: The Scatchard Plot
`26. Spectrophotometric Analysis of a Mixture: Caffeine and
`Benzoic Acid in a Soft Drink
`27. Mn2⫹ Standardization by EDTA Titration
`28. Measuring Manganese in Steel by Spectrophotometry with
`Standard Addition
`29. Measuring Manganese in Steel by Atomic Absorption Using
`a Calibration Curve
`30. Properties of an Ion-Exchange Resin
`31. Analysis of Sulfur in Coal by Ion Chromatography
`32. Measuring Carbon Monoxide in Automobile Exhaust by
`Gas Chromatography
`33. Amino Acid Analysis by Capillary Electrophoresis
`34. DNA Composition by High-Performance Liquid
`Chromatography
`35. Analysis of Analgesic Tablets by High-Performance Liquid
`Chromatography
`36. Anion Content of Drinking Water by Capillary
`Electrophoresis
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`CHAPTER8
`
`Introducing Acids
`and Bases
`
`The chemistry of acids and bases is probably the most important topic you will
`
`study in chemical equilibrium. It is difficult to have a meaningful discussion of sub-
`jects ranging from protein folding to the weathering of rocks without understanding
`acids and bases. It will take us several chapters to provide meaningful detail to the
`study of acid-base chemistry.
`
`8-1 What Are Acids and Bases?
`In aqueous chemistry, an acid is a substance that increases the concentration of
`H3O⫹ (hydronium ion). Conversely, a base decreases the concentration of H3O⫹ in
`aqueous solution. As we shall see shortly, a decrease in H3O⫹ concentration neces-
`sarily requires an increase in OH⫺ concentration. Therefore, a base is also a sub-
`stance that increases the concentration of OH⫺ in aqueous solution.
`The species H⫹ is called a proton because a proton is all that remains when a
`hydrogen atom loses its electron. Hydronium ion, H3O⫹, is a combination of H⫹
`with H2O (Figure 8-1). Although H3O⫹ is a more accurate representation than H⫹
`for the hydrogen ion in aqueous solution, we will use H3O⫹ and H⫹ interchangeably
`in this book.
`A more general definition of acids and bases given by Brønsted and Lowry is
`that an acid is a proton donor and a base is a proton acceptor. This definition
`includes the one already stated. For example, HCl is an acid because it donates a pro-
`ton to H2O to form H3O⫹:
`
`HCl ⫹ H2O
`
`34
`
`H3O⫹ ⫹ Cl⫺
`
`The Brønsted-Lowry definition can be extended to nonaqueous solvents and to the
`gas phase:
`
`102 pm
`
`110°
`
`172 pm
`
`Figure 8-1 Structure of
`hydronium ion, H3O⫹.
`
`HCl(g)
`Hydrochloric acid
`(acid: proton donor)
`
`⫹
`
`NH3(g)
`Ammonia
`(base: proton acceptor)
`
`34
`
`⫹Cl⫺(s)
`NH4
`Ammonium chloride
`(salt)
`
`Brønsted-Lowry acid: proton donor
`Brønsted-Lowry base: proton acceptor
`
`171
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`172
`8 Introducing Acids and Bases
`
`Salts
`Any ionic solid, such as ammonium chloride, is called a salt. In a formal sense, a
`salt can be thought of as the product of an acid-base reaction. When an acid and
`a base react stoichiometrically, they are said to neutralize each other. Most salts
`are strong electrolytes, meaning that they dissociate almost completely into their
`component ions when dissolved in water. Thus, ammonium chloride gives NH⫹
`4 and
`Cl⫺ in aqueous solution:
`
`⫹Cl⫺(s) ¡ NH⫹
`4 (aq) ⫹ Cl⫺(aq)
`NH4
`
`Conjugate Acids and Bases
`The products of a reaction between an acid and a base also are acids and bases:
`
`⫹
`
`⫺
`
`CH3
`
`H
`⫹ N
`ð(
`H
`Methylammonium ion
`
`H
`
`ý
`O
`
` k
`
`34
`
`CH3
`
`C
`
`O
`½
`ý
`Acetate ion
`
`⫹
`
`š
`CH3 N
`H
`(
`H
`Methylamine
`
`½ý
`
`O
`
`
`CH3
`
`C
`
`k
`HO
`Acetic acid
`
`A solid wedge is a bond coming out
`of the page toward you. A dashed
`wedge is a bond going behind the
`page.
`
`Conjugate acids and bases are related
`by the gain or loss of one proton.
`
`Conjugate pair
`
`Conjugate pair
`
`Acid
`
`Base
`
`Base
`
`Acid
`
`Acetate is a base because it can accept a proton to make acetic acid. The methylam-
`monium ion is an acid because it can donate a proton and become methylamine.
`Acetic acid and the acetate ion are said to be a conjugate acid-base pair.
`Methylamine and the methylammonium ion are likewise conjugate. Conjugate acids
`and bases are related to each other by the gain or loss of one H⫹.
`
`Ask Yourself
`8-A. When an acid and base react, they are said to __________ each other. Acids
`and bases related by the gain or loss of one proton are said to be __________.
`
`8-2 Relation Between [Hⴙ], [OHⴚ], and pH
`In autoprotolysis, one substance acts as both an acid and a base:
`
`Autoprotolysis
`of water:
`
`H2O ⫹ H2O
`
`Kw
`H3O⫹ ⫹ OH⫺
`34
`Hydronium ion
`Hydroxide ion
`
`We abbreviate Reaction 8-1a in the following manner:
`
`H2O
`
`Kw
`34
`
`H⫹ ⫹ OH⫺
`
`(8-1a)
`
`(8-1b)
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`and we designate its equilibrium constant as Kw.
`
`Autoprotolysis constant
`for water:
`
`Kw ⫽ [H⫹][OH⫺] ⫽ 1.0 ⫻ 10⫺14 at 25⬚C
`
`(8-2)
`
`Equation 8-2 provides a tool with which we can find the concentration of H⫹ and
`OH⫺ in pure water. Also, given that the product [H⫹][OH⫺] is constant, we can
`always find the concentration of either species if the concentration of the other is
`known. Because the product is a constant, as the concentration of H⫹ increases, the
`concentration of OH⫺ necessarily decreases, and vice versa.
`
`173
`8-2 Relation Between [Hⴙ],
`[OHⴚ], and pH
`
`Example Concentration of Hⴙ and OHⴚ in Pure Water at 25ⴗC
`Calculate the concentrations of H⫹ and OH⫺ in pure water at 25⬚C.
`
`SOLUTION H⫹ and OH⫺ are produced in a 1:1 mole ratio in Reaction 8-1b.
`Calling each concentration x, we write
`
`21.0 ⫻ 10⫺14 ⫽ 1.0 ⫻ 10⫺7 M
`
`Kw ⫽ 1.0 ⫻ 10⫺14 ⫽ [H⫹][OH⫺] ⫽ [x][x] ⇒ x ⫽
`
`The concentrations of H⫹ and OH⫺ are both 1.0 ⫻ 10⫺7 M.
`
`Test Yourself At 0⬚C, the equilibrium constant Kw has the value 1.2 ⫻
`10⫺15. Find [H⫹] and [OH⫺] in pure water at 0⬚C. (Answer: both 3.5 ⫻ 10⫺8 M)
`
`Example Finding [OHⴚ] When [Hⴙ] Is Known
`What is the concentration of OH⫺ if [H⫹] ⫽ 1.0 ⫻ 10⫺3 M at 25⬚C?
`
`SOLUTION Setting [H⫹] ⫽ 1.0 ⫻ 10⫺3 M gives
`
`Kw ⫽ [H⫹][OH⫺] ⇒ [OH⫺] ⫽
`
`Kw
`[H⫹]
`
`⫽
`
`1.0 ⫻ 10⫺14
`1.0 ⫻ 10⫺3
`
`⫽ 1.0 ⫻ 10⫺11 M
`
`When [H⫹] ⫽ 1.0 ⫻ 10⫺3 M, [OH⫺] ⫽ 1.0 ⫻ 10⫺11 M. If [OH⫺] ⫽ 1.0 ⫻ 10⫺3 M,
`then [H⫹] ⫽ 1.0 ⫻ 10⫺11 M. As one concentration increases, the other decreases.
`
`Test Yourself Find [H+] in water when [OH–] ⫽ 1.0 ⫻ 10⫺4 M. (Answer:
`1.0 ⫻ 10⫺10 M)
`
`To simplify the writing of H⫹ concentration, we define pH as
`
`Approximate definition of pH:
`
`pH ⫽ ⫺log[H⫹]
`
`(8-3)
`
`Here are some examples:
`
`⇒ pH ⫽ ⫺log(10⫺3) ⫽ 3
`[H⫹] ⫽ 10⫺3 M
`⇒ pH ⫽ ⫺log(10⫺10) ⫽ 10
`[H⫹] ⫽ 10⫺10 M
`[H⫹] ⫽ 3.8 ⫻ 10⫺8 M ⇒ pH ⫽ ⫺log(3.8 ⫻ 10⫺8) ⫽ 7.42
`
`pH is really defined in terms of the
`activity of H⫹, which is related to
`concentration. Section 12-2 dis-
`cusses activity.
`
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`Page 13
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`
`

`

`Baking soda
`Lake Ontario
`Human urine
`Saliva, pH 5.7–7.1
`Tomato juice
`Average pH of rainfall,
`Toronto, February 1979
`Apples
`Lemon juice
`
`2
`
`1
`
`0
`
`Acidic
`
`1
`
`–
`
`2
`
`–
`
`3
`
`–
`
`174
`8 Introducing Acids and Bases
`
`Figure 8-2 pH values of various
`substances. The most acidic rainfall
`in the United States is more acidic
`than lemon juice.
`
`Example: An acidic solution has
`pH ⫽ 4, which means [H⫹] ⫽ 10⫺4 M
`and [OH⫺] ⫽ Kw/[H⫹] ⫽ 10⫺10 M.
`Therefore, [H⫹] ⬎ [OH⫺].
`
`Alkaline
`
`1
`
`1
`
`0
`
`1
`
`9
`
`8
`
`7
`
`6
`
`5
`
`4
`
`3
`
`4
`
`1
`
`3
`
`1
`
`2
`
`1
`
`Lye
`Ammonia
`Milk of magnesia
`Seawater
`Human blood
`Neutral
`
`Milk
`Theoretical “pure” rain, pH 5.6
`Most fish species die, pH 4.5–5.0
`Vinegar
`Most acidic rainfall recorded in U.S. at Wheeling, W. Va.
`Battery acid
`Acidic mine water, Iron Mountain, Calif.
`
`Changing the pH by 1 unit changes [H⫹] by a factor of 10. When the pH changes
`from 3 to 4, [H⫹] changes from 10⫺3 to 10⫺4 M.
`A solution is acidic if [H⫹] ⬎ [OH⫺]. A solution is basic if [H⫹] ⬍ [OH⫺]. An
`earlier example demonstrated that in pure water (which is neither acidic nor basic
`and is said to be neutral), [H⫹] ⫽ [OH⫺] ⫽ 10⫺7 M, so the pH is ⫺log(10⫺7) ⫽ 7.
`At 25⬚C, an acidic solution has a pH below 7, and a basic solution has a pH above
`7 (Figure 8-2).
`
`pH
`
`⫺1
`
`[H+] (M)
`
`0
`
`1
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`
`11
`
`12
`
`13
`
`14
`
`15
`
`10⫺2
`Acidic
`
`10⫺4
`
`10⫺6
`
`10⫺8
`
`10⫺10
`
`Neutral
`
`10⫺12
`Basic
`
`10⫺14
`
`Although pH generally falls in the range 0 to 14, these are not limits. A pH of
`⫺1, for example, means ⫺log[H⫹] ⫽ ⫺1, or [H⫹] ⫽ 10⫹1 ⫽ 10 M. This pH is
`attained in a concentrated solution of a strong acid such as HCl.
`
`Ask Yourself
`8-B. A solution of 0.050 M Mg2⫹ is treated with NaOH until Mg(OH)2 precipitates.
`(a) At what concentration of OH⫺ does this occur? (Remember the solubility
`product in Section 6-4. Use Ksp for brucite Mg(OH)2 in Appendix A.)
`(b) At what pH does this occur?
`
`8-3 Strengths of Acids and Bases
`Acids and bases are classified as strong or weak, depending on whether they react
`“completely” or only “partly” to produce H⫹ or OH⫺. Because there is a continuous
`range for a “partial” reaction, there is no sharp distinction between weak and strong.
`
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`Page 14
`
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`Page 14
`
`

`

`However, some compounds react so completely that they are unquestionably strong
`acids or bases—and everything else is defined as weak.
`
`Strong Acids and Bases
`Common strong acids and bases are listed in Table 8-1, which you must memorize.
`Note that even though HCl, HBr, and HI are strong acids, HF is not. A strong acid
`or strong base is completely dissociated in aqueous solution. That is, the equilib-
`rium constants for the following reactions are very large:
`
`HCl(aq) ¡ H⫹ ⫹ Cl⫺
`KOH(aq) ¡ K⫹ ⫹ OH⫺
`
`Virtually no undissociated HCl or KOH exists in aqueous solution. Demonstration 8-1
`shows one consequence of the strong-acid behavior of HCl.
`
`Weak Acids and Bases
`All weak acids, HA, react with water by donating a proton to H2O:
`
`HA ⫹ H2O
`
`Ka
`34
`
`H3O⫹ ⫹ A⫺
`
`which means exactly the same as
`
`Dissociation of
`weak acid:
`
`Ka H⫹ ⫹ A⫺
`34
`
`HA
`
`Ka ⫽
`
`[H⫹][A⫺]
`[HA]
`
`(8-4)
`
`The equilibrium constant, Ka, is called the acid dissociation constant. A weak acid
`is only partly dissociated in water, which means that some undissociated HA remains.
`Weak bases, B, react with water by abstracting (grabbing) a proton from H2O:
`
`Base
`hydrolysis:
`
`B ⫹ H2O
`
`Kb BH⫹ ⫹ OH⫺
`34
`
`Kb ⫽
`
`[BH⫹][OH⫺]
`[B]
`
`(8-5)
`
`The equilibrium constant, Kb, is called the base hydrolysis constant. A weak base
`is one for which some unreacted B remains.
`
`Table 8-1 Common strong
`acids and bases
`Formula
`
`Name
`
`ACIDS
`HCl
`
`HBr
`HI
`H2SO4
`HNO3
`HClO4
`
`a
`
`BASES
`LiOH
`NaOH
`KOH
`
`RbOH
`
`CsOH
`R4NOHb
`
`Hydrochloric acid
`(hydrogen
`chloride)
`Hydrogen bromide
`Hydrogen iodide
`Sulfuric acid
`Nitric acid
`Perchloric acid
`
`Lithium hydroxide
`Sodium hydroxide
`Potassium
`hydroxide
`Rubidium
`hydroxide
`Cesium hydroxide
`Quaternary
`ammonium
`hydroxide
`
`a. For H2SO4, only the first proton
`ionization is complete. Dissociation of
`the second proton has an equilibrium
`constant of 1.0 ⫻ 10⫺2.
`b. This is a general formula for any
`hydroxide salt of an ammonium cation
`containing four organic groups. An
`example is tetrabutylammonium
`hydroxide: (CH3CH2CH2CH2)4N⫹OH⫺.
`
`Carboxylic Acids Are Weak Acids
`and Amines Are Weak Bases
`Acetic acid is a typical weak acid:
`
`Roughly speaking, an acid is weak if
`Ka ⬍ 1 and a base is weak if Kb ⬍ 1.
`
`O
`
`CH3 C
`
`34
`
`CH3 C
`
`O H
`Acetic acid
`HA
`
`Acetate
`A⫺
`
`O
`
`O⫺
`
`⫹
`
`H⫹
`
`Ka ⫽ 1.75 ⫻ 10⫺5
`
`(8-6)
`
`175
`
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`Page 15
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`Page 15
`
`

`

`Demonstration 8-1 HCl Fountain
`
`The complete dissociation of HCl into H⫹ and Cl⫺
`makes HCl(g) extremely soluble in water.
`
`HCl(g)
`
`34
`
`HCl(aq)
`
`HCl(aq) —→ H⫹(aq) ⫹ Cl⫺(aq)
`
`(A)
`
`(B)
`
`Reaction B consumes the product of reaction A, thereby
`pulling reaction A to the right.
`An HCl fountain is assembled as shown below.2 In
`panel a, an inverted 250-mL round-bottom flask
`containing air is set up with its inlet tube leading to a
`source of HCl(g) and its outlet tube directed into an
`inverted bottle of water. As HCl is admitted to the flask,
`
`air is displaced into the bottle of water. When the bottle
`is filled with air, the flask contains mostly HCl(g).
`The hoses are disconnected and replaced with a
`beaker of indicator and a rubber bulb (panel b). For an
`indicator, we use slightly alkaline, commercial methyl
`purple solution, which is green above pH 5.4 and purple
`below pH 4.8. When 1 mL of water is squirted from the
`rubber bulb into the flask, a vacuum is created and
`indicator solution is drawn up into the flask, creating a
`colorful fountain (Color Plate 3).
`
`Questions Why is vacuum created when water is
`squirted into the flask? Why does the indicator change
`color when it enters the flask?
`
`250-mL
`round-bottom
`flask
`
`Glass
`tubes
`
`250-mL
`bottle
`
`Constriction
`
`Rubber
`stopper
`
`Hoses
`
`Beaker containing
`your favorite
`indicator
`
`2-mL
`rubber bulb
`
`HCl(g) in
`from tank
`
`(a)
`
`Water
`
`(b)
`
`Acetic acid is representative of carboxylic acids, which have the general structure
`shown below, where R is an organic substituent. Most carboxylic acids are weak
`acids, and most carboxylate anions are weak bases.
`
`O
`
`R C
`
`O H
`A carboxylic acid
`(weak acid, HA)
`
`O
`
`R C
`
`O⫺
`A carboxylate anion
`(weak base, A⫺)
`
`176
`
`Flat Line Capital Exhibit 1018
`Page 16
`
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`
`

`

`Methylamine is a typical weak base. It forms a bond to H⫹ by sharing the lone
`pair of electrons from the nitrogen atom of the amine:
`
`⫹
`
`H2O
`
`34
`
`M
`N H
`CH3
`H
`Methylamine
`B
`
`⫹
`
`H
`N H
`CH3
`H
`Methylammonium ion
`BH⫹
`
`⫹
`
`OH⫺
`
`Kb ⫽ 4.42 ⫻ 10⫺4
`
`(8-7)
`
`177
`8-3 Strengths of Acids
`and Bases
`
`Carboxylic acids (RCO2H) and ammo-
`nium ions (R3NH⫹) are weak acids.
`⫺) and
`Carboxylate anions (RCO2
`amines (R3N) are weak bases.
`
`Methylamine is a representative amine, a nitrogen-containing compound:
`
`RN!H2
`R2N!H
`R3N!
`
`a primary amine
`a secondary amine
`a tertiary amine
`
`⫹
`RNH 3
`⫹
`R2NH2
`R3NH⫹
`
`ammonium ions
`
`u
`
`Amines are weak bases, and ammonium ions are weak acids. The “parent” of all
`amines is ammonia, NH3. When methylamine reacts with water, the product is the con-
`jugate acid. That is, the methylammonium ion produced in Reaction 8-7 is a weak acid:
`Ka CH3N!H2 ⫹ Hⴙ
`34
`
`CH3N⫹H3
`BH⫹
`
`B
`
`Ka ⫽ 2.26 ⫻ 10⫺11
`
`(8-8)
`
`The methylammonium ion (BH⫹) is the conjugate acid of methylamine (B).
`You should learn to recognize whether a compound is acidic or basic. For exam-
`ple, the salt methylammonium chloride dissociates completely in water to give
`methylammonium cation and chloride anion:
`
`CH3N⫹H3Cl⫺(s) —→ CH3N⫹H3(aq) ⫹ Cl⫺(aq)
`Methylammonium
`chloride
`
`The methylammonium ion, being the conjugate acid of methylamine, is a weak acid
`(Reaction 8-8). The chloride ion is neither an acid nor a base. It is the conjugate base
`of HCl, a strong acid. In other words, Cl⫺ has virtually no tendency to associate with
`H⫹; otherwise, HCl would not be classified as a strong acid. We predict that methyl-
`ammonium chloride solution is acidic, because the methylammonium ion is an acid
`and Cl⫺ is not a base.
`
`Metal Ions with Charge ⱖ2 Are Weak Acids
`Metal ions with a charge of ⫹2 or higher are acidic. In aqueous solution, metal ions
`n⫹ in which electrons from oxygen are
`bind several water molecules to form M(H2O)w
`shared with the metal ion. Many metal ions bind w ⫽ 6 water molecules, but large
`n⫹ to reduce
`metal ions can bind more water. A proton can dissociate from M(H2O)w
`the positive charge on the metal complex.
`Ka M(H2O)w–1(OH)(n–1)⫹ ⫹ Hⴙ
`34
`
`n⫹
`M(H2O)w
`
`(8-9)
`
`Weak acids: HA and BHⴙ
`Weak bases: Aⴚ and B
`
`Methylammonium chloride is a weak
`acid because
`1. It dissociates into CH3NH3
`⫹ and
`Cl⫺.
`2. CH3NH 3
`⫹ is a weak acid, being
`conjugate to CH3NH2, a weak
`base.
`3. Cl⫺ has no basic properties. It
`is conjugate to HCl, a strong
`acid. That is, HCl dissociates
`completely.
`
`Challenge Phenol (C6H5OH) is
`a weak acid. Explain why a solution
`of the ionic compound potassium
`phenolate (C6H5O⫺K⫹) is basic.
`
`Electron pair
`to donate
`MS
`OH
`H
`
`Empty orbital
`accepts electrons
`Mn⫹
`
`M
`O⫺Mn⫹
`
`HH
`
`The higher the charge on the metal, the more acidic it tends to be. For example, Ka
`for Fe2⫹ is 4 ⫻ 10–10, but Ka for Fe3⫹ is 6.5 ⫻ 10–3. Cations with a charge of ⫹1
`have negligible acidity. Now you should understand why solutions of metal salts
`such as Fe(NO3)3 are acidic.
`
`Flat Line Capital Exhibit 1018
`Page 17
`
`KVK-Tech, Flat Line Capital Exhibit 1018
`Page 17
`
`

`

`178
`8 Introducing Acids and Bases
`
`Relation Between Ka and Kb
`An important relation exists between Ka and Kb of a conjugate acid-base pair in aque-
`ous solution. We can derive this result with the acid HA and its conjugate base A⫺.
`
`HA
`
`34
`
`H⫹ ⫹
`
`A⫺
`
`Ka ⫽
`
`A⫺
`
`⫹ H2O
`
`34
`
`HA
`
`⫹ OH⫺
`
`H2O
`
`34
`
`H⫹ ⫹ OH⫺
`
`[H⫹][A⫺]
`[HA]
`[HA][OH⫺]
`[A⫺]
`
`Kb ⫽
`#
`Ka Kb ⫽
`[H⫹][A⫺]
`[HA]
`
`[HA][OH⫺]
`[A⫺]
`
`⫽ Kw
`
`When reactions are added, their equilibrium constants must be multiplied,
`thereby giving a most useful result:
`
`#
`Ka Kb ⫽ Kw for a conjugate acid-
`base pair in aqueous solution.
`
`Relation between Ka and Kb
`for a conjugate pair:
`
`#
`Ka Kb ⫽ Kw
`
`(8-10)
`
`Equation 8-10 applies to any acid and its conjugate base in aqueous solution.
`
`Example Finding Kb for the Conjugate Base
`The value of Ka for acetic acid is 1.75 ⫻ 10⫺5 (Reaction 8-6). Find Kb for acetate
`ion.
`
`SOLUTION
`
`Kb ⫽
`
`Kw
`Ka
`
`⫽
`
`1.0 ⫻ 10⫺14
`1.75 ⫻ 10⫺5
`
`⫽ 5.7 ⫻ 10⫺10
`
`
`Test Yourself Ka for ammonium ion (NH 4⫹) is 5.7 ⫻ 10⫺10. Find Kb for
`ammonia (NH3). (Answer: 1.8 ⫻ 10⫺5 M)
`
`Example Finding Ka for the Conjugate Acid
`Kb for methylamine is 4.42 ⫻ 10⫺4 (Reaction 8-7). Find Ka for methylammo-
`nium ion.
`
`SOLUTION
`
`Ka ⫽
`
`Kwᎏ
`Kb
`
`Test Yourself Kb for formate (HCO2–) is 5.6 ⫻ 10⫺11. Find Ka for formic
`acid (HCO2H). (Answer: 1.8 ⫻ 10⫺4 M)
`
`1.0 ⫻ 10⫺14
`ᎏᎏ
`4.42 ⫻ 10⫺4
`
`⫽
`
`⫽ 2.3 ⫻ 10⫺11
`
`Ask Yourself
`8-C. Which is a stronger acid, A or B? Write the Ka reaction for each.
`
`O
`
`O
`
`A
`
`Cl2HCCOH
`Dichloroacetic acid
`Ka ⫽ 8 ⫻ 10⫺2
`
`B
`
`ClH2CCOH
`Chloroacetic acid
`Ka ⫽ 1.36 ⫻ 10⫺3
`
`Flat Line Capital Exhibit 1018
`Page 18
`
`KVK-Tech, Flat Line Capital Exhibit 1018
`Page 18
`
`

`

`Which is a stronger base, C or D? Write the Kb reaction for each.
`
`O
`
`C
`
`H2NNH2
`Hydrazine
`Kb ⫽ 3.0 ⫻ 10⫺6
`
`D
`
`H2NCNH2
`Urea
`Kb ⫽ 1.5 ⫻ 10⫺14
`
`179
`8-4 pH of Strong Acids
`and Bases
`
`8-4 pH of Strong Acids and Bases
`The principal components that make rainfall acidic are nitric and sulfuric acids,
`which are strong acids. Each molecule of strong acid or strong base in aqueous solu-
`tion dissociates completely to provide one molecule of H⫹ or OH⫺. Nitric acid is a
`strong acid, so the reaction
`
`HNO3 ¡ H⫹ ⫹ NO 3
`Nitric acid
`Nitrate
`
`⫺
`
`goes to completion. In the case of sulfuric acid, one proton is completely dissociated,
`but the second is only partly dissociated (depending on conditions):
`
`H2SO4 ¡ H⫹ ⫹ HSO4
`Sulfuric acid
`Hydrogen sulfate
`(also called bisulfate)
`
`⫺
`
`Ka ⫽ 0.010
`
`2⫺
`H⫹ ⫹ SO4
`Sulfate
`
`pH of a Strong Acid
`Because HBr is completely dissociated, the pH of 0.010 M HBr is
`
`pH ⫽ ⫺log[H⫹] ⫽ ⫺log(0.010) ⫽ 2.00
`
`Is pH 2 sensible? (Always ask yourself that question at the end of a calculation.)
`Yes—because pH values below 7 are acidic and pH values above 7 are basic.
`
`Acid: pH ⬍ 7
`Base: pH ⬎ 7
`
`Example pH of a Strong Acid
`Find the pH of 4.2 ⫻ 10⫺3 M HClO4.
`
`SOLUTION HClO4 is completely dissociated, so [H⫹] ⫽ 4.2 ⫻ 10⫺3 M.
`
`pH ⫽ ⫺log[H⫹] ⫽ ⫺log(4.2 ⫻ 10⫺3) ⫽ 2.38
`
`}
`2 significant
`figures
`
`}
`2 digits
`in mantissa
`
`How about significant figures? The two significant figures in the mantissa
`of the logarithm correspond to the two significant figures in the number 4.2 ⫻
`10⫺3.
`
`Test Yourself What is the pH of 0.055 M HBr? (Answer: 1.26)
`
`Flat Line Capital Exhibit 1018
`Page 19
`
`KVK-Tech, Flat Line Capital Exhibit 1018
`Page 19
`
`

`

`180
`8 Introducing Acids and Bases
`
`For consistency in working problems in this book, we are generally going to
`express pH values to the 0.01 decimal place regardless of what is justified by
`significant figures. Real pH measurements are rarely more accurate than ⫾0.02,
`although differences in pH between two solutions can be accurate to ⫾0.002 pH
`units.
`
`pH of a Strong Base
`Now we ask, “What is the pH of 4.2 ⫻ 10⫺3 M KOH?” The concentration of OH⫺
`is 4.2 ⫻ 10⫺3 M, and we can calculate [H⫹] from the Kw equation, 8-2:
`
`[H⫹] ⫽
`
`⫽
`
`Kw
`1.0 ⫻ 10⫺14
`[OH⫺]
`4.2 ⫻ 10⫺3
`pH ⫽ ⫺log[H⫹] ⫽ ⫺log(2.38 ⫻ 10⫺12) ⫽ 11.62
`
`⫽ 2.38 ⫻ 10⫺12 M
`
`Her