Survival Guide to
General Chemistry

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Survival Guide to
General Chemistry

Patrick E. McMahon
Rosemary F. McMahon
Bohdan B. Khomtchouk

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CRC Press
Taylor & Francis Group
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Library of Congress Cataloging‑in‑Publication Data
Names: McMahon, Patrick E., author. | McMahon, Rosemary Fischer, author. |
Khomtchouk, Bohdan B., author.
Title: Survival guide to general chemistry / Patrick E. McMahon, Rosemary F.
McMahon, Bohdan Khomtchouk.
Other titles: General chemistry
Description: Boca Raton, Florida : CRC Press, 2019. | Includes
bibliographical references and index.
Identifiers: LCCN 2018039429| ISBN 9781138333727 (hardback : alk. paper) |
ISBN 9780429445828 (ebook) | ISBN 9781138333628 (pbk. : alk. paper)
Subjects: LCSH: Chemistry--Textbooks.
Classification: LCC QD33.2 .M3545 2019 | DDC 540--dc23
LC record available at />Visit the Taylor & Francis Web site at

and the CRC Press Web site at



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Dedication
To our twins, Patrick and Grace, who are now ten, and to Professor Paul Robert
Young of the University of Illinois, who was a mentor and a friend to both of us.
Patrick E. McMahon and
Rosemary F. McMahon
To my daughter, Bogdana Bohdanovna Khomtchouk.
In loving memory of my dear uncle, Taras Khomtchouk.
Bohdan B. Khomtchouk

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Contents
Preface............................................................................................................................................xvii
Authors.............................................................................................................................................xix
Chapter 1 Unit Conversion and Density: An Introduction to Problem-Solving Methods.............1
I General Techniques for Performing Unit Conversions......................................1
II General Procedures for Solving Density Problems............................................3
Process for Density Problems.............................................................................3
III General Examples for Density with Unit Conversions.......................................3
IV Practice Problems...............................................................................................6
V Answers to Practice Problems............................................................................7
Chapter 2 Atomic Particles, Isotopes, and Ions: An Initial Look at Atomic Structure............... 11

I General Concepts............................................................................................. 11
II Atomic Symbols and Isotopes.......................................................................... 13
Isotopes: Atoms with the Same Value of Z But with a Different Value for A......14
III Atomic Symbols and Ion Symbols................................................................... 15
Additional Practice Examples.......................................................................... 16
IV Practice Problems............................................................................................. 17
V Answers to Practice Problems.......................................................................... 17
Chapter 3 Working with Atomic Mass and Nuclear Mass.......................................................... 19
I
II
III
IV
V

General Concepts............................................................................................. 19
Potential Energy, Kinetic Energy, and Forces.................................................. 19
Energy, Mass Loss, and the Strong Nuclear Force...........................................20
Calculating Mass Using the Atomic Mass Unit............................................... 22
Calculating the Approximate Mass of an Atom in amu, kg, or g.................... 23
Process for Calculating Atomic Masses........................................................... 23
VI Average Atomic Mass for an Element..............................................................25
VII Practice Problems.............................................................................................26
VIII Answers to Practice Problems.......................................................................... 27
Chapter 4 Procedures for Writing Formulas and Naming Compounds...................................... 31
I
II
III
IV

General Concepts............................................................................................. 31

Elemental Ions for Ionic Compounds............................................................... 32
Writing Formulas for Binary Ionic Compounds.............................................. 33
Naming Binary Ionic Compounds................................................................... 36
Procedure for Naming a Binary Ionic Compound............................................ 36
Additional Concepts......................................................................................... 37
Additional Practice Examples.......................................................................... 38
V Writing Formulas for Ionic Compounds with Polyatomic Ions....................... 39
Procedure for Writing Formulas for Ionic Compounds with
Polyatomic Ions......................................................................................... 39

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Contents

VI Naming Ionic Compounds with Polyatomic Ions.............................................40
Procedure for Naming Ionic Compounds Containing Polyatomic Ions........... 41
VII Naming Binary Covalent Compounds............................................................. 41
Covalent System for Naming Binary Covalent Compounds............................ 42
VIII Additional Combination Practice Examples.................................................... 43
IX Practice Problems.............................................................................................46
X Answers to Practice Problems..........................................................................46
Chapter 5 An Introduction to Moles and Molar Mass................................................................. 49
I General Concepts............................................................................................. 49
Counting Numbers............................................................................................ 49
II Mass/Mole/Atom Conversions for Elements.................................................... 51

Procedure for Solving Mole Problems (Elements)........................................... 51
III Mass/Mole/Molecule Conversions for Compounds......................................... 53
Procedure for Solving Mole Problems (Compounds)...................................... 54
IV Concepts for Using Ratios in Formulas............................................................ 55
V Mass Percent of an Element in a Compound.................................................... 58
VI Practice Problems.............................................................................................60
VII Answers to Practice Problems.......................................................................... 61
Chapter 6 Procedures for Calculating Empirical and Molecular Formulas................................ 69
I General Concept............................................................................................... 69
Concepts of Empirical or Molecular Formulas................................................ 69
II  Procedure for Calculation of Simplest (Empirical) Formula of
Any Compound............................................................................................ 69
III Determination of the Simplest Formula from Element Mass Percent.............. 71
IV Determination of the True Molecular Formula for Molecules......................... 72
Determining and Using the Multiple................................................................ 72
Procedure for Finding the Simplest Formula and True Molecular Formula........ 73
V Experimental Determination of Compound Formulas..................................... 73
VI Practice Problems............................................................................................. 76
VII Answers to Practice Problems.......................................................................... 77
Chapter 7 Writing Chemical Equations....................................................................................... 83
I General Concepts............................................................................................. 83
Conservation Laws........................................................................................... 83
II Writing Balanced Equations............................................................................. 83
Process for Writing Balanced Equations from Descriptions............................84
III Practice Problems............................................................................................. 86
IV Answers to Practice Problems.......................................................................... 86
Chapter 8 Techniques for Performing Stoichiometric Calculations............................................ 89
I General Concepts............................................................................................. 89
II  General Process for Stoichiometric Calculations Based on Balanced
Equations.....................................................................................................90

Diagram Form.................................................................................................. 91
Viewing Each Step............................................................................................92

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Contents

III
IV
V
VI
VII

Percent Yield...................................................................................................... 93
Limiting Reagent...............................................................................................94
Calculation of All Products and Reactants in a Limiting Reagent Problem.....96
Practice Problems............................................................................................ 100
Answers to Practice Problems......................................................................... 102

Chapter 9 Precipitation and Acid/Base Aqueous Reactions: Concepts and Methods to
Design Complete Balanced Equations...................................................................... 109
I General Concepts............................................................................................. 109
II Solubility Equations and Aqueous Solution Formats...................................... 109
Solution Formation Equations......................................................................... 110
Formula Format............................................................................................... 110
Ionic Format..................................................................................................... 111
Equation Formats for Complete Aqueous Solution Reactions........................ 111

Formula Format Equation................................................................................ 111
Total Ionic Format Equation............................................................................ 111
Net Ionic Equation........................................................................................... 112
III Precipitation Reactions.................................................................................... 113
Determining Ionic Compound Solubility........................................................ 113
General Solubility Guideline Rules................................................................. 114
Examples from the Previous Reactions........................................................... 114
Predicting Products for Precipitation Reactions and Writing Equations......... 114
Process for Completing and Writing Precipitation Reaction Equations.......... 114
IV Acid/Base Reactions: General Concepts......................................................... 118
Properties of Acids........................................................................................... 119
Properties of Bases.......................................................................................... 120
V Aqueous Acid/Base Reactions......................................................................... 121
Acid Ionization Reaction and Acid Strength................................................... 121
Aqueous Base Reactions.................................................................................. 122
Completing Acid/Base Reactions and Equations............................................ 122
Examination of Reaction Requirements.......................................................... 123
A Specific Process for Completing and Writing Acid/Base
Reaction Equations..................................................................................... 124
VI Practice Problems............................................................................................ 127
VII Answers to Practice Problems......................................................................... 128
Chapter 10 Oxidation Numbers: A First Look at Redox Reactions............................................ 131
I General Concepts............................................................................................. 131
II Oxidation Numbers.......................................................................................... 133
General Rules for Oxidation Numbers............................................................ 133
III Process for the Analysis of Redox Reactions Using Oxidation Numbers........ 135
IV Practice Problems............................................................................................ 138
V Answers to Practice Problems......................................................................... 138
Chapter 11 Solution Concentration, Molarity, and Solution Stoichiometry................................ 141
I General Concepts............................................................................................. 141

II Concentration Calculations Based on Molarity............................................... 142
General Procedure for Solving Molarity Problems......................................... 142

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Contents

III Solution Stoichiometry................................................................................... 145
Process for Solution Stoichiometry................................................................ 145
IV Practice Problems........................................................................................... 148
V Answers to Practice Problems........................................................................ 149
Chapter 12 Light, Matter, and Spectroscopy............................................................................... 153
I General Properties of Light............................................................................ 153
Wave Properties.............................................................................................. 153
The Wave Nature of Light.............................................................................. 153
II Energy and the Quantum Theory of Light..................................................... 154
Energy and Light Calculations....................................................................... 155
III Electrons and Atoms...................................................................................... 156
IV Energy States, Light Interaction, and Electron Transitions............................ 157
V Spectroscopy Calculations............................................................................. 157
VI Spectra Calculations Using [E (Final Level) − E (Initial Level)]................... 159
VII Practice Problems........................................................................................... 161
VIII Answers to Practice Problems........................................................................ 162
Chapter 13 Atomic Orbitals and the Electronic Structure of the Atom...................................... 167
I Quantum Theory and Electron Orbitals......................................................... 167
Orbital Architecture and Electron Spin.......................................................... 169
II Determining Electron Configurations of Elements........................................ 170

Rules for Ground State Electron Configurations............................................ 171
Closed Shells and the Noble Gas Electron Configuration.............................. 173
III Electron Configurations and Organization of the Periodic Table.................. 175
Process to Read the Electron Configuration Directly from the
Periodic Table............................................................................................ 176
Valence Shell Electrons.................................................................................. 177
IV Ionization Energy and Electron Configuration Relationship......................... 178
V Determination of Electron Configuration for Ions......................................... 180
Electron Configuration for Negative Ions....................................................... 180
Electron Configuration for Most Fixed-Charge Positive Ions........................ 181
Ion Formation for Metals in Groups 4A and 5A............................................ 182
Ion Formation for Transition Metals (B Groups)........................................... 182
VI Practice Problems........................................................................................... 183
VII Answers to Practice Problems........................................................................ 183
Chapter 14 Alternate Methods for Visualizing and Constructing: Lewis Structures of
Covalent Molecules................................................................................................... 185
I Introduction to Interpretation of Lewis Structures......................................... 185
II Common Bonding Behavior for Non-Metals in Covalent Molecules............ 186
General Concept of Normal Bonding in Covalent Molecules........................ 186
Normal Neutral Bonding Rules...................................................................... 187
Summary of Normal Neutral Bond Numbers for H, Be, B, C, N, O, F......... 188
Summary of Normal Neutral Bond Numbers for Elements in Rows 3–5...... 190

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III  Constructing Lewis Structures for Covalent Molecules from H and the
Row-2 Elements: Bonding That Follows Normal Neutral Bonding Rules...... 190
Lewis Structure Concepts................................................................................ 190
Process for Molecules Containing H, Be, B, C, N, O, F................................. 191
IV  Constructing Lewis Structures for Covalent Molecules Using Elements
from Rows 3–5: Bonding Patterns That Follow Normal Neutral
Bonding Rules............................................................................................. 195
V  Constructing Molecules That Require Exceptions to Normal Neutral
Bonding Rules............................................................................................. 198
Bonding Patterns through Exception Rules..................................................... 199
Exception Rule #1..............................................................................200
Exception Rule #2..............................................................................200
Exception Rule #3..............................................................................200
Working with Exception Rule #1.....................................................................200
Lewis Structures for Polyatomic Ions.............................................................. 201
Using Exception Rule #3.................................................................................203
Other Uses for Exception Rules......................................................................204
Resonance Structures.......................................................................................204
VI Practice Problems............................................................................................205
VII Answers to Practice Problems.........................................................................206
Chapter 15 Additional Techniques for Designing and Representing Structures of
Large Molecules........................................................................................................209
I Techniques for Understanding and Designing Isomers of
Large Molecules..................................................................................209
General Rule #1 for the Number of Multiple Bonds (or Rings)......................209
II Using Condensed Structural Formulas............................................................ 213
Guidelines for Converting a Full Structure to a Condensed
Structural Formula...................................................................................... 213
Guidelines for Expanding Condensed Formulas: Reconstructing the
Complete Molecule..................................................................................... 216

III Concept of Ring Structures and Line Drawings.............................................. 217
Structural Notation: Guidelines for Producing Line Drawings....................... 218
Converting Line Drawings to Structural Formulas.......................................... 219
IV Practice Problems............................................................................................ 219
V Answers to Practice Problems......................................................................... 220
Chapter 16 Determining and Drawing Molecular Geometry and Polarity................................. 223
I Concepts of Molecular Geometry................................................................... 223
Types of Geometry Analysis for Central Atoms.............................................. 223
Counting Electron Regions.............................................................................. 223
Summary of E.R. Count...................................................................................224
II Process for Complete Determination of Molecular Geometry and Polarity...... 224
Descriptions of Geometric Figures for 2 to 4 Electron Regions...................... 225
Descriptions of Geometric Figures for 5 and 6 Electron Regions................... 225

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Contents

III Atom Geometry Determination from Electron Region Geometry................ 228
Additional Atom Geometries Derived from Trigonal Planar
and Tetrahedral........................................................................................ 229
Additional Atom Geometries Derived from Trigonal Bipyramidal
and Octahedral........................................................................................... 230
IV Molecular Polarity.......................................................................................... 233
V Practice Problems........................................................................................... 238
VI Answers to Practice Problems........................................................................ 238
Chapter 17 Summary Analysis of Central Atom Bonding, Hybridization, and Geometry......... 243

I Concept of Sigma Bonds and Pi Bonds.......................................................... 243
II Concept of Hybridization...............................................................................244
Electron Configuration and Hybridization of Carbon in CH4........................ 245
III Summary Tables.............................................................................................248
IV Practice Problems........................................................................................... 250
V Answers to Practice Problems........................................................................ 251
Chapter 18 Concepts of Potential Energy, Enthalpy, and Bond Energy Calculations................. 253
I Concept of Energy.......................................................................................... 253
II Chemical Bond Energetics............................................................................. 254
Bond Strengths and Bond Dissociation Energy (BDE).................................. 255
III Energy and Chemical Reactions.................................................................... 256
Potential Energy Changes and Enthalpy........................................................ 256
IV Potential Energy Diagrams............................................................................ 257
Activation Energy........................................................................................... 258
V Calculating Reaction Enthalpy Values...........................................................260
Process for Calculation of ΔH (Reaction) for a Balanced Equation...............260
VI Reading an Energy Diagram..........................................................................264
VII Practice Problems........................................................................................... 265
VIII Answers to Practice Problems........................................................................266
Chapter 19 Thermochemistry Calculations: Heat Capacity and Enthalpy.................................. 269


I General Concepts of Thermodynamics.......................................................... 269
The First Law of Thermodynamics................................................................ 270
II Heat Capacity and Heat Transfer between Substances.................................. 271
Simple Heat Transfer for One Substance....................................................... 273
Simple Heat Transfer between Two Substances............................................. 274
III Energy and Enthalpy in Chemical Reactions................................................. 278
IV Calorimetry.................................................................................................... 279
Determining ∆H and ∆E from Calorimetry...................................................280

General Procedures for Solving Calorimetry Problems.................................280
V Enthalpy and Hess’s Law................................................................................284
Process for Applying Hess’s Law Calculations.............................................. 285
VI Calculation of ∆H (Reaction) from Enthalpies of Formation........................ 287
VII Enthalpy and Stoichiometric Calculations..................................................... 291
VIII Practice Problems........................................................................................... 294
IX Answers to Practice Problems........................................................................ 297

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Contents

Chapter 20 Working with Gas Laws............................................................................................307
I

II


III
IV

V
VI
VII

Kinetic Theory of Gases.................................................................................307
Kinetic Energy, Temperature, and Graham’s Law for Diffusion...................307

The Ideal Gas Law......................................................................................... 310
Measurements of Gas Pressure....................................................................... 310
Solving Ideal Gas Law Problems................................................................... 311
Condition Changes for a Specific Gas Sample............................................... 313
Solving Additional Problems Using Gas Laws.............................................. 315
Stoichiometric Calculations Using Gas Laws................................................ 316
Gas Mixtures and Law of Partial Pressures................................................... 316
Practice Problems........................................................................................... 319
Answers to Practice Problems........................................................................ 320

Chapter 21 Guideline for Analyzing Intermolecular Forces and Calculating
Phase Change Enthalpies.......................................................................................... 325
I


II


III
IV



V
VI
VII

Overview of Interparticle and Intermolecular Forces.................................... 325
Phase Changes and Temperature.................................................................... 325
Descriptions of Interparticle Forces............................................................... 326

A Guideline for Comparing Total Strength of Intermolecular Forces
in Individual Compounds.......................................................................... 328
Strengths of Interparticle Forces.................................................................... 328
Process for Comparing Total Intermolecular Forces for Different
Compounds................................................................................................ 328
Enthalpy of Phase Changes............................................................................ 333
Interparticle and Intermolecular Forces for Solutions................................... 336
Solubility Requirements................................................................................. 336
Interparticle and Intermolecular Forces between Solutes and Solvents......... 337
Process for Comparing Total Intermolecular Forces for Solutions................ 337
Enthalpies of Solutions................................................................................... 339
Practice Problems...........................................................................................340
Answers to Practice Problems........................................................................ 341

Chapter 22 Kinetics Part 1: Rate Laws, Rate Equations, and an Introduction to Reaction
Mechanisms............................................................................................................... 345
I


II
III

IV





General Concept of Kinetics.......................................................................... 345
Additional Variables Affecting Reaction Rates............................................. 345

Information Relationships for Kinetics and Mechanisms..............................346
Introduction to Reaction Mechanisms............................................................346
Description of Reactions by Mechanisms...................................................... 347
Variability of Mechanisms............................................................................. 347
Experimental Kinetics: Determining Reactant Orders and Rate
Constants from Integrated Rate Equations................................................348
Zero-Order Reactants..................................................................................... 349
First-Order Reactants..................................................................................... 349
Second-Order Reactants................................................................................. 352
Experimental Determination of Reactant Orders in MultipleConcentration Rate Expressions................................................................ 354

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V








VI
VII


Determining Rate Expressions from Initial Rate Data Calculations............. 356
Relative Rate Measurements in the Balanced Equation................................. 356
Working with Initial Rate Data Tables........................................................... 357
Techniques for Solving for Reactant Orders by Comparing Data Sets.......... 357
Reactant Order Determination by Simple Inspection.................................... 358
Reactant Order Determination by Logarithmic Analysis............................... 359
Determining the Complete Rate Expressions................................................ 361
Determining the Value for the Rate Constant................................................ 361
Determining the Value for Any Unknown Rate............................................. 361
Determining Reactant Orders from Limited Data Sets................................. 363
Practice Problems...........................................................................................364
Answers to Practice Problems........................................................................ 365

Chapter 23 General Techniques for Solving Equilibrium Problems........................................... 371


I Concentration Quotient and Equilibrium Expression.................................... 371
Equilibrium Types and Expressions............................................................... 372
II Techniques for Performing Equilibrium Calculations: Calculating K........... 374
Process for Calculating the Numerical Value of the Equilibrium
Constant (K) from Concentrations............................................................ 375
III Techniques for Performing Equilibrium Calculations................................... 380
Process for Calculating Equilibrium Concentrations of All
Reactants and Products from the Numerical Value of the
Equilibrium Constant (K)..........................................................................380
IV Techniques for Performing Equilibrium Calculations................................... 384
Using the Quadratic Formula......................................................................... 384
V Techniques for Performing Equilibrium Calculations................................... 388
Using the Simplification Technique............................................................... 388
The Common Ion Effect................................................................................. 390

VI Shifts in Equilibrium...................................................................................... 391
VII Practice Problems........................................................................................... 393
VIII Answers to Practice Problems........................................................................ 395
Chapter 24 Kinetics Part 2: Application of Rate Laws and Rate Variables to Reaction
Mechanisms...............................................................................................................407


I Predicting Rate Expressions from Mechanisms.............................................407
II General Concepts for Rate Expression Comparison: Identification of
the Rate Determining Step........................................................................407
III Rules and Procedures for Predicting Rate Expressions.................................408
Rule 4 Procedure for Predicting Rate Expressions for Multi-Step
Reactions....................................................................................................409
IV Determining Rate Expressions from Mechanism Descriptions.....................409
Notation for Mechanisms Written in Equation Form.....................................409
Comparison of Rate Expressions for Mechanisms #1, #2, #3........................ 411
V General Construction of Potential Energy Diagrams..................................... 414
VI Energy, Temperature, and Chemical Reactions............................................. 416
Bonding Changes and Activation Energy...................................................... 416
Bonding Changes and Temperature............................................................... 416
Relationship between Rate Constant, Temperature, and Ea.......................... 417

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VII Reading Potential Energy Diagrams.............................................................. 418

III Rates and Catalysis......................................................................................... 422
V
IX Practice Problems........................................................................................... 423
X Answers to Practice Problems........................................................................ 426
Chapter 25 Thermodynamics: Entropy and Free Energy............................................................ 433
I

II
III
IV




V




VI

VII
VIII
IX
X

General Concepts of Entropy......................................................................... 433
Predicting Entropy Changes for a Chemical Process..................................... 433
Entropy and the Second Law of Thermodynamics........................................ 436
Calculation of Entropy and the Third Law of Thermodynamics................... 438

Enthalpy, Entropy, and Chemical Spontaneity............................................... 441
Enthalpy and Chemical Spontaneity.............................................................. 442
Entropy and Chemical Spontaneity................................................................ 442
Combining Enthalpy and Entropy as Spontaneity Measures......................... 442
Spontaneity and Temperature......................................................................... 443
Reaction Spontaneity and Free Energy.......................................................... 445
Definition of Free Energy (ΔG)...................................................................... 445
Enthalpy, Entropy, and Temperature Contributions to Free Energy..............446
Standard Free Energy (ΔG°)........................................................................... 447
Calculation of ΔG° at Variable Temperatures................................................ 450
Non-Standard Free Energy (ΔG) and Concentrations.................................... 454
Calculating Non-Standard Free Energy (ΔGT)............................................... 455
Non-Standard Free Energy (ΔG) and Equilibrium Constants........................ 457
Comprehensive Examples..............................................................................460
Practice Problems........................................................................................... 463
Answers to Practice Problems........................................................................465

Chapter 26 Acid/Base Equilibrium, pH, and Buffers.................................................................. 473
I

II
III
IV
V
VI
VII
VIII
IX
X


Acid and Base Dissociation Reactions: Acid and Base Strength................... 473
Autoionization of Water................................................................................. 476
Relationship between Acid (pka) and Conjugate Base Strength..................... 476
Process for Determining the Equilibrium Position for Acid/Base
Reactions................................................................................................. 478
pH Calculations in Aqueous Solutions: General Concept of pH.................... 481
pH Calculations in Aqueous Solutions: Reactions of One Acid or
Base with Water......................................................................................... 482
pH Calculations in Aqueous Solutions: Solving General Acid/Base
Reactions........................................................................................................ 488
The Common Ion Effect and Acid/Base Buffers........................................... 494
The Hendersen–Hasselbach Equation............................................................ 496
Practice Problems........................................................................................... 497
Answers to Practice Problems........................................................................ 498

Index...............................................................................................................................................507

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Preface
Similar to our companion book, Survival Guide to Organic Chemistry, this work evolved over
30 years of teaching both introductory and major level general chemistry to a variety of student
demographics at Benedictine University, Elmhurst College, Dominican University, and Triton
College in Illinois. The topics and descriptions in this book offer detailed step-by-step methods and
procedures for solving the major types of problems in general chemistry, whether mathematical or
conceptual. Included are every major topic in the first semester of general chemistry and most of

the major topics from the second semester. The approach to the format in this book is based on a
viewpoint that answers the question, “If I were first learning this material myself, how would I want
it explained to me and how would I want examples and problem solutions presented?” The explanations, instructional process sequences, solved examples, and completely solved practice problems in
this book are greatly expanded with special emphasis placed on overcoming deficiencies and correcting problems that my experience suggests as the most common or most insidious.
Chapter 1 introduces the process of problem solving using density and unit conversion as a central theme. Chapters 4, 7, 9, and 10 provide a solid foundation for writing correct compound formulas, correctly naming compounds, writing balanced equations, as well as understanding the basic
concepts for determining and analyzing acid/base, precipitation, and redox equations. Chapters 5,
6, 8, and 11 form the corresponding foundation for working with moles and stoichiometric calculations. Thermochemistry and thermodynamic problems are analyzed in Chapters 19 and 25.
Many chapters also provide alternative viewpoints as a way to help students better understand
certain chemical concepts. For example, Chapter 3 includes problems of nuclear mass loss and
nuclear energy as a way to grasp the ideas of mass number, atomic mass, and the definition of the
atomic mass unit. Chapters 14 and 15 describe alternative methods for constructing Lewis structures,
including large covalent molecules. These viewpoints help explain the role of bonding electrons and
lone electron pairs for atoms bonding in typical patterns and include ways of viewing electron roles
in polyatomic ions, unusual ions, and resonance structures. Included in Chapter 15 is a description
of methods for structure notation for large (organic) molecules (condensed structures and line drawings), which are necessary for working with more complicated structures. Chapter 16 includes a
description of the skill for drawing geometrical shapes as an aid to determining and picturing electron region and molecular geometry, a technique critical for branching out into organic chemistry.
Chapters 22 and 24 provide a much expanded discussion of kinetic processes, reaction mechanisms,
and their relationship to reaction rate laws. Chapter 23 deals with all equilibrium calculation types;
in this case, unified by problem-solving techniques rather than reaction concepts.

Patrick E. McMahon

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Authors
Patrick E. McMahon, PhD, holds a PhD in organic chemistry from the University of Illinois and
a Masters of Arts for Teachers from Indiana University. For the past 25 years he has taught both
general chemistry and organic chemistry at several Chicago area colleges and universities. Prior to
that, he was a research scientist for Amoco Chemical Company at their Naperville, Illinois c­ ampus.
He has over 30 years of experience teaching both introductory and science major level ­general
chemistry to a variety of student demographics at Benedictine University, Elmhurst College,
Dominican University, and Triton College. He is a member of the American Legion and served
in the United States Army from 1970 to 1972. Awards that can be accredited to his name include
the B.J. Babler award for outstanding contribution to undergraduate instruction at the University
of Illinois, the Dean’s Award for Teaching Excellence at Benedictine University, and first recipient
of the Shining Star award given by the student senate for outstanding contribution to students at
Benedictine University.
Rosemary F. McMahon, PhD, earned a BS with highest distinction in chemistry and an MS and
PhD in organic chemistry at the University of Illinois. Her industrial career at Amoco Chemical and
British Petroleum (BP) spanned chemicals process research and development, chemicals manufacturing, technical service, and customer support. She worked in oxidation chemistry, environmental
catalyst chemistry, catalyst recovery processes, and manufacturing for product lines which included
purified terephthalic acid, dimethyl 2,6-naphthalenedicarboxylate, and acrylonitrile. Her career
later branched out to information technology as a patent and technical literature specialist supporting all technologies at BP worldwide. She is the co-author of four United States patents.
Bohdan B. Khomtchouk, PhD, is an American Heart Association (AHA) Postdoctoral Fellow in
the Department of Biology and Department of Medicine at Stanford University. Previously, he was
an NIH/NIA Postdoctoral Research Scholar, National Institute on Aging of the National Institutes
of Health (Stanford Training Program in Aging Research) at Stanford University and a National
Defense Science and Engineering Graduate (NDSEG) Fellow at the University of Miami Miller
School of Medicine.

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1 An Introduction to Problem-

Unit Conversion and Density
Solving Methods

I  GENERAL TECHNIQUES FOR PERFORMING UNIT CONVERSIONS
Principle #1: Adjust any conversion factor ratio so that the unit to be calculated is on top of the
ratio fraction (numerator), and the unit to be cancelled out is on the bottom of the ratio fraction
(denominator).
Principle #2: Volumes in certain problem types may be calculated from the corresponding equations
for a rectangular object (V = l × w × h), a cylinder (V = π r2 h), or a sphere (V = 4/3 π r3). It is
easier to convert all linear dimensions to the required units before multiplication to generate volume
in the required units. Alternatively, a unit conversion comparing two different volume units must be
generated.
Principle #3: A unit conversion for different volume units can be derived from linear dimensions; any linear dimension cubed produces the corresponding volume unit.
Example: Convert cubic inches to cubic centimeters; use 1 inch (in) = 2.54 centimeters (cm). 1 cubic
inch (in3) is the volume of a cube, which is 1 inch on all three sides based on


V(rectangular object) = length (l) × width (w) × height (h)



V(1 inch-sided cube) = 1 inch × 1 inch × 1 inch = 1 in3

Since 1 inch = 2.54 cm; the volume of the identical cube can be expressed as V (1 inch-sided cube) =

2.54 cm × 2.54 cm × 2.54 cm = 16.39 cm3
Therefore, 1 in3 = 16.39 cm3
Principle #4: To perform a complete unit conversion for a ratio, it is easiest to convert the numerator and denominator separately, then reform the ratio and divide through.
Example: A common highway speed limit is 70 miles per hour; convert 70.0 miles/hour to meters
per second. 1 kilometer = 0.6214 miles; 1 mile = 1.609 kilometers
Step (1): Convert the numerator:


70.0 miles ×

1 km
1000 m
×
= 1.1265 × 105 m
1 km
0.6214 miles


Principle #1: Regardless of which conversion factor is used to convert miles to km, km is on top of
the ratio fraction, and miles is on the bottom of the ratio fraction. Therefore, the following conversion setup is equivalent.


70.0 miles ×

1.6093 km 1000 m
×
= 1.1265 × 105 m
1 mile
1 km


1

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2

Survival Guide to General Chemistry

Step (2): Convert the denominator:
1 hour ×



60 minutes 60 sec
×
= 3.600 × 103 sec
1 hour
1 min


Step (3): Reform the ratio for distance divided by time:
70 miles 1.1265 × 105 m
=
= 31.3 m /sec
1 hour
3.600 × 103 sec





Example: The density of visible matter in the universe (i.e., ignoring dark matter) is estimated to be
equivalent to 3 hydrogen atoms per cubic meter (m3) of space. Calculate the density of the universe
in units of grams/cm3. Although the estimate is very general, express the final answer to three
significant figures (extra significant figures can and, often, should be carried through a calculation
until the final answer).


mass of 1 hydrogen (H) atom = 1.674 × 10−27 kilogram



1 kilogram (kg) = 1000 grams (g); 1 meter (m) = 100 centimeters (cm)

The ratio is expressed as





(mass)
(Volume)

The starting complete unit to be converted is

3 hydrogen atoms
( numerator )
=

(denominator )

1 m3

The complete unit to be calculated is

grams
( numerator )
=

1 cm 3 (denominator )

Use Principle #4: Convert the numerator and denominator separately, then reform the ratio.
Step (1): Convert the numerator from the mass of 3 H atoms to the mass in grams:



(3 H atoms) ×

(1.674 × 10 −27 kg) (1000 g)
×
= 5.02 × 10 −24 grams
1 H atom
1 kg


Step (2): Convert the denominator from 1 m3 to 1 cm3:
No direct conversion unit for m3 to cm3 is provided.
Use Principle #3:
1 m = 100 cm is used as the linear conversion;
1 cubic meter (m3) is the volume a cube, which is 1 meter on all three sides.



V (1 meter-sided cube) = 1 m × 1 m × 1 m = 1 m3

Since 1 m = 100 cm; the volume of the identical cube can be expressed as


V (1 meter-sided cube) = 100 cm × 100 cm × 100 cm = 1 × 106 cm3

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3

Unit Conversion and Density

Therefore 1 m3 = 1 × 106 cm3
Step (3): Reform the

( mass)
ratio.
( Volume)

The converted units from steps (1) and (2) are used; the bottom number of the ratio must be 1.
density of universe (g /cm3 ) =



(5.02 × 10 −24 g)
= 5.02 × 10 −30 g /cm3
(1× 106 cm 3 )



II  GENERAL PROCEDURES FOR SOLVING DENSITY PROBLEMS
Density (d) measures the mass (m) of an object relative to its volume (V):
density (d)
=



mass (m)
m
==
or d
volume ( V)
V

Density units of mass: usually grams (g);
Density units of volume: cubic centimeters (cm3) for solids; milliliters (mL) for liquids; Liters
(L) for gases.
The density equation can be solved for each possible variable.
d=

m
: solves for density as the unknown variable when mass and volume are known
V variables.

m = V × d: solves for mass as the unknown variable when density and volume are known
variables.
m
V = : solves for volume as the unknown variable when density and mass are known

d variables.

Process for Density Problems
Step (1): Identify the correct form of the density equation that is needed to solve for the desired
unknown variable.
Step (2): Identify or calculate the required values for the known variables in the correct units based
on the density units given or required.
Step (3): Complete the calculation for the unknown variable based on the results from step (1)
and step (2).
Step (4): When necessary, use the calculated variable from step (3) to solve for additional
information related to a more complex problem.

III  GENERAL EXAMPLES FOR DENSITY WITH UNIT CONVERSIONS
Example: A 1.75-liter jug is filled with liquid mercury; what is the mass of the mercury in pounds?
Density of Hg = 13.6 g/mL; 1 pound = 454 grams.
Step (1): Mass is the unknown variable; equation is m = V × d
Step (2): d is given as 13.6 g/mL;

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Survival Guide to General Chemistry

volume must be converted to units of mL:



V = (1.75 L) ×


(1000 mL)
= 1, 750 mL
1L


Principle #1: mL is the unit to be calculated and is on top of the ratio fraction; L is the unit to be
cancelled out and is on the bottom of the ratio fraction.
Step (3): m = V × d : m (grams) = (1.750 mL) × (13.6 g/mL) = 23, 800 grams
= 2.38 × 10 4 g
Step (4): Mass in grams = 23, 800 g; convert to find the mass in pounds:
mass (lbs) = (23, 800 g) × (1 lb/454 g) = 52.4 lbs
Example: Calculate the mass in kilograms of a mahogany wooden block with ­dimensions of 1.05 
meters × 0.650 meters × 0.110 meters; density of mahogany = 0.770 g/cm3;


1 kilogram (kg) = 1000 grams (g); 1 meter (m) = 100 centimeters (cm).



V(rectangular object) = length (l) × width (w) × height (h).

Step (1): Mass is the unknown variable; equation is m = V × d
Step (2): The density, d, is given as 0.770 g/cm3;
volume in cm3 must be calculated from the dimensions.
Principle #2: Convert each meter unit in the problem to centimeters using (100 cm /1 m) before
multiplying through using each dimension unit to find volume. If the volume is calculated in cubic
meters, the conversion factor for m3 to cm3 must be calculated.



V in cm3 = (105 cm) × (65.0 cm) × (11.0 cm) = 75075 cm3

Step (3): m = V × d: m (g) = (75075 cm3) × (0.770 g/cm3) = 5.78 × 104 g
Step (4): mass ( kg) = (5.78 × 10 4 g) ×

(1 kg)
= 57.8 kg
1000 g

Example: Titanium metal rods are often used in human joint replacement due to their low density
but high strength and tissue unreactivity. Calculate the length (height) in centimeters (cm) of a
cylindrical rod of titanium, which has a diameter of 3.20 cm and a mass of 2.44 pounds; density
of titanium (Ti) = 4.51 grams/cm3; 1 pound (lb) = 454 grams (g); V (cylinder) = π r2 h (r = radius;
h = height); radius = (½) diameter.
Steps 1 through 3 are used to find the volume of the rod using the density; step 4 then calculates the
length (height).
Step (1): Volume is the unknown variable; equation is V =
Step (2): The density, d, is given as 4.51 g/cm3;

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m
d