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Chemistry in Quantitative Language

CHEMISTRY IN QUANTITATIVE LANGUAGE Fundamentals of General Chemistry Calculations ............................................................................

Christopher O. Oriakhi, CChem, FRSC

1

3

Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford.

It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Christopher O. Oriakhi 2021 The moral rights of the author have been asserted First Edition published in 2009 Second Edition published in 2021 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2021937954 ISBN 978–0–19–886778–4 DOI: 10.1093/oso/9780198867784.001.0001 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

Preface

This is the second edition of Chemistry in Quantitative Language. I am pleased that the first edition, published in 2009, was so well received by both instructors and students. However, as is typical with most books in their first edition, the users graciously provided several constructive suggestions to make the book more useful for the intended audience. In addition, on my part, a decade later I find the need to add a few topics and concepts that were left out of the first edition, as well as the need to reorganize the chapters and update the worked examples and end-of-chapter problems to make the book more useful. All of these have armed me with the motivation and insights necessary to prepare this second edition. Formulating and solving quantitative chemistry problems remains a concern for many students. This edition shares the same objective of making problem-solving in chemistry more pleasurable and exciting, so students can hopefully face their examinations with ease and pass with flying colors.

This second edition has been revised extensively and incorporates many minor changes than can be included here. The most significant changes include: • The original first two chapters (Essential Mathematics and System of Measurement) have been removed and made available in the Appendix.

• I have added principal new materials broken down into two new chapters (Chemical Bonding 1: Basic Concepts, and Chemical Bonding 2: Modern Theories of Chemical Bonding) as these are foundational college chemistry materials; the latter chapter deals specifically with molecular shapes and structure.

• Throughout the book I have added new problems with varying degree of difficulties, while others have been combined, revised, or replaced.

Throughout the book I have adhered to the philosophy behind the first edition, which was to introduce the concepts of the underlying chemistry followed by a series of worked example to show students how the calculations are done and to hopefully enable them to appreciate what is involved. At the end of each chapter are a series of problems that range from very simple to those requiring more time and energy. Each problem in the book has been solved and checked independently by Ted LaPage. Answers for all the problems are in the Solutions to Problems chapter at the end of the book.

If you have used this book and found any errors or have comments, suggestions, and recommendations for future revisions and additions, please feel free to reach out to me by email at oriakhi@gmail.com or by contacting Oxford University Press.

v

Acknowledgement

Preparation of the second edition of Chemistry in Quantitative Language benefited greatly from the immense support and encouragement of my family and some amazing friends, colleagues, and students.

I begin by expressing my sincere appreciation to Ted LaPage for his indispensable contributions to this edition. In addition to his great sense of humor, dedication, and friendship, Ted read the entire manuscript, solved the problems, and suggested many improvements in both content and style.

Suggestions and constructive feedback from students and faculty who have used the book are particularly helpful and deeply appreciated. Many of your suggestions have been incorporated into this revision.

I also thank the various persons at Oxford University Press especially Katherine Ward, Sonke Adlung, and Harriet Konishi for their dedication and friendly support in getting this project to the finish line in a record time.

Finally, this acknowledgement would be incomplete without saying how much I appreciate the love, patience, support, and encouragement I received from my family and friends at all times.

In particular, I dedicate this edition to the memory of mother, Mrs Ikhiwi Oriakhi, who inspired this work.

vii

Contents

1 Atomic Structure and Isotopes 1.1 Atomic Theory 1.2 The Structure of the Atom 1.3 Isotopes 1.4 Relative Atomic Mass 1.5 Problems

1 1 2 4 5 7

2 Formula and Molecular Mass 2.1 Formula Mass 2.2 Molecular Mass 2.3 Molar Mass 2.4 Problems

9 9 9 10 11

3 The Mole and Avogadro’s Number 3.1 The Mole and Avogadro’s Number (NA ) 3.2 The Mole and Molar Mass 3.3 Calculating the Number of Moles 3.4 Problems

13 13 13 13 18

4 Formulas of Compounds and Percent Composition 4.1 Percent Composition 4.2 Types of Chemical Formula 4.3 Empirical Formula from Combustion Analysis 4.4 Molecular Formula 4.5 Problems

19 19 22 25 27 29

5 Chemical Formulas and Nomenclature 5.1 General Background 5.2 Chemical Formula 5.3 Oxidation Numbers 5.4 Writing the Formulas of Compounds 5.5 Nomenclature of Inorganic Compounds 5.6 Problems

31 31 32 32 34 37 40

ix

x

Contents

6 Chemical Equations 6.1 Writing Chemical Equations 6.2 Balancing Chemical Equations 6.3 Types of Chemical Reactions 6.4 Problems

43 43 43 46 48

7 Stoichiometry 7.1 Reaction Stoichiometry 7.2 Information From a Balanced Equation 7.3 Types of Stoichiometric Problem 7.4 Limiting Reagents 7.5 Reaction Yields: Theoretical, Actual, and Percent Yields 7.6 Problems

50 50 50 50 57 59 60

8 Structure of the Atom 8.1 Electronic Structure of the Atom 8.2 Electromagnetic Radiation 8.3 The Nature of Matter and Quantum Theory 8.4 The Hydrogen Atom 8.5 The Quantum-Mechanical Description of the Hydrogen Atom 8.6 Quantum Mechanics and Atomic Orbitals 8.7 Electronic Configuration of Multielectron Atoms 8.8 Problems

64 64 64 66 67 70 71 75 78

9 Chemical Bonding 1: Basic Concepts 9.1 Introduction: Types of Chemical Bonds 9.2 Lewis Dot Symbols 9.3 Ionic Bonding: Formation of Ionic Compounds 9.4 Covalent Bonding: Lewis Structures for Molecules 9.5 Covalent Bonding: Writing Lewis Structures 9.6 Resonance and Formal Charge 9.7 Exceptions to the Octet Rule 9.8 Polar Covalent Bonds: Bond Polarity and Electronegativity 9.9 Problems

81 81 81 83 86 86 88 91 93 98

10 Chemical Bonding 2: Modern Theories of Chemical Bonding 10.1 VSPER Theory: Molecular Geometry and the Shapes of Molecules 10.2 VSEPR Theory: Predicting Electron Group Geometry and Molecular Shape with the VSEPR Model 10.3 VSEPR Theory: Predicting Molecular Shape and Polarity 10.4 Valence Bond Theory 10.5 Valence Bond Theory: Types of Overlap 10.6 Hybridization

102 102

103 107 110 111 112

Contents

10.7 Limitations of Valence Bond Theory 10.8 Molecular Orbital Theory 10.9 Problems

xi

119 120 125

11 Gas Laws 11.1 Standard Temperature and Pressure 11.2 Boyle’s Law: Volume vs Pressure 11.3 Charles’s Law: Volume vs Temperature 11.4 The Combined Gas Law 11.5 Gay-Lussac’s Law and Reactions Involving Gases 11.6 Avogadro’s Law 11.7 The Ideal Gas Law 11.8 Density and Molecular Mass of a Gas 11.9 Molar Volume of an Ideal Gas 11.10 Dalton’s Law of Partial Pressure 11.11 Partial Pressure and Mole Fraction 11.12 Real Gases and Deviation from the Gas Laws 11.13 Graham’s Law of Diffusion 11.14 Problems

129 129 129 130 132 134 136 137 139 140 142 143 144 146 148

12 Liquids and Solids 12.1 The Liquid State 12.2 Vapor Pressure and the Clausius–Clapeyron Equation 12.3 The Solid State 12.4 The Crystal System 12.5 Calculations Involving Unit Cell Dimensions 12.6 Ionic Crystal Structure 12.7 The Radius Ratio Rule for Ionic Compounds 12.8 Determination of Crystal Structure by X-Ray Diffraction 12.9 Problems

152 152 152 155 156 159 165 167 171 174

13 Solution Chemistry 13.1 Solution and Solubility 13.2 Concentration of Solutions 13.3 Solving Solubility Problems 13.4 Effect of Temperature on Solubility 13.5 Solubility Curves 13.6 Effect of Pressure on Solubility 13.7 Problems

177 177 178 188 191 191 193 194

14 Volumetric Analysis 14.1 Introduction 14.2 Applications of Titration

199 199 199

xii

Contents

14.3 Calculations Involving Acid-Base Titration 14.4 Back Titrations 14.5 Kjeldahl Nitrogen Determination 14.6 Problems

200 206 210 212

15 Ideal Solutions and Colligative Properties 15.1 Colligative Properties 15.2 Vapor Pressure and Raoult’s Law 15.3 Elevation of Boiling Point 15.4 Depression of Freezing Point 15.5 Osmosis and Osmotic Pressure 15.6 Problems

214 214 214 217 220 222 225

16 Chemical Kinetics 16.1 Rates of Reaction 16.2 Measurement of Reaction Rates 16.3 Reaction Rates and Stoichiometry 16.4 Collision Theory of Reaction Rates 16.5 Rate Laws and the Order of Reactions 16.6 Experimental Determination of Rate Law Using Initial Rates 16.7 The Integrated Rate Equation 16.8 Half-Life of a Reaction 16.9 Reaction Rates and Temperature: The Arrhenius Equation 16.10 Problems

228 228 228 233 234 235 236 240 246 248 250

17 Chemical Equilibrium 17.1 Reversible and Irreversible Reactions 17.2 The Equilibrium Constant 17.3 The Reaction Quotient 17.4 Predicting the Direction of Reaction 17.5 Position of Equilibrium 17.6 Homogeneous vs Heterogeneous Equilibria 17.7 Calculating Equilibrium Constants 17.8 Calculating Equilibrium Concentrations from K 17.9 Qualitative Treatment of Equilibrium: Le Chatelier’s Principle 17.10 Problems

255 255 255 259 259 260 261 262 263 268 273

18 Ionic Equilibria and pH 18.1 The Ionization of Water 18.2 Definition of Acidity and Basicity 18.3 The pH of a Solution 18.4 The pOH of a Solution 18.5 The Acid Ionization Constant, Ka

276 276 276 277 278 280

Contents

xiii

18.6 Calculating pH and Equilibrium Concentrations in Solutions of Weak Acids 18.7 Percent Dissociation of Weak Acids 18.8 The Base Dissociation Constant, Kb 18.9 Relationship Between Ka and Kb 18.10 Salt Hydrolysis: Acid–Basis Properties of Salts 18.11 The Common Ion Effect 18.12 Buffers and pH of Buffer Solutions 18.13 Polyprotic Acids and Bases 18.14 More Acid–Base Titration 18.15 pH Titration Curves 18.16 Problems

280 283 285 286 288 292 293 298 301 303 308

19 Solubility and Complex-Ion Equilibria 19.1 Solubility Equilibria 19.2 The Solubility Product Principle 19.3 Determining Ksp from Molar Solubility 19.4 Calculating Molar Solubility from Ksp 19.5 Ksp and Precipitation 19.6 Complex-Ion Equilibria 19.7 Problems

313 313 313 314 316 318 320 323

20 Thermochemistry 20.1 Introduction 20.2 Calorimetry and Heat Capacity 20.3 Enthalpy 20.4 Hess’s Law of Heat Summation 20.5 Lattice Energy and the Born–Haber Cycle 20.6 Bond Energies and Enthalpy 20.7 Problems

325 325 325 327 331 333 335 338

21 Chemical Thermodynamics 21.1 Definition of Terms 21.2 The First Law of Thermodynamics 21.3 Expansion Work 21.4 Entropy 21.5 The Second Law of Thermodynamics 21.6 Calculation of Entropy Changes in Chemical Reactions 21.7 Free Energy 21.8 The Standard Free Energy Change 21.9 Enthalpy and Entropy Changes during a Phase Change 21.10 Free Energy and the Equilibrium Constant 21.11 Variation of G0 and Equilibrium Constant with Temperature 21.12 Problems

344 344 344 345 348 348 348 352 352 355 356 358 361

xiv

Contents

22 Oxidation and Reduction Reactions 22.1 Introduction 22.2 Oxidation and Reduction in Terms of Electron Transfer 22.3 Oxidation Numbers (ON) 22.4 Oxidation and Reduction in Terms of Oxidation Number 22.5 Disproportionation Reactions 22.6 Oxidizing and Reducing Agents 22.7 Half-Cell Reactions 22.8 Balancing Redox Equations 22.9 Oxidation-Reduction Titration 22.10 Problems

365 365 365 366 368 369 369 371 372 381 385

23 Fundamentals of Electrochemistry 23.1 Galvanic Cells 23.2 The Cell Potential 23.3 Standard Electrode Potential 23.4 The Electrochemical Series (ECS) 23.5 Applications of Electrode Potential 23.6 Cell Diagrams 0 from Electrode Potential 23.7 Calculating Ecell 23.8 Relationship of the Standard Electrode Potential, the Gibbs Free Energy, and the Equilibrium Constant 23.9 Dependence of Cell Potential on Concentration (the Nernst Equation) 23.10 Electrolysis 23.11 Faraday’s Laws of Electrolysis 23.12 Problems

389 389 389 390 391 391 393 394

24 Radioactivity and Nuclear Reactions 24.1 Definitions 24.2 Radioactive Decay and Nuclear Equations 24.3 Nuclear Transmutations 24.4 Rates of Radioactive Decay and Half-Life 24.5 Energy of Nuclear Reactions 24.6 Problems

412 412 412 415 416 419 423

Appendix A A.1 Essential mathematics A.2 Significant figures and mathematical operations A.3 Scientific notation and exponents A.4 Logarithms A.5 Algebraic equations

427 427 428 429 432 434

396 399 402 402 408

Contents

xv

Appendix B B.1 Systems of measurement B.2 Measurement of mass, length, and time B.3 Temperature B.4 Derived units B.5 Density and specific gravity B.6 Dimensional analysis and conversion factors

445 445 446 447 448 449 451

Solutions Index

457 495

1 Atomic Structure and Isotopes ............................................................................

1.1 Atomic Theory In 1808, based on experimental data and chemical laws known in his day, Dalton proposed his theory of the atom. The theory states that: 1. All chemical elements are made up of tiny indivisible particles called atoms.

2. Atoms cannot be created or destroyed. Chemical reactions only rearrange the way that the atoms are combined.

3. Atoms of the same element are identical in all respects and have the same masses and physical and chemical properties. Atoms of different elements have different masses as well as different physical and chemical properties.

4. A combination of elements to form a compound occurs between small, whole-number ratios of atoms.

Dalton’s theory resulted in the formulation of the law of conservation of mass and the law of multiple proportions. Along with the law of definite proportion and the law of reciprocal proportion, these form the basis of reaction stoichiometry (see Chapter 7).

1.1.1 The law of conservation of mass In a chemical reaction, matter is neither created nor destroyed. The total mass of reactants is equal to the total mass of the products. This law was first stated by Lavoisier, based on his findings from combustion experiments.

1.1.2 The law of definite proportion The law of definite proportions (also known as Proust’s law or the law of constant composition) states that a given chemical compound is always composed of the same elements in the same proportions by mass. When elements combine to form a particular compound, they do so in fixed and constant proportions by mass, regardless of the source of the compound. For example, a sample of pure water, regardless of its source, always contains 11.1% hydrogen and 88.9% oxygen.

Chemistry in Quantitative Language: Fundamentals of General Chemistry Calculations. Second Edition.

Christopher O. Oriakhi, Oxford University Press. © Christopher O. Oriakhi 2021.

DOI: 10.1093/oso/9780198867784.003.0001

2

Chemistry in Quantitative Language

1.1.3 The law of multiple proportions If two elements can form more than one compound between them, the masses of one element, which combine with a fixed mass of the second element, are in a ratio of whole numbers. For example, nitrogen and oxygen combine to form compounds such as NO, NO2 , and N2 O, in which the ratio of nitrogen atoms per oxygen atom is respectively 1, ½, and 2. This is one of the basic laws of stoichiometry, as we discuss in Chapter 7.

1.1.4 The law of reciprocal proportions According to the Law of Reciprocal Proportions (also known as the law of equivalent proportions or the law of permanent ratios), if two different elements, A and B, chemically combine separately with a fixed mass of a third element, D, the ratio of the masses in which they do so are either the same as or a simple multiple (or simple fraction) of the ratio of the masses in which A and B combine with each other. For example, carbon reacts with sulfur to form carbon disulfide (CS2 ) and with oxygen to form carbon dioxide (CO2 ). Sulfur and oxygen, meanwhile, combine to form sulfur dioxide (SO2 ), in which the ratio of sulfur to oxygen is 1:2, which is ½ the 1:1 ratio of sulfur to oxygen in the carbon compounds.

1.2 The Structure of the Atom An atom consists of a central nucleus, which contains roughly 99.9% of the total mass of the atom, and a surrounding cloud of electrons. The nucleus is composed of two kinds of particles, protons and neutrons, which are collectively known as nucleons. The proton is positively charged, while the neutron is electrically neutral. The electrons have a negative charge and surround the nucleus in “shells” of definite energy levels. (Note: energy level is discussed in Chapter 8.) In a neutral (unreacted) atom, the number of electrons equals the number of protons, so the atom has a charge of zero. It must be mentioned that the chemistry of a given atom comes from its electrons; all chemical changes take place entirely with regard to the electrons—the nucleus is never affected by chemical reactions. The properties of the three sub-atomic particles are summarized in Table 1.1.

1.2.1 Atomic number (Z) The atomic number of an element is defined as the number of protons in the nucleus of an atom of the element. It is also equal to the number of electrons in a neutral atom. Atomic number is a characteristic of a given element and determines its chemical properties.

Table 1.1

Properties of subatomic particles

Fundamental particle Symbol Electron Proton Neutron

e p n

Location

Mass (g)

Mass (amu)

Charge

Outside the nucleus Inside the nucleus Inside the nucleus

9.110 × 10−28

0.00549 1.0073 1.0087

−1 1 0

1.673 × 10−24 1.675 × 10−24

Atomic Structure and Isotopes

3

1.2.2 Mass number (A) The mass number of an element is the sum of protons and neutrons in the nucleus of the atom.

Mass number (A) = No. of protons (Z) + No. of neutrons (N) A = Z+N The general symbol for an element, showing its mass number and atomic number, is: A ZE

A = mass number in atomic mass units (amu) Z = atomic number E = symbol of the element as shown on the periodic table For example, the symbols for C and Mg, showing their mass and atomic numbers, are: 12 6C

and

24 12 Mg

1.2.3 Ions An ion is an atom or group of atoms that has gained or lost electron(s). A positively charged ion results when an atom loses one or more electrons. Conversely, a negatively charged ion is formed when an atom gains one or more electrons. For example, a sodium atom, Na, loses one electron to form a sodium ion, Na+ ; a nitrogen atom, N, gains three electrons to form a nitrogen (or nitride) ion, N3− .

Let us try to determine the number of protons, electrons, and neutrons in the Ca2+ ion. A neutral Ca atom has twenty electrons and twenty protons (atomic number = 20). A Ca2+ ion however, has twenty protons and eighteen electrons (for a net charge of +2). The mass number, which is the sum of protons and neutrons, is forty; since the ion has twenty protons, it must have 40 – 20 = 20 neutrons.

Example 1.1 Determine the number of protons, neutrons, and electrons in (a) 23 11 Na

(b) 168 O2−

3+ (c) 56 26 Fe

(d) 63 29 Cu

Solution The solutions are summarized in the following table.

(a) (b) (c) (d)

Symbol

Protons

Neutrons

Electrons

23 Na 11 16 O2− 8 56 Fe3+ 26 63 Cu 29

11

12

11

8

8

10

26

30

23

29

34

29

4

Chemistry in Quantitative Language

Example 1.2 Complete the following table.

Particle A B C D E F G H

Atomic number

Mass number

protons 25

13 35 15

Number of neutrons electrons 30 14

80 31 39

82 19

9

125

25

26

Symbol En± Mn Al3+

36 18 80 0 −1

10 56

Net charge

K

23

Solution To complete this table, you need to recall the basic definitions and the general equation: Mass number (A) = No. of protons (Z) + No. of neutrons (N). Use the periodic table to identify the corresponding symbols. Also remember that atomic number is equal to the number of protons in the nucleus of an atom. In a neutral atom (zero charge), the number of electrons is always equal to the number of protons. The difference between the number of protons and the number of electrons is the charge on the atomic particle. If the number of protons is greater than the number of electrons, the particle takes on a net positive charge, and vice-versa. The complete table is Particle

Atomic number

Mass number

A B C D E F G H

25 13 35 15 82 19 9 26

55 27 80 31 207 39 19 56

Net charge

Symbol En±

protons

Number of neutrons electrons

25 13 35 15 82 19 9 26

30 14 45 16 125 20 10 30

0 3 −1 −3 2 0 −1 3

Mn Al3+ Br− P3− Pb2+ K F− Fe3+

25 10 36 18 80 19 10 23

1.3 Isotopes Isotopes are atoms that have the same atomic number, and hence are the same element, but that have different mass numbers (that is, different numbers of neutrons). The difference in mass is due to the variation in the neutron number. Isotopes have practically the same chemical properties but differ slightly in physical properties. Most elements exhibit isotopy. For example, hydrogen has three isotopes: hydrogen, deuterium, and tritium. The atomic numbers and mass numbers are shown in Table 1.2.

Atomic Structure and Isotopes

5

Table 1.2 The hydrogen isotopes

Atomic number Mass number

Hydrogen (H)

Deuterium (D)

Tritium (D)

1 1

1 2

1 3

Example 1.3 Which of the following are isotopes?

18 a) 18 9 F and 10 Ne

b) 21 H and 31 H 40 c) 40 19 K and 20 Ca 25 d) 24 12 Mg and 12 Mg

Solution Isotopes are atoms with the same atomic number but different mass number. Here only (b) and (d) are isotopes.

1.4 Relative Atomic Mass The relative mass of an atom is called atomic mass (older textbooks call it “atomic weight”) and is characteristic of each element. The mass of an individual atom is difficult to measure, but the relative masses of the atoms of different elements can be measured, and this determines the atomic mass.

The masses of individual atoms and molecules are exceedingly small and cannot be conveniently expressed in grams or kilograms. For example, one atom of Ca has a mass of 6.64 × 10−23 g. For this reason, scientists instead use a relative atomic mass scale. Scientists have chosen the carbon-12 isotope as a reference, and its mass is defined as exactly twelve atomic mass 1 of the mass of the carbon-12 atom. units (amu). Therefore one atomic mass unit is equal to 12 One amu has been determined experimentally to be 1.66 × 10−24 g.

The relative atomic mass of an element is defined as the mass of an atom of that element 1 of the mass of the carbon-12 isotope. compared with 12 The atomic masses of elements given in the periodic table are not the same as mass number. In nature, most elements occur as a mixture of isotopes. Therefore, the atomic mass of an element is an average mass based on the abundance of the isotopes.

1.4.1 Calculating atomic masses The information needed to calculate the atomic masses of elements includes: the number of isotopes for the element, the relative mass of each isotope on the carbon-12 scale, and the percent abundance of each isotope.

The atomic mass of a given element is then obtained as the sum of the product of the exact mass of each isotope and its percent abundance. For example, naturally occurring carbon consists of

6

Chemistry in Quantitative Language

13 a mixture of 98.89% carbon-12 (12 6 C) with a mass of 12.00000 amu, and 1.11% carbon-13 (6 C) with a mass of 13.00335 amu. The atomic mass is obtained as follows:

Atomic mass = (12.00000 amu)

1.11 98.89 + (13.00335 amu) = 12.011 amu 100 100

An instrument called the mass spectrometer measures the exact mass of each isotope and its relative abundance.

Example 1.4 Calculate the average atomic mass of lithium, which is a mixture of 7.5% 6 Li and 92.5% 7 Li. The exact masses of these isotopes are 6.01 amu and 7.02 amu.

Solution Multiplying the abundance of each isotope by its atomic mass and then adding these products gives the average atomic mass.

92.5 7.5 + (7.02 amu) = 6.94 amu Average atomic mass of Li = (6.01 amu) 100 100

Example 1.5 Boron, B, with an atomic mass of 10.81, is composed of two isotopes, 10 B and 11 B, weighing 10.01294 and 11.00931 amu, respectively. What is the fraction and percentage of each isotope in the mixture?

Solution Let the abundance of 10 B be X and that of 11 B be 1 − X since there are only two isotopes of boron. Therefore, Atomic mass = 10.81 = (X) (10.01294) + (1 − X) (11.00931) Now solve for X: 10.81 = 10.01294 X + 11.0093 − 11.0093 X 10.0129 X − 11.0093 X = 10.81 − 11.0093 − 0.9964 X = −0.1993 X = 0.20 or 20% and 1 − X = 0.80 or 80% The fraction and % of 10 B is 0.20 or 20%. Also, the fraction of 11 B is 0.80 or 80%.

Atomic Structure and Isotopes

7

1.5 Problems 1. How many protons, neutrons, and electrons are in each of the following?

10 40 163 (a) 197 79 Au (b) 5 B (c) 20 Ca (d) 66 Dy 2. How many protons, neutrons, and electrons are in each of the following?

24 69 75 (a) 84 36 Kr (b) 12 Mg (c) 31 Ga (d) 33 As 3. Find the number of protons, neutrons, and electrons in the following ions: 2+ 2+ 3+ 2+ (a) 59 (b) 24 (c) 69 (d) 118 50 Sn 27 Co 31 Ga 12 Mg 4. Identify the following atoms or ions. (a) A halogen (an element in group VII of the periodic table) anion with thirty-six electrons and thirty-five protons. (b) An alkali metal (an element in group I of the periodic table) cation with fifty-five protons and fifty-four electrons. (c) A transition metal cation with twenty-five protons and twenty-three electrons. (Note: Transition elements are those elements embedded between groups II and III in the periodic table).

5. Complete the following table.

79 S e2− 34

137 B a2+ 56

238

15

146 88

8

40 C a2+ 20

Symbol Mass number Protons Neutrons Electrons Net charge

15 16 −3

−3

6. With the aid of a periodic table, identify the following elements: (a) 56 26 X;

(b) 131 53 X;

(c) 202 80 X;

(d) 19 9 X

7. Fill in the blanks in the following table: Particle A B C D E F G H

Atomic number

Mass number

35

80 31

protons 13 15

24 54

Number of neutrons electrons

P3− 24

17 81 40

Symbol

−1 3

14 28

35 131 204

Net charge

0 0 80 51

4

Zr4+

8

Chemistry in Quantitative Language

8. Find the number of protons, neutrons, and electrons in the following ions: 2− 3− − 2− (a) 32 (b) 80 (c) 128 (d) 147 N 16 S 35 Br 52 Te 9. Naturally occurring chlorine has two isotopes, which occur in the following abundance: 37 75.76% 35 17 Cl, with an isotopic mass of 34.9689 amu, and 24.24% 17 Cl, with a isotopic mass 36.9659 amu. Calculate the atomic mass of chlorine.

10 10. Boron has two naturally occurring isotopes: 80% of 11 5 B, and 20% of 5 B, which has an isotopic mass of 10.02 amu. If the atomic mass of boron is 10.81, what is the isotopic mass of 11 5 B?

11. Naturally occurring oxygen gas consist of three isotopes. Use the information in the table to calculate the atomic mass of oxygen gas.

Isotope

Exact mass

Abundance

16 O 8 17 O 8 18 O 8

15.995

99.96%

16.999

0.037%

17.999

0.024%

12. Naturally occurring gallium (Ga) exists in two isotopic forms, 69 Ga and 71 Ga. The atomic mass of Ga is 69.72. What is the percentage abundance of each isotope? (The exact isotopic masses of 69 Ga and 71 Ga are 68.9259 and 70.9249, respectively).

2 Formula and Molecular Mass ............................................................................

Many chemists use the terms formula mass and molecular mass interchangeably when dealing with chemical compounds of known formula. This chapter explains the slight difference between the two terms.

2.1 Formula Mass The formula mass of a compound is the sum of the atomic masses of all the atoms in a formula unit of the compound, whether it is ionic or molecular (covalent).

The formula mass is based on the ratio of different elements in a formula, as opposed to the molecular mass, which depends on the actual number of each kind of atom (compare to Section 4.2). Formula masses are relative since they are derived from relative atomic masses.

For example, the formula mass of phosphoric acid, H3 PO4 , is 97.98 atomic mass units (amu) and is obtained by adding the atomic masses (taken from the periodic table) of the elements in one formula unit (i.e. 3 H + 1 P + 4 O).

(3 × At. wt. of H) + (1 × At. wt. of P) + (4 × At. wt. of O) = (3 × 1.00) + (1 × 30.97) + (4 × 16.00) = 97.97

2.2 Molecular Mass Once the actual formula of a chemical substance is known, the molecular mass can be determined in a manner similar to that for calculating the formula mass. The molecular mass of a compound is the sum of the atomic masses of all the atoms in one molecule of the compound. The term applies only to compounds that exist as molecules such as H2 O, SO2 , and glucose, C6 H12 O6 .

For example, the molecular mass of ethanol, C2 H5 OH, is (2 × C) + (6 × H) + (1 × O) = (2 × 12.0) + (6 × 1.0) + (1 × 16.0) = 46

Chemistry in Quantitative Language: Fundamentals of General Chemistry Calculations. Second Edition.

Christopher O. Oriakhi, Oxford University Press. © Christopher O. Oriakhi 2021.

DOI: 10.1093/oso/9780198867784.003.0002