ADVANCED 1

Philip Matthews

B&& CAMBRIDGE UNIVERSITY PRESS Contents

Acknowledgements pagex 5 Radioactive decay 28 How to use this book xi 5.1 Detection of radiation 28 5.2 Half-lives 29 5.3 The radioactive decay law 31 5.4 Decay schemes 31 PHYSICAL CHEMISTRY 6 Nuclear energy 34 1 Elements, and electrons: basic 6.1 Discovery of nuclear energy 34 ideas 3 6.2 Fission reactions 34 1.1 's 3 6.3 Nuclear power 35 1.2 Evidence for atoms 5 6.4 Fusion reactions 37 1.3 Cathode rays 6 6.5 Nuclear weapons 38 1.4 Millikan's experiment 6 1.5 Electric Charge is quantised 7 7 Applications of radioactivity 41 7.1 Industrial uses of radioactivity 41 2 Energy levels 9 7.2 Medical uses of radioactivity 42 2.1 Energy changes 9 7.3 Radiocarbon dating 42 2.2 Energy levels 9 7.4 Chemical applications 43 2.3 Max Planck and energy levels 11 2.4 Light energy 11 8 Bohr's model of the 46 8.1 Energy levels of the atom 46 3 Atoms and the nucleus 13 8.2 How to calculate the ionisation energy of 3.1 A plum pudding 13 hydrogen 47 3.2 How the nucleus was discovered 13 8.3 What are Orbitals? 48 3.3 The discovery of protons 14 8.4 What are stationary states? 48 3.4 Moseley and 15 8.5 Ground and excited states 49 3.5 Discovery of 15 3.6 A comparison of electrons, protons and 9 The hydrogen atom spectrum 51 neutrons 16 9.1 Balmer's formula for the hydrogen atom 51 3.7 17 9.2 Bohr's explanation 51 3.8 Atomic units 17 9.3 Other lines in the hydrogen spectrum 51 3.9 Relative atomic and molecular masses 18 3.10 Einstein's equation 18 10 Waves and particles 54 3.11 20 10.1 Experimental evidence about the nature 3.12 Mass defect and mass excess 21 of light 54 10.2 What is wave—particle duality? 56 4 Discovery of radioactivity 23 10.3 de Broglie's equation 56 4.1 The discovery of radioactivity 23 4.2 New elements 24 11 Schrödinger's theory of the atom 58 4.3 Some properties of radiation 24 11.1 Schrödinger's theory of the hydrogen 4.4 Units of radioactivity 25 atom 58 4.5 Nuclear reactions 25 11.2 What do the quantum numbers teil us? 59 4.6 Artificially prepared elements 26 11.3 Different types of orbital 59 4.7 A sad ending 27 11.4 Wavefunctions and what they mean 60 11.5 The shapes of orbitals 61 18.2 Ionic substances have some covalent 11.6 The spin quantum number 63 character 101 18.3 Other evidence that a substance contains 12 The aufbau method and electron ions 102 structures 66 18.4 Which elements make ionic Compounds? 103 12.1 What is the aufbau method? 66 18.5 Why do ionic Compounds exist? 103 12.2 More about orbital energies 66 18.6 Ionic Compounds and electron structures 104 12.3 Filling orbitals - the importance of energy 67 12.4 The Pauli exclusion principle 67 19 Polar molecules and polar bonds 107 12.5 Hund's rule 68 19.1 What is a polar molecule? 107 12.6 Background to Hund's rule 68 19.2 Polar bonds and 107 12.7 The aufbau method in action 68 19.3 Polar molecules and dipole moments 108 19.4 Polarisability 111 13 Electron structures, ionisation energies and shielding 71 20 Intermolecular forces 113 13.1 What is shielding? 71 20.1 Where are intermolecular forces found? 113 13.2 Ionisation energies down a 71 20.2 What causes intermolecular forces? 113 13.3 Ionisation energies across a 72 20.3 Dispersion forces and polarisability 114 13.4 How ionisation energies are linked to 20.4 Intermolecular forces are also produced Groups in the 73 by permanent dipoles 114 20.5 Some words of warning 114 14 Bonding in molecules: valence bond theory 77 21 Hydrogen bonding 117 14.1 Valence bond theory 77 21.1 What is hydrogen bonding? 117 14.2 Dot-and-cross diagrams for diatomic 21.2 Evidence for hydrogen bonding 117 molecules 78 21.3 Intermolecular and intramolecular 14.3 Dot-and-cross diagrams for triatomic and hydrogen bonding 119 quadratomic molecules 78 21.4 Hydrogen bonding in biochemistry 120 14.4 Dot-and-cross diagrams for hydrocarbons 79 21.5 Hydrogen bonding in solids 120 14.5 Showing bonds by lines 79 14.6 Bonding in oxoanions 80 22 Metallic bonding 122 14.7 Resonance structures 80 22.1 How can you recognise a ? 122 22.2 What is the band structure of ? 122 15 Coordinate bonding 84 22.3 Why do metals conduct electricity? 123 15.1 What is coordinate bonding? 84 22.4 Semiconductors 123 22.5 Why do metals conduct heat? 126 16 Molecular orbital theory 87 22.6 Metal atoms exist in a sea of electrons 126 16.1 Wavefunctions can be positive or negative 87 23 The three states of matter 128 16.2 How wavefunctions can be combined 87 23.1 The three states of matter 128 16.3 Bonding and antibonding orbitals using s 23.2 How do we know that gases are disorderly? 129 orbitals 87 23.3 Differences in properties of solids, liquids 16.4 Bonding and antibonding orbitals using p and gases 129 orbitals 88 23.4 The potential energy curve for two 16.5 Energies of bonding and antibonding neighbouring molecules 130 orbitals 89 23.5 Some remarkable substances 130 16.6 Molecular orbitals for homopolar diatomic molecules 90 24 Three types of spectroscopy 136 16.7 Molecular orbitals for heteropolar 24.1 Emission and absorption spectra 136 diatomic molecules 91 24.2 Electronic spectroscopy 136 16.8 Molecular orbitals for hydrocarbons 92 24.3 Vibrational spectroscopy 136 24.4 Rotational spectroscopy 136 17 Shapes of molecules 95 24.5 Translations 138 17.1 Molecular modeis 95 24.6 Electromagnetic waves 138 17.2 Electron repulsion theory 95 24.7 The electric field and electrons 139 17.3 The isoelectronic rule 96 24.8 The magnetic field and electrons 139 17.4 Hybridisation 97 24.9 Selection rules 140

18 Ionic bonding 101 25 Visible spectroscopy 142 18.1 Covalent substances have some ionic 25.1 Why does copper(n) sulphate Solution character 101 lookblue? 142

IV Contents 25.2 The visible spectrum of copper(n) 32 Unit cells 179 sulphate Solution 142 32.1 The seven crystal Systems 179 25.3 How does a visible light spectrometer 32.2 The fourteen Bravais lattices 179 work? 143 32.3 What are unit cells? 179 25.4 What happens to the photons absorbed 32.4 Radius ratio rules 184 by copper(n) sulphate Solution? 144 32.5 The number of atoms or ions in a unit 25.5 Why vibrations are important in visible cell 185 spectra 144 33 Sizes of atoms, ions and molecules 188 26 Ultraviolet spectroscopy 146 33.1 How can we estimate the size of an 26.1 The ultra violet spectrum of alkenes 146 atom? 188 26.2 The ultraviolet spectrum of arenes 147 33.2 Metallic and covalent radii 188 26.3 The ultraviolet spectrum of aldehydes 33.3 Van der Waals radii 189 and ketones 147 33.4 Ionic radii 190 33.5 Bondlengths 191 27 Vibrational spectroscopy 149 27.1 Why is vibrational spectroscopy useful? 149 34 Real and ideal gases 193 27.2 What are group frequencies? 151 34.1 The gas laws 193 27.3 Making sense of vibrational spectra 151 34.2 Real gases and the van der Waals 27.4 Vibrational spectra can teil us about the equation 195 strengths of bonds 155 34.3 How good is the van der Waals equation? 196 35 Kinetic theory of gases 200 28 Nuclear magnetic resonance 157 What is the kinetic theory of gases? 200 28.1 The importance of nuclear spin 157 35.1 The pressure of an ideal gas 200 28.2 The patterns in an n.m.r. spectrum 158 35.2 The connection between energy and 28.3 Why do protons appear in different 35.3 temperature 201 places in the spectrum? 158 The spread of energies in a gas 202 28.4 N.m.r. spectra can teil us how many 35.4 protons are present 158 35.5 Kinetic theory and Avogadro's theory 203 28.5 Not only hydrogen atoms can show up in 36 n.m.r. 159 Chemistry and gases 205 36.1 Gay-Lussac's law of combining volumes 205 36.2 Avogadro's theory 205 29 161 36.3 Dalton's law of partial pressures 206 29.1 What are mass spectrometers? 161 36.4 Graham's law of diffusion 206 29.2 The design of a mass spectrometer 161 29.3 The whole number rule and Standards of 37 The mole 209 mass 162 37.1 What is the mole? 209 29.4 Mass spectra and isotopes 164 37.2 How to work with moles of Compounds 210 29.5 Calculating relative atomic masses from 37.3 Moles and equations 210 mass spectra 164 37.4 Moles and balancing equations 211 29.6 What are fragmentation patterns? 164 37.5 The empirical formula and molecular 29.7 The effect of isotopes in a molecule's mass formula of a Compound 212 spectrum 165 37.6 Percentage compositions 213

30 X-ray diffraction 168 38 Molar masses of gases and liquids 216 30.1 What causes X-ray diffraction? 168 38.1 Measuring the molar mass of a gas 216 30.2 More about diffraction 168 38.2 Measuring the molar mass of a soluble 30.3 Bragg's equation 169 gas 217 30.4 Different types of X-ray diffraction 38.3 Measuring the molar mass of a volatile experiment 169 liquid 218 30.5 Explanation of powder photographs 170 30.6 The arrangement of planes in crystals 171 39 Moles and titrations 221 30.7 The arrangements of individual atoms 172 39.1 Standard Solutions 221 39.2 The concentration of a Solution 223 31 Crystallography 174 39.3 Concentration and molarity 224 31.1 What is crystallography? 174 39.4 How to do calculations involving 31.2 The dosest packing of atoms 174 concentrations 224 31.3 Structures that are not close-packed 176 31.4 C oordination numbers 176 40 Four types of titration 227 31.5 Metal crystals 176 40.1 Acid-base titrations 227

Contents v 40.2 Redox titrations 227 49.2 The Boltzmann distribution 281 40.3 Titrations involving iodine 229 49.3 More about energy levels 281 40.4 Silver nitrate titrations 230 49.4 Entropy changes and mixing of gases 282 49.5 Entropy and disorder 283 41 Oxidation numbers and oxidation 49.6 Reversible and irreversible changes 285 states 234 49.7 Some changes are spontaneous, some are 41.1 What are oxidation and reduction not 285 reactions? 234 49.8 Entropy and reversible changes 286 41.2 What are oxidation numbers? 235 49.9 Entropy and non-reversible changes 286 41.3 Oxidation numbers of elements in 49.1(0 Standard entropies 288 covalent Compounds 235 49.149.11 Calculating entropy changes 289 41.4 Oxidation numbers of elements in ions 236 41.5 Rules for assigning oxidation numbers 237 50 Free energy 291 41.6 Oxidation states 237 50.1 What is free energy? 291 41.7 Using oxidation numbers with equations 238 50.2 Standard free energies 293 41.8 Half-equations 240 50.3 Free energy values do not teil us how fast a reaction will occur 294 42 Energy changes 243 50.4 Free energy changes under non-standard 42.1 Energy changes and chemical bonds 243 conditions 294 42.2 Energy changes and energy diagrams 244 50.5 Ellingham diagrams and the extraction of 42.3 Exothermic and endothermic reactions 245 metals 295

43 Enthalpy 247 51 Equilibrium and free energy 299 43.1 What is enthalpy? 247 51.1 What is the effect of concentration and 43.2 Enthalpy and Standard states 248 pressure on free energy? 299 43.3 Enthalpy and State functions 249 51.2 What is the connection between free 43.4 Hess's law 250 energy and equilibrium? 300 51.3 Equilibrium and equilibrium constants 301 44 Standard enthalpies 252 44.1 Standard enthalpy of an dement 252 52 Chemical equilibrium 304 44.2 Standard heats of formation 252 52.1 Equilibrium constants 304 44.3 Standard heats of combustion 253 52.2 Equilibrium constants and their units 305 44.4 Enthalpy changes when substances break 52.3 Are equilibrium constants really apart 255 constant? 306 44.5 Bond energies and average bond energies 255 52.4 How does temperature affect an 44.6 Heats of hydrogenation 256 equilibrium reaction? 306 52.5 How can the connection between 45 Calculations using Hess's law 259 equilibrium constants and temperature 45.1 Using heats of formation 259 be made more exact? 307 45.2 Impossible reactions 260 52.6 Pressure can change the proportions of reactants and products at equilibrium 308 46 Lattice energies 263 46.1 What is meant by lattice energy? 263 53 Some equilibrium reactions 314 46.2 The Born-Haber cycle 263 53.1 What this unit is about 314 46.3 What do lattice energies teil us? 265 53.2 The bismuth trichloride—water reaction 314 53.3 The chromate(vi)-dichromate(vi) reaction 314 47 Enthalpy changes in Solutions 271 53.4 The iodine—iodine trichloride reaction 314 47.1 Heats of neutralisation 271 53.5 The iodine—triiodide reaction 315 47.2 Hydration energies 273 53.6 The nitrogen dioxide-dinitrogen 47.3 Heats of Solution 273 tetraoxide reaction 315 47.4 Enthalpies of formation of ions in 53.7 The decomposition of ammonium salts 315 Solution 274 53.8 Reactions involving complex ions 315

48 Internal energy 276 54 Measuring equilibrium constants 318 48.1 What is internal energy? 276 54.1 How can equilibrium constants be 48.2 Taking account of work 276 measured? 318 48.3 Measuring internal energy with a bomb 54.2 The ester equilibrium 318 calorimeter 277 54.3 The hydrogen iodide equilibrium 320

49 Entropy 279 55 Equilibria between phases 323 49.1 A first look at entropy 279 55.1 What is a phase? 323

vi Contents 55.2 How to interpret a phase diagram 323 63 Distillation 365 55.3 The phase diagram of sulphur 324 63.1 The boiling points of mixtures 365 55.4 The phase diagram of helium 324 63.2 How distillation works 366 63.3 Industrial distillation 368 56 Chromatography 327 63.4 Does distillation always work? 369 56.1 What is chromatography? 327 63.5 Steam distillation 370 56.2 Paper chromatography 328 56.3 Thin layer chromatography (TLC) 330 64 Solubility product 373 56.4 Column chromatography 330 64.1 What is a solubility product? 373 56.5 Ion exchange chromatography 331 64.2 Using solubility products to calculate 56.6 Gas-liquid chromatography (GLC) 331 solubilities 373 56.7 High pressure liquid chromatography 64.3 The common ion effect 375 (HPLC) 332 64.4 Solubility products teil us when a precipitate will be made 375 57 Polymorphism and allotropy 335 64.5 Using solubility products in chemical 57.1 What is polymorphism? 335 analysis 376 57.2 What is allotropy? 336 65 Colligative properties 379 58 Equilibrium between a solid and 65.1 What are colligative properties? 379 liquid 340 65.2 Why does a solute influence the vapour 58.1 What happens when a liquid freezes? 340 pressure of water? 379 58.2 Cooling curves 341 65.3 Elevation of boiling point 379 58.3 Cooling curves for mixtures 341 65.4 How to make use of the boiling point constant 380 59 Solubility of salts in water 345 65.5 Depression of freezing point 381 59.1 The solubility of a solid in water 345 65.6 Osmotic pressure 382 59.2 Fractional crystallisation 346 65.7 Methods of measuring osmotic pressure 382 59.3 Crystals that contain water of 65.8 How might we explain osmosis? 383 crystallisation 346 65.9 How to calculate molar masses from 59.4 Saturated and supersaturated Solutions 347 osmotic pressure experiments 383 65.10 Some examples of osmosis 384 60 Explaining solubilities 349 65.11 Abnormal molar masses 384 60.1 Why is water a good solvent for ionic 65.12 Calculating the degree of dissociation crystals? 349 from abnormal molar masses 385 60.2 Entropy changes are important when a 65.13 The thermodynamic explanation of crystal dissolves 350 colligative properties 386 60.3 The sizes of the ions in a crystal are 65.14 Raoult's law and solids in Solution 387 important in explaining solubilities 351 60.4 Why is water a good solvent for many 66 Electrochemical cells 389 covalent substances? 351 66.1 How an equilibrium is set up between a 60.5 Covalent liquids often dissolve covalent metal and Solution 389 solids 352 66.2 The Standard hydrogen electrode 390 60.6 Volume changes when solids dissolve 352 66.3 Standard electrode potentials 390 66.4 Combining half-cells 391 61 Mixtures of liquids 355 66.5 How to work out cell reactions 392 61.1 What is the difference between miscible 66.6 A quick way of writing cells 393 and immiscible liquids? 355 66.7 The anode and cathode in a cell 393 61.2 Raoult's law and ideal Solutions 355 66.8 More about salt bridges 393 61.3 Solutions that do not obey Raoult's law 356 66.9 The electrochemical series 394 61.4 Why are there deviations from Raoult's 66.10 Some useful cells 395 law? 357 61.5 Why do some liquids mix and others 67 Cells and concentration changes 400 not? 357 67.1 How cell e.m.f.s change with concentration 400 62 Competition between solvents 362 67.2 How to work out equilibrium constants 62.1 Solvent extraction 362 from cell e.m.f.s 401 62.2 Solvent extraction is an equilibrium 67.3 Concentration cells 403 process 362 67.4 pH and the glass electrode 404 62.3 Partition coefficients 363 62.4 Why do some results not fit the partition 68 Corrosion 408 law? 363 68.1 An example of corrosion 408

Contents vn 68.2 The rusting of iron 409 75.9 How to work out the pH of a weak acid 450 68.3 How does a layer of zinc prevent iron 75.10 Buffer Solutions 450 rusting? 409 68.4 Why does tin protect iron from corrosion? 410 76 Neutralisation and titrations 455 76.1 Salt hydrolysis 455 69 Cells and thermodynamics 412 76.2 Salts of a strong acid and a strong base 455 69.1 The link between free energy and cell 76.3 Salts of a strong acid and a weak base 455 e.m.f.s 412 76.4 Salts of a weak acid and a strong base 455 69.2 Calculating Standard e.m.f.s from free 76.5 Salts of a weak acid and a weak base 456 energy values 412 76.6 Endpoints in titrations depend on the 69.3 Calculating free energy values from strength of the acid and base 456 Standard e.m.f.s 413 76.7 Indicators 456

70 Redox potentials 415 77 Rates of reactions 459 70.1 Standard redox potentials 415 77.1 Why do we study the rates of reactions? 459 70.2 Predicting redox reactions 416 77.2 What makes reactions take place? 459 70.3 Predicting reactions in the laboratory 77.3 What can prevent reactions taking place? 460 from redox potentials 416 77.4 How can we make reactions go faster? 461 70.4 Redox titrations 417 78 Two theories of reaction rates 465 71 Redox Charts 420 78.1 Collision theory 465 71.1 What is a redox chart? 420 78.2 More about the activation energy 466 71.2 How to use redox charts 420 78.3 Catalysts and activation energy 467 71.3 What is disproportionation? 422 78.4 Transition State theory 467

72 Electrolysis 426 79 Measuring the rates of reactions 471 72.1 What is an electric current? 426 79.1 An example of measuring a rate 471 72.2 What happens during electrolysis? 427 79.2 Six ways of measuring rates 472 72.3 Examples of electrolysis 428 79.3 Measuring the rates of very fast reactions 476 72.4 How to calculate the mass of a substance liberated in electrolysis 430 80 Rate laws 480 72.5 Why is electrolysis used in industry? 431 80.1 What is a rate law? 480 80.2 How can we discover the rate law? 481 73 Conductivity of Solutions 433 80.3 Quick ways of finding the rate law 482 73.1 How do we measure conductivity? 433 80.4 The contribution of individual Orders to 73.2 Molar conductivities 434 the overall rate law 484 73.3 Molar conductivities and the degree of dissociation 435 81 Reaction mechanisms 487 73.4 How individual ions contribute to 81.1 What is a reaction mechanism? 487 conductivities 435 81.2 Bonds can break in two ways 487 73.5 How can we make use of conductivity 81.3 The slowest Step in a reaction governs the measurements? 436 rate 488 81.4 Free radical reactions 489 74 Acids and bases 439 81.5 Mechanisms of the hydrolysis of 74.1 Early ideas about acids 439 halogenoalkanes 490 74.2 Acids give hydrogen ions in Solution 439 81.6 The influence of catalysts 491 74.3 The Brensted theory of acids and bases 440 81.7 The kinetics of enzyme reactions 492 74.4 The Lewis theory of acids and bases 441

75 Strong and weak acids 443 75.1 What is the difference between strong INDUSTRIAL CHEMISTRY and weak acids? 443 75.2 Conjugate acids and bases 443 82 The chemical industry 497 75.3 The ionic produet of water 444 82.1 Why is the chemical industry important? 497 75.4 Acid dissociation equilibrium constants 445 82.2 The stages in producing a new produet 498 75.5 What makes an acid strong? 446 82.3 The economics of produetion 499 75.6 What is the connection between pH and 82.4 Cash flow in the produetion cycle 500 PKa? 448 82.5 Running a chemical plant 501 75.7 Base dissociation constants and p/Cb 449 82.6 Designing a chemical plant 502 75.8 How to work out the degree of 82.7 Energy and mass balances 502 dissociation of a weak acid 449 82.8 Continuous and batch processing 503

vm Contents 83 Chemical processes 506 85.4 Reducing an oxide ore 520 83.1 Examples of modern chemical 85.5 The extraction of reactive metals 521 manufacture 506 83.2 Manufacture of sulphuric acid 506 86 The oil industry 525 83.3 The Haber process for the manufacture of 86.1 Why is the oil industry important? 525 ammonia 508 86.2 Catalytic re-forming 526 83.4 The manufacture of nitric acid 510 86.3 Catalytic cracking 527 86.4 Thermal cracking 528 84 The chlor-alkali industry 512 Appendix A The laws of thermodynamics 533 84.1 What is the chlor-alkali industry? 512 84.2 The production of chlorine and sodium Appendix B Table of ionisation energies 535 hydroxide 512 Appendix C Table of atomic masses 536 Appendix D Values of some universal 84.3 The ammonia-soda (Solvay) process 514 constants 538 Bibliography 539 85 The extraction of metals 518 Examination questions 540 85.1 The methods of extraction 518 Answers to examination questions 558 85.2 Extracting the noble metals 518 Subject index 559 85.3 Reducing sulphide ores 520 Index of names 569