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Pharmaceutical Analysis E-Book

Pharmaceutical Analysis E-Book

David G. Watson

(2015)

Additional Information

Book Details

Abstract

Pharmaceutical analysis determines the purity, concentration, active compounds, shelf life, rate of absorption in the body, identity, stability, rate of release etc. of a drug. Testing a pharmaceutical product involves a variety of chemical, physical and microbiological analyses. It is reckoned that over £10 billion is spent annually in the UK alone on pharmaceutical analysis, and the analytical processes described in this book are used in industries as diverse as food, beverages, cosmetics, detergents, metals, paints, water, agrochemicals, biotechnological products and pharmaceuticals.

This is the key textbook in pharmaceutical analysis, now revised and updated for its fourth edition.

  • Worked calculation examples
  • Self-assessment
  • Additional problems (self tests)
  • Practical boxes
  • Key points boxes
  • New chapter on Biotech products.
  • New chapter on electrochemical methods in diagnostics.
  • Greatly extended chapter on molecular emission spectroscopy to accommodate developments and innovations in the area.
  • Now on StudentConsult

Table of Contents

Section Title Page Action Price
Front Cover cover
IFC_StudentConsult IFC2
Pharmaceutical Analysis i
Copyright Page iv
Preface v
Table Of Contents vii
Learning resources xiii
1 Control of the quality of analytical methods 1
Introduction 1
Control of errors in analysis 2
Accuracy and precision 4
Validation of analytical procedures 7
The analytical procedure 7
Levels of precision 7
Repeatability 8
Intermediate precision 10
Reproducibility 10
Accuracy 10
Standard operating procedure (SOP) for the assay of paracetamol tablets 11
Compound random errors 11
Reporting of results 13
Other terms used in the control of analytical procedures 14
System suitability 14
Analytical blank 14
Calibration 14
Limit of detection 14
Limit of quantification 15
Linearity 15
Range 17
Robustness 18
Selectivity 18
Sensitivity 18
Weighing by difference 19
Basic calculations in pharmaceutical analysis 19
Percentage volume/volume (%v/v) 20
Percentage weight in volume (%w/v) 20
Dilutions 20
Preparation of standard stock solutions 21
Percentage weight/weight (%w/w) 22
Parts per million (ppm) calculations 23
Working between weights and molarity 23
Definitions 23
References 25
Further reading 25
2 Physical and chemical properties of drug molecules 26
Introduction 26
Calculation of pH value of aqueous solutions of strong and weak acids and bases 27
Dissociation of water 27
Strong acids and bases 27
Weak acids and bases 27
Acidic and basic strength and pKa 29
Henderson–Hasselbalch equation 29
Ionisation of drug molecules (see Animation 2.1) 30
Diphenhydramine 31
Ibuprofen 31
Buffers 32
Salt hydrolysis 36
Activity, ionic strength and dielectric constant 36
Partition coefficient 38
Effect of pH on partitioning (see Animation 2.1) 39
Drug stability 41
Zero-order degradation 42
First-order degradation 42
Stereochemistry of drugs 43
Geometrical isomerism 44
Chirality and optical isomerism 44
Diastereoisomers 47
Measurement of optical rotation (see Animation 2.3) 48
Profiles of physico-chemical properties of some drug molecules 50
Procaine 50
Paracetamol 50
Aspirin 51
Benzylpenicillin 51
5-Fluorouracil 52
Acebutolol 53
Sulfadiazine 53
Isoprenaline 54
Prednisolone 54
Guanethidine 55
Pyridostigmine bromide 55
References 57
Further reading 57
3 Titrimetric and chemical analysis methods 58
Introduction 59
Instrumentation and reagents 59
Glassware 59
Primary standards and standard solutions 59
Direct acid/base titrations in the aqueous phase 60
Strong acid/strong base titrations 60
Weak acid/strong base and weak base/strong acid titrations (see Animation 3.2) 61
Titrations of the salts of weak bases in mixed aqueous/non-aqueous media 63
Indirect titrations in the aqueous phase 64
Estimation of esters by back titration 64
Saponification value (see Animation 3.3) 64
Estimation of alcohols and hydroxyl values by reaction with acetic anhydride (AA) 65
Non-aqueous titrations 66
Theory 66
Non-aqueous titration of weak bases 67
Non-aqueous titration of weak acids 68
Argentimetric titrations 68
Compleximetric titrations 68
Redox titrations 69
Theory 69
Iodometric titrations 71
Direct titrations 71
Iodine displacement titrations 72
Iodine-absorbing substances in penicillins 73
Ion pair titrations 73
Titrations using indicator dyes 74
Titrations using iodide as a lipophilic anion 74
Diazotisation titrations 74
Potentiometric titrations 75
Potentiometric end-point detection 75
Use of potentiometric titration to determine pKa values (see Animation 3.4) 77
Karl Fischer titration (coulometric end-point detection) 78
Automation of wet chemical methods 80
Automatic titration (Fig. 3.21) 80
Flow injection analysis 81
Applications of FIA in pharmaceutical analysis 82
Determination of chloroxine 82
Determination of captopril 83
Determination of non-steroidal anti-inflammatory drugs 83
Determination of promethazine 83
Determination of chlorocresol 83
Limit test for heavy metals 83
Use of segmented flow in determination of partition coefficients 84
Automated dissolution testing 84
References 87
Further reading 87
4 Ultraviolet and visible spectroscopy 88
Introduction 89
Factors governing absorption of radiation in the UV/visible region (see Animation 4.1 and Animation 4.2) 90
Beer–Lambert Law 92
Instrumentation 93
Diode array instruments 93
Instrument calibration 94
Calibration of absorbance scale 94
Calibration of wavelength scale 95
Determination of instrumental resolution 95
Determination of stray light 95
UV spectra of some representative drug molecules 96
Steroid enones 96
Ephedrine: the benzoid chromophore 96
Ketoprofen: extended benzene chromophore 97
Procaine: amino group auxochrome 97
Phenylephrine: hydroxyl group auxochrome 98
Use of UV/visible spectrophotometry to determine pKa values 99
Applications of UV/visible spectroscopy to pharmaceutical quantitative analysis 100
Assay examples 101
Furosemide (frusemide) in tablet form 101
Assay of cyclizine lactate in an injection 101
Assay of penicillins by derivatisation (Fig. 4.12) 103
Assay of adrenaline in lidocaine (lignocaine) adrenaline injection 104
Difference spectrophotometry 105
Analysis of aspirin in dextropropoxyphene compound tablets 105
Derivative spectra 106
Applications of UV/visible spectroscopy in preformulation and formulation 109
Partition coefficient 109
Solubility 110
Release of a drug from a formulation 110
Reference 112
Further reading 112
5 Infrared spectrophotometry 113
Introduction 114
Factors determining intensity and energy level of absorption in IR spectra 115
Intensity of absorption 115
Energy level of absorption 116
Instrumentation 116
Instrument calibration 118
Sample preparation 118
Application of IR spectrophotometry in structure elucidation 121
Examples of IR spectra of drug molecules 122
IR spectrophotometry as a fingerprint technique 125
Preparation of samples for fingerprint determination 125
Infrared spectrophotometry as a method for identifying polymorphs 128
Near-infrared analysis (NIRA) 128
Introduction 129
Examples of NIRA applications 129
Determination of particle size in United States Pharmacopoeia (USP) grade aspirin 130
Determination of blend uniformity 130
Determination of active ingredients in multicomponent dosage forms 131
In-pack determination of active ingredients 131
Determination of polymorphs 131
Moisture determination 132
Process control of components in a shampoo 132
References 134
Further reading 134
Additional reading 135
6 Atomic spectrophotometry 136
Atomic emission spectrophotometry (AES) 136
Introduction 136
Instrumentation 137
Examples of quantitation by AES 138
Assay of sodium and potassium ions in an i.v. infusion 138
Interferences in AES analysis (see Animation 6.3) 140
Ionisation 140
Viscosity 140
Anionic interference 140
Assays based on the method of standard additions 141
Assay for KCl, NaCl and glucose i.v. infusion 141
Atomic absorption spectrophotometry (AAS) 143
Introduction 143
Instrumentation 144
Examples of assays using AAS (see Animation 6.4) 144
Assay of calcium and magnesium in haemodialysis fluid 144
Some examples of limit tests employing AAS 146
Assay of lead in sugars 146
Trace metals in a silicone foam cavity wound dressing 147
Applications of AAS in BP assays 148
Inductively coupled plasma emission spectroscopy 148
References 149
Further reading 149
7 Molecular emission spectroscopy 150
Fluorescence spectrophotometry 150
Introduction 151
Instrumentation 151
Molecules which exhibit fluorescence 152
Factors interfering with fluorescence intensity 154
Applications of fluorescence spectrophotometry in pharmaceutical analysis 154
Determination of ethinylestradiol in tablets 154
Determination of the dissolution rate of digoxin tablets 155
Determination of aluminium in water for injection as a fluorescent complex 155
Determination of stability of peptide drugs in solution 156
Fluorescent derivatives and flow injection analysis 156
Raman spectroscopy 157
Introduction 157
Instrumentation 158
Applications 159
Rapid fingerprinting of drugs 159
Analysis of drugs in their formulations 159
A quantitative application 159
Control of the polymorphic forms of drugs in tablets 160
The development of spatially offset Raman spectroscopy (SORS) as a process control tool 160
Further reading 162
8 Nuclear magnetic resonance spectroscopy 163
Introduction 164
Instrumentation 165
Proton (1H) NMR 166
Chemical shifts 166
Integration and equivalence 171
Multiplicity and spin–spin coupling 174
Splitting diagrams and spin systems 178
Application of NMR to structure confirmation in some drug molecules 185
Proton NMR spectrum of paracetamol 185
Proton NMR spectrum of aspirin 185
Proton NMR spectrum of salbutamol: a more complex example 186
Carbon NMR 189
Chemical shifts 189
An example of a 13C spectrum 190
Two-dimensional NMR spectra 191
Simple examples 191
A more complex example 192
Application of NMR to quantitative analysis 195
Other specialised applications of NMR 197
NMR in drug metabolism and related areas 199
Further reading 199
9 Mass spectrometry 200
Introduction 201
Ion generation 201
Electrospray ionisation (ESI) (see Animation 9.1) 201
Atmospheric pressure chemical ionisation (APCI) 205
Electron impact ionisation (EI) (see Animation 9.4) 205
Matrix assisted laser desorption ionisation (MALDI) 208
Other ionisation methods 210
Ion separation techniques 210
Magnetic sector mass spectrometry 210
Magnetic sector instruments 210
Quadrupole instruments (see Animation 9.5) 211
Time of flight (TOF) ion separation (see Animation 9.6) 212
Ion trap separation (see Animation 9.8) 213
Fourier transform mass spectrometry 214
Calibration of the mass axes of mass spectrometers 214
A more detailed consideration of mass spectra 216
Mass spectra obtained under electron impact (EI) ionisation conditions 216
Molecular fragmentation patterns 216
Homolytic α-cleavage (see Animation 9.9) 216
Heterolytic cleavage (see Animation 9.10) 217
Fragmentation of aliphatic rings involving hydrogen transfer (see Animation 9.11) 220
Retro Diels–Alder fragmentation (see Animation 9.12) 220
McLafferty rearrangement (see Animation 9.13) 221
EI mass spectra where the molecular ion is abundant 224
Gas chromatography–mass spectrometry (GC–MS) 227
Applications of GC–MS with EI 228
Analysis of an essential oil 228
GC–MS of process intermediates and degradation products 230
Tandem mass spectrometry (see Animation 9.16) 232
High-resolution mass spectrometry 240
Mass spectrometry of proteins 242
Mass spectrometry in drug discovery 244
Reference 246
Further reading 246
10 Chromatographic theory 248
Introduction 248
Void volume and capacity factor 248
Calculation of column efficiency 249
Origins of band broadening in HPLC 251
Van Deemter equation in liquid chromatography 251
Van Deemter equation in gas chromatography 253
Parameters used in evaluating column performance 254
Resolution 255
Peak asymmetry 258
Data acquisition 258
Report generation 260
Reference 260
11 Gas chromatography 261
Introduction (see Animation 11.1) 262
Instrumentation 262
Syringes 263
Injection systems 264
Packed column injections 264
Split/splitless injection 264
Cool on-column injection 266
Programmable temperature vapouriser (see Animation 11.4) 266
GC oven 267
Types of columns 267
Packed columns 267
Capillary columns 268
Selectivity of liquid stationary phases 268
Kovats indices and column polarity 268
Examples of the separation of mixtures by GC 269
Analysis of peppermint oil on two GC phases 269
Analysis of the fatty acid composition of a fixed oil by GC 272
Chiral selectivity 273
Use of derivatisation in GC 275
Summary of parameters governing capillary GC performance 279
Carrier gas type/flow 279
Column temperature 279
Column length 279
Film thickness phase loading 279
Internal diameter 279
GC detectors (see Animation 11.5) 280
Applications of GC in quantitative analysis 280
Analysis of methyltestosterone in tablets 282
Data from analysis of methyltestosterone tablets 283
Analysis of atropine in eyedrops 284
Brief description of the assay 285
Data from analysis of eyedrop formulation 285
Quantification of ethanol in a formulation 286
Determination of manufacturing and degradation residues by GC 287
Determination of pivalic acid in dipivefrin eyedrops 287
Determination of dimethylaniline in bupivacaine injection (Fig. 11.25) 287
Determination of N,N-dimethylaniline in penicillins 287
Determination of a residual glutaraldehyde in a polymeric film 289
Determination of residual solvents 289
Typical BP procedures 289
Determination of residual solvents and volatile impurities by headspace analysis (see Animation 11.6) 290
Purge trap analysis 292
Solid-phase microextraction (SPME) (see Animation 11.7) 292
Applications of GC in bioanalysis 293
References 295
Further reading 295
12 High-performance liquid chromatography 296
Introduction 297
Instrumentation (see Animation 12.2 and Animation 12.3) 297
Stationary and mobile phases 298
Structural factors which govern rate of elution of compounds from HPLC columns 300
Elution of neutral compounds 300
Control of elution rate of ionisable compounds by adjustment of pH of mobile phase 303
More advanced consideration of solvent selectivity in reverse-phase chromatography 307
Effect of temperature on HPLC 310
Summary of stationary phases used in HPLC 311
A more advanced consideration of reverse-phase stationary phases 312
(i) Retention factor for the lipophilic compound pentylbenzene, kPB 313
(ii) Hydrophobic selectivity αCH2 = kPB/kBB 314
(iii) Shape selectivity αT/O = kT/kO 314
(iv) Hydrogen bonding capacity αC/P = kC/kP 314
(v) Total ion exchange capacity aB/P = kB/kP (pH 7.6) 315
(vi) The acidic ion exchange capacity aB/P = kB/kP (pH 2.7) 315
Summary of detectors used in HPLC 316
Performance of a diode array detector 317
Applications of HPLC to the quantitative analysis of drugs in formulations 321
Analyses based on calibration with an external standard 321
Analysis of paracetamol tablets using a calibration curve 322
Tablets 322
Explanation of the assay 322
Assay 322
Data obtained 323
Assay of paracetamol and aspirin in tablets using a narrow-range calibration curve 323
Tablets 323
Explanation of the assay 323
Brief outline of the assay 325
Data obtained 326
Dilution of sample 326
Assay of active ingredients in an anaesthetic gel using a single-point calibration curve 327
Content per 100 g of gel 327
Explanation of the assay 327
Brief outline of the assay 327
Assays using calibration against an internal standard 329
Assay of hydrocortisone cream with one-point calibration against an internal standard 330
Explanation of the assay 330
Brief outline of the assay 331
Data obtained 332
Assay of miconazole cream with calibration against an internal standard over a narrow concentration range 333
Explanation of the assay 333
Brief outline of the assay 333
Data obtained 334
Assays involving more specialised HPLC techniques 334
Assay of adrenaline injection by chromatography with an anionic ion-pairing agent 335
Explanation of the assay 335
Assay of ascorbic acid by chromatography with a cationic ion-pairing agent and electrochemical detection 335
Assay of ascorbic acid by hydrophilic interaction chromatography 336
Assay of hyaluronic acid by size-exclusion chromatography (see Animation 12.10) 337
Methods used for the assay of proteins by HPLC 339
Analysis of non-ionic surfactants with an evaporative light scattering detector and gradient elution 341
Derivatisation in HPLC analysis 342
Separation of enantiomers by chiral HPLC 343
Ion chromatography 345
Ultra-high-performance liquid chromatography 347
References 350
Further reading 350
13 Thin-layer chromatography 351
Introduction 352
Instrumentation 352
TLC chromatogram 353
Stationary phases 354
Elutropic series and mobile phases 354
Modification of TLC adsorbant 357
Treatment of silica gel with KOH 357
Silanised silica gel 358
Keiselguhr as an inert support 358
Detection of compounds on TLC plates following development 359
Ultraviolet light 359
Location reagents 359
Iodine vapour 359
Potassium permanganate 360
Ninhydrin solution 360
Alkaline tetrazolium blue 360
Ethanol/sulphuric acid 20% 360
Applications of TLC analysis 360
Qualitative identity tests 360
Limit tests 360
Where the structure of the impurity is known 360
Where the structure of the impurity is unknown 363
Tests in which known and unknown standards are used 364
High-performance TLC (HPTLC) 365
Applications of HPTLC 365
References 367
Further reading 367
14 High-performance capillary electrophoresis 368
Introduction 369
Electrophoresis 369
Electro-osmotic flow (EOF) (see Animation 14.1) 370
Migration in Capillary electrophoresis (CE) (see Animation 14.2) 371
Instrumentation 372
Control of separation 372
Migration time 372
Dispersion 374
Longitudinal diffusion 374
Injection plug length 374
Joule heating 374
Solute/wall interactions 374
Electrodispersion 375
Applications of CE in pharmaceutical analysis 375
Separation of atenolol and related impurities predominantly on the basis of charge 375
Separation predominantly on the basis of ionic radius 376
Analysis of non-steroidal anti-inflammatory drugs (NSAIDs) by CE and separation of anions on the basis of ionic radius 378
Separation of peptides 378
Use of additives in the running buffer 379
Applications of cyclodextrins in producing improvements in separation 380
Separation of pilocarpine from its epimer 380
Separation of chiral local anaesthetics 380
Micellar electrokinetic chromatography (MEKC) 382
Separation of cefotaxime from related impurities 382
Analysis of flavonoids by MEKC 383
Capillary electrophoresis with indirect detection 384
Affinity capillary electrophoresis 386
Capillary electro-chromatography (CEC) 386
References 387
Further reading 388
15 Extraction methods in pharmaceutical analysis 389
Introduction 390
Commonly used excipients in formulations 390
Tablets and capsules 390
Suspensions and solutions 391
Creams and ointments 391
Solvent extraction methods 391
Extraction of organic bases and acids utilising their ionised and un-ionised forms 391
Partitioning between organic solvents 392
Ion pair extraction 393
Derivatisation prior to extraction 393
Supercritical fluid extraction 394
Microdialysis extraction 395
Solid-phase extraction (SPE) 395
Introduction 396
Methodology 396
Types of adsorbants used in SPE 398
Lipophilic silica gels 398
Typical extraction methodologies using lipophilic silica gels 399
Polar surface-modified silica gels 399
Typical methodologies using straight-phase adsorbants 399
Anion exchangers based on surface-modified silica gels 400
Cation exchangers based on surface-modified silica gels 401
Factors requiring attention in SPE with silica gels 402
Borate gels (Fig. 15.12) 402
Immunoaffinity gels 403
Adaptation of SPE for automated on-line extraction prior to HPLC analysis 403
Recent developments in solid-phase and on-line extraction 404
References 405
Further reading 405
16 Methods used in the quality control of biotechnologically produced drugs 406
Protein drugs 407
Protein structure 408
Amino acids and amino acid sequences 408
Polar amino acids 409
Hydrophobic amino acids 409
Charged amino acids 410
The peptide bond and the primary structure of proteins 411
Protein secondary structure 414
Protein tertiary structure 416
Instrumental techniques used in the analysis of biotechnologically produced drugs 417
Introduction 417
Size exclusion chromatography (SEC) 418
Sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDSPAGE) 420
Isoelectric focusing 422
Alteplase glycoforms 424
Molgramostim identification test 424
Other pharmacopoeial tests using isoelectric focusing 424
Binding assays used in pharmacopoeial tests on protein drugs 425
Enzyme-linked immunosorbant assay (ELISA) 425
Applications of ELISA in the pharmacopoeias 425
Radio-immunoassay (RIA) 425
Polymerase chain reaction (PCR) 426
Capillary electrophoresis 427
Fingerprinting by HPLC and HPLC-MS 428
The Edman reaction 430
Methods used to assess the secondary and tertiary structure of protein drugs 430
Circular dichroism 431
Other techniques used to assess protein secondary structure 433
Reference 434
Further reading 434
17 Electrochemical biosensors 435
Introduction 435
Basic principles of electrochemistry 436
Types of electrochemical biosensors 438
First-generation biosensors 439
Second-generation biosensors 440
Third-generation biosensors 440
Instrumentation 441
Examples of biosensors utilised for pharmaceutical analysis 442
Detection of blood glucose levels 442
Detection of cholesterol 445
Detection of pharmaceutical drugs 445
Limitations of biosensors in pharmaceutical analysis 446
References 447
Further reading 447
Answers to Self-tests e1
Chapter 1 e1
Self-test 1.1 e1
Self-test 1.2 e1
Self-test 1.3 e1
Self-test 1.4 e1
Self-test 1.5 e1
Self-test 1.6 e1
Self-test 1.7 e1
Self-test 1.8 e2
Self-test 1.9 e2
Self-test 1.10 e2
Self-test 1.11 e2
Chapter 2 e2
Self-test 2.1 e2
Self-test 2.2 e2
Self-test 2.3 e2
Self-test 2.4 e2
Self-test 2.5 e2
Self-test 2.6 e2
Self-test 2.7 e2
Self-test 2.8 e3
Self-test 2.9 e3
Self-test 2.10 e3
Self-test 2.11 e3
Self-test 2.12 e3
Self-test 2.13 e3
Self-test 2.14 e3
Self-test 2.15 e3
Self-test 2.16 e3
Self-test 2.17 e3
Chapter 3 e3
Self-test 3.1 e3
Self-test 3.2 e3
Self-test 3.3 e3
Self-test 3.4 e3
Self-test 3.5 e4
Self-test 3.6 e4
Self-test 3.7 e4
Self-test 3.8 e4
Self-test 3.9 e4
Self-test 3.10 e4
Chapter 4 e4
Self-test 4.1 e4
Self-test 4.2 e4
Self-test 4.3 e4
Self-test 4.4 e4
Self-test 4.5 e4
Self-test 4.6 e4
Self-test 4.7 e4
Chapter 5 e5
Self-test 5.1 e5
Self-test 5.2 e5
Self-test 5.3 e5
Self-test 5.4 e5
Chapter 6 e5
Self-test 6.1 e5
Self-test 6.2 e5
Self-test 6.3 e5
Self-test 6.4 e5
Self-test 6.5 e5
Self-test 6.6 e5
Chapter 8 e5
Self-test 8.1 e5
Self-test 8.2 e5
Self-test 8.3 e6
Self-test 8.4 e6
Self-test 8.5 e6
Self-test 8.6 e6
Self-test 8.7 e6
Self-test 8.8 e6
Self-test 8.9 e6
Self-test 8.10 e6
Chapter 9 e6
Self-test 9.1 e6
Self-test 9.2 e7
Self-test 9.3 e7
Self-test 9.4 e7
Self-test 9.5 e7
Self-test 9.6 e8
Self-test 9.7 e8
Self-test 9.8 e8
Self-test 9.9 e8
Self-test 9.10 e8
Self-test 9.11 e9
Self-test 9.12 e9
Self-test 9.13 e9
Chapter 10 e9
Self-test 10.1 e9
Self-test 10.2 e9
Self-test 10.3 e9
Self-test 10.4 e10
Chapter 11 e10
Self-test 11.1 e10
Self-test 11.2 e10
Self-test 11.3 e10
Self-test 11.4 e10
Self-test 11.5 e10
Self-test 11.6 e10
Self-test 11.7 e10
Chapter 12 e10
Self-test 12.1 e10
Self-test 12.2 e10
Self-test 12.3 e10
Self-test 12.5 e11
Self-test 12.6 e11
Self-test 12.7 e11
Self-test 12.8 e11
Self-test 12.9 e11
Self-test 12.10 e11
Self-test 12.11 e11
Chapter 13 e11
Self-test 13.1 e11
Self-test 13.2 e11
Self-test 13.3 e11
Self-test 13.4 e11
Self-test 13.5 e11
Chapter 14 e12
Self-test 14.1 e12
Chapter 16 e12
Self-test 16.1 e12
Self-test 16.2 e12
Self-test 16.3 e12
Self-test 16.4 e12
Self-test 16.5 e12
Self-test 16.6 e12
Self-test 16.7 e13
Chapter 17 e13
Self-test 17.1 e13
Self-test 17.2 e13
Index 448
A 448
B 449
C 450
D 451
E 452
F 452
G 453
H 453
I 454
J 455
K 455
L 455
M 455
N 456
O 457
P 457
Q 458
R 458
S 459
T 460
U 460
V 461
W 461
X 461
Z 461