Contemporary Instrumental Analysis

K E N N E T H A. R U B I N S O N

J U D I T H F. R U B I N S O N

Contemporary Instrumental

Analysis

PRENTICE HALL Upper Saddle River, NJ 07458

C O N T E N T S

Preface xviii About the Authors xx

C H A I T E R

Preliminaries

Eliminate expected interferents 1

1 Runassay . .

calibratkm Standards : sample

T " Data reduction to numericai answer 1

J Statistical analysis 1

} .- Numerical answers with error limits 1

1 ::: Iriterpretto get Solution to: probiem 1

l . i 1.2

1.3 1.4

1.5

1.6

Introduction 3

Some Definitions 3 Identification, Determination, Analysis, Assay, Quantitation, and Analyte 3 Validation 4 Methods, Protocols, and Techniques 4

Solving a Problem 4 A Brief Review of Basic Measures 8

Atomic Mass 8 Mole 9 Prefix Notation 9

Measures of Composition: Units of Content 10 Weight-to-Weight Measures 10 Weight-to-Volume Measures 11 Number-to-Volume Measures 12 Volume-to-Volume Measures 13 The pH and Other Logarithmic Scales 13

Experiments and Mathematical Equations 13

Suggestions for Further Reading 15 Exercises 16

Concept Review 16

C H A A T E R

Statistical Tests and Error Analysis

| f / F ^ ~~1 I •. Belaßve • / V ' ••' 1

frequertey • •. • i ^ ~ ^ L

1 y/TJVS^ L^42^Xß^Z,

2.1 2.2

2.3 2.4

2.5 2.6

2.7

2.8

Introduction 19 Finding Errors 19

A Simple Analysis by Chromatography 19 Am I at Least in the Ballpark? 20

Measuring Errors 20 Absolute and Relative Measures 23 Precision and Accuracy 24 Random Errors and the Normal (Gaussian) Distribution

Properties of Gaussian Distributions 28 The Confidence Limit 29

Confidence Limits when a Is Known 29 Confidence Limits when er Is Unknown 30

Standards, Blanks, and Accuracy 32

25

IV

Contents

2.9 Finding Errors 33 The Analysis Procedure 33

2.10 Unacceptable Methodologies 37 2.11 Pooling Data and the Difference between Two Means 37

The Difference between Two Means 38 Comparing Two Different Methods Using Sets of Samples 40 Comparing an Experimental Mean with a True Value 43

2.12 Propagation of Uncertainty 44 Total Differential Determinate Error 45 Total Differential Random Errors 46 What To Do with Error Information 49

2.13 Significant Figures 50 Rules of Rounding Off 50 Significant Digits and Arithmetic Operations 50 Addition and Subtraction 51 Multiplication and Division 51 Logarithms 52

2.14 Discordant Data 53 2.15 The Median 55

2.16 Least Squares 55

A DEEPER LOOK

2A The F-test for Equality of Variances 58

Suggestions for Further Reading 60 • Exercises 61

C H A j T E R

Sampling

fl~ l iE:

"*•;""" %? TL-^-

\ TfP^-C^fW

ÄsrJ

—

3.1 Factors Involved in Effective Sampling 67 3.2 Good Samples: Representative and Homogeneous 68

Making the Sample Representative 68 Multiple Hierarchical Sampling 70 Making the Sample Homogeneous 71

3.3 A Pictorial Model 75 3.4 Samples of Mixtures 77 3.5 Sample Integrity 77 3.6 Physical Separations in Sampling 78

Sampling Gases and Volatile Species 79

3.7 How Many Samples Do I Need? 80

A DEEPER LOOK

3A The Binomial Distribution 82 A postscript 85


Concept Review 86

VI Contents

C H Ä 4 T E R

Sample Treatment, Interferences, and Standards

4.1 Sample Preparation 91 4.2 Maximize Recovery 92

Loss of Analyte 93 Correction for Loss of Analyte 95

4.3 Optimize the Chemical Form 96 Working Directly with Solid Samples 96 Adding or Removing Heat 96 Dissolution 97 Digestion 97 Integrated Vaporization 100

4.4 Minimize the Interferences 101 Extraction 102 Dialysis 107 Precipitation and Flotation 107 Purge and Trap 109

4.5 Optimize the Concentration 109

4.6 Calibration and Standards 111 4.7 Types of Standards 112

External Standards 112

Added Standards 114

A DEEPER LOOK

4A The Basis of Ultrasound-Assisted Dissolution and Digestion 4B Microwave-Assisted Sample Preparation 119 4C Supercritical Fluid Extraction 122 4D Purge and Trap 123 4E Flow Injection Analysis 126 4F Standard Reference Materials 128

Definitions 130

118


Concept Review 132

C H A J T E R

Sample Size and Major, Minor,

Trace, and Ultratrace

Components

5.1 Sample Classification by Size and Analyte Level 139 5.2 Limits of Trace Analysis 140 5.3 Trace, Ultratrace, and Microanalysis Compared 145

Preconcentration of Trace Analytes 146 5.4 Four Cases 146

Case 1: A Sample of High Purity 146 Case 2: A Milligram Sample to be Analyzed for Its Elemental

Composition 146

Contents vii

Case 3: Micro-Organic Analysis 148 Case 4: A Solid and the Distribution of Elements in Its Structure

5.5 Signals, Noise, and Detection Limits 150 5.6 Figures of Merit and the Detection Limit 152

Comparing Detection Limits 153 5.7 The Limit of Detection in More Detail 154

149


Concept Review 158

C H A| T E R

Electronics and Noise

Ed \ V-

\ ^ Output

1 Load i _ i

6.1 Introduction 163 6.2 DC Current,Voltage, and Resistance 164 6.3 Power 165 6.4 Kirchhoff's Laws 166

Resistors in Series: Voltage Dividers 167 Resistors in Parallel 169 Wheatstone Bridge Circuit: Resistors Combined in Series and in Parallel 169

6.5 Time-Dependent Responses of Circuits 171 6.6 Signal-to-Noise Ratios 174 6.7 Types of Noise 175

Thermal Noise 176 Shot Noise 178 l//Noise 179 Electrical Interference 179

6.8 Amplifiers and Amplification 180 A Few Common Operational Amplifier Circuits 182

6.9 Detection Limit with a Multichannel Detector 187

A DEEPER LOOK

6A Schematic Symbols in Electronics 188 6B A Brief Introduction to the Nomenclature

of Digital Logic 189 A Flip-Flop Network 191 The D-block Latch 192 A Binary Counter 195

6C Capacitors, Inductors, and Alternating Current (AC) 196

Capacitors and AC 196 Inductors and AC 198 LC Circuits and Resonance 199


viii Contents

C H A f T E R

Electrochemical Methods

J7-Auxiliary

Working

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

The Variety of Electrochemical Methods 205

A Review: Electrochemical Potentials and the Nernst Equation 205 Chemical Activities 205

The Nernst Equation 206

Concentration Cells 208

pH and the Electrochemical Potential 208

The Formal Potential 209

Toward Measurements 211

How an Inert Electrode Senses the Potential of a Redox Couple 211

The Experimental Measurement 213

Potentiometry and Ion-Selective Electrodes 215

Reference Half-Cells 215

Ion-Selective Interfaces and Ion-Selective Electrodes 217

Range of Response of Ion-Selective Electrodes 222

Ion-Selective Field-Effect Transistors 223

Interferences and Ion-Selective Electrodes 224

Potentiometrie Precision 226

Electrochemical Methods Using Current Flow 226 Behavior of an Electrochemical Cell with an Applied Potential 226

The Linear Region 227

The Nonlinear Region 228

Kinetic Overpotential 229

Three-Electrode Potentiostat 231

Conductimetry 233

Conductivity and Ionic Concentration 234

Conductimetry in Practice 235

Coulometry 238 Background Currents: Competitive Electrolysis 240

Coulometric Titrations 242

Amperometry 243

Fixed-Potential Amperometry: Amperometric Titrations 244

The Two-Electrode System 244

"One-Electrode" System 247

Chromatography/Amperometry 248

7.10 Voltammetry 248 DC Polarography and the Dropping Mercury Electrode 250

Pulsed Voltammetry 250

Differential Pulse Voltammetry 254

Cyclic Voltammetry 255

7.11 Stripping Voltammetry 258

A DEEPER LOOK

7A Notation for Electrochemical Cells 260

7B H o w Selectivity Coefficients Are Determined 263

Contents ix

7C Salt Bridges 264 7D Voltages, Current Measurement, and Time in Differential-Pulse

Voltammetry 265


Concept Review 269

C H A « T E R

Introduction to Spectrometry

^ A-SJ : : ,

hvim

(luminescence, Emission)

^ g ^ yS (photoelectric Effect, \f ftiermoelectron Emission,

i ondary dectrons)

^ - ] *BT«II

*-* (nonradiative energy loss)

8.1 Spectrometry, from Radiofrequency to y-Rays 275 8.2 Review of Energy, Wavelength, Frequency, and Temperature 276 8.3 The Transformations of Light Energy 280

Spectrometric Names 281

8.4 Spectral Purity and Spectral Resolution 282 Monochromators and Polychromators in the Optical Range 284 Bandwidth and Spectral Slit Width 285 Resolution 285

8.5 Measurement of Spectra 286 8.6 Light Scattering 289

Geometry of Scattering 289 Elastic Scattering Origins and Behavior 290 Inelastic Scattering 291

8.7 Emission Spectrometry 292 8.8 Absorption Spectrometry 293

Absorbance and Concentration 295 Absorbance, Concentration, and Precision 296 Spectral Resolution and Error in Concentration Measurements 297 Sample Cells and Solvents 298 Other Limits to Photometrie Precision 299

8.9 Fluorescence/Phosphorescence Spectrometry 301 Comparisons of the Methods 304

8.10 Spectral Interference and the Spectra of Mixtures 305 Background Correction 307 Quantifying Two Species with Spectral Interference Present 308

8.11 Chemical Interference 311 Isosbestic Points 311

8.12 Instrument Interference 312 8.13 Total Internal Reflection and Fiber Optics 314

Attenuated Total Reflection 317

8.14 Diffuse Reflectance Spectrometry 321 8.15 Derivative Spectrometry 325 A DEEPER LOOK

8A Wavelength Separation: Interference, Diffraction, Grätings, and Filters 326 Constructive and Destructive Interference of Two Stationary Waves 327

Contents

333

Two-Slit Diffraction 328 Multislit Diffraction 329 Grätings 330 Gräting Monochromators Interferometers 334

8B Sources of Electromagnetic Radiation: 190 nm to 50 /xm Lasers and Laser Safety 335 The Ultraviolet Region, 190 to 320 nm: Deuterium, Xenon, and Mercury Ares 335 The Visible Region, 320 to -750 nm: Tungsten Filament Lamps The Infrared Region, 2.5 to 50 /am: Nernst Glower 339

8C Representative Transducers for Electromagnetic Radiation Rectifiers for Radiofrequency 339 Infrared Devices 340 Phototubes and Photomultipliers 341 CCDs and CIDs 343 X-ray and Gamma Detectors 345

8D Derivation of the Beer-Lambert Law 346 Luminescence and its Dependence on Concentration 348

8E The Nomenclature of Molecular Absorption and Luminescence 349


335

337

339

C H A R T E R

Spectrometry for Elemental Analysis

9.1 9.2

9.3

9.4

9.5

9.6 9.7 9.8

9.9

Atomic Spectrometry 363 Nomenclature of Atomic Spectrometry 363 Spectra and Spectral Notation 364

Intensities and Linewidths of Gas Phase Atomic Spectra Linewidth Dependence on Temperature and Pressure 366 Simultaneous Emission and Absorption and Lineshape Changes

Factors Affecting Atomization/Ionization 370 Solid Samples 370 Atoms or Ions? 371 Liquid Samples 373 Gaseous Samples 375

Isolated Atoms or Ions from Samples 376 Furnaces 376 Plasmas 377 Flames 380

Causes of Spectral Interferences in Gases 380 Atomic Emission Methodology 383 Atomic Absorption Methodology 385

The Light Source in Atomic Absorption 386 Background Correction 389

366

367

9.10 Bulk Analysis Without Atomization 392

Contents

9.11 X-ray Methods of Analysis 392 Nomenclature of X-ray Radiation 392 Absorption of X-rays 393 Mass Absorption Coefficients 397 Spurious Peaks and Anomalous Fluorescence Intensities 399 Proton-Induced X-ray Fluorescence (PIXE) 399

9.12 Neutron Activation Analysis 400 9.13 Furnace or Plasma? Absorption or Emission?

Optical, X-ray, y-ray? Which to Use? 404 9.14 Surface-Sensitive Spectrometries 406 9.15 Photoelectron and Auger Spectroscopies 409

Electrons Emitted from Samples 409 Which Electrons Are Emitted? 411 Auger Emission Spectrometry (AES) 412 Auger Nomenclature 415

9.16 Rutherford Backscattering 416

A DEEPER LOOK

9A Emission and Absorption Spectra and the Boltzmann Distribution 419

Temperature Fluctuations and Noise 423 9B Doppler Spectroscopic Line Broadening 424 9C Wavelength-Dispersive X-ray Spectrometers (WDX) 427 9D Energy-Dispersive X-ray Spectrometers (EDX) 429 9E Electron Spectrometers 430


c H 4w E R

10.1 Introduction 439 Infrared Spectra 439

10.2 Vibrational Frequencies 441 10.3 Normal Vibrational Modes 445 10.4 Qualitative Information from IR Spectra 448 10.5 Raman Spectra 452 10.6 Samples for Infrared and Raman Spectrometries 455

Samples for Infrared Spectrometry 455 Samples for Raman Spectrometry 456

10.7 Band Intensities of Vibrational Spectra 458 10.8 Quantitation 461 10.9 Infrared and Raman Microspectrometry 462

A DEEPER LOOK

10A Raman Spectrometers 463 10B Characteristic Frequencies 466

Infrared and Raman

Spectrometries: Vibrational

Spectrometries


xii Contents

H A| P|T E R

Nuclear Magnetic Resonance

Spectrometry

11.1 Introduction 477 11.2 General Principles of NMR 477

Signal Magnitude and Concentration 480

11.3 Chemical Shifts: Origins andValues 482 Origin of er, the Shielding Parameter 482

11.4 Nuclear Equivalence and Inequivalence 486 11.5 Nuclear Spin-Nuclear Spin Interaction 487

The Heights and Areas of Split Peaks 490 General Splitting Patterns 491 Some Complications 493 Splitting by More Than One Set of Equivalent Nuclei 496 Spin-Spin Splitting from Nonresonant Nuclei 499

11.6 13C-NMR 499 11.7 Quantitation 501 11.8 NMR of Solids 504

11.9 Multidimensional NMR 505

A DEEPER LOOK

IIA NMR Instruments and Samples 507


c H 4EJ E R

Mass Spectrometry

12.1 12.2 12.3

12.4 12.5 12.6 12.7 12.8 12.9 12.10

Introduction 515 Mass Spectra and the Mass-to-Charge Ratio 518 Analysis of Organic-Molecule Mass Spectra 518 Identify the Molecular Ion 519 Study the Isotope Distribution Patterns 520 Explain the Fragmentation Patterns 523

Mass Spectral Resolving Power and Spectral Resolution 525 Exact Masses and Chemical Formula Determination 526 Sequential Mass Spectrometry: MS/MS 528 Separations/Mass Spectrometry 529 High-Mass Mass Spectrometry 533 Spatial Distribution by Mass Spectrometry 536 The Variety of Ion Sources 540 Common Factors in Ion Sources: Stability Control of Ion Motion 540 Electron Ionization (EI) and Chemical Ionization (CI) 542 Electrospray (ES, ESI) 543 Inductively Coupled Plasma Source (ICP) 548 Pulsed-Laser-Based Sources 550 Fast-Atom Bombardment (FAB) 550

Contents xiii

Ion Impact Desorption/Ionization: SIMS, Plasma Desorption, Glow Discharge, Sputtered Neutrais 552

Thermal Ionization 555

12.11 Mass Analyzers for Mass Spectrometry 555 Magnetic Sector 556

Double Sector 556

Quadrupole Mass Filter 557

Quadrupole Ion Trap 559

Time-of-Flight 560

Fourier Transform Mass Spectrometry (Fourier Transform Ion Cyclotron Resonance) 562

12.12 High-Precision Analyses by Mass Spectrometry: Isotope Dilution 565 The Equation of Mass Spectral Isotope Dilution Analysis 566

A DEEPER LOOK

12A Natural Isotopic Abundances 568


C H A| OT E R

The Chromatography Experiment 577

Nomenclature of Chromatographie Separations 579

Descriptions of Experimental Chromatograms 580

Parameters of Chromatography 581

Parameters for Individual Bands 582

Efficiency 583

Parameters Describing Pairs of Bands 584

Comparing Column Efficiencies 587

Mass Resolution versus Peak Resolution 587

Quantitation in Chromatography 589

Loss of Material on the Column 589

Detector Response 590

Quantitation Techniques 590

Explaining Chromatographie Separations 592

Extractions 592 Sample Loading 593

KD and Elution Times 594

A More Complete Model 596

Zone Broadening: The van Deemter Equation 598

Zone Broadening in More Detail 601

The Broadening Process Accounted for by B/ü 601

The Broadening Process Accounted for by Cw 602

Packing of the Stationary Phase and the A-term 604

Improving Separations 606 Varying N by Changing the Flow Rate 607

General Introduction to Separations and Chromatography

Band broadening mostly due to

diffusion

t

1 I

1 H

«~--j-H :

HE

TP

0

Band broadening mostly due to slow

niass transfer

t

: / ; : : i ' ~'<\, „ " • "

'\^ff^%m * C»S

B.

' (flow velocity)

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

xiv Contents

Improve the Separation by Changing a! 608 Batch Separations 608 Other Strategies 609

13.9 Asymmetrical Peaks 609 Sample Loading 610 Isotherms and Asymmetry 611

13.10 Multidimensional Techniques 612 Multidimensional Separations 612 Multidimensional Detection 613

A DEEPER LOOK

13A Proof That Wt = 4o-, for Gaussian Peaks 617 13B Reduced Plate Height and Reduced Flow Velocity 618 13C How Good is the Resolution in High-Resolution

Chromatograms? 619


C H Aff l% E R

Types of Liquid Chromatography 629 Normal-Phase Liquid Chromatography 630 Reversed-Phase Liquid Chromatography 633 Ion-Exchange Liquid Chromatography (Ion Chromatography) 636 Ion Chromatography 638 Ion-Pairing Chromatography 641

Size-Exclusion Liquid Chromatography 641 Chiral Separations 644 Gradients 645 Effects of Temperature 648

Particie Size, Column Size, Pressure, and HETP 650 Detectors for Column LC 653 UV-Visible Adsorption Detectors 654 Fluorescence Detectors 656 Differential Refractive Index Detector 656 Amperometric Detector 658 Conductivity Detector 659 Evaporative Light Scattering (ELS) 659 Light Scattering in Liquids 661 Viscometric Detector for Polymer Solutions 662

Batch Separations 663 Planar Chromatography 664 High-Performance Thin-Layer Chromatography 664 Detection and Quantitation for TLC 666

tions for Further Reading 668 • Exercises 669

Liquid Chromatography

14.1 14.2 14.3 14.4

14.11 14.12

Suggest

Contents xv

T E R

Gas Chromatography and Supercritical

Fluid Chromatography

Output

Makeup gas in

] Capillary column

686 686

689

15.1 Comparison between Gas, Supercritical Fluid, and Liquid Chromatographies 673

15.2 The Nomenclature of Gas Chromatography 674 15.3 Samples Analyzed 675 15.4 Sample Introduction, Splitters, and Columns 676

Sample Introduction and Splitters 676 Columns and Stationary Phases 677 Temperature in GC 681 Flow Rate in GC 683 GC Detectors 684

15.5 Detectors for Gas Chromatography Thermal Conductivity Detector (TCD) Flame Ionization Detector (FID) 688 Electron Capture Detector (ECD) 689 Nitrogen-Phosphorus Detector (NPD) Photoionization Detector (PID) 690 Pulsed Discharge Helium Ionization Detector (PDHID) 690 Flame Photometrie Detector (FPD) 691 Hall (Conductivity) Detector (ELCD) 692 Other Detectors 694 Effluent Flow Rates 694

15.6 Supercritical Fluid Chromatography 694 Analytes 694 The Mobile Phase 695 Sample Form and Sample Injection 695 Columns and Packings 695 Detectors 696

A DEEPER LOOK

15A Stationary Phases for Gas Liquid Chromatography: Classification Schemes 696 Homologous Series 696 Retention Index 697 McReynolds Constants 699

Optimization of Gas Chromatography Separations 701 15B


E R

Separations by Applied Voltage:

Electroseparations

16.1 The Basis of Electroseparations 709 16.2 Negative, Neutral, or Positive? 711 16.3 Electrophoretic Separations within a Gel Matrix

The Gels 713 713

xvi Contents

Some Modes of Operation 715 Improving the Resolution 716

16.4 Some Detection Methods for Gel Electrophoresis 717

16.5 Isoelectric Focusing 720 16.6 Capillary Electrophoresis 721

Temperature Differences and Convection 722 Electroosmotic Flow in Capillaries 724 Efficiency 727 Resolution 728 Sample Injection 728 Modes of Operation 729 Detection 729

16.7 Micellar Electrokinetic Capillary Chromatography 730

16.8 Ion Mobility Spectrometry 733

A DEEPER LOOK

16A The Origin of Electroosmotic Flow 736


C H 4 / T E R

Digitization 741 Resolution 741 Least and Most Significant Bits 744

Signal Averaging 746

Time and Frequency: How Often to Sample the Voltage 748 Eliminating Aliasing with Filters 749 When an Anti-Aliasing Filter Is Not Needed 751

Time and Frequency: HowThey Are Related 752 Adding Together and Extracting Sine Waves 753 Mathematical Preliminaries: Fourier Transforms 755 Complex Variables: A Convenient Shorthand Notation 756 The Inverse Transform 757

Frequencies, Filters, and Aliasing 757 Digression on the Characteristics of Noise in Spectrometry 759 Fluctuation Noise (<* I) and Photon Emission Noise (« Iin) 761 Multichannel is Not Multiplex 762 A Simple Example of Multiplexing 762 Multiplexing in Infrared Spectrometry 763 Spectral Elements 763 Distributions of Noise 765 How to Get Enough Signal 765

Some Instrument Principles 767 Power Brought to the Detector 767 "Instantaneous" Collection of Spectra 768 Resolution, S/N, and Data Collection Time 768 Sampling Time, Digital Resolution, and Spectral Range 769

Digital Signal 17.1 Acquisition and Signal Treatment 17 2

17.3

Wavelength

17.4

17.5 17.6

17.7

Contents XVII

17.8 The Experimental Uses of Fourier Transforms 773 FT-NMR 773 FT-Mass Spectrometry 775 FT-IR 777 Digital Resolution and the Maximum Retardation 780 The Throughput Advantage 780 The Multiplex Advantage 780 Precautions 781

A DEEPER LOOK

17A The Phasor Representation of Voltage 781

17B The Fourier Transform ofaTransient Signal 783 Apodization (Windowing) 785


C H AJCJT E R

Kinetic Methods

Time, arbitrary units

18.1 The Chemistries of Kinetic Analyses 789 18.2 Why Kinetic Methods? 789 18.3 A Brief Review of the Mathematics of Rates of Reactions, Decay

Times, and Half-Lives 790 18.4 Assay Kinetics and AssayTypes 794

The Catalytic Method 795 The Direct Method 796

18.5 Methods for Determining [A]0 or fccataiytic from Rates 796 The Derivative Method 797 Fixed-Time Method 798 Variable-Time Method 800

A DEEPER LOOK

18A Obtaining Simple Kinetic Behavior Pseudo First-Order Behavior 803 Pseudo Zero-Order Behavior 804

802

Suggestions for Further Reading 804 • Concept Review 805 • Exercises 805

Appendices 808 Answers 828 Index 831

Documents

Contemporary Instrumental Analysis