Spectrometric Titrations

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1 Jürgen Polster Heinrich Lachmann Spectrometric Titrations Analysis of Chemical Equilibria VCH

Contents Part I The Theoretical and Methodological Basis of Spectrometric Titration 1 Basic Principles and the Classification of Titration Methods.. 3 1.1 Definitions 3 1.

2 Contents Part I The Theoretical and Methodological Basis of Spectrometric Titration 1 Basic Principles and the Classification of Titration Methods Definitions The Classification of Spectrometric Titration Methods 5 Literature 7 2 Graphic Treatment of the Data from a Spectrometric Titration 9 Literature 12 3 Basic Principles of Multiple Wavelength Spectrometry as Applied to Titration Systems Generalized Lambert-Beer-Bouguer Law Matrix-Rank Analysis of a Titration System Numeric Matrix-Rank Analysis Graphic Methods of Matrix-Rank Analysis 16 Literature 20 4 Thermodynamic and Electrochemical Principles of Spectrometric Titration Systems 23 Literature 25 Part II The Formal Treatment and Evaluation of Titration Systems - Analysis of Chemical Equilibria 5 The Goal of a Spectrometric Titration 29

XII Contents 6 Single-Step Acid-Base Equilibria 33 6.1 Basic Equations 33 6.2 Graphic Matrix-Rank Analysis 34 6.3 Determination of Absolute pk Values 39 6.3.1 Inflection Point Analysis 39 6.3.2 Determining the Midpoint of Overall Change in Absorbance (the "Halving Method") 42 6.

3 XII Contents 6 Single-Step Acid-Base Equilibria Basic Equations Graphic Matrix-Rank Analysis Determination of Absolute pk Values Inflection Point Analysis Determining the Midpoint of Overall Change in Absorbance (the "Halving Method") Linearization of Spectrometric Titration Curves Numeric Evaluation of pk Through the Use of Linear Equations Non-linear Curve-Fitting Methods Photometrie Determination of pa' in the Absence of ph Measurements The Treatment of Non-overlapping, Multi-Step Titration Systems as Combinations of Single-Step Subsystems Summary Single-Step (s = 1) Titrations Non-overlapping, Multi-Step Titration Systems 64 Literature 66 7 Two-Step Acid-Base Equilibria Basic Equations Graphic Matrix-Rank Analysis (ADQ-Diagrams) The Determination of Absolute pk Values Inflection Point Analysis (First Approximate Method) Uniform Subregions in an Absorbance Diagram (Second Approximate Method) Dissociation Diagrams Bisection of the Sides of an Absorbance Triangle Pencils of Rays in an Absorbance Triangle Linear and Non-linear Regression Methods Determining the Quotient Ki/K 2 (ApK = pk 2 - pki) Distance Relationships Within an Absorbance Triangle Non-linear Regression Analysis The Characteristic Concentration Diagram Second-Order Curves (Conic Sections) Poles and Polars of Conic Sections Pencils of Rays, and Lines Bisecting the Sides of the Triangle Distance Relationships Geometrie Relationships Between Concentration Diagrams and Absorbance Diagrams Concentration Difference Quotient (CDQ) Diagrams Geometrie Relationships Between ADQ-, CDQ-, and A-Diagrams.. 121

Contents XIII 7.9 Summary and Tabular Overview 126 Literature 129 8 Three-Step Acid-Base Equilibria 133 8.1 Basic Equations 133 8.2 Graphic Matrix-Rank Analysis (ADQ3-Diagrams) 135 8.

4 Contents XIII 7.9 Summary and Tabular Overview 126 Literature Three-Step Acid-Base Equilibria Basic Equations Graphic Matrix-Rank Analysis (ADQ3-Diagrams) Absolute pk Determination Analysis of Inflection Points Uniform Subregions Within Absorbance Diagrams Dissociation Diagrams Pencils of Rays in an Absorbance Tetrahedron Pencils of Planes in the Absorbance Tetrahedron Correlation of Two-dimensional A- and ADQ-Diagrams Determining the Molar Absorptivities of BH2 and BH 2 " Reducing the System by One Stage of Equilibrium Determining pk Values from the Three Separate Equilibria Linear and Non-linear Regression Analysis The Determination of Ki/K 2 and K2/K3, with the Aid of the Absorbance Tetrahedron The Characteristic Concentration Diagram Tangents and Osculating Planes Pencils of Rays Pencils of Planes Determining KJK2 and K2IK?, from the Concentration Tetrahedron Geometrical Relationships Between A- and ADQ-Diagrams Summary and Tabular Overview 180 Literature s-step Overlapping Acid-Base Equilibria Basic Equations Characteristic Concentration Diagrams and Absorbance Diagrams The Generalized Form of an ADQ-Diagram The Establishment of Absorbance Polyhedra The Determination of Absolute pk- Values Summary 197 Literature Non-Linear Curve-Fitting of Spectrometric Data from s-step Acid-Base Equilibrium Systems Basic Equations Iterative Curve-Fitting Procedures 202

XTV Contents 10.3 Statistical Analysis 207 10.4 Summary 208 Literature 210 11 Simultaneous Titrations 211 11.1 Basic Equations 211 11.2 Graphic Matrix-Rank Analysis 214 11.

5 XTV Contents 10.3 Statistical Analysis Summary 208 Literature Simultaneous Titrations Basic Equations Graphic Matrix-Rank Analysis The Determination of Relative pk Values Creation of a Dissociation-Degree Diagram Points of Bisection in a Dissociation-Degree Diagram Terminal Slope in a Dissociation-Degree Diagram Complete Evaluation of a Dissociation-Degree Diagram The Diagonal of a Dissociation-Degree Diagram A Comparison of the Various Methods 221 Literature Branched Acid-Base Equilibrium Systems Macroscopic and Microscopic pk Values: The Problem of Assignment pk Assignments Based on Extrapolations from Unbranched Systems Assignment of Spectral Features to Specific Dissociable Groups UV-VIS Spectroscopy IR and Raman Spectroscopy NMR Spectroscopy The Dependence of Spectra on Solvent and Temperature; Band Shape Analysis Summary 237 Literature Metal-Complex Equilibria The System BH i^ B (H), M + B ^ MB Concentration Diagrams Absorbance Diagrams Determination of Overall Stability Constants for Metal Complexes Related to Multi-Step Acid-Base Equilibria The Method of Continuous Variation ("Job's Method") The System M + B ^ MB, MB + B ^ MB Concentration Diagrams Excess-Absorbance Diagrams The System Daphnetin/FeCl lon-selective Electrodes in the Determination of Stability Constants. 270

Contents XV 13.6 Summary 272 Literature 273 14 Association Equilibria 277 14.1 Establishing Association Constants for Dimerism Equilibria Related to Protolysis Systems 277 14.

6 Contents XV 13.6 Summary 272 Literature Association Equilibria Establishing Association Constants for Dimerism Equilibria Related to Protolysis Systems Determining Association Constants for the System 2B ^ C by Successively Increasing the Dye Concentration Absorbance Diagrams A Practical Example Based on the Eosine System Excess Absorbance and Reduced Absorbance Diagrams Reduced Absorbance Difference Quotient Diagrams and Excess Absorbance Quotient Diagrams (2B t* C, C + B *=* E) Determining Association Constants of Charge-Transfer Complexes Summary 296 Literature Redox Equilibria Determining Standard Electrode Potentials The Redox System Redi + Ox 2 ^ Oxi + Red Evaluating the Equilibrium Constant by Successively Increasing the Concentration of One Component (First Method) Determining the Equilibrium Constant by the Method of Continuous Variation (Second Method) Determining the Equilibrium Constant for an NADH-Dependent Dehydrogenase Reaction Summary 313 Literature 313 Part III Instrumental Methods 16 Suitable Apparatus for Spectrometric Titration m Experiments, Each Performed in a Different Buffer Medium Discontinuous Spectrometric Titration in the Strictest Sense Titration Outside the Spectrometer Titration Inside the Spectrometer Optimal Sample Size for Spectrometric Titration Introducing the Titrant: Burets and Other Alternatives 326 Literature 327

XVI Contents 17 Electrochemical Methods 329 17.1 Problems Associated with the Conventional ph Scale 329 17.2 Calibrating a ph Meter Using Standard Buffers 331 17.

7 XVI Contents 17 Electrochemical Methods Problems Associated with the Conventional ph Scale Calibrating a ph Meter Using Standard Buffers ph Measurements 334 Literature Spectrometric Methods UV-VIS Absorption Spectrometric Data Collection The Lambert-Beer-Bouguer Law and its Associated Error Function Fluorescence Spectrometric Data Collection Quantitative Fluorescence Spectrometry and Predictable Sources of Error Protolysis Equilibria: The Electronic Ground State vs. Excited States Circular Dichroism (CD) and Optical Rotatory Dispersion (ORD) Spectrometric Data Collection Quantitative CD and ORD Spectrometry IR Absorption Spectrometric Data Collection Quantitative Spectrometry in Aqueous Solution Raman Scattering Spectrometric Data Collection Quantitative Spectrometry in Aqueous Solution Nuclear Magnetic Resonance (NMR) Basic Principles and Spectrometric Data Collection Quantitative NMR Analysis of Titration Equilibria 379 Literature Automation and Data Processing 391 Literature 394 Appendix 395 A Source Listing ofedia 395 B Source Listing of TIFIT 405 Index 425

Reflection = EM strikes a boundary between two media differing in η and bounces back

Reflection = EM strikes a boundary between two media differing in η and bounces back Incident ray θ 1 θ 2 Reflected ray Medium 1 (air) η = 1.00 Medium 2 (glass) η = 1.50 Specular reflection = situation