The Determination of Ionization Constants The Determination of Ionization Constants A Laboratory Manual THIRD EDITION Adrien Albert D.Sc. (Lond.), F.R.I.e. Fellow of the Australian Academy of Science Emeritus Professor, Department of Chemistry, Australian National University Research Professor, Department of Pharmacological Sciences, School of Medicine, State University of New York, Stony Brook E.P. Serjeant M.Sc. (N.S.W.) Senior Lecturer in Chemistry, Faculty of Military Studies, University of New South Wales, Duntroon, A. C. T LONDON NEW YORK CHAPMAN AND HAll First published 1962 as Ionization Constants of Acids and Bases by Methuen & Co Ltd Second edition published 1971 by Chapman and Hall Ltd II New Fetter Lane, London EC4P 4EE Third edition 1984 Published in the USA by Chapman and Hall 733 Third Avenue, New York NYI0017 (C) 1984 Adrien Albert and E.P. Serjeant Softcover reprint of the hardcover I st edition 1984 ISBN-13: 978-94-010-8948-7 All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from the Publisher. British Library Cataloguing in Publication Data Albert, Adrien The determination of ionization constants. ~ 3rd ed. I. Ionization 2. Acids 3. Bases I. Title II. Serjeant, E. P. 546'24 QD561 ISBN-13: 978-94-010-8948-7 Library of Congress Cataloging in Publication Data Albert, Adrien, 1907 ~ The determination of ionization constants. Bibliography: p. Includes index. I. Ionization constants~ Measurement~ Laboratory manuals. I. Serjeant, E. P. II. Title. QD56I.A366 1984 541.3'722'028 84-7497 ISBN-13: 978-94-010-8948-7 e-ISBN-13: 978-94-009-5548-6 DOl: 10.1007/978-94-009-5548-6 Contents Preface 1 Introduction page 2 1.1 What is meant by 'ionization constants'? 2 1.2 Why do we determine ionization constants? 2 1.3 Brief summary of the chemistry of ionization 4 1.4 The nature of pKa values 6 1.5 The shape of a titration curve 7 1.6 Methods commonly used for determining ionization constants 8 1.7 What degree of precision is required? 10 1.8 The effect of temperature on ionization constants II 1.9 Molality and molarity 12 2 Determination of Ionization Constants by Potentiometric Titration using a Glass Electrode 14 2.1 Apparatus for general use 15 2.2 Preparation of solutions 22 2.3 Choice of concentration for the titration 24 2.4 Details of the titration method 25 2.5 Derivation and choice of equations for calculating pKa 26 2.6 Some typical titrations (worked examples) 29 2.7 Precision and accuracy. Checking the precision obtained 31 2.8 Common sources of error, and their elimination 31 2.9 False constants 35 2.10 Partly aqueous solvents 35 3 Refinements of Potentiometric Titration: Apparatus and Calculations 40 A Apparatus 3.1 Semi-micro titrations 40 3.2 Micro titrations 43 3.3 The rapid-flow method 46 3.4 The hydrogen electrode 46 B Calculations 3.5 Monofunctional acids and bases 47 v vi Contents 3.6 Method of calculation 51 3.7 Diacidic bases, dibasic acids and ampholytes 53 3.8 Overlapping ionization processes 56 3.9 Polyelectrolytes 61 3.10 Accuracy of the potentiometric method 62 3.11 Non-aqueous solvents 64 4 Determination of Ionization Constants by Spectrophotometry 70 4.1 Introduction 70 4.2 Apparatus 73 4.3 Buffers 73 4.4 Acidity functions 75 4.5 Preparation of the stock solution of the unknown 78 4.6 The search for the spectra of two pure ionic species 79 4.7 The choice of an analytical wavelength 79 4.8 Preliminary search for an approximate value of pKa 80 4.9 Exact determination of pKa 80 4.10 Worked examples 81 4.11 Activity corrections 84 4.12 Extensions of the spectrometric method 84 (a) Tbe pKa of a very weak acid (graphical treatment) 84 (b) Overlapping pKa values 86 (c) Computer program for overlapping values 89 4.13 Errors, precision and accuracy 93 4.14 Common sources of error 94 4.15 Spectrophotometric determination of the pKa of a substance that lacks an absorption spectrum 94 4.16 A rapid method for the approximate measurement of pKa 95 5 Relations between Ionization and Solubility. Determination of Ionization Constants by Phase Equilibria 102 5.1 Ionization constants in preparative work 102 5.2 Prediction of solubility from ionization constants 103 5.3 Determination of ionization constants from solubilities 105 5.4 Determination of ionization constants from vapour pressure, by partitioning between a pair of solvents, or by other phase equilibria 107 6 Determination of Ionization Constants by Conductimetry 110 6.1 Scope of the method 111 6.2 Apparatus 113 6.3 Procedure 115 6.4 Refinements of calculation 117 Contents vii 7 Some Other Methods for the Determination of Ionization Constants 120 7.1 Raman spectrometry 120 7.2 Proton nuclear magnetic resonance 121 7.3 Nuclear magnetic resonance using other atoms 123 7.4 Thermometric methods 124 8 Zwitterions (Dipolar Ions) 126 8.1 Zwitterions compared to ordinary amphoteric substances 126 8.2 How to distinguish zwitterions from ordinary ampholytes 128 8.3 Zwitterionicequilibria: macroscopic and microscopic constants 130 9 The Ionization Constants of Typical Acids and Bases 136 A Organic Section 9.1 The oxygen acids (monobasic) 137 (a) Aliphatic carboxylic acids 137 (b) Aromatic carboxylic acids 140 (c) Aliphatic hydroxylic acids 142 (d) Aromatic hydroxylic acids (phenols) 144 (e) Other oxygen acids 144 9.2 The oxygen acids (dibasic) 147 9.3 Sulphur acids, nitrogen acids and carbon acids 150 (a) Mercaptans 150 (b) Nitrogen acids 150 (c) Carbon acids 150 9.4 The nitrogen bases (mono acidic) 150 (a) Aliphatic bases 150 (b) Aromatic and heteroaromatic bases 153 9.5 The nitrogen bases (diacidic) 156 9.6 Carbinolamine bases 157 9.7 Oxygen bases and carbon bases 160 9.8 Amphoteric substances 160 B Inorganic Section 9.9 Inorganic acids 162 9.10 Inorganic bases 164 C Biologically-Active Substances 166 10 Chelation and the Stability Constants of Metal Complexes 176 10.1 The nature of chelation 178 10.2 Methods of calculation 179 10.3 Choice of ionic medium and the preparation of standard solutions 184 10.4 Measurement of pH and the calculation of pC 188 H 10.5 Common difficulties and how they can be overcome 190 viii Contents 11 Appendices 192 An outline of the BflzSnsted-Lowry Theory 192 II Comparison of classical and thermodynamic quantities 196 III Calculations of hydrogen ion activity and concentration: also of hydroxyl ion activity and concentration 197 IV Some effects of temperature on ionization constants 199 V How percentage ionized may be calculated, given pKa and pH 203 VI An outline of the theory of pH 203 References 208 Subject index 216 Preface This practical manual is devised for organic chemists and biochemists who, in the course of their researches and without previous experience, need to determine an ionization constant. We are gratified that earlier editions were much used for this purpose and that they also proved adequate for the in service training of technicians and technical officers to provide a Department with a pK service. The features of previous editions that gave this wide appeal have been retained, but the subject matter has been revised, extended, and brought up to date. We present two new chapters, one of which describes the determination of the stability constants of the complexes which organic ligands form with metal cations. The other describes the use of more recently introduced techniques for the determination of ionization constants, such as Raman and nuclear magnetic resonance spectroscopy, thermometric titrations, and paper electro phoresis. Chapter 1 gives enhanced help in choosing between alternative methods for determining ionization constants. The two chapters on potentiometric methods have been extensively revised in the light of newer understanding of electrode processes and of the present state of the art in instrumen tation. In the spectrometric methods chapter, the newer IUPAC symbols replace the old. Also the treatment of Hammett's acidity function has been brought up to date. This chapter concludes with help for the preparative organic chemist, namely a rapid spectrometric titration. This yields an approximate pK, know ledge of which will suggest conditions under which the new substance can be extracted and purified in higher yields. The chapter on zwitterions and other ampholytes has been largely rewritten to give a clearer presentation, and much new information has been incorporat ed. The tables of typical ionization constants, in Chapter 9, have been re-com piled from the most reliable of available values, and many additional substances will be found there. This chapter has a new section on substances which modify their ionization by equilibrating with pseudo bases (e.g. acridinium and pyrylium salts, also triphenylmethane dyes). The chapter concludes with a new table of the ionization constants of 370 commonly prescribed drugs and other bio logically active substances. ix x Preface Help in the interpretation of ionization constants is provided. It is shown how these are related to solubility (Chapter 5), how the degree of ionization at any pH can be calculated (Appendix V), and how ionization constants can aid in deciphering an unknown structure (Chapter 1). We advise a beginner, before he tackles any unknown substance, to 'enroll' in a course by repeating, in the order printed, each worked example in Chapters 2 and 4, both the practical work and the calculations (only easily procurable substances are needed). Much time can be saved in the calculations if the results are set out as shown in these worked examples. The first examples require only a few, very simple calculations. We have taken care to define the parameters within which these simple methods suffice, and to state clearly when refinements of calculation are needed. We have introduced the more complicated calculations as gradually as possible, and with full explanatory detail. To lessen the tedium of the lengthier calculations, we have devised computer programs. These are presented in a form which clearly shows the pathways of their derivation, to help those who would like to use a desk (electronic) calculator instead of a computer. Because this is a practical manual, we have touched only lightly on the theory of ionization (Chapter 1 and Appendices I and II). For theoretical study, E.1. King's book Acid-Base Equilibria (1965) and R.G. Bates' Determination of pH, Theory and Practice (1973) are recommended. Many useful data will also be found in Electrolyte Solutions by R.A. Robinson and R.H. Stokes (1959), and Solution Equilibria by F.R. Hartley, C. Burgess and R. Alcock (1980), the latter being particularly helpful with the experimental approach to finding stability constants of metal complexes. We thank Dr D.D. Perrin for helpful discussions.