Analytical Chemistry PDF

www.FreeEngineeringbooksPdf.com  11 0111 Analytical Chemistry 0111 0111 0111 0 11 www.FreeEngineeringbooksPdf.com ii Section K – Lipid metabolism The INSTANT NOTES series Series editor B.D. Ha...

www.FreeEngineeringbooksPdf.com  11 0111 Analytical Chemistry 0111 0111 0111 0 11 www.FreeEngineeringbooksPdf.com ii Section K – Lipid metabolism The INSTANT NOTES series Series editor B.D. Hames School of Biochemistry and Molecular Biology, University of Leeds, Leeds, UK Animal Biology Biochemistry 2nd edition Chemistry for Biologists Developmental Biology Ecology 2nd edition Genetics Immunology Microbiology Molecular Biology 2nd edition Neuroscience Plant Biology Psychology Forthcoming titles Bioinformatics The INSTANT NOTES Chemistry series Consulting editor: Howard Stanbury Analytical Chemistry Inorganic Chemistry Medicinal Chemistry Organic Chemistry Physical Chemistry www.FreeEngineeringbooksPdf.com  11 Analytical Chemistry 0111 D. Kealey School of Biological and Chemical Sciences Birkbeck College, University of London, UK 0111 and Department of Chemistry University of Surrey, Guildford, UK and 0111 P. J. Haines Oakland Analytical Services, Farnham, UK 0111 0 11 www.FreeEngineeringbooksPdf.com © BIOS Scientific Publishers Limited, 2002 First published 2002 (ISBN 1 85996 189 4) This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” All rights reserved. No part of this book may be reproduced or transmitted, in any form or by any means, without permission. A CIP catalogue record for this book is available from the British Library. ISBN 0-203-64544-8 Master e-book ISBN ISBN 0-203-68109-6 (Adobe eReader Format) ISBN 1 85996 189 4 (Print Edition) BIOS Scientific Publishers Ltd 9 Newtec Place, Magdalen Road, Oxford OX4 1RE, UK Tel. +44 (0)1865 726286. Fax +44 (0)1865 246823 World Wide Web home page: http://www.bios.co.uk/ Distributed exclusively in the United States, its dependent territories, Canada, Mexico, Central and South America, and the Caribbean by Springer-Verlag New York Inc, 175 Fifth Avenue, New York, USA, by arrangement with BIOS Scientific Publishers, Ltd, 9 Newtec Place, Magdalen Road, Oxford OX4 1RE, UK www.FreeEngineeringbooksPdf.com  C ONTENTS 11 Abbreviations vii Preface ix Section A – The nature and scope of analytical chemistry 1 0111 A1 Analytical chemistry, its functions and applications 1 A2 Analytical problems and procedures 3 A3 Analytical techniques and methods 5 A4 Sampling and sample handling 10 A5 Calibration and standards 15 A6 Quality in analytical laboratories 18 Section B − Assessment of data 21 B1 Errors in analytical measurements 21 B2 Assessment of accuracy and precision 26 0111 B3 Significance testing 34 B4 Calibration and linear regression 41 B5 Quality control and chemometrics 49 Section C − Analytical reactions in solution 55 C1 Solution equilibria 55 C2 Electrochemical reactions 61 C3 Potentiometry 66 C4 pH and its control 74 0111 C5 Titrimetry I: acid–base titrations 80 C6 Complexation, solubility and redox equilibria 85 C7 Titrimetry II: complexation, precipitation and redox titrations 90 C8 Gravimetry 95 C9 Voltammetry and amperometry 98 C10 Conductimetry 104 Section D − Separation techniques 109 D1 Solvent and solid-phase extraction 109 0111 D2 Principles of chromatography 119 D3 Thin-layer chromatography 131 D4 Gas chromatography: principles and instrumentation 137 D5 Gas chromatography: procedures and applications 149 D6 High-performance liquid chromatography: principles and instrumentation 155 D7 High-performance liquid chromatography: modes, procedures and applications 166 D8 Electrophoresis and electrochromatography: principles and instrumentation 174 0 D9 Electrophoresis and electrochromatography: modes, 11 procedures and applications 182 www.FreeEngineeringbooksPdf.com vi Contents Section E − Spectrometric techniques 189 E1 Electromagnetic radiation and energy levels 189 E2 Atomic and molecular spectrometry 195 E3 Spectrometric instrumentation 201 E4 Flame atomic emission spectrometry 206 E5 Inductively coupled plasma spectrometry 209 E6 X-ray emission spectrometry 214 E7 Atomic absorption and atomic fluorescence spectrometry 218 E8 Ultraviolet and visible molecular spectrometry: principles and instrumentation 223 E9 Ultraviolet and visible molecular spectrometry: applications 228 E10 Infrared and Raman spectrometry: principles and instrumentation 233 E11 Infrared and Raman spectrometry: applications 242 E12 Nuclear magnetic resonance spectrometry: principles and instrumentation 248 E13 Nuclear magnetic resonance spectrometry: interpretation of proton and carbon-13 spectra 261 E14 Mass spectrometry 270 Section F − Combined techniques 283 F1 Advantages of combined techniques 283 F2 Sample identification using multiple spectrometric techniques data 285 F3 Gas chromatography–mass spectrometry 294 F4 Gas chromatography–infrared spectrometry 298 F5 Liquid chromatography–mass spectrometry 302 Section G − Thermal methods 305 G1 Thermogravimetry 305 G2 Differential thermal analysis and differential scanning calorimetry 311 G3 Thermomechanical analysis 316 G4 Evolved gas analysis 320 Section H – Sensors, automation and computing 323 H1 Chemical sensors and biosensors 323 H2 Automated procedures 328 H3 Computer control and data collection 331 H4 Data enhancement and databases 333 Further reading 337 Index 339 www.FreeEngineeringbooksPdf.com  A BBREVIATIONS 11 AAS atomic absorption spectrometry ICP-MS ICP-mass spectrometry ADC analog-to-digital converter IEC ion-exchange chromatography AFS atomic fluorescence spectrometry ISE ion-selective electrode ANOVA analysis of variance LVDT linear variable differential ATR attenuated total reflectance transformer 0111 BPC bonded-phase chromatography MEKC micellar electrokinetic CC chiral chromatography chromatography CGE capillary gel electrophoresis MIR multiple internal reflectance CI confidence interval MS mass spectrometry CIEF capillary isoelectric focusing NIR near infrared CL confidence limits NMR nuclear-magnetic resonance CPU central processing unit NPD nitrogen-phosphorus detector CRM certified reference material PAH polycyclic aromatic hydrocarbons CZE capillary zone electrophoresis PC paper chromatography DAC digital-to-analog converter PCA principal component analysis 0111 DAD diode array detector PCR principal component regression DMA dynamic mechanical analysis PDMS polydimethylsiloxane DME dropping mercury electrode PLS partial least squares DSC differential scanning calorimetry QA quality assurance DTA differential thermal analysis QC quality control DTG derivative thermogravimetry RAM random access memory DVM digital voltmeter RF radiofrequency ECD electron-capture detector RI refractive index EDAX energy dispersive analysis ROM read only memory of X-rays RMM relative molecular mass 0111 EDTA ethylenediaminetetraacetic acid SCE saturated calomel electrode EGA evolved gas analysis SDS sodium dodecyl sulfate FA factor analysis SDS-PAGE SDS-polyacrylamide gel FAES flame atomic emission electrophoresis spectometry SE solvent extraction FFT fast Fourier transform SEC size-exclusion chromatography FID flame ionization detector SHE standard hydrogen electrode or free induction decay SIM selected ion monitoring GC gas chromatography SPE solid phase extraction GLC gas liquid chromatography SPME solid phase microextraction 0111 GSC gas solid chromatography SRM standard reference material HATR horizontal attenuated total TCD thermal conductivity detector reflectance TG thermogravimetry HPLC high-performance liquid TIC total ion current chromatography TISAB total ionic strength adjustment IC ion chromatography buffer ICP inductively coupled plasma TLC thin-layer chromatography ICP-AES ICP-atomic emission spectrometry TMA thermomechanical analysis ICP-OES ICP-optical emission spectrometry 0 11 www.FreeEngineeringbooksPdf.com www.FreeEngineeringbooksPdf.com P REFACE Analytical chemists and others in many disciplines frequently ask questions such as: What is this substance?; How concentrated is this solution?; What is the structure of this molecule? The answers to these and many other similar questions are provided by the techniques and methods of analytical chemistry. They are common to a wide range of activities, and the demand for analytical data of a chemical nature is steadily growing. Geologists, biologists, environmental and materials scientists, physicists, pharmacists, clinicians and engineers may all find it necessary to use or rely on some of the techniques of analysis described in this book. If we look back some forty or fifty years, chemical analysis concentrated on perhaps three main areas: qualitative testing, quantitative determinations, particularly by ‘classical’ techniques such as titrimetry and gravimetry, and structural analysis by procedures requiring laborious and time-consuming calcu- lations. The analytical chemist of today has an armoury of instrumental techniques, automated systems and computers which enable analytical measurements to be made more easily, more quickly and more accurately. However, pitfalls still exist for the unwary! Unless the analytical chemist has a thorough understand- ing of the principles, practice and limitations of each technique he/she employs, results may be inaccu- rate, ambiguous, misleading or invalid. From many years of stressing the importance of following appropriate analytical procedures to a large number of students of widely differing abilities, backgrounds and degrees of enthusiasm, the authors have compiled an up-to-date, unified approach to the study of analytical chemistry and its applications. Surveys of the day-to-day operations of many industrial and other analytical laboratories in the UK, Europe and the USA have shown which techniques are the most widely used, and which are of such limited application that extensive coverage at this level would be inappropriate. The text therefore includes analytical techniques commonly used by most analytical laboratories at this time. It is intended both to complement those on inorganic, organic and physical chemistry in the Instant Notes series, and to offer to students in chemistry and other disciplines some guid- ance on the use of analytical techniques where they are relevant to their work. We have not given extended accounts of complex or more specialized analytical techniques, which might be studied beyond first- and second-year courses. Nevertheless, the material should be useful as an overview of the subject for those studying at a more advanced level or working in analytical laboratories, and for revision purposes. The layout of the book has been determined by the series format and by the requirements of the overall analytical process. Regardless of the discipline from which the need for chemical analysis arises, common questions must be asked: How should a representative sample be obtained? What is to be determined and with what quantitative precision? What other components are present and will they interfere with the analytical measurements? How much material is available for analysis, and how many samples are to be analyzed? What instrumentation is to be used? How reliable is the data generated? These and related questions are considered in Sections A and B. Most of the subsequent sections provide notes on the principles, instrumentation and applications of both individual and groups of techniques. Where suitable supplementary texts exist, reference is made to them, and some suggestions on consulting the primary literature are made. We have assumed a background roughly equivalent to UK A-level chemistry or a US general chemistry course. Some simplification of mathematical treatments has been made; for example, in the sections on statistics, and on the theoretical basis of the various techniques. However, the texts listed under Further Reading give more comprehensive accounts and further examples of applications. www.FreeEngineeringbooksPdf.com x Preface We should like to thank all who have contributed to the development of this text, especially the many instrument manufacturers who generously provided examples and illustrations, and in particular Perkin Elmer Ltd. (UK) and Sherwood Scientific Ltd. (UK). We would like also to thank our colleagues who allowed us to consult them freely and, not least, the many generations of our students who found questions and problems where we had thought there were none! DK PJH www.FreeEngineeringbooksPdf.com Section A – The nature and scope of analytical chemistry A1 A NALYTICAL CHEMISTRY, ITS FUNCTIONS AND APPLICATIONS Key Notes Definition Analytical chemistry is a scientific discipline used to study the chemical composition, structure and behavior of matter. Purpose The purpose of chemical analysis is to gather and interpret chemical information that will be of value to society in a wide range of contexts. Scope and Quality control in manufacturing industries, the monitoring of clinical applications and environmental samples, the assaying of geological specimens, and the support of fundamental and applied research are the principal applications. Related topics Analytical problems and Computer control and data procedures (A2) collection (H3) Chemical sensors and biosensors Data enhancement and databases (H1) (H4) Automated procedures (H2) Definition Analytical chemistry involves the application of a range of techniques and methodologies to obtain and assess qualitative, quantitative and structural information on the nature of matter. Qualitative analysis is the identification of elements, species and/or compounds present in a sample. Quantitative analysis is the determination of the absolute or relative amounts of elements, species or compounds present in a sample. Structural analysis is the determination of the spatial arrangement of atoms in an element or molecule or the identification of characteristic groups of atoms (functional groups). An element, species or compound that is the subject of analysis is known as an analyte. The remainder of the material or sample of which the analyte(s) form(s) a part is known as the matrix. Purpose The gathering and interpretation of qualitative, quantitative and structural infor- mation is essential to many aspects of human endeavor, both terrestrial and extra-terrestrial. The maintenance of, and improvement in, the quality of life throughout the world, and the management of resources rely heavily on the information provided by chemical analysis. Manufacturing industries use analytical data to monitor the quality of raw materials, intermediates and www.FreeEngineeringbooksPdf.com 2 Section A – The nature and scope of analytical chemistry finished products. Progress and research in many areas is dependent on estab- lishing the chemical composition of man-made or natural materials, and the monitoring of toxic substances in the environment is of ever increasing impor- tance. Studies of biological and other complex systems are supported by the collection of large amounts of analytical data. Scope and Analytical data are required in a wide range of disciplines and situations that applications include not just chemistry and most other sciences, from biology to zoology, but the arts, such as painting and sculpture, and archaeology. Space exploration and clinical diagnosis are two quite disparate areas in which analytical data is vital. Important areas of application include the following. Quality control (QC). In many manufacturing industries, the chemical composition of raw materials, intermediates and finished products needs to be monitored to ensure satisfactory quality and consistency. Virtually all consumer products from automobiles to clothing, pharmaceuticals and food- stuffs, electrical goods, sports equipment and horticultural products rely, in part, on chemical analysis. The food, pharmaceutical and water industries in particular have stringent requirements backed by legislation for major compo- nents and permitted levels of impurities or contaminants. The electronics industry needs analyses at ultra-trace levels (parts per billion) in relation to the manufacture of semi-conductor materials. Automated, computer-controlled procedures for process-stream analysis are employed in some industries. Monitoring and control of pollutants. The presence of toxic heavy metals (e.g., lead, cadmium and mercury), organic chemicals (e.g., polychlorinated biphenyls and detergents) and vehicle exhaust gases (oxides of carbon, nitrogen and sulfur, and hydrocarbons) in the environment are health hazards that need to be monitored by sensitive and accurate methods of analysis, and remedial action taken. Major sources of pollution are gaseous, solid and liquid wastes that are discharged or dumped from industrial sites, and vehicle exhaust gases. Clinical and biological studies. The levels of important nutrients, including trace metals (e.g., sodium, potassium, calcium and zinc), naturally produced chemicals, such as cholesterol, sugars and urea, and administered drugs in the body fluids of patients undergoing hospital treatment require monitoring. Speed of analysis is often a crucial factor and automated procedures have been designed for such analyses. Geological assays. The commercial value of ores and minerals is determined by the levels of particular metals, which must be accurately established. Highly accurate and reliable analytical procedures must be used for this purpose, and referee laboratories are sometimes employed where disputes arise. Fundamental and applied research. The chemical composition and structure of materials used in or developed during research programs in numerous disciplines can be of significance. Where new drugs or materials with potential commercial value are synthesized, a complete chemical characterization may be required involving considerable analytical work. Combinatorial chemistry is an approach used in pharmaceutical research that generates very large numbers of new compounds requiring confirmation of identity and structure. www.FreeEngineeringbooksPdf.com Section A – The nature and scope of analytical chemistry A2 A NALYTICAL PROBLEMS AND PROCEDURES Key Notes Analytical problems Selecting or developing and validating appropriate methods of analysis to provide reliable data in a variety of contexts are the principal problems faced by analytical chemists. Analytical Any chemical analysis can be broken down into a number of stages that procedures include a consideration of the purpose of the analysis, the quality of the results required and the individual steps in the overall analytical procedure. Related topics Analytical chemistry, its functions Automated procedures (H2) and applications (A1) Computer control and data Sampling and sample handling collection (H3) (A4) Data enhancement and databases Chemical sensors and biosensors (H4) (H1) Analytical The most important aspect of an analysis is to ensure that it will provide useful problems and reliable data on the qualitative and/or quantitative composition of a material or structural information about the individual compounds present. The analyt- ical chemist must often communicate with other scientists and nonscientists to establish the amount and quality of the information required, the time-scale for the work to be completed and any budgetary constraints. The most appropriate analytical technique and method can then be selected from those available or new ones devised and validated by the analysis of substances of known composition and/or structure. It is essential for the analytical chemist to have an appreciation of the objectives of the analysis and an understanding of the capabilities of the various analytical techniques at his/her disposal without which the most appro- priate and cost-effective method cannot be selected or developed. Analytical The stages or steps in an overall analytical procedure can be summarized as procedures follows. Definition of the problem. Analytical information and level of accuracy required. Costs, timing, availability of laboratory instruments and facilities. Choice of technique and method. Selection of the best technique for the required analysis, such as chromatography, infrared spectrometry, titrimetry, thermogravimetry. Selection of the method (i.e. the detailed stepwise instruc- tions using the selected technique). Sampling. Selection of a small sample of the material to be analyzed. Where this is heterogeneous, special procedures need to be used to ensure that a genuinely representative sample is obtained (Topic A4). www.FreeEngineeringbooksPdf.com 4 Section A – The nature and scope of analytical chemistry Sample pre-treatment or conditioning. Conversion of the sample into a form suitable for detecting or measuring the level of the analyte(s) by the selected technique and method. This may involve dissolving it, converting the analyte(s) into a specific chemical form or separating the analyte(s) from other components of the sample (the sample matrix) that could interfere with detec- tion or quantitative measurements. Qualitative analysis. Tests on the sample under specified and controlled conditions. Tests on reference materials for comparison. Interpretation of the tests. Quantitative analysis. Preparation of standards containing known amounts of the analyte(s) or of pure reagents to be reacted with the analyte(s). Calibration of instruments to determine the responses to the standards under controlled conditions. Measurement of the instrumental response for each sample under the same conditions as for the standards. All measurements may be replicated to improve the reliability of the data, but this has cost and time implications. Calculation of results and statistical evaluation. Preparation of report or certificate of analysis. This should include a summary of the analytical procedure, the results and their statistical assess- ment, and details of any problems encountered at any stage during the analysis. Review of the original problem. The results need to be discussed with regard to their significance and their relevance in solving the original problem. Sometimes repeat analyses or new analyses may be undertaken. www.FreeEngineeringbooksPdf.com Section A – The nature and scope of analytical chemistry A3 A NALYTICAL TECHNIQUES AND METHODS Key Notes Analytical Chemical or physico-chemical processes that provide the basis for techniques analytical measurements are described as techniques. Analytical methods A method is a detailed set of instructions for a particular analysis using a specified technique. Method validation A process whereby an analytical method is checked for reliability in terms of accuracy, reproducibility and robustness in relation to its intended applications. Related topic Quality in analytical laboratories (A6) Analytical There are numerous chemical or physico-chemical processes that can be used to techniques provide analytical information. The processes are related to a wide range of atomic and molecular properties and phenomena that enable elements and compounds to be detected and/or quantitatively measured under controlled conditions. The underlying processes define the various analytical techniques. The more important of these are listed in Table 1, together with their suitability for qualitative, quantitative or structural analysis and the levels of analyte(s) in a sample that can be measured. Atomic and molecular spectrometry and chromatography, which together comprise the largest and most widely used groups of techniques, can be further subdivided according to their physico-chemical basis. Spectrometric techniques may involve either the emission or absorption of electromagnetic radiation over a very wide range of energies, and can provide qualitative, quantitative and structural information for analytes from major components of a sample down to ultra-trace levels. The most important atomic and molecular spectrometric techniques and their principal applications are listed in Table 2. Chromatographic techniques provide the means of separating the compo- nents of mixtures and simultaneous qualitative and quantitative analysis, as required. The linking of chromatographic and spectrometric techniques, called hyphenation, provides a powerful means of separating and identifying unknown compounds (Section F). Electrophoresis is another separation tech- nique with similarities to chromatography that is particularly useful for the separation of charged species. The principal separation techniques and their applications are listed in Table 3. Analytical An analytical method consists of a detailed, stepwise list of instructions to be methods followed in the qualitative, quantitative or structural analysis of a sample for one or more analytes and using a specified technique. It will include a summary and www.FreeEngineeringbooksPdf.com 6 Section A – The nature and scope of analytical chemistry Table 1. Analytical techniques and principal applications Technique Property measured Principal areas of application Gravimetry Weight of pure analyte or compound Quantitative for major or minor of known stoichiometry components Titrimetry Volume of standard reagent solution Quantitative for major or minor reacting with the analyte components Atomic and molecular Wavelength and intensity of Qualitative, quantitative or structural spectrometry electromagnetic radiation emitted or for major down to trace level absorbed by the analyte components Mass spectrometry Mass of analyte or fragments of it Qualitative or structural for major down to trace level components isotope ratios Chromatography and Various physico-chemical properties Qualitative and quantitative electrophoresis of separated analytes separations of mixtures at major to trace levels Thermal analysis Chemical/physical changes in the Characterization of single or mixed analyte when heated or cooled major/minor components Electrochemical analysis Electrical properties of the analyte Qualitative and quantitative for major in solution to trace level components Radiochemical analysis Characteristic ionizing nuclear Qualitative and quantitative at major radiation emitted by the analyte to trace levels Table 2. Spectrometric techniques and principal applications Technique Basis Principal applications Plasma emission spectrometry Atomic emission after excitation in high Determination of metals and some temperature gas plasma non-metals mainly at trace levels Flame emission spectrometry Atomic emission after flame excitation Determination of alkali and alkaline earth metals Atomic absorption spectrometry Atomic absorption after atomization Determination of trace metals and by flame or electrothermal means some non-metals Atomic fluorescence Atomic fluorescence emission after Determination of mercury and spectrometry flame excitation hydrides of non-metals at trace levels X-ray emission spectrometry Atomic or atomic fluorescence Determination of major and minor emission after excitation by electrons elemental components of or radiation metallurgical and geological samples γ-spectrometry γ-ray emission after nuclear excitation Monitoring of radioactive elements in environmental samples Ultraviolet/visible spectrometry Electronic molecular absorption in Quantitative determination of solution unsaturated organic compounds Infrared spectrometry Vibrational molecular absorption Identification of organic compounds Nuclear magnetic resonance Nuclear absorption (change of spin Identification and structural analysis spectrometry states) of organic compounds Mass spectrometry Ionization and fragmentation of Identification and structural analysis molecules of organic compounds www.FreeEngineeringbooksPdf.com A3 – Analytical techniques and methods 7 Table 3. Separation techniques and principal applications Technique Basis Principal applications 冧 Thin-layer chromatography Qualitative analysis of mixtures Differential rates of migration of Gas chromatography Quantitative and qualitative analytes through a stationary phase determination of volatile compounds by movement of a liquid or gaseous High-performance liquid mobile phase Quantitative and qualitative chromatography determination of nonvolatile compounds Electrophoresis Differential rates of migration of Quantitative and qualitative analytes through a buffered medium determination of ionic compounds lists of chemicals and reagents to be used, laboratory apparatus and glassware, and appropriate instrumentation. The quality and sources of chemicals, including solvents, and the required performance characteristics of instruments will also be specified as will the procedure for obtaining a representative sample of the material to be analyzed. This is of crucial importance in obtaining mean- ingful results (Topic A4). The preparation or pre-treatment of the sample will be followed by any necessary standardization of reagents and/or calibration of instruments under specified conditions (Topic A5). Qualitative tests for the analyte(s) or quantitative measurements under the same conditions as those used for standards complete the practical part of the method. The remaining steps will be concerned with data processing, computational methods for quantitative analysis and the formatting of the analytical report. The statistical assessment of quantitative data is vital in establishing the reliability and value of the data, and the use of various statistical parameters and tests is widespread (Section B). Many standard analytical methods have been published as papers in analyt- ical journals and other scientific literature, and in textbook form. Collections by trades associations representing, for example, the cosmetics, food, iron and steel, pharmaceutical, polymer plastics and paint, and water industries are available. Standards organizations and statutory authorities, instrument manufacturers’ applications notes, the Royal Society of Chemistry and the US Environmental Protection Agency are also valuable sources of standard methods. Often, labora- tories will develop their own in-house methods or adapt existing ones for specific purposes. Method development forms a significant part of the work of most analytical laboratories, and method validation and periodic revalidation is a necessity. Selection of the most appropriate analytical method should take into account the following factors: the purpose of the analysis, the required time scale and any cost constraints; the level of analyte(s) expected and the detection limit required; the nature of the sample, the amount available and the necessary sample preparation procedure; the accuracy required for a quantitative analysis; the availability of reference materials, standards, chemicals and solvents, instrumentation and any special facilities; possible interference with the detection or quantitative measurement of the analyte(s) and the possible need for sample clean-up to avoid matrix interference; www.FreeEngineeringbooksPdf.com 8 Section A – The nature and scope of analytical chemistry the degree of selectivity available − methods may be selective for a small number of analytes or specific for only one; quality control and safety factors. Method validation Analytical methods must be shown to give reliable data, free from bias and suit- able for the intended use. Most methods are multi-step procedures, and the process of validation generally involves a stepwise approach in which optimized experimental parameters are tested for robustness (ruggedness), that is sensi- tivity to variations in the conditions, and sources of errors investigated. A common approach is to start with the final measurement stage, using cali- bration standards of known high purity for each analyte to establish the perfor- mance characteristics of the detection system (i.e. specificity, range, quantitative response (linearity), sensitivity, stability and reproducibility). Robustness in terms of temperature, humidity and pressure variations would be included at this stage, and a statistical assessment made of the reproducibility of repeated identical measurements (replicates). The process is then extended backwards in sequence through the preceding stages of the method, checking that the optimum conditions and performance established for the final measurement on analyte calibration standards remain valid throughout. Where this is not the case, new conditions must be investigated by modification of the procedure and the process repeated. A summary of this approach is shown in Figure 1 in the form of a flow diagram. At each stage, the results are assessed using appropriate statistical tests (Section B) and compared for consistency with those of the previous stage. Where unacceptable variations arise, changes to the procedure are implemented and the assessment process repeated. The performance and robustness of the overall method are finally tested with field trials in one or more routine analytical laboratories before the method is considered to be fully validated. www.FreeEngineeringbooksPdf.com A3 – Analytical techniques and methods 9 Step 1 Performance characteristics of detector for single analyte calibration standards Step 2 Process repeated for mixed analyte calibration standards Step 3 Process repeated for analyte calibration standards with possible interfering substances and for reagent blanks Step 4 Process repeated for analyte calibration standards with anticipated matrix components to evaluate matrix interference Step 5 Analysis of 'spiked' simulated sample matrix. i.e. matrix with added known amounts of analyte(s), to test recoveries Step 6 Field trials in routine laboratory with more junior personnel to test ruggedness Fig. 1. Flow chart for method validation. www.FreeEngineeringbooksPdf.com Section A – The nature and scope of analytical chemistry A4 S AMPLING AND SAMPLE HANDLING Key Notes Representative A representative sample is one that truly reflects the composition of the sample material to be analyzed within the context of a defined analytical problem. Sample storage Due to varying periods of time that may elapse between sample collection and analysis, storage conditions must be such as to avoid undesirable losses, contamination or other changes that could affect the results of the analysis. Sample Preliminary treatment of a sample is sometimes necessary before it is in a pre-treatment suitable form for analysis by the chosen technique and method. This may involve a separation or concentration of the analytes or the removal of matrix components that would otherwise interfere with the analysis. Sample preparation Samples generally need to be brought into a form suitable for measurements to be made under controlled conditions. This may involve dissolution, grinding, fabricating into a specific size and shape, pelletizing or mounting in a sample holder. Related topic Analytical problems and procedures (A2) Representative The importance of obtaining a representative sample for analysis cannot be sample overemphasized. Without it, results may be meaningless or even grossly misleading. Sampling is particularly crucial where a heterogeneous material is to be analyzed. It is vital that the aims of the analysis are understood and an appro- priate sampling procedure adopted. In some situations, a sampling plan or strategy may need to be devised so as to optimize the value of the analytical information collected. This is necessary particularly where environmental samples of soil, water or the atmosphere are to be collected or a complex indus- trial process is to be monitored. Legal requirements may also determine a sampling strategy, particularly in the food and drug industries. A small sample taken for analysis is described as a laboratory sample. Where duplicate analyses or several different analyses are required, the laboratory sample will be divided into sub-samples which should have identical compositions. Homogeneous materials (e.g., single or mixed solvents or solutions and most gases) generally present no particular sampling problem as the composition of any small laboratory sample taken from a larger volume will be representative of the bulk solution. Heterogeneous materials have to be homogenized prior to obtaining a laboratory sample if an average or bulk composition is required. Conversely, where analyte levels in different parts of the material are to be www.FreeEngineeringbooksPdf.com A4 – Sampling and sample handling 11 measured, they may need to be physically separated before laboratory samples are taken. This is known as selective sampling. Typical examples of hetero- geneous materials where selective sampling may be necessary include: surface waters such as streams, rivers, reservoirs and seawater, where the concentrations of trace metals or organic compounds in solution and in sedi- ments or suspended particulate matter may each be of importance; materials stored in bulk, such as grain, edible oils, or industrial organic chem- icals, where physical segregation (stratification) or other effects may lead to variations in chemical composition throughout the bulk; ores, minerals and alloys, where information about the distribution of a partic- ular metal or compound is sought; laboratory, industrial or urban atmospheres where the concentrations of toxic vapors and fumes may be localized or vary with time. Obtaining a laboratory sample to establish an average analyte level in a highly heterogeneous material can be a lengthy procedure. For example, sampling a large shipment of an ore or mineral, where the economic cost needs to be determined by a very accurate assay, is typically approached in the following manner. (i) Relatively large pieces are randomly selected from different parts of the shipment. (ii) The pieces are crushed, ground to coarse granules and thoroughly mixed. (iii) A repeated coning and quartering process, with additional grinding to reduce particle size, is used until a laboratory-sized sample is obtained. This involves creating a conical heap of the material, dividing it into four equal portions, discarding two diagonally opposite portions and forming a new conical heap from the remaining two quarters. The process is then repeated as necessary (Fig. 1). 2 2 2 1 3 1 3 1 3 4 4 4 Fig. 1. A diagrammatic representation of coning and quartering (quarters 1 and 3, or 2 and 4 are discarded each time). www.FreeEngineeringbooksPdf.com 12 Section A – The nature and scope of analytical chemistry The distribution of toxic heavy metals or organic compounds in a land rede- velopment site presents a different problem. Here, to economize on the number of analyses, a grid is superimposed on the site dividing it up into approximately one- to five-metre squares. From each of these, samples of soil will be taken at several specified depths. A three-dimensional representation of the distribution of each analyte over the whole site can then be produced, and any localized high concentrations, or hot spots, can be investigated by taking further, more closely- spaced, samples. Individual samples may need to be ground, coned and quartered as part of the sampling strategy. Repeated sampling over a period of time is a common requirement. Examples include the continuous monitoring of a process stream in a manufacturing plant and the frequent sampling of patients’ body fluids for changes in the levels of drugs, metabolites, sugars or enzymes, etc., during hospital treatment. Studies of seasonal variations in the levels of pesticide, herbicide and fertilizer residues in soils and surface waters, or the continuous monitoring of drinking water supplies are two further examples. Having obtained a representative sample, it must be labeled and stored under appropriate conditions. Sample identification through proper labeling, increas- ingly done by using bar codes and optical readers under computer control, is an essential feature of sample handling. Sample storage Samples often have to be collected from places remote from the analytical labora- tory and several days or weeks may elapse before they are received by the labo- ratory and analyzed. Furthermore, the workload of many laboratories is such that incoming samples are stored for a period of time prior to analysis. In both instances, sample containers and storage conditions (e.g., temperature, humidity, light levels and exposure to the atmosphere) must be controlled such that no significant changes occur that could affect the validity of the analytical data. The following effects during storage should be considered: increases in temperature leading to the loss of volatile analytes, thermal or biological degradation, or increased chemical reactivity; decreases in temperature that lead to the formation of deposits or the precipi- tation of analytes with low solubilities; changes in humidity that affect the moisture content of hygroscopic solids and liquids or induce hydrolysis reactions; UV radiation, particularly from direct sunlight, that induces photochemical reactions, photodecomposition or polymerization; air-induced oxidation; physical separation of the sample into layers of different density or changes in crystallinity. In addition, containers may leak or allow contaminants to enter. A particular problem associated with samples having very low (trace and ultra-trace) levels of analytes in solution is the possibility of losses by adsorp- tion onto the walls of the container or contamination by substances being leached from the container by the sample solvent. Trace metals may be depleted by adsorption or ion-exchange processes if stored in glass containers, whilst sodium, potassium, boron and silicates can be leached from the glass into the sample solution. Plastic containers should always be used for such samples. www.FreeEngineeringbooksPdf.com A4 – Sampling and sample handling 13 Conversely, sample solutions containing organic solvents and other organic liquids should be stored in glass containers because the base plastic or additives such as plasticizers and antioxidants may be leached from the walls of plastic containers. Sample pre- Samples arriving in an analytical laboratory come in a very wide assortment of treatment sizes, conditions and physical forms and can contain analytes from major constituents down to ultra-trace levels. They can have a variable moisture content and the matrix components of samples submitted for determinations of the same analyte(s) may also vary widely. A preliminary, or pre-treatment, is often used to condition them in readiness for the application of a specific method of analysis or to pre-concentrate (enrich) analytes present at very low levels. Examples of pre- treatments are: drying at 100°C to 120°C to eliminate the effect of a variable moisture content; weighing before and after drying enables the water content to be calculated or it can be established by thermogravimetric analysis (Topic G1); separating the analytes into groups with common characteristics by dis- tillation, filtration, centrifugation, solvent or solid phase extraction (Topic D1); removing or reducing the level of matrix components that are known to cause interference with measurements of the analytes; concentrating the analytes if they are below the concentration range of the analytical method to be used by evaporation, distillation, co-precipitation, ion exchange, solvent or solid phase extraction or electrolysis. Sample clean-up in relation to matrix interference and to protect special- ized analytical equipment such as chromatographic columns and detection systems from high levels of matrix components is widely practised using solid phase extraction (SPE) cartridges (Topic D1). Substances such as lipids, fats, proteins, pigments, polymeric and tarry substances are particularly detri- mental. Sample A laboratory sample generally needs to be prepared for analytical measurement preparation by treatment with reagents that convert the analyte(s) into an appropriate chem- ical form for the selected technique and method, although in some instances it is examined directly as received or mounted in a sample holder for surface analysis. If the material is readily soluble in aqueous or organic solvents, a simple dissolution step may suffice. However, many samples need first to be decom- posed to release the analyte(s) and facilitate specific reactions in solution. Sample solutions may need to be diluted or concentrated by enrichment so that analytes are in an optimum concentration range for the method. The stabilization of solu- tions with respect to pH, ionic strength and solvent composition, and the removal or masking of interfering matrix components not accounted for in any pre-treat- ment may also be necessary. An internal standard for reference purposes in quantitative analysis (Topic A5 and Section B) is sometimes added before adjust- ment to the final prescribed volume. Some common methods of decomposition and dissolution are given in Table 1. www.FreeEngineeringbooksPdf.com 14 Section A – The nature and scope of analytical chemistry Table 1. Some methods for sample decomposition and dissolution Method of attack Type of sample Heated with concentrated mineral Geological, metallurgical acids (HCl, HNO3, aqua regia) or strong alkali, including microwave digestion Fusion with flux (Na2O2, Na2CO3, Geological, refractory materials LiBO2, KHSO4, KOH) Heated with HF and H2SO4 or HClO4 Silicates where SiO2 is not the analyte Acid leaching with HNO3 Soils and sediments Dry oxidation by heating in a furnace Organic materials with inorganic analytes or wet oxidation by boiling with concentrated H2SO4 and HNO3 or HClO4 www.FreeEngineeringbooksPdf.com Section A – The nature and scope of analytical chemistry A5 C ALIBRATION AND STANDARDS Key Notes Calibration Calibration or standardization is the process of establishing the response of a detection or measurement system to known amounts or concentrations of an analyte under specified conditions, or the comparison of a measured quantity with a reference value. Chemical standard A chemical standard is a material or substance of very high purity and/or known composition that is used to standardize a reagent or calibrate an instrument. Reference material A reference material is a material or substance, one or more properties of which are sufficiently homogeneous and well established for it to be used for the calibration of apparatus, the assessment of a measurement method or for assigning values to materials. Related topic Calibration and linear regression (B4) Calibration With the exception of absolute methods of analysis that involve chemical reac- tions of known stoichiometry (e.g., gravimetric and titrimetric determinations), a calibration or standardization procedure is required to establish the relation between a measured physico-chemical response to an analyte and the amount or concentration of the analyte producing the response. Techniques and methods where calibration is necessary are frequently instrumental, and the detector response is in the form of an electrical signal. An important consideration is the effect of matrix components on the analyte detector signal, which may be supressed or enhanced, this being known as the matrix effect. When this is known to occur, matrix matching of the calibration standards to simulate the gross composition expected in the samples is essential (i.e. matrix components are added to all the analyte standards in the same amounts as are expected in the samples). There are several methods of calibration, the choice of the most suitable depending on the characteristics of the analytical technique to be employed, the nature of the sample and the level of analyte(s) expected. These include: External standardization. A series of at least four calibration standards containing known amounts or concentrations of the analyte and matrix components, if required, is either prepared from laboratory chemicals of guar- anteed purity (AnalaR or an equivalent grade) or purchased as a concentrated standard ready to use. The response of the detection system is recorded for each standard under specified and stable conditions and additionally for a blank, sometimes called a reagent blank (a standard prepared in an identical www.FreeEngineeringbooksPdf.com 16 Section A – The nature and scope of analytical chemistry fashion to the other standards but omitting the analyte). The data is either plotted as a calibration graph or used to calculate a factor to convert detector responses measured for the analyte in samples into corresponding masses or concentrations (Topic B4). Standard addition. Internal standardization. The last two methods of calibration are described in Topic B4. Instruments and apparatus used for analytical work must be correctly main- tained and calibrated against reference values to ensure that measurements are accurate and reliable. Performance should be checked regularly and records kept so that any deterioration can be quickly detected and remedied. Microcomputer and microprocessor controlled instrumentation often has built-in performance checks that are automatically initiated each time an instrument is turned on. Some examples of instrument or apparatus calibration are manual calibration of an electronic balance with certified weights; calibration of volumetric glassware by weighing volumes of pure water; calibration of the wavelength and absorbance scales of spectrophotometers with certified emission or absorption characteristics; calibration of temperature scales and electrical voltage or current readouts with certified measurement equipment. Chemical Materials or substances suitable for use as chemical standards are generally standard single compounds or elements. They must be of known composition, and high purity and stability. Many are available commercially under the name AnalaR. Primary standards, which are used principally in titrimetry (Section C) to standardize a reagent (titrant) (i.e. to establish its exact concentration) must be internationally recognized and should fulfil the following requirements: be easy to obtain and preserve in a high state of purity and of known chemical composition; be non-hygroscopic and stable in air allowing accurate weighing; have impurities not normally exceeding 0.02% by weight; be readily soluble in water or another suitable solvent; react rapidly with an analyte in solution; other than pure elements, to have a high relative molar mass to minimize weighing errors. Primary standards are used directly in titrimetric methods or to standardize solutions of secondary or working standards (i.e. materials or substances that do not fulfill all of the above criteria, that are to be used subsequently as the titrant in a particular method). Chemical standards are also used as reagents to effect reactions with analytes before completing the analysis by techniques other than titrimetry. Some approved primary standards for titrimetric analysis are given in Table 1. Reference Reference materials are used to demonstrate the accuracy, reliability and com- material parability of analytical results. A certified or standard reference material (CRM or SRM) is a reference material, the values of one or more properties of which have been certified by a technically valid procedure and accompanied by a trace- able certificate or other documentation issued by a certifying body such as the www.FreeEngineeringbooksPdf.com A5 – Calibration and standards 17 Table 1. Some primary standards used in titrimetric analysis Type of titration Primary standard Acid-base Sodium carbonate, Na2CO3 Sodium tetraborate, Na2B4O7.10H2O Potassium hydrogen phthalate, KH(C8H4O4) Benzoic acid, C6H5COOH Redox Potassium dichromate, K2Cr2O7 Potassium iodate, KIO3 Sodium oxalate, Na2C2O4 Precipitation (silver halide) Silver nitrate, AgNO3 Sodium chloride, NaCl Complexometric (EDTA) Zinc, Zn Magnesium, Mg EDTA (disodium salt), C10H14N2O8Na2 Bureau of Analytical Standards. CRMs or SRMs are produced in various forms and for different purposes and they may contain one or more certified compo- nents, such as pure substances or solutions for calibration or identification; materials of known matrix composition to facilitate comparisons of analytical data; materials with approximately known matrix composition and specified components. They have a number of principal uses, including validation of new methods of analysis; standardization/calibration of other reference materials; confirmation of the validity of standardized methods; support of quality control and quality assurance schemes. www.FreeEngineeringbooksPdf.com Section A – The nature and scope of analytical chemistry A6 Q UALITY IN ANALYTICAL LABORATORIES Key Notes Quality control Quality control (QC) is the process of ensuring that the operational techniques and activities used in an analytical laboratory provide results suitable for the intended purpose. Quality assurance Quality assurance (QA) is the combination of planned and systematic actions necessary to provide adequate confidence that the process of quality control satisfies specified requirements. Accreditation This is a system whereby the quality control and quality assurance system procedures adopted by a laboratory are evaluated by inspection and accredited by an independent body. Related topics Analytical techniques and Quality control and chemometrics methods (A3) (B5) Quality control Analytical data must be of demonstrably high quality to ensure confidence in the results. Quality control (QC) comprises a system of planned activities in an analytical laboratory whereby analytical methods are monitored at every stage to verify compliance with validated procedures and to take steps to eliminate the causes of unsatisfactory performance. Results are considered to be of sufficiently high quality if they meet the specific requirements of the requested analytical work within the context of a defined problem; there is confidence in their validity; the work is cost effective. To implement a QC system, a complete understanding of the chemistry and operations of the analytical method and the likely sources and magnitudes of errors at each stage is essential. The use of reference materials (Topic A5) during method validation (Topic A3) ensures that results are traceable to certified sources. QC processes should include: checks on the accuracy and precision of the data using statistical tests (Section B); detailed records of calibration, raw data, results and instrument performance; observations on the nature and behavior of the sample and unsatisfactory aspects of the methodology; control charts to determine system control for instrumentation and repeat analyses (Topic B5); www.FreeEngineeringbooksPdf.com A6 – Quality in analytical laboratories 19 provision of full documentation and traceability of results to recognized reference materials through recorded identification; maintenance and calibration of instrumentation to manufacturers’ specifica- tions; management and control of laboratory chemicals and other materials including checks on quality; adequate training of laboratory personnel to ensure understanding and competence; external verification of results wherever possible; accreditation of the laboratory by an independent organization. Quality assurance The overall management of an analytical laboratory should include the provision of evidence and assurances that appropriate QC procedures for laboratory activ- ities are being correctly implemented. Quality assurance (QA) is a managerial responsibility that is designed to ensure that this is the case and to generate confidence in the analytical results. Part of QA is to build confidence through the laboratory participating in interlaboratory studies where several laboratories analyze one or more identical homogeneous materials under specified condi- tions. Proficiency testing is a particular type of study to assess the performance of a laboratory or analyst relative to others, whilst method performance studies and certification studies are undertaken to check a particular analytical method or reference material respectively. The results of such studies and their statistical assessment enable the performances of individual participating laboratories to be demonstrated and any deficiencies in methodology and the training of personnel to be addressed. Accreditation Because of differences in the interpretation of the term quality, which can be system defined as fitness for purpose, QC and QA systems adopted by analyical labora- tories in different industries and fields of activity can vary widely. For this reason, defined quality standards have been introduced by a number of organi- zations throughout the world. Laboratories can design and implement their own quality systems and apply to be inspected and accredited by the organization for the standard most appropriate to their activity. A number of organizations that offer accreditation suitable for analytical laboratories and their corresponding quality standards are given in Table 1. Table 1. Accreditation organizations and their quality standards Name of accreditation organization Quality standard Organization for Economic Co-operation Good Laboratory Practice (GLP) and Development (OECD) The International Organization for ISO 9000 series of quality standards Standardization (ISO) ISO Guide 25 general requirements for competence of calibration and testing laboratories European Committee for Standardization EN 29000 series (CEN) EN 45000 series British Standards Institution (BSI) BS 5750 quality standard BS 7500 series National Measurement Accreditation NAMAS Service (NAMAS) www.FreeEngineeringbooksPdf.com www.FreeEngineeringbooksPdf.com Section B – Assessment of data B1 E RRORS IN ANALYTICAL MEASUREMENTS Key Notes Measurement errors All measurement processes are subject to measurement errors that affect numerical data and which arise from a variety of sources. Absolute and An absolute error is the numerical difference between a measured value relative errors and a true or accepted value. A relative error is the absolute error divided by the true or accepted value. Determinate errors Also known as systematic errors, or bias, these generally arise from determinate or identifiable sources causing measured values to differ from a true or accepted value. Indeterminate errors Also known as random errors, these arise from a variety of uncontrolled sources and cause small random variations in a measured quantity when the measurement is repeated a number of times. Accumulated errors Where several different measurements are combined to compute an overall analytical result, the errors associated with each individual measurement contribute to a total or accumulated error. Related topic Assessment of accuracy and precision (B2) Measurement The causes of measurement errors are numerous and their magnitudes are vari- errors able. This leads to uncertainties in reported results. However, measurement errors can be minimized and some types eliminated altogether by careful exper- imental design and control. Their effects can be assessed by the application of statistical methods of data analysis and chemometrics (Topic B5). Gross errors may arise from faulty equipment or bad laboratory practice; proper equipment maintenance and appropriate training and supervision of personnel should eliminate these. Nevertheless, whether it is reading a burette or thermometer, weighing a sample or timing events, or monitoring an electrical signal or liquid flow, there will always be inherent variations in the measured parameter if readings are repeated a number of times under the same conditions. In addition, errors may go undetected if the true or accepted value is not known for comparison purposes. Errors must be controlled and assessed so that valid analytical measurements can be made and reported. The reliability of such data must be demonstrated so that an end-user can have an acceptable degree of confidence in the results of an analysis. www.FreeEngineeringbooksPdf.com 22 Section B – Assessment of data Absolute and The absolute error, EA, in a measurement or result, xM, is given by the equation relative errors EA = xM - xT where xT is the true or accepted value. Examples are shown in Figure 1 where a 200 mg aspirin standard has been analyzed a number of times. The absolute errors range from -4 mg to +10 mg. The relative error, ER, in a measurement or result, xM, is given by the equation ER = (xM - xT)/xT Often, ER is expressed as a percentage relative error, 100ER. Thus, for the aspirin results shown in Figure 1, the relative error ranges from -2% to +5%. Relative errors are particularly useful for comparing results of differing magnitude. Aspirin (mg) 195 200 205 210 –5 0 5 10 Absolute error (EA; mg) –2.5 0 2.5 5 Relative error (ER; %) Fig. 1. Absolute and relative errors in the analysis of an aspirin standard. Determinate There are three basic sources of determinate or systematic errors that lead to a errors bias in measured values or results: the analyst or operator; the equipment (apparatus and instrumentation) and the laboratory environ- ment; the method or procedure. It should be possible to eliminate errors of this type by careful observation and record keeping, equipment maintenance and training of laboratory personnel. Operator errors can arise through carelessness, insufficient training, illness or disability. Equipment errors include substandard volumetric glassware, faulty or worn mechanical components, incorrect electrical signals and a poor or insufficiently controlled laboratory environment. Method or procedural errors are caused by inadequate method validation, the application of a method to samples or concentration levels for which it is not suitable or unexpected varia- tions in sample characteristics that affect measurements. Determinate errors that lead to a higher value or result than a true or accepted one are said to show a positive bias; those leading to a lower value or result are said to show a nega- tive bias. Particularly large errors are described as gross errors; these should be easily apparent and readily eliminated. www.FreeEngineeringbooksPdf.com B1 – Errors in analytical measurements 23 Determinate errors can be proportional to the size of sample taken for analysis. If so, they will have the same effect on the magnitude of a result regardless of the size of the sample, and their presence can thus be difficult to detect. For example, copper(II) can be determined by titration after reaction with potassium iodide to release iodine according to the equation 2Cu2+ + 4I- Æ 2CuI + I2 However, the reaction is not specific to copper(II), and any iron(III) present in the sample will react in the same way. Results for the determination of copper in an alloy containing 20%, but which also contained 0.2% of iron are shown in Figure 2 for a range of sample sizes. The same absolute error of +0.2% or relative error of 1% (i.e. a positive bias) occurs regardless of sample size, due to the presence of the iron. This type of error may go undetected unless the constituents of the sample and the chemistry of the method are known. 21 Copper found (%) Positive bias 20 True value 19 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Sample size (g) Fig. 2. Effect of a proportional error on the determination of copper by titration in the presence of iron. Constant determinate errors are independent of sample size, and therefore become less significant as the sample size is increased. For example, where a visual indicator is employed in a volumetric procedure, a small amount of titrant is required to change the color at the end-point, even in a blank solution (i.e. when the solution contains none of the species to be determined). This indicator blank (Topic C5) is the same regardless of the size of the titer when the species being determined is present. The relative error, therefore, decreases with the magnitude of the titer, as shown graphically in Figure 3. Thus, for an indicator blank of 0.02 cm3, the relative error for a 1 cm3 titer is 2%, but this falls to only 0.08% for a 25 cm3 titer. Indeterminate Known also as random errors, these arise from random fluctuations in errors measured quantities, which always occur even under closely controlled condi- tions. It is impossible to eliminate them entirely, but they can be minimized by careful experimental design and control. Environmental factors such as temper- ature, pressure and humidity, and electrical properties such as current, voltage and resistance are all susceptible to small continuous and random variations described as noise. These contribute to the overall indeterminate error in any www.FreeEngineeringbooksPdf.com 24 Section B – Assessment of data 2.5 2 Relative error (%) 1.5 1 0.5 0 0 10 20 30 Size of titer (cm3) Fig. 3. Effect of a constant error on titers of differing magnitudes. physical or physico-chemical measurement, but no one specific source can be identified. A series of measurements made under the same prescribed conditions and represented graphically is known as a frequency distribution. The frequency of occurrence of each experimental value is plotted as a function of the magnitude of the error or deviation from the average or mean value. For analytical data, the values are often distributed symmetrically about the mean value, the most common being the normal error or Gaussian distribution curve. The curve (Fig. 4) shows that small errors are more probable than large ones, positive and negative errors are equally probable, and the maximum of the curve corresponds to the mean value. The normal error curve is the basis of a number of statistical tests that can be applied to analytical data to assess the effects of indeterminate errors, to compare values and to establish levels of confidence in results (Topics B2 and B3). Frequency of occurrence of each deviation – 0 + Deviation from mean, µ Fig. 4. The normal error or Gaussian distribution curve. www.FreeEngineeringbooksPdf.com B1 – Errors in analytical measurements 25 Accumulated Errors are associated with every measurement made in an analytical procedure, errors and these will be aggregated in the final calculated result. The accumulation or propagation of errors is treated similarly for both determinate (systematic) and indeterminate (random) errors. Determinate (systematic) errors can be either positive or negative, hence some cancellation of errors is likely in computing an overall determinate error, and in some instances this may be zero. The overall error is calculated using one of two alternative expressions, that is where only a linear combination of individual measurements is required to compute the result, the overall absolute determinate error, ET, is given by ET = E1 + E2 + E3 + ……. E1 and E2 etc., being the absolute determinate errors in the individual measurements taking sign into account where a multiplicative expression is required to compute the result, the overall relative determinate error, ETR, is given by ETR = E1R + E2R + E3R + ……. E1R and E2R etc., being the relative determinate errors in the individual measure- ments taking sign into account. The accumulated effect of indeterminate (random) errors is computed by combining statistical parameters for each measurement (Topic B2). www.FreeEngineeringbooksPdf.com Section B – Assessment of data B2 A SSESSMENT OF ACCURACY AND PRECISION Key Notes Accuracy and Accuracy is the closeness of an experimental measurement or result to precision the true or accepted value. Precision is the closeness of agreement between replicated measurements or results obtained under the same prescribed conditions. Standard deviation The standard deviation of a set of values is a statistic based on the normal error (Gaussian) curve and used as a measure of precision. Relative standard Relative standard deviation (coefficient of variation) is the standard deviation deviation expressed as a percentage of the measured value. Pooled standard A standard deviation can be calculated for two or more sets of data by deviation pooling the values to give a more reliable measure of precision. Variance This is the square of the standard deviation, which is used in some statistical tests. Overall precision An estimate of the overall precision of an analytical procedure can be made by combining the precisions of individual measurements. Confidence interval This is the range of values around an experimental result within which the true or accepted value is expected to lie with a defined level of probability. Related topic Errors in analytical measurements (B1) Accuracy and These two characteristics of numerical data are the most important and the most precision frequently confused. It is vital to understand the difference between them, and this is best illustrated diagrammatically as in Figure 1. Four analysts have each performed a set of five titrations for which the correct titer is known to be 20.00 cm3. The titers have been plotted on a linear scale, and inspection reveals the following: the average titers for analysts B and D are very close to 20.00 cm3 - these two sets are therefore said to have good accuracy; the average titers for analysts A and C are well above and below 20.00 cm3 respectively - these are therefore said to have poor accuracy; the five titers for analyst A and the five for analyst D are very close to one another within each set – these two sets therefore both show good precision; the five titers for analyst B and the five for analyst C are spread widely within each set - these two sets therefore both show poor precision. www.FreeEngineeringbooksPdf.com B2 – Assessment of accuracy and precision 27 Correct result A B C D 19.70 20.00 20.30 Titer (cm3) Fig. 1. Plots of titration data to distinguish accuracy and precision. It should be noted that good precision does not necessarily produce good accuracy (analyst A) and poor precision does not necessarily produce poor accuracy (analyst B). However, confidence in the analytical procedure and the