Modern Analytical Cheymistry - Chapter 3

Chapter 3 The Language of Analytical Chemistry Analytical chemists converse using terminology that conveys specific meaning to other analytical chemists. To discuss and learn analytical chemistry you must first understand its language. You are probably already familiar with some analytical terms, such as ÒaccuracyÓ and Òprecision,Ó but you may not have placed them in their appropriate analytical context. Other terms, such as ÒanalyteÓ and Òmatrix,Ó may be less familiar. This chapter introduces many important terms routinely used by analytical chemists. Becoming comfortable with these terms will make the material in the chapters that follow easier to read and understand. 35 36 Modern Analytical Chemistry analysis A process that provides chemical or physical information about the constituents in the sample or the sample itself. analytes The constituents of interest in a sample. matrix All other constituents in a sample except for the analytes. determination An analysis of a sample to find the identity, concentration, or properties of the analyte. measurement An experimental determination of an analyte’s chemical or physical properties. technique A chemical or physical principle that can be used to analyze a sample. method A means for analyzing a sample for a specific analyte in a specific matrix. procedure Written directions outlining how to analyze a sample. 3A Analysis, Determination, and Measurement The first important distinction we will make is among the terms “analysis,” “deter-mination,” and “measurement.” An analysis provides chemical or physical infor-mation about a sample. The components of interest in the sample are called ana-lytes, and the remainder of the sample is the matrix. In an analysis we determine the identity, concentration, or properties of the analytes. To make this determina-tion we measure one or more of the analyte’s chemical or physical properties. An example helps clarify the differences among an analysis, a determination, and a measurement. In 1974, the federal government enacted the Safe Drinking Water Act to ensure the safety of public drinking water supplies. To comply with this act municipalities regularly monitor their drinking water supply for potentially harmful substances. One such substance is coliform bacteria. Municipal water de-partments collect and analyze samples from their water supply. To determine the concentration of coliform bacteria, a portion of water is passed through a mem-brane filter. The filter is placed in a dish containing a nutrient broth and incu-bated. At the end of the incubation period the number of coliform bacterial colonies in the dish is measured by counting (Figure 3.1). Thus, municipal water departments analyze samples of water to determine the concentration of coliform bacteria by measuring the number of bacterial colonies that form during a speci-fied period of incubation. 3B Techniques, Methods, Procedures, and Protocols Suppose you are asked to develop a way to determine the concentration of lead in drinking water. How would you approach this problem? To answer this question it helps to distinguish among four levels of analytical methodology: techniques, meth-ods, procedures, and protocols.1 A technique is any chemical or physical principle that can be used to study an analyte. Many techniques have been used to determine lead levels.2 For example, in graphite furnace atomic absorption spectroscopy lead is atomized, and the ability of the free atoms to absorb light is measured; thus, both a chemical principle (atom-ization) and a physical principle (absorption of light) are used in this technique. Chapters 8–13 of this text cover techniques commonly used to analyze samples. A method is the application of a technique for the determination of a specific analyte in a specific matrix. As shown in Figure 3.2, the graphite furnace atomic ab-sorption spectroscopic method for determining lead levels in water is different from that for the determination of lead in soil or blood. Choosing a method for deter-mining lead in water depends on how the information is to be used and the estab-lished design criteria (Figure 3.3). For some analytical problems the best method might use graphite furnace atomic absorption spectroscopy, whereas other prob-lems might be more easily solved by using another technique, such as anodic strip-ping voltammetry or potentiometry with a lead ion-selective electrode. A procedure is a set of written directions detailing how to apply a method to a particular sample, including information on proper sampling, handling of interfer-ents, and validating results. A method does not necessarily lead to a single proce-dure, as different analysts or agencies will adapt the method to their specific needs. As shown in Figure 3.2, the American Public Health Agency and the American Soci-ety for Testing Materials publish separate procedures for the determination of lead levels in water. Chapter 3 The Language of Analytical Chemistry 37 Techniques Graphite furnace atomic absorption spectroscopy Methods Pb in Pb in Pb in Water Soil Blood Procedures APHA ASTM Protocols EPA Figure 3.1 Membrane filter showing colonies of coliform bacteria. The number of colonies are counted and reported as colonies/100 mL of sample. PourRite™ is a trademark of Hach Company/photo courtesy of Hach Company. Figure 3.2 Chart showing hierarchical relationship among a technique, methods using that technique, and procedures and protocols for one method. (Abbreviations: APHA = American Public Health Association, ASTM = American Society for Testing Materials, EPA = Environmental Protection Agency) Finally, a protocol is a set of stringent written guidelines detailing the proce-dure that must be followed if the agency specifying the protocol is to accept the re-sults of the analysis. Protocols are commonly encountered when analytical chem-istry is used to support or define public policy. For purposes of determining lead levels in water under the Safe Drinking Water Act, labs follow a protocol specified by the Environmental Protection Agency. There is an obvious order to these four facets of analytical methodology. Ide-ally, a protocol uses a previously validated procedure. Before developing and vali-dating a procedure, a method of analysis must be selected. This requires, in turn, an initial screening of available techniques to determine those that have the potential for monitoring the analyte. We begin by considering a useful way to classify analyti-cal techniques. 3C Classifying Analytical Techniques Analyzing a sample generates a chemical or physical signal whose magnitude is pro-portional to the amount of analyte in the sample. The signal may be anything we can measure; common examples are mass, volume, and absorbance. For our pur-poses it is convenient to divide analytical techniques into two general classes based on whether this signal is proportional to an absolute amount of analyte or a relative amount of analyte. Consider two graduated cylinders, each containing 0.01 M Cu(NO3)2 (Fig-ure 3.4). Cylinder 1 contains 10 mL, or 0.0001 mol, of Cu2+; cylinder 2 contains 20 mL, or 0.0002 mol, of Cu2+. If a technique responds to the absolute amount of analyte in the sample, then the signal due to the analyte, SA, can be expressed as 1. Identify the problem Determine type of information needed (qualitative, quantitative, or characterization) Identify context of the problem 2. Design the experimental procedure Establish design criteria (accuracy, precision, scale of operation, sensitivity, selectivity, cost, speed) Identify interferents Select method Establish validation criteria Establish sampling strategy Figure 3.3 Subsection of the analytical approach to problem solving (see Figure 1.3), of relevance to the selection of a method and the design of an analytical procedure. SA = knA 3.1 protocol where nA is the moles or grams of analyte in the sample, and k is a proportionality constant. Since cylinder 2 contains twice as many moles of Cu2+ as cylinder 1, an-alyzing the contents of cylinder 2 gives a signal that is twice that of cylinder 1. A set of written guidelines for analyzing a sample specified by an agency. signal An experimental measurement that is proportional to the amount of analyte (S). 38 Modern Analytical Chemistry A second class of analytical techniques are those that respond to the relative amount of analyte; thus SA = kCA 3.2 total analysis techniques A technique in which the signal is proportional to the absolute amount of analyte; also called “classical” techniques. concentration techniques A technique in which the signal is proportional to the analyte’s concentration; also called “instrumental” techniques. (a) (b) Figure 3.4 Graduated cylinders containing 0.01 M Cu(NO3)2. (a) Cylinder 1 contains 10 mL, or 0.0001 mol, of Cu2+. (b) Cylinder 2 contains 20 mL, or 0.0002 mol, of Cu2+. © David Harvey/Marilyn Culler, photographer. accuracy A measure of the agreement between an experimental result and its expected value. where CA is the concentration of analyte in the sample. Since the solutions in both cylinders have the same concentration of Cu2+, their analysis yields identical signals. Techniques responding to the absolute amount of analyte are called total analysis techniques. Historically, most early analytical methods used total analysis techniques, hence they are often referred to as “classical” techniques. Mass, volume, and charge are the most common signals for total analysis techniques, and the cor-responding techniques are gravimetry (Chapter 8), titrimetry (Chapter 9), and coulometry (Chapter 11). With a few exceptions, the signal in a total analysis tech-nique results from one or more chemical reactions involving the analyte. These re-actions may involve any combination of precipitation, acid–base, complexation, or redox chemistry. The stoichiometry of each reaction, however, must be known to solve equation 3.1 for the moles of analyte. Techniques, such as spectroscopy (Chapter 10), potentiometry (Chapter 11), and voltammetry (Chapter 11), in which the signal is proportional to the relative amount of analyte in a sample are called concentration techniques. Since most concentration techniques rely on measuring an optical or electrical signal, they also are known as “instrumental” techniques. For a concentration technique, the rela-tionship between the signal and the analyte is a theoretical function that depends on experimental conditions and the instrumentation used to measure the signal. For this reason the value of k in equation 3.2 must be determined experimentally. 3D Selecting an Analytical Method A method is the application of a technique to a specific analyte in a specific matrix. Methods for determining the concentration of lead in drinking water can be devel-oped using any of the techniques mentioned in the previous section. Insoluble lead salts such as PbSO4 and PbCrO4 can form the basis for a gravimetric method. Lead forms several soluble complexes that can be used in a complexation titrimetric method or, if the complexes are highly absorbing, in a spectrophotometric method. Lead in the gaseous free-atom state can be measured by an atomic ab-sorption spectroscopic method. Finally, the availability of multiple oxidation states (Pb, Pb2+, Pb4+) makes coulometric, potentiometric, and voltammetric methods feasible. The requirements of the analysis determine the best method. In choosing a method, consideration is given to some or all the following design criteria: accuracy, precision, sensitivity, selectivity, robustness, ruggedness, scale of operation, analysis time, availability of equipment, and cost. Each of these criteria is considered in more detail in the following sections. 3D.1 Accuracy Accuracy is a measure of how closely the result of an experiment agrees with the ex-pected result. The difference between the obtained result and the expected result is usually divided by the expected result and reported as a percent relative error obtained result – expected result expected result Chapter 3 The Language of Analytical Chemistry 39 Analytical methods may be divided into three groups based on the magnitude of their relative errors.3 When an experimental result is within 1% of the correct result, the analytical method is highly ac-curate. Methods resulting in relative errors between 1% and 5% are moderately accurate, but methods of low accuracy produce rel-ative errors greater than 5%. The magnitude of a method’s relative error depends on how accurately the signal is measured, how accurately the value of k in equations 3.1 or 3.2 is known, and the ease of handling the sample without loss or contamination. In general, total analysis methods produce results of high accuracy, and concentration methods range from high to low accuracy. A more detailed discussion of accuracy is presented in Chapter 4. 3D.2 Precision 5.8 5.9 6.0 6.1 6.2 ppm K+ (a) 5.8 5.9 6.0 6.1 6.2 ppm K+ (b) Figure 3.5 Two determinations of the concentration of K+ in serum, showing the effect of precision. The data in (a) are less scattered and, therefore, more precise than the data in (b). When a sample is analyzed several times, the individual results are rarely the same. Instead, the results are randomly scattered. Precision is a measure of this variability. The closer the agreement between individual analyses, the more precise the results. For example, in determining the concentration of K+ in serum, the results shown in Figure 3.5(a) are more precise than those in Figure 3.5(b). It is important to realize that precision does not imply accuracy. That the data in Figure 3.5(a) are more pre-cise does not mean that the first set of results is more accurate. In fact, both sets of results may be very inaccurate. As with accuracy, precision depends on those factors affecting the relationship between the signal and the analyte (equations 3.1 and 3.2). Of particular impor-tance are the uncertainty in measuring the signal and the ease of handling samples reproducibly. In most cases the signal for a total analysis method can be measured with a higher precision than the corresponding signal for a concentration method. Precision is covered in more detail in Chapter 4. 3D.3 Sensitivity The ability to demonstrate that two samples have different amounts of analyte is an essential part of many analyses. A method’s sensitivity is a measure of its ability to establish that such differences are significant. Sensitivity is often confused with a method’s detection limit.4 The detection limit is the smallest amount of analyte that can be determined with confidence. The detection limit, therefore, is a statisti-cal parameter and is discussed in Chapter 4. Sensitivity is the change in signal per unit change in the amount of analyte and is equivalent to the proportionality constant, k, in equations 3.1 and 3.2. If ΔSA is the smallest increment in signal that can be measured, then the smallest difference in the amount of analyte that can be detected is precision An indication of the reproducibility of a measurement or result. sensitivity A measure of a method’s ability to distinguish between two samples; reported as the change in signal per unit change in the amount of analyte (k). detection limit A statistical statement about the smallest amount of analyte that can be determined with confidence. ΔnA = ΔSA ΔCA = ΔSA (total analysis method) (concentration method) Suppose that for a particular total analysis method the signal is a measurement of mass using a balance whose smallest increment is ±0.0001 g. If the method’s ... - tailieumienphi.vn