Chapter 3 The Vocabulary of Analytical Chemistry.pdf

CHAPTER OVERVIEW 3: The Vocabulary of Analytical Chemistry If you browse through an issue of the journal Analytical Chemistry, you will discover that the authors and readers share a common vocabulary of analytical terms. You probably are familiar with some of these terms, such as accuracy and prec...

CHAPTER OVERVIEW 3: The Vocabulary of Analytical Chemistry If you browse through an issue of the journal Analytical Chemistry, you will discover that the authors and readers share a common vocabulary of analytical terms. You probably are familiar with some of these terms, such as accuracy and precision, but other terms, such as analyte and matrix, are perhaps less familiar to you. In order to participate in any community, one must first understand its vocabulary; the goal of this chapter, therefore, is to introduce some important analytical terms. Becoming comfortable with these terms will make the chapters that follow easier to read and to understand. 3.1: Analysis, Determination, and Measurement 3.2: Techniques, Methods, Procedures, and Protocols 3.3: Classifying Analytical Techniques 3.4: Selecting an Analytical Method 3.5: Developing the Procedure 3.6: Protocols 3.7: The Importance of Analytical Methodology 3.8: Problems 3.9: Additional Resources 3.10: Chapter Summary and Key Terms This page titled 3: The Vocabulary of Analytical Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 3.1: Analysis, Determination, and Measurement The first important distinction we will make is among the terms analysis, determination, and measurement. An analysis provides chemical or physical information about a sample. The component in the sample of interest to us is called the analyte, and the remainder of the sample is the matrix. In an analysis we determine the identity, the concentration, or the properties of an analyte. To make this determination we measure one or more of the analyte’s chemical or physical properties. An example will help clarify the difference between an analysis, a determination and a measurement. In 1974 the federal government enacted the Safe Drinking Water Act to ensure the safety of the nation’s public drinking water supplies. To comply with this act, municipalities monitor their drinking water supply for potentially harmful substances, such as fecal coliform bacteria. Municipal water departments collect and analyze samples from their water supply. To determine the concentration of fecal coliform bacteria an analyst passes a portion of water through a membrane filter, places the filter in a dish that contains a nutrient broth, and incubates the sample for 22–24 hrs at 44.5 oC ± 0.2 oC. At the end of the incubation period the analyst counts the number of bacterial colonies in the dish and reports the result as the number of colonies per 100 mL (Figure 3.1.1 ). Thus, a municipal water department analyzes samples of water to determine the concentration of fecal coliform bacteria by measuring the number of bacterial colonies that form during a carefully defined incubation period Figure 3.1.1 : Colonies of fecal coliform bacteria from a water supply. Source: Susan Boyer. Photo courtesy of ARS–USDA (www.ars.usda.gov). A fecal coliform count provides a general measure of the presence of pathogenic organisms in a water supply. For drinking water, the current maximum contaminant level (MCL) for total coliforms, including fecal coliforms is less than 1 colony/100 mL. Municipal water departments must regularly test the water supply and must take action if more than 5% of the samples in any month test positive for coliform bacteria. This page titled 3.1: Analysis, Determination, and Measurement is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.1: Analysis, Determination, and Measurement by David Harvey is licensed CC BY-NC-SA 4.0. 3.1.1 https://chem.libretexts.org/@go/page/401329 3.2: Techniques, Methods, Procedures, and Protocols Suppose you are asked to develop an analytical method to determine the concentration of lead in drinking water. How would you approach this problem? To provide a structure for answering this question, it is helpful to consider four levels of analytical methodology: techniques, methods, procedures, and protocols [Taylor, J. K. Anal. Chem. 1983, 55, 600A–608A]. A technique is any chemical or physical principle that we can use to study an analyte. There are many techniques for that we can use to determine the concentration of lead in drinking water [Fitch, A.; Wang, Y.; Mellican, S.; Macha, S. Anal. Chem. 1996, 68, 727A–731A]. In graphite furnace atomic absorption spectroscopy (GFAAS), for example, we first convert aqueous lead ions into free atoms—a process we call atomization. We then measure the amount of light absorbed by the free atoms. Thus, GFAAS uses both a chemical principle (atomization) and a physical principle (absorption of light). See Chapter 10 for a discussion of graphite furnace atomic absorption spectroscopy. A method is the application of a technique for a specific analyte in a specific matrix. As shown in Figure 3.2.1 , the GFAAS method for determining the concentration of lead in water is different from that for lead in soil or blood. Figure 3.2.1 : Chart showing the hierarchical relationship between a technique, methods that use the technique, and procedures and protocols for a method. The abbreviations are APHA: American Public Health Association, ASTM: American Society for Testing Materials, EPA: Environmental Protection Agency. A procedure is a set of written directions that tell us how to apply a method to a particular sample, including information on how to collect the sample, how to handle interferents, and how to validate results. A method may have several procedures as each analyst or agency adapts it to a specific need. As shown in Figure 3.2.1 , the American Public Health Agency and the American Society for Testing Materials publish separate procedures for determining the concentration of lead in water. Finally, a protocol is a set of stringent guidelines that specify a procedure that an analyst must follow if an agency is to accept the results. Protocols are common when the result of an analysis supports or defines public policy. When determining the concentration of lead in water under the Safe Drinking Water Act, for example, the analyst must use a protocol specified by the Environmental Protection Agency. There is an obvious order to these four levels of analytical methodology. Ideally, a protocol uses a previously validated procedure. Before developing and validating 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. This page titled 3.2: Techniques, Methods, Procedures, and Protocols is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.2.1 https://chem.libretexts.org/@go/page/401330 3.3: Classifying Analytical Techniques The analysis of a sample generates a chemical or physical signal that is proportional to the amount of analyte in the sample. This signal may be anything we can measure, such as volume or absorbance. It is convenient to divide analytical techniques into two general classes based on whether the signal is proportional to the mass or moles of analyte, or is proportional to the analyte’s concentration Consider the two graduated cylinders in Figure 3.3.1 , each of which contains a solution of 0.010 M Cu(NO3)2. Cylinder 1 contains 10 mL, or 1.0 × 10 moles of Cu2+, and cylinder 2 contains 20 mL, or 2.0 × 10 moles of Cu2+. If a technique responds to the −4 −4 absolute amount of analyte in the sample, then the signal due to the analyte SA SA = kA nA (3.3.1) where nA is the moles or grams of analyte in the sample, and kA is a proportionality constant. Because cylinder 2 contains twice as many moles of Cu2+ as cylinder 1, analyzing the contents of cylinder 2 gives a signal twice as large as that for cylinder 1. Figure 3.3.1 : Two graduated cylinders, each containing 0.10 M Cu(NO3)2. Although the cylinders contain the same concentration of Cu2+, the cylinder on the left contains 1.0 × 10 mol Cu2+ and the cylinder on the right contains 2.0 × 10 mol Cu2+. −4 −4 A second class of analytical techniques are those that respond to the analyte’s concentration, CA SA = kA CA (3.3.2) 2+ Since the solutions in both cylinders have the same concentration of Cu , their analysis yields identical signals. A technique that responds to the absolute amount of analyte is a total analysis technique. Mass and volume are the most common signals for a total analysis technique, and the corresponding techniques are gravimetry (Chapter 8) and titrimetry (Chapter 9). With a few exceptions, the signal for a total analysis technique is the result of one or more chemical reactions, the stoichiometry of which determines the value of kA in Equation 3.3.1. Historically, most early analytical methods used a total analysis technique. For this reason, total analysis techniques are often called “classical” techniques. Spectroscopy (Chapter 10) and electrochemistry (Chapter 11), in which an optical or an electrical signal is proportional to the relative amount of analyte in a sample, are examples of concentration techniques. The relationship between the signal and the analyte’s concentration is a theoretical function that depends on experimental conditions and the instrumentation used to measure the signal. For this reason the value of kA in Equation 3.3.2 is determined experimentally. Since most concentration techniques rely on measuring an optical or electrical signal, they also are known as “instrumental” techniques. This page titled 3.3: Classifying Analytical Techniques is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.3.1 https://chem.libretexts.org/@go/page/401331 3.4: Selecting an Analytical Method A method is the application of a technique to a specific analyte in a specific matrix. We can develop an analytical method to determine the concentration of lead in drinking water using any of the techniques mentioned in the previous section. A gravimetric method, for example, might precipiate the lead as PbSO4 or as PbCrO4, and use the precipitate’s mass as the analytical signal. Lead forms several soluble complexes, which we can use to design a complexation titrimetric method. As shown in Figure 3.2.1, we can use graphite furnace atomic absorption spectroscopy to determine the concentration of lead in drinking water. Finally, lead’s multiple oxidation states (Pb0, Pb2+, Pb4+) makes feasible a variety of electrochemical methods. Ultimately, the requirements of the analysis determine the best method. In choosing among the available methods, we give consideration to some or all the following design criteria: accuracy, precision, sensitivity, selectivity, robustness, ruggedness, scale of operation, analysis time, availability of equipment, and cost. Accuracy Accuracy is how closely the result of an experiment agrees with the “true” or expected result. We can express accuracy as an absolute error, e e = obtained result − expected result or as a percentage relative error, %er obtained result − expected result %er = × 100 expected result A method’s accuracy depends on many things, including the signal’s source, the value of kA in Equation 3.3.1 or Equation 3.3.2, and the ease of handling samples without loss or contamination. A total analysis technique, such as gravimetry and titrimetry, often produce more accurate results than does a concentration technique because we can measure mass and volume with high accuracy, and because the value of kA is known exactly through stoichiometry. Because it is unlikely that we know the true result, we use an expected or accepted result to evaluate accuracy. For example, we might use a standard reference material, which has an accepted value, to establish an analytical method’s accuracy. You will find a more detailed treatment of accuracy in Chapter 4, including a discussion of sources of errors. Precision When a sample is analyzed several times, the individual results vary from trial-to-trial. Precision is a measure of this variability. The closer the agreement between individual analyses, the more precise the results. For example, the results shown in the upper half of Figure 3.4.1 for the concentration of K+ in a sample of serum are more precise than those in the lower half of Figure 3.4.1. It is important to understand that precision does not imply accuracy. That the data in the upper half of Figure 3.4.1 are more precise does not mean that the first set of results is more accurate. In fact, neither set of results may be accurate. Figure 3.4.1 : Two determinations of the concentration of K+ in serum, showing the effect of precision on the distribution of individual results. The data in (a) are less scattered and, therefore, more precise than the data in (b). 3.4.1 https://chem.libretexts.org/@go/page/401332 A method’s precision depends on several factors, including the uncertainty in measuring the signal and the ease of handling samples reproducibly. In most cases we can measure the signal for a total analysis technique with a higher precision than is the case for a concentration method. Confusing accuracy and precision is a common mistake. See Ryder, J.; Clark, A. U. Chem. Ed. 2002, 6, 1–3, and Tomlinson, J.; Dyson, P. J.; Garratt, J. U. Chem. Ed. 2001, 5, 16–23 for discussions of this and other common misconceptions about the meaning of error. You will find a more detailed treatment of precision in Chapter 4, including a discussion of sources of errors. 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 a difference is significant. Sensitivity is often confused with a method’s detection limit, which is the smallest amount of analyte we can determine with confidence. Confidence, as we will see in Chapter 4, is a statistical concept that builds on the idea of a population of results. For this reason, we will postpone our discussion of detection limits to Chapter 4. For now, the definition of a detection limit given here is sufficient. Sensitivity is equivalent to the proportionality constant, kA, in Equation 3.3.1 and Equation 3.3.2 [IUPAC Compendium of Chemical Terminology, Electronic version]. If ΔS is the smallest difference we can measure between two signals, then the A smallest detectable difference in the absolute amount or the relative amount of analyte is ΔSA ΔSA ΔnA = or ΔCA = kA kA Suppose, for example, that our analytical signal is a measurement of mass using a balance whose smallest detectable increment is ±0.0001 g. If our method’s sensitivity is 0.200, then our method can conceivably detect a difference in mass of as little as ±0.0001 g ΔnA = = ±0.0005 g 0.200 For two methods with the same ΔS , the method with the greater sensitivity—that is, the method with the larger kA—is better able A to discriminate between smaller amounts of analyte. Specificity and Selectivity An analytical method is specific if its signal depends only on the analyte [Persson, B-A; Vessman, J. Trends Anal. Chem. 1998, 17, 117–119; Persson, B-A; Vessman, J. Trends Anal. Chem. 2001, 20, 526–532]. Although specificity is the ideal, few analytical methods are free from interferences. When an interferent contributes to the signal, we expand Equation 3.3.1 and Equation 3.3.2 to include its contribution to the sample’s signal, Ssamp Ssamp = SA + SI = kA nA + kI nI (3.4.1) Ssamp = SA + SI = kA CA + kI CI (3.4.2) where SI is the interferent’s contribution to the signal, kI is the interferent’s sensitivity, and nI and CI are the moles (or grams) and the concentration of interferent in the sample, respectively. Selectivity is a measure of a method’s freedom from interferences [Valcárcel, M.; Gomez-Hens, A.; Rubio, S. Trends Anal. Chem. 2001, 20, 386–393]. A method’s selectivity for an interferent relative to the analyte is defined by a selectivity coefficient, KA,I kI KA,I = (3.4.3) kA which may be positive or negative depending on the signs of kI and kA. The selectivity coefficient is greater than +1 or less than –1 when the method is more selective for the interferent than for the analyte. 3.4.2 https://chem.libretexts.org/@go/page/401332  Although kA and kI usually are positive, they can be negative. For example, some analytical methods work by measuring the concentration of a species that remains after is reacts with the analyte. As the analyte’s concentration increases, the concentration of the species that produces the signal decreases, and the signal becomes smaller. If the signal in the absence of analyte is assigned a value of zero, then the subsequent signals are negative. Determining the selectivity coefficient’s value is easy if we already know the values for kA and kI. As shown by Example 3.4.1 , we also can determine KA,I by measuring Ssamp in the presence of and in the absence of the interferent.  Example 3.4.1 A method for the analysis of Ca2+ in water suffers from an interference in the presence of Zn2+. When the concentration of Ca2+ is 100 times greater than that of Zn2+, an analysis for Ca2+ has a relative error of +0.5%. What is the selectivity coefficient for this method? Solution Since only relative concentrations are reported, we can arbitrarily assign absolute concentrations. To make the calculations easy, we will let CCa = 100 (arbitrary units) and CZn = 1. A relative error of +0.5% means the signal in the presence of Zn2+ is 0.5% greater than the signal in the absence of Zn2+. Again, we can assign values to make the calculation easier. If the signal for Ca2+ in the absence of Zn2+ is 100 (arbitrary units), then the signal in the presence of Zn2+ is 100.5. The value of kCa is determined using Equation 3.3.2 SCa 100 kCa = = =1 CCa 100 In the presence of Zn2+ the signal is given by Equation 3.4.2; thus Ssamp = 100.5 = kCa CCa + kZn CZn = (1 × 100) + kZn × 1 Solving for kZn gives its value as 0.5. The selectivity coefficient is kZn 0.5 KCa,Zn = = = 0.5 kCa 1 If you are unsure why, in the above example, the signal in the presence of zinc is 100.5, note that the percentage relative error for this problem is given by obtained result − 100 × 100 = +0.5% 100 Solving gives an obtained result of 100.5.  Exercise 3.4.1 Wang and colleagues describe a fluorescence method for the analysis of Ag+ in water. When analyzing a solution that contains 1.0 × 10 M Ag+ and 1.1 × 10 M Ni2+, the fluorescence intensity (the signal) was +4.9% greater than that obtained for a −9 −7 sample of 1.0 × 10 M Ag+. What is KAg,Ni for this analytical method? The full citation for the data in this exercise is Wang, −9 L.; Liang, A. N.; Chen, H.; Liu, Y.; Qian, B.; Fu, J. Anal. Chim. Acta 2008, 616, 170-176. Answer Because the signal for Ag+ in the presence of Ni2+ is reported as a relative error, we will assign a value of 100 as the signal for 1 × 10 M Ag+. With a relative error of +4.9%, the signal for the solution of 1 × 10 M Ag+ and 1.1 × 10 M Ni2+ −9 −9 −7 is 104.9. The sensitivity for Ag+ is determined using the solution that does not contain Ni2+; thus SAg 100 11 −1 kAg = = = 1.0 × 10 M −9 CAg 1 × 10 M 3.4.3 https://chem.libretexts.org/@go/page/401332  Substituting into Equation 3.4.2values for kAg, Ssamp , and the concentrations of Ag+ and Ni2+ 11 −1 −9 −7 104.9 = (1.0 × 10 M ) × (1 × 10 M) + kNi × (1.1 × 10 M) and solving gives kNi as 4.5 × 10 M–1. The selectivity coefficient is 7 7 −1 kNi 4.5 × 10 M −4 KAg,Ni = = = 4.5 × 10 11 −1 kAg 1.0 × 10 M A selectivity coefficient provides us with a useful way to evaluate an interferent’s potential effect on an analysis. Solving Equation 3.4.3 for kI kI = KA,I × kA (3.4.4) and substituting in Equation 3.4.1 and Equation 3.4.2, and simplifying gives Ssamp = kA { nA + KA,I × nI } (3.4.5) Ssamp = kA { CA + KA,I × CI } (3.4.6) An interferent will not pose a problem as long as the term K A,I × nI in Equation 3.4.5 is significantly smaller than nA, or if K A,I×C Iin Equation 3.4.6 is significantly smaller than CA.  Example 3.4.2 Barnett and colleagues developed a method to determine the concentration of codeine (structure shown below) in poppy plants [Barnett, N. W.; Bowser, T. A.; Geraldi, R. D.; Smith, B. Anal. Chim. Acta 1996, 318, 309– 317]. As part of their study they evaluated the effect of several interferents. For example, the authors found that equimolar solutions of codeine and the interferent 6-methoxycodeine gave signals, respectively of 40 and 6 (arbitrary units). (a) What is the selectivity coefficient for the interferent, 6-methoxycodeine, relative to that for the analyte, codeine. (b) If we need to know the concentration of codeine with an accuracy of ±0.50%, what is the maximum relative concentration of 6-methoxy-codeine that we can tolerate? Solution (a) The signals due to the analyte, SA, and the interferent, SI, are SA = kA CA SI = kI CI Solving these equations for kA and for kI, and substituting into Equation 3.4.4 gives SI / CI KA,I = SA / CI Because the concentrations of analyte and interferent are equimolar (CA = CI), the selectivity coefficient is SI 6 KA,I = = = 0.15 SA 40 (b) To achieve an accuracy of better than ±0.50% the term K A,I × CI in Equation 3.4.6 must be less than 0.50% of CA; thus KA,I × CI ≤ 0.0050 × CA Solving this inequality for the ratio CI/CA and substituting in the value for KA,I from part (a) gives 3.4.4 https://chem.libretexts.org/@go/page/401332  CI 0.0050 0.0050 ≤ = = 0.033 CA KA,I 0.15 Therefore, the concentration of 6-methoxycodeine must be less than 3.3% of codeine’s concentration. When a method’s signal is the result of a chemical reaction—for example, when the signal is the mass of a precipitate—there is a good chance that the method is not very selective and that it is susceptible to an interference.  Exercise 3.4.2 Mercury (II) also is an interferent in the fluorescence method for Ag+ developed by Wang and colleagues (see Practice Exercise 3.4.1). The selectivity coefficient, KAg,Hg has a value of −1.0 × 10. −3 (a) What is the significance of the selectivity coefficient’s negative sign? (b) Suppose you plan to use this method to analyze solutions with concentrations of Ag+ no smaller than 1.0 nM. What is the maximum concentration of Hg2+ you can tolerate if your percentage relative errors must be less than ±1.0%? Answer (a) A negative value for KAg,Hg means that the presence of Hg2+ decreases the signal from Ag+. (b) In this case we need to consider an error of –1%, since the effect of Hg2+ is to decrease the signal from Ag+. To achieve this error, the term K × C in Equation 3.4.6must be less than –1% of CA; thus A,I I KAg,Hg × CHg = −0.01 × CAg Substituting in known values for KAg,Hg and CAg, we find that the maximum concentration of Hg2+ is 1.0 × 10 −8 M. Problems with selectivity also are more likely when the analyte is present at a very low concentration [Rodgers, L. B. J. Chem. Educ. 1986, 63, 3–6]. Look back at Figure 1.1.1, which shows Fresenius’ analytical method for the determination of nickel in ores. The reason there are so many steps in this procedure is that precipitation reactions generally are not very selective. The method in Figure 1.1.2 includes fewer steps because dimethylglyoxime is a more selective reagent. Even so, if an ore contains palladium, additional steps are needed to prevent the palladium from interfering. Robustness and Ruggedness For a method to be useful it must provide reliable results. Unfortunately, methods are subject to a variety of chemical and physical interferences that contribute uncertainty to the analysis. If a method is relatively free from chemical interferences, we can use it to analyze an analyte in a wide variety of sample matrices. Such methods are considered robust. Random variations in experimental conditions introduces uncertainty. If a method’s sensitivity, k, is too dependent on experimental conditions, such as temperature, acidity, or reaction time, then a slight change in any of these conditions may give a significantly different result. A rugged method is relatively insensitive to changes in experimental conditions. Scale of Operation Another way to narrow the choice of methods is to consider three potential limitations: the amount of sample available for the analysis, the expected concentration of analyte in the samples, and the minimum amount of analyte that will produce a measurable signal. Collectively, these limitations define the analytical method’s scale of operations. We can display the scale of operations visually (Figure 3.4.2 ) by plotting the sample’s size on the x-axis and the analyte’s concentration on the y-axis. For convenience, we divide samples into macro (>0.1 g), meso (10 mg–100 mg), micro (0.1 mg–10 mg), and ultramicro (1% w/w), minor (0.01% w/w–1% w/w), trace (10–7% w/w–0.01% w/w), and ultratrace (