CChhaapptteerr 3 35 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 “accuracy” and “precision,” but you may not have placed them in their appropriate analytical context. Other terms, such as “analyte” and “matrix,” 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. 1400-CH03 9/8/99 3:51 PM Page 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. 3 A 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. 3 B 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. 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. 1400-CH03 9/8/99 3:51 PM Page 36 Chapter 3 The Language of Analytical Chemistry 37 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. Graphite furnace atomic absorption spectroscopy Pb in Soil Procedures Techniques Methods Protocols Pb in Blood Pb in Water EPA APHA ASTM 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 3.2 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) 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. protocol 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). 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. 3 C 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(NO 3 ) 2 (Fig- ure 3.4). Cylinder 1 contains 10 mL, or 0.0001 mol, of Cu 2+ ; cylinder 2 contains 20 mL, or 0.0002 mol, of Cu 2+ . If a technique responds to the absolute amount of analyte in the sample, then the signal due to the analyte, S A , can be expressed as S A = kn A 3.1 where n A 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 Cu 2+ as cylinder 1, an- alyzing the contents of cylinder 2 gives a signal that is twice that of cylinder 1. 1400-CH03 9/8/99 3:51 PM Page 37 38 Modern Analytical Chemistry 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. Figure 3.4 Graduated cylinders containing 0.01 M Cu(NO 3 ) 2 . (a) Cylinder 1 contains 10 mL, or 0.0001 mol, of Cu 2+ . (b) Cylinder 2 contains 20 mL, or 0.0002 mol, of Cu 2+ . © David Harvey/Marilyn Culler, photographer. (a) (b) accuracy A measure of the agreement between an experimental result and its expected value. A second class of analytical techniques are those that respond to the relative amount of analyte; thus S A = kC A 3.2 where C A is the concentration of analyte in the sample. Since the solutions in both cylinders have the same concentration of Cu 2+ , 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. 3 D 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 PbSO 4 and PbCrO 4 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, Pb 2+ , Pb 4+ ) 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. 3 D.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 % Error = obtained result – expected result expected result × 100 1400-CH03 9/8/99 3:51 PM Page 38 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). 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. 3 D.2 Precision 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. 3 D. 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 ∆S A is the smallest increment in signal that can be measured, then the smallest difference in the amount of analyte that can be detected is 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 ∆ ∆ ∆ ∆ n S k C S k A A A A = = () () total analysis method concentration method Chapter 3 The Language of Analytical Chemistry 39 5.8 (a) (b) 5.9 6.0 ppm K + 6.1 6.2 5.8 5.9 6.0 ppm K + 6.1 6.2 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. 1400-CH03 9/8/99 3:51 PM Page 39 40 Modern Analytical Chemistry selectivity A measure of a method’s freedom from interferences as defined by the method’s selectivity coefficient. selectivity coefficient A measure of a method’s sensitivity for an interferent relative to that for the analyte (K A,I ). sensitivity is 0.200, then the method can conceivably detect a difference of as little as in the absolute amount of analyte in two samples. For methods with the same ∆S A , the method with the greatest sensitivity is best able to discriminate among smaller amounts of analyte. 3 D. 4 Selectivity An analytical method is selective if its signal is a function of only the amount of an- alyte present in the sample. In the presence of an interferent, equations 3.1 and 3.2 can be expanded to include a term corresponding to the interferent’s contribution to the signal, S I , S samp = S A + S I = k A n A + k I n I (total analysis method) 3.3 S samp = S A + S I = k A C A + k I C I (concentration method) 3.4 where S samp is the total signal due to constituents in the sample; k A and k I are the sensitivities for the analyte and the interferent, respectively; and n I and C I are the moles (or grams) and concentration of the interferent in the sample. The selectivity of the method for the interferent relative to the analyte is de- fined by a selectivity coefficient, K A,I 3.5 which may be positive or negative depending on whether the interferent’s effect on the signal is opposite that of the analyte.* A selectivity coefficient greater than +1 or less than –1 indicates that the method is more selective for the interferent than for the analyte. Solving equation 3.5 for k I k I = K A,I × k A 3.6 substituting into equations 3.3 and 3.4, and simplifying gives S samp = k A (n A + K A,I × n I ) (total analysis method) 3.7 S samp = k A (C A + K A,I × C I ) (concentration method) 3.8 The selectivity coefficient is easy to calculate if k A and k I can be independently determined. It is also possible to calculate K A,I by measuring S samp in the presence and absence of known amounts of analyte and interferent. EXAMPLE 3 .1 A method for the analysis of Ca 2+ in water suffers from an interference in the presence of Zn 2+ . When the concentration of Ca 2+ is 100 times greater than that of Zn 2+ , an analysis for Ca 2+ gives a relative error of +0.5%. What is the selectivity coefficient for this method? K k k A,I A = I ∆n A = 0.0001 g 0.200 0.0005 g ± =± *Although k A and k I are usually positive, they also may be negative. For example, some analytical methods work by measuring the concentration of a species that reacts with the analyte. As the analyte’s concentration increases, the concentration of the species producing 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. 1400-CH03 9/8/99 3:51 PM Page 40 Chapter 3 The Language of Analytical Chemistry 41 SOLUTION Since only relative concentrations are reported, we can arbitrarily assign absolute concentrations. To make the calculations easy, let C Ca = 100 (arbitrary units) and C Zn = 1. A relative error of +0.5% means that the signal in the presence of Zn 2+ is 0.5% greater than the signal in the absence of zinc. Again, we can assign values to make the calculation easier. If the signal in the absence of zinc is 100 (arbitrary units), then the signal in the presence of zinc is 100.5. The value of k Ca is determined using equation 3.2 In the presence of zinc the signal is S samp = 100.5 = k Ca C Ca + k Zn C Zn = (1)(100) + k Zn (1) Solving for k Zn gives a value of 0.5. The selectivity coefficient, therefore, is Knowing the selectivity coefficient provides a useful way to evaluate an inter- ferent’s potential effect on an analysis. An interferent will not pose a problem as long as the term K A,I × n I in equation 3.7 is significantly smaller than n A , or K A,I × C I in equation 3.8 is significantly smaller than C A. EXAMPLE 3 .2 Barnett and colleagues 5 developed a new method for determining the concentration of codeine during its extraction from poppy plants. As part of their study they determined the method’s response to codeine relative to that for several potential interferents. For example, the authors found that the method’s signal for 6-methoxycodeine was 6 (arbitrary units) when that for an equimolar solution of codeine was 40. (a) What is the value for the selectivity coefficient K A,I when 6-methoxycodeine is the interferent and codeine is the analyte? (b) If the concentration of codeine is to be determined with an accuracy of ±0.50%, what is the maximum relative concentration of 6-methoxycodeine (i.e., [6-methoxycodeine]/[codeine]) that can be present? SOLUTION (a) The signals due to the analyte, S A, and the interferent, S I , are S A = k A C A S I = k I C I Solving these two expressions for k A and k I and substituting into equation 3.6 gives K SC SC AI II AA , / / = K k k Ca Zn/ == . = 0.5 Zn Ca 05 1 k S C Ca Ca Ca = == 100 100 1 1400-CH03 9/8/99 3:51 PM Page 41 Since equimolar concentrations of analyte and interferent were used (C A = C I ), we have (b) To achieve an accuracy of better than ±0.50% the term K A,I × C I in equation 3.8 must be less than 0.50% of C A; thus 0.0050 × C A ≥ K A,I × C I Solving this inequality for the ratio C I /C A and substituting the value for K A,I determined in part (a) gives Therefore, the concentration of 6-methoxycodeine cannot exceed 3.3% of codeine’s concentration. Not surprisingly, methods whose signals depend on chemical reactivity are often less selective and, therefore, more susceptible to interferences. Problems with selec- tivity become even greater when the analyte is present at a very low concentration. 6 3 D. 5 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 uncer- tainty to the analysis. When a method is relatively free from chemical interferences, it can be applied to the determination of analytes in a wide variety of sample matri- ces. Such methods are considered robust. Random variations in experimental conditions also introduce uncertainty. If a method’s sensitivity is highly dependent on experimental conditions, such as tem- perature, acidity, or reaction time, then slight changes in those conditions may lead to significantly different results. A rugged method is relatively insensitive to changes in experimental conditions. 3 D.6 Scale of Operation Another way to narrow the choice of methods is to consider the scale on which the analysis must be conducted. Three limitations of particular importance are the amount of sample available for the analysis, the concentration of analyte in the sample, and the absolute amount of analyte needed to obtain a measurable signal. The first and second limitations define the scale of operations shown in Figure 3.6; the last limitation positions a method within the scale of operations. 7 The scale of operations in Figure 3.6 shows the analyte’s concentration in weight percent on the y-axis and the sample’s size on the x-axis. For convenience, we divide analytes into major (>1% w/w), minor (0.01% w/w – 1% w/w), trace (10 –7 % w/w – 0.01% w/w) and ultratrace (<10 –7 % w/w) components, and we divide samples into macro (>0.1 g), meso (10 mg – 100 mg), micro (0.1 mg – 10 mg) and ultramicro (<0.1 mg) sample sizes. Note that both the x-axis and the y-axis use a logarithmic scale. The analyte’s concentration and the amount of C CK I AAI ≤== 0 0050 0 0050 015 0 033 . . , K S S AI I A , .=== 6 40 015 42 Modern Analytical Chemistry rugged A method that is insensitive to changes in experimental conditions is considered rugged. robust A method that can be applied to analytes in a wide variety of matrices is considered robust. 1400-CH03 9/8/99 3:51 PM Page 42 Figure 3.6 Scale of operation for analytical methods. Adapted from references 7a and 7b. sample used provide a characteristic description for an analysis. For example, samples in a macro–major analysis weigh more than 0.1 g and contain more than 1% analyte. Diagonal lines connecting the two axes show combinations of sample size and concentration of analyte containing the same absolute amount of analyte. As shown in Figure 3.6, for example, a 1-g sample containing 1% analyte has the same amount of analyte (0.010 g) as a 100-mg sample containing 10% analyte or a 10-mg sample containing 100% analyte. Since total analysis methods respond to the absolute amount of analyte in a sample, the diagonal lines provide an easy way to define their limitations. Consider, for example, a hypothetical total analysis method for which the minimum de- tectable signal requires 100 mg of analyte. Using Figure 3.6, the diagonal line repre- senting 100 mg suggests that this method is best suited for macro samples and major analytes. Applying the method to a minor analyte with a concentration of 0.1% w/w requires a sample of at least 100 g. Working with a sample of this size is rarely practical, however, due to the complications of carrying such a large amount of material through the analysis. Alternatively, the minimum amount of required analyte can be decreased by improving the limitations associated with measuring the signal. For example, if the signal is a measurement of mass, a decrease in the minimum amount of analyte can be accomplished by switching from a con- ventional analytical balance, which weighs samples to ±0.1 mg, to a semimicro (±0.01 mg) or microbalance (±0.001 mg). Chapter 3 The Language of Analytical Chemistry 43 Ultratrace Trace Minor g mg µg ng 1 g sample, 1% analyte ppm ppb 100 mg 10 mg 1 mg 100 µg 10 µg 1 µg 0.1 g sample, 10% analyte 0.01 g sample, 100% analyte Macro Micro Meso Ultramicro Major 10 –10 % 10 –9 % 10 –8 % 10 –7 % 10 –6 % 10 –5 % 10 –4 % 10 –3 % 10 –2 % 0.1% 1% 10% 100% –log(% analyte as %w/w) –log(Weight of sample) 1 0.1 0.01 0.1 0.01 0.1 0.01 100 10 1 100 100 10 10 1 1 1400-CH03 9/8/99 3:51 PM Page 43 Concentration methods frequently have both lower and upper limits for the amount of analyte that can be determined. The lower limit is dictated by the small- est concentration of analyte producing a useful signal and typically is in the parts per million or parts per billion concentration range. Upper concentration limits exist when the sensitivity of the analysis decreases at higher concentrations. An upper concentration level is important because it determines how a sam- ple with a high concentration of analyte must be treated before the analysis. Con- sider, for example, a method with an upper concentration limit of 1 ppm (micro- grams per milliliter). If the method requires a sample of 1 mL, then the upper limit on the amount of analyte that can be handled is 1 µg. Using Figure 3.6, and following the diagonal line for 1 µg of analyte, we find that the analysis of an ana- lyte present at a concentration of 10% w/w requires a sample of only 10 µg! Ex- tending such an analysis to a major analyte, therefore, requires the ability to ob- tain and work with very small samples or the ability to dilute the original sample accurately. Using this example, analyzing a sample for an analyte whose concen- tration is 10% w/w requires a 10,000-fold dilution. Not surprisingly, concentra- tion methods are most commonly used for minor, trace, and ultratrace analytes, in macro and meso samples. 3 D. 7 Equipment, Time, and Cost Finally, analytical methods can be compared in terms of their need for equipment, the time required to complete an analysis, and the cost per sample. Methods relying on instrumentation are equipment-intensive and may require significant operator training. For example, the graphite furnace atomic absorption spectroscopic method for determining lead levels in water requires a significant capital investment in the instrument and an experienced operator to obtain reliable results. Other methods, such as titrimetry, require only simple equipment and reagents and can be learned quickly. The time needed to complete an analysis for a single sample is often fairly simi- lar from method to method. This is somewhat misleading, however, because much of this time is spent preparing the solutions and equipment needed for the analysis. Once the solutions and equipment are in place, the number of samples that can be analyzed per hour differs substantially from method to method. This is a significant factor in selecting a method for laboratories that handle a high volume of samples. The cost of an analysis is determined by many factors, including the cost of necessary equipment and reagents, the cost of hiring analysts, and the number of samples that can be processed per hour. In general, methods relying on instruments cost more per sample than other methods. 3 D.8 Making the Final Choice Unfortunately, the design criteria discussed earlier are not mutually independent. 8 Working with smaller amounts of analyte or sample, or improving selectivity, often comes at the expense of precision. Attempts to minimize cost and analysis time may decrease accuracy. Selecting a specific method requires a careful balance among these design criteria. Usually, the most important design criterion is accuracy, and the best method is that capable of producing the most accurate results. When the need for results is urgent, as is often the case in clinical labs, analysis time may be- come the critical factor. The best method is often dictated by the sample’s properties. Analyzing a sam- ple with a complex matrix may require a method with excellent selectivity to avoid 44 Modern Analytical Chemistry 1400-CH03 9/8/99 3:51 PM Page 44 [...]... phosphorus, EPA-approved procedures provided poorer reproducibility than nonapproved methods 3H KEY TERMS accuracy (p 38 ) analysis (p 36 ) analytes (p 36 ) calibration (p 47) calibration curve (p 47) concentration techniques (p 38 ) detection limit (p 39 ) determination (p 36 ) matrix (p 36 ) measurement (p 36 ) method (p 36 ) method blank (p 45) precision (p 39 ) procedure (p 36 ) protocol (p 37 ) quality assurance... assume that Sreag is zero under both conditions SOLUTION Using equation 3. 12, we write the following simultaneous equations 33 .4 = (76 ppm–1)CA + (186 ppm–1)CB 29.7 = (33 ppm–1)CA + (2 43 ppm–1)CB Multiplying the first equation by the ratio 33 /76 gives the two equations as 14.5 = (33 ppm–1)CA + (80.8 ppm–1)CB 29.7 = (33 ppm–1)CA + (2 43 ppm–1)CB Subtracting the first equation from the second gives 15.2... 242–250 Further details on evaluating analytical methods may be found in Wilson, A L “The Performance-Characteristics of Analytical Methods,” Part I-Talanta, 1970, 17, 21–29; Part II-Talanta, 1970, 17, 31 –44; Part III-Talanta, 19 73, 20, 725– 732 ; Part IVTalanta, 1974, 21, 1109–1121 Several texts provide numerous examples of analytical procedures for specific analytes in well-defined matrices Basset, J.; Denney,... Anal Chim Acta 1996, 31 8, 30 9 31 7 6 Rogers, L B J Chem Ed 1986, 63, 3 6 7 (a) Sandell, E B.; Elving, P J In Kolthoff, I M.; Elving, P J., eds Treatise on Analytical Chemistry, Interscience: New York; Part 1, Vol 1, 8 9 10 11 12 13 14 Chapter 1, pp 3 6; (b) Potts, L W Quantitative Analysis—Theory and Practice Harper and Row: New York, 1987, p 12 Valcárcel, M.; Ríos, A Anal Chem 19 93, 65, 781A–787A Valcárcel,... included as an additional term Smeas = kAnA + kInI + Sreag (total analysis method) 3. 11 Smeas = kACA + kICI + Sreag (concentration method) 3. 12 method blank A sample that contains all components of the matrix except the analyte 45 1400-CH 03 9/8/99 3: 51 PM Page 46 46 Modern Analytical Chemistry Solving either equation 3. 11 or 3. 12 for the amount of analyte can be accomplished by separating the analyte and... equations of the general form of equation 3. 11 or 3. 12 EXAMPLE 3. 3 A sample was analyzed for the concentration of two analytes, A and B, under two sets of conditions Under condition 1, the calibration sensitivities are kA,1 = 76 ppm–1 kB,1 = 186 ppm–1 kA,2 = 33 ppm–1 kB,2 = 2 43 ppm–1 and for condition 2 The signals under the two sets of conditions are Smeas,1 = 33 .4 Smeas,2 = 29.7 Determine the concentration... a solution of 10-ppb glutathione and 1.5-ppb ascorbic acid, the signal was 5. 43 times greater than that obtained for the analysis of 10-ppb glutathione.12 What is the selectivity coefficient for this analysis? The same study found that when analyzing a solution of 35 0-ppb methionine and 10-ppb glutathione the signal was 0.906 times less than that obtained for the analysis of 10 ppb-glutathione What... obtained using a method of known accuracy Chapter 14 provides a more detailed discussion of validation techniques validation The process of verifying that a procedure yields acceptable results 1400-CH 03 9/8/99 3: 51 PM Page 48 48 Modern Analytical Chemistry 3F Protocols quality assurance and quality control Those steps taken to ensure that the work conducted in an analytical lab is capable of producing... as 0.094 ppm Substituting this concentration back into either of the two original equations gives the concentration of A, CA, as 0.21 ppm 1400-CH 03 9/8/99 3: 51 PM Page 47 Chapter 3 The Language of Analytical Chemistry 47 3E.2 Calibration and Standardization Analytical chemists make a distinction between calibration and standardization.9 Calibration ensures that the equipment or instrument used to measure... experimental design may result in data that has little value 1400-CH 03 9/8/99 3: 51 PM Page 49 Chapter 3 The Language of Analytical Chemistry 49 Start Standardization ICV, ICB OK? No Identify and correct problem Yes CCV, CCB OK? No Yes Run 10 samples Discard results for last set of samples CCV, CCB OK? No Yes Yes More samples? No End Figure 3. 7 Schematic diagram of a portion of the Contract Laboratory . matrix. procedure Written directions outlining how to analyze a sample. 1400-CH 03 9/8/99 3: 51 PM Page 36 Chapter 3 The Language of Analytical Chemistry 37 Figure 3. 1 Membrane filter showing colonies of coliform bacteria require a method with excellent selectivity to avoid 44 Modern Analytical Chemistry 1400-CH 03 9/8/99 3: 51 PM Page 44 Chapter 3 The Language of Analytical Chemistry 45 interferences. Samples in which. method) 3. 12 method blank A sample that contains all components of the matrix except the analyte. 1400-CH 03 9/8/99 3: 51 PM Page 45 46 Modern Analytical Chemistry Solving either equation 3. 11 or 3. 12