D. Harvey - Modern Analytical Chemistry (794078), страница 19
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What is the selectivity coefficient forthis analysis? In what way do these interferents behavedifferently?7. Oungpipat and Alexander described a new method fordetermining the concentration of glycolic acid (GA)in a variety of samples, including physiological fluidssuch as urine.13 In the presence of only GA, the signalis given asSsamp,1 = kGACGAand in the presence of both glycolic acid and ascorbic acid(AA), the signal isSsamp,2 = kGACGA + kAACAAWhen the concentration of glycolic acid is 1.0 × 10–4 M andthe concentration of ascorbic acid is 1.0 × 10–5 M, the ratio ofthe two signals was found to beSsamp ,2= 1.44Ssamp ,1a. Using the ratio of the two signals, determine the value ofthe selectivity ratioK GA, AA =k AAkGAb. Is the method more selective toward glycolic acid orascorbic acid?c.
If the concentration of ascorbic acid is 1.0 × 10–5 M,what is the smallest concentration of glycolic acid thatcan be determined such that the error introduced byfailing to account for the signal from ascorbic acid is lessthan 1%?1400-CH03 9/8/99 3:51 PM Page 5252Modern Analytical Chemistry8. Ibrahim and co-workers developed a new method for thequantitative analysis of hypoxanthine, a natural compound ofsome nucleic acids.14 As part of their study they evaluated themethod’s selectivity for hypoxanthine in the presence ofseveral possible interferents, including ascorbic acid.a.
When analyzing a solution of 1.12 × 10–6 M hypoxanthine,the authors obtained a signal of 7.45 × 10–5 amperes (A).What is the sensitivity for hypoxanthine? You mayassume that the signal has been corrected for the methodblank.b. When a solution containing 1.12 × 10–6 M hypoxanthineand 6.5 × 10–5 M ascorbic acid was analyzed a signal of4.04 × 10–5 A was obtained. What is the selectivitycoefficient for this method?c. Is the method more selective for hypoxanthine or forascorbic acid?d. What is the largest concentration of ascorbic acid that maybe present if a concentration of 1.12 × 10–6 Mhypoxanthine is to be determined within ±1%?9. A sample was analyzed for the concentration of two analytes,C and D, under two sets of conditions. Under condition 1 thecalibration sensitivities arekC,1 = 23 ppm–1kD,1 = 415 ppm–1and for condition 2kC,2 = 115 ppm–1kD,2 = 45 ppm–1The signals under the two sets of conditions areSmeas,1 = 78.6Smeas,2 = 47.9Determine the concentration of C and D.
You may assumethat Sreag is zero under both conditions.10. Examine a procedure from Standard Methods for the Analysisof Waters and Wastewaters (or another manual of standardanalytical methods), and identify the steps taken tocompensate for interferences, to calibrate equipment andinstruments, to standardize the method, and to acquire arepresentative sample.3K SUGGESTED READINGSThe following papers provide alternative schemes for classifyinganalytical methodsBooksh, K. S.; Kowalski, B.
R. “Theory of Analytical Chemistry,”Anal. Chem. 1994, 66, 782A–791A.Phillips, J. B. “Classification of Analytical Methods,” Anal. Chem.1981, 53, 1463A–1470A.Valcárcel, M.; Luque de Castro, M. D. “A Hierarchical Approach toAnalytical Chemistry,” Trends Anal. Chem., 1995, 14, 242–250.Further details on evaluating analytical methods may be found inWilson, A. L. “The Performance-Characteristics of AnalyticalMethods,” Part I-Talanta, 1970, 17, 21–29; Part II-Talanta,1970, 17, 31–44; Part III-Talanta, 1973, 20, 725–732; Part IVTalanta, 1974, 21, 1109–1121.Several texts provide numerous examples of analytical proceduresfor specific analytes in well-defined matrices.Basset, J.; Denney, R. C.; Jeffery, G.
H.; et al. Vogel’s Textbook ofQuantitative Inorganic Analysis, 4th ed. Longman: London, 1981.Csuros, M. Environmental Sampling and Analysis for Technicians,Lewis: Boca Raton, 1994.Keith, L. H., ed. Compilation of EPA’s Sampling and AnalysisMethods, Lewis: Boca Raton, 1996.Rump, H. H.; Krist, H. Laboratory Methods for the Examination ofWater, Wastewater and Soil. VCH Publishers: New York, 1988.Standard Methods for the Analysis of Waters and Wastewaters,19th ed. American Public Health Association: Washington,DC, 1995.3L REFERENCES1. Taylor, J.
K. Anal. Chem. 1983, 55, 600A–608A.2. Fitch, A.; Wang, Y.; Mellican, S.; et al. Anal. Chem. 1996, 68,727A–731A.3. Basset, J.; Denney, R. C.; Jeffery, G. H.; et al. Vogel’s Textbook ofQuantitative Inorganic Analysis, 4th ed. Longman: London,1981, p. 8.4. Ingle, J. D.; Crouch, S. R. Spectrochemical Analysis. Prentice-Hall:Englewood, NJ, 1988, pp. 171–172.5. Barnett, N. W.; Bowser, T. A.; Gerardi, R.
D.; et al. Anal. Chim. Acta1996, 318, 309–317.6. 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 andPractice. Harper and Row: New York, 1987, p. 12.Valcárcel, M.; Ríos, A. Anal. Chem. 1993, 65, 781A–787A.Valcárcel, M.; Ríos, A. Analyst, 1995, 120, 2291–2297.(a) Amore, F. Anal. Chem. 1979, 51, 1105A–1110A; (b) Taylor, J. K.Anal. Chem. 1981, 53, 1588A–1593A.D’Elia, C. F.; Sanders, J. G.; Capone, D. G. Environ. Sci. Technol. 1989,23, 768–774.Jiménez-Prieto, R.; Velasco, A.; Silva, M.; et al.
Anal. Chim. Acta 1992,269, 273–279.Oungpipat, W.; Alexander, P. W. Anal. Chim. Acta 1994, 295, 36–46.Ibrahim, M. S.; Ahmad, M. E.; Temerk, Y. M.; et al. Anal. Chim. Acta1996, 328, 47–52.1400-CH04 9/8/99 3:53 PM Page 534ChapterEvaluating Analytical DataAproblem dictates the requirements we place on ourmeasurements and results.
Regulatory agencies, for example, placestringent requirements on the reliability of measurements and resultsreported to them. This is the rationale for creating a protocol forregulatory problems. Screening the products of an organic synthesis,on the other hand, places fewer demands on the reliability ofmeasurements, allowing chemists to customize their procedures.When designing and evaluating an analytical method, we usuallymake three separate considerations of experimental error.1 First, beforebeginning an analysis, errors associated with each measurement areevaluated to ensure that their cumulative effect will not limit the utilityof the analysis. Errors known or believed to affect the result can then beminimized.
Second, during the analysis the measurement process ismonitored, ensuring that it remains under control. Finally, at the endof the analysis the quality of the measurements and the result areevaluated and compared with the original design criteria. This chapteris an introduction to the sources and evaluation of errors in analyticalmeasurements, the effect of measurement error on the result of ananalysis, and the statistical analysis of data.531400-CH04 9/8/99 3:53 PM Page 5454Modern Analytical Chemistry4A Characterizing Measurements and ResultsLet’s begin by choosing a simple quantitative problem requiring a single measurement. The question to be answered is—What is the mass of a penny? If you thinkabout how we might answer this question experimentally, you will realize that thisproblem is too broad.
Are we interested in the mass of United State pennies or Canadian pennies, or is the difference in country of importance? Since the composition ofa penny probably differs from country to country, let’s limit our problem to penniesminted in the United States. There are other considerations. Pennies are minted atseveral locations in the United States (this is the meaning of the letter, or absence of aletter, below the date stamped on the lower right corner of the face of the coin).Since there is no reason to expect a difference between where the penny was minted,we will choose to ignore this consideration. Is there a reason to expect a differencebetween a newly minted penny not yet in circulation, and a penny that has been incirculation? The answer to this is not obvious.
Let’s simplify the problem by narrowing the question to—What is the mass of an average United States penny in circulation? This is a problem that we might expect to be able to answer experimentally.A good way to begin the analysis is to acquire some preliminary data. Table 4.1shows experimentally measured masses for seven pennies from my change jar athome. Looking at these data, it is immediately apparent that our question has nosimple answer.
That is, we cannot use the mass of a single penny to draw a specificconclusion about the mass of any other penny (although we might conclude that allpennies weigh at least 3 g). We can, however, characterize these data by providing ameasure of the spread of the individual measurements around a central value.4A.1 Measures of Central TendencyOne way to characterize the data in Table 4.1 is to assume that the masses of individual pennies are scattered around a central value that provides the best estimate ofa penny’s true mass.
Two common ways to report this estimate of central tendencyare the mean and the median.mean–The average value of a set of data (X).–Mean The mean, X, is the numerical average obtained by dividing the sum of theindividual measurements by the number of measurements∑i =1 XinX =where Xi is theTable 4.1ithnmeasurement, and n is the number of independent measurements.Masses of Seven United StatesPennies in CirculationPennyMass (g)12345673.0803.0943.1073.0563.1123.1743.1981400-CH04 9/8/99 3:53 PM Page 55Chapter 4 Evaluating Analytical DataEXAMPLE 4.1What is the mean for the data in Table 4.1?SOLUTIONTo calculate the mean, we add the results for all measurements3.080 + 3.094 + 3.107 + 3.056 + 3.112 + 3.174 + 3.198 = 21.821and divide by the number of measurementsX =21.821= 3.117 g7The mean is the most common estimator of central tendency. It is not considered a robust estimator, however, because extreme measurements, those muchlarger or smaller than the remainder of the data, strongly influence the mean’svalue.2 For example, mistakenly recording the mass of the fourth penny as 31.07 ginstead of 3.107 g, changes the mean from 3.117 g to 7.112 g!Median The median, Xmed, is the middle value when data are ordered from thesmallest to the largest value.
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