D. Harvey - Modern Analytical Chemistry (794078), страница 21
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Other types of volumetric glassware, such as beakers and graduated cylinders, are unsuitable for accurately measuring volumes.Determinate measurement errors can be minimized by calibration. A pipet canbe calibrated, for example, by determining the mass of water that it delivers andusing the density of water to calculate the actual volume delivered by the pipet. Although glassware and instrumentation can be calibrated, it is never safe to assumethat the calibration will remain unchanged during an analysis. Many instruments,in particular, drift out of calibration over time.
This complication can be minimizedby frequent recalibration.personal errorAn error due to biases introduced by theanalyst.constant determinate errorA determinate error whose value is thesame for all samples.Table 4.5Personal Errors Finally, analytical work is always subject to a variety of personalerrors, which can include the ability to see a change in the color of an indicatorused to signal the end point of a titration; biases, such as consistently overestimating or underestimating the value on an instrument’s readout scale; failing to calibrate glassware and instrumentation; and misinterpreting procedural directions.Personal errors can be minimized with proper care.Identifying Determinate Errors Determinate errors can be difficult to detect.Without knowing the true value for an analysis, the usual situation in any analysiswith meaning, there is no accepted value with which the experimental result can becompared.
Nevertheless, a few strategies can be used to discover the presence of adeterminate error.Some determinate errors can be detected experimentally by analyzing severalsamples of different size. The magnitude of a constant determinate error is thesame for all samples and, therefore, is more significant when analyzing smaller samples. The presence of a constant determinate error can be detected by running several analyses using different amounts of sample, and looking for a systematic changein the property being measured. For example, consider a quantitative analysis inwhich we separate the analyte from its matrix and determine the analyte’s mass.Let’s assume that the sample is 50.0% w/w analyte; thus, if we analyze a 0.100-gsample, the analyte’s true mass is 0.050 g. The first two columns of Table 4.5 givethe true mass of analyte for several additional samples.
If the analysis has a positiveconstant determinate error of 0.010 g, then the experimentally determined mass forEffect of Constant Positive Determinate Error on Analysisof Sample Containing 50% Analyte (%w/w)Mass Sample(g)True Mass of Analyte(g)Constant Error(g)Mass of Analyte Determined(g)Percent Analyte Reported(%w/w)0.1000.2000.4000.8001.0000.0500.1000.2000.4000.5000.0100.0100.0100.0100.0100.0600.1100.2100.4100.51060.055.052.551.251.01400-CH04 9/8/99 3:53 PM Page 61Chapter 4 Evaluating Analytical Data61% w/w analyteany sample will always be 0.010 g, larger than its true mass (column four of Table4.5).
The analyte’s reported weight percent, which is shown in the last column ofTable 4.5, becomes larger when we analyze smaller samples. A graph of % w/w analyte versus amount of sample shows a distinct upward trend for small amounts ofsample (Figure 4.1). A smaller concentration of analyte is obtained when analyzingsmaller samples in the presence of a constant negative determinate error.proportional determinate errorA proportional determinate error, in which the error’s magnitude depends onA determinate error whose valuethe amount of sample, is more difficult to detect since the result of an analysis is independs on the amount of sampledependent of the amount of sample.
Table 4.6 outlines an example showing the efanalyzed.fect of a positive proportional error of 1.0% on the analysis of a sample that is50.0% w/w in analyte. In terms of equations 4.4 and 4.5, the reagent blank, Sreag, isan example of a constant determinate error, and the sensitivity, k, may be affectedby proportional errors.Potential determinate errors also can be identified by analyzing a standard sample containing a known amount of analyte in a matrix similar to that of the samplesstandard reference materialbeing analyzed.
Standard samples are available from a variety of sources, such as theA material available from the NationalNational Institute of Standards and Technology (where they are called standardInstitute of Standards and Technologyreference materials) or the American Society for Testing and Materials. For examcertified to contain knownconcentrations of analytes.ple, Figure 4.2 shows an analysis sheet for a typical reference material. Alternatively,the sample can be analyzed by an independentmethod known to give accurate results, and the results of the two methods can be compared. Onceidentified, the source of a determinate error can bePositive constant errorcorrected.
The best prevention against errors affecting accuracy, however, is a well-designed procedurethat identifies likely sources of determinate errors,True % w/w analytecoupled with careful laboratory work.The data in Table 4.1 were obtained using acalibrated balance, certified by the manufacturer tohave a tolerance of less than ±0.002 g. Suppose theTreasury Department reports that the mass of a1998 U.S. penny is approximately 2.5 g. Since theNegative constant errormass of every penny in Table 4.1 exceeds the reported mass by an amount significantly greaterAmount of samplethan the balance’s tolerance, we can safely concludethat the error in this analysis is not due to equipFigure 4.1ment error.
The actual source of the error is reEffect of a constant determinate error on the reported concentration ofanalyte.vealed later in this chapter.Table 4.6Effect of Proportional Positive Determinate Error on Analysisof Sample Containing 50% Analyte (%w/w)Mass Sample(g)True Mass of Analyte(g)Proportional Error(%)Mass of Analyte Determined(g)Percent Analyte Reported(%w/w)0.2000.4000.6000.8001.0000.1000.2000.3000.4000.5001.001.001.001.001.000.1010.2020.3030.4040.50550.550.550.550.550.51400-CH04 9/8/99 3:53 PM Page 6262Modern Analytical ChemistrySimulated Rainwater (liquid form)This SRM was developed to aid in the analysis of acidic rainwater by providing a stable,homogeneous material at two levels of acidity.Figure 4.2Analysis sheet for Simulated Rainwater (SRM2694a). Adapted from NIST SpecialPublication 260: Standard ReferenceMaterials Catalog 1995–96, p.
64; U.S.Department of Commerce, TechnologyAdministration, National Institute ofStandards and Technology.SRMTypeUnit of issue2694aSimulated rainwaterSet of 4: 2 of 50 mL at each of 2 levelsConstituent element parameter2694a-I2694a-IIpH, 25°CElectrolytic Conductivity (S/cm, 25°C)Acidity, meq/LFluoride, mg/LChloride, mg/LNitrate, mg/LSulfate, mg/LSodium, mg/LPotassium, mg/LAmmonium, mg/LCalcium, mg/LMagnesium, mg/L4.3025.40.05440.057(0.23)*(0.53)*2.690.2080.056(0.12)*0.01260.02423.60129.30.2830.108(0.94)*7.1910.60.4230.108(1.06)*0.03640.0484* Values in parentheses are not certified and are given for information only.4B.2 PrecisionrepeatabilityThe precision for an analysis in whichthe only source of variability is theanalysis of replicate samples.reproducibilityThe precision when comparing resultsfor several samples, for several analystsor several methods.indeterminate errorAny random error that causes somemeasurements or results to be too highwhile others are too low.Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance.
Precision is commonlydivided into two categories: repeatability and reproducibility. Repeatability is theprecision obtained when all measurements are made by the same analyst during asingle period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a singleanalyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability.Errors affecting the distribution of measurements around a central value arecalled indeterminate and are characterized by a random variation in both magnitude and direction.
Indeterminate errors need not affect the accuracy of an analysis. Since indeterminate errors are randomly scattered around a central value, positive and negative errors tend to cancel, provided that enough measurements aremade. In such situations the mean or median is largely unaffected by the precisionof the analysis.Sources of Indeterminate Error Indeterminate errors can be traced to severalsources, including the collection of samples, the manipulation of samples duringthe analysis, and the making of measurements.When collecting a sample, for instance, only a small portion of the availablematerial is taken, increasing the likelihood that small-scale inhomogeneities in thesample will affect the repeatability of the analysis.
Individual pennies, for example,are expected to show variation from several sources, including the manufacturingprocess, and the loss of small amounts of metal or the addition of dirt during circulation. These variations are sources of indeterminate error associated with the sampling process.1400-CH04 9/8/99 3:53 PM Page 63Chapter 4 Evaluating Analytical DataDuring the analysis numerous opportunities arise for random variations in theway individual samples are treated. In determining the mass of a penny, for example, each penny should be handled in the same manner. Cleaning some pennies butnot cleaning others introduces an indeterminate error.Finally, any measuring device is subject to an indeterminate error in reading itsscale, with the last digit always being an estimate subject to random fluctuations, orbackground noise.
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