D. Harvey - Modern Analytical Chemistry (794078), страница 40
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J. Anal. Chem. 1986, 58, 433–438.aW = weight of analyte used to prepare standard solution by diluting to a fixed volume, V.sbW = weight of sample used to prepare sample solution by diluting to a fixed volume, V.xcAnalyte-free sample prepared in the same fashion as samples, but without the analyte being present.1400-CH05 9/8/99 3:59 PM Page 129Chapter 5 Calibrations, Standardizations, and Blank Correctionstions between the analyte and the sample matrix.
Both the calibration blank andthe reagent blank correct for signals due to the reagents and solvents. Any difference in their values is due to the number and composition of samples contributing to the determination of the blank.Unfortunately, neither the calibration blank nor the reagent blank can correct for bias due to analyte–matrix interactions because the analyte is missing inthe reagent blank, and the sample’s matrix is missing from the calibration blank.The true method blank must include both the matrix and the analyte and, consequently, can only be determined using the sample itself.
One approach is to measure the signal for samples of different size and determine the regression linefrom a plot of signal versus the amount of sample. The resulting y-intercept givesthe signal for the condition of no sample and is known as the total Youdenblank.13 This is the true blank correction. The regression line for the sample datain Table 5.3 is129total Youden blankA blank that corrects the signal foranalyte–matrix interactions.Ssamp = 0.009844 × Wx + 0.185giving a true blank correction of 0.185. Using this value to correct the signalsgives identical values for the concentration of analyte in all three samples (seeTable 5.4, bottom row).The total Youden blank is not encountered frequently in analytical work,because most chemists rely on a calibration blank when using calibration curvesand rely on reagent blanks when using a single-point standardization.
As longas any constant bias due to analyte–matrix interactions can be ignored, whichis often the case, the accuracy of the method will not suffer. It is always agood idea, however, to check for constant sources of error, by analyzingsamples of different sizes, before relying on either a calibration or reagentblank.Table 5.4Equations and Resulting Concentrations for Different Approaches to Correctingfor the Method BlankConcentration of Analyte inEquationaApproach for Correcting Method BlankSample 1Sample 2Sample 3Ignore blank correctionsCA =SsampWa=WxkW x0.17070.16100.1552Use calibration blankCA =Ssamp – CBWa=WxkW x0.14410.14090.1390Use reagent blankCA =Ssamp – RBWa=WxkW x0.14940.14490.1422Use both calibration and reagent blankCA =Ssamp – CB – RBWa=WxkW x0.12270.12480.1261Use total Youden blankCA =Ssamp – TYBWa=WxkW x0.13130.13130.1313aC = concentration of analyte; W = weight of analyte; W = weight of sample; k = slope of calibration curve = 0.075 (see Table 5.3).AaxAbbreviations: CB = calibration blank = 0.125 (see Table 5.3); RB = reagent blank = 0.100 (see Table 5.3); TYB = total Youden blank = 0.185 (see text).1400-CH05 9/8/99 3:59 PM Page 130130Modern Analytical Chemistry5E KEY TERMSaliquot (p.
111)external standard (p. 109)internal standard (p. 116)linear regression (p. 118)matrix matching (p. 110)method of standard additionsmultiple-point standardization (p. 109)normal calibration curve (p. 109)primary reagent (p. 106)reagent grade (p. 107)residual error (p. 118)secondary reagent (p. 107)single-point standardization (p. 108)standard deviation about theregression (p.
121)total Youden blank (p. 129)(p. 110)5F SUMMARYIn a quantitative analysis, we measure a signal and calculate theamount of analyte using one of the following equations.Smeas = knA + SreagSmeas = kCA + SreagTo obtain accurate results we must eliminate determinate errorsaffecting the measured signal, Smeas, the method’s sensitivity, k,and any signal due to the reagents, Sreag.To ensure that Smeas is determined accurately, we calibratethe equipment or instrument used to obtain the signal.
Balancesare calibrated using standard weights. When necessary, we canalso correct for the buoyancy of air. Volumetric glassware canbe calibrated by measuring the mass of water contained or delivered and using the density of water to calculate the true volume.
Most instruments have calibration standards suggested bythe manufacturer.An analytical method is standardized by determining its sensitivity. There are several approaches to standardization, includingthe use of external standards, the method of standard addition,and the use of an internal standard. The most desirable standardization strategy is an external standardization.
The method ofstandard additions, in which known amounts of analyte are addedto the sample, is used when the sample’s matrix complicates theanalysis. An internal standard, which is a species (not analyte)added to all samples and standards, is used when the proceduredoes not allow for the reproducible handling of samples andstandards.Standardizations using a single standard are common, but alsoare subject to greater uncertainty. Whenever possible, a multiplepoint standardization is preferred.
The results of a multiple-pointstandardization are graphed as a calibration curve. A linear regression analysis can provide an equation for the standardization.A reagent blank corrects the measured signal for signals due toreagents other than the sample that are used in an analysis. Themost common reagent blank is prepared by omitting the sample.When a simple reagent blank does not compensate for all constantsources of determinate error, other types of blanks, such as thetotal Youden blank, can be used.Experiments5G Suggested EXPERIMENTSThe following exercises and experiments help connect the material in this chapter to the analytical laboratory.Calibration—Volumetric glassware (burets, pipets, andvolumetric flasks) can be calibrated in the manner describedin Example 5.1. Most instruments have a calibration samplethat can be prepared to verify the instrument’s accuracy andprecision.
For example, as described in this chapter, asolution of 60.06 ppm K2Cr2O7 in 0.0050 M H2SO4 shouldgive an absorbance of 0.640 ± 0.010 at a wavelength of350.0 nm when using 0.0050 M H2SO4 as a reagentblank. These exercises also provide practice with usingvolumetric glassware, weighing samples, and preparingsolutions.Standardization—External standards, standard additions,and internal standards are a common feature of manyquantitative analyses.
Suggested experiments using thesestandardization methods are found in later chapters. A goodproject experiment for introducing external standardization,standard additions, and the importance of the sample’smatrix is to explore the effect of pH on the quantitativeanalysis of an acid–base indicator. Using bromothymol blueas an example, external standards can be prepared in a pH 9buffer and used to analyze samples buffered to different pHsin the range of 6–10.
Results can be compared with thoseobtained using a standard addition.1400-CH05 9/8/99 3:59 PM Page 131131Chapter 5 Calibrations, Standardizations, and Blank Corrections5H PROBLEMS1. In calibrating a 10-mL pipet, a measured volume of water wastransferred to a tared flask and weighed, yielding a mass of9.9814 g. (a) Calculate, with and without correcting forbuoyancy, the volume of water delivered by the pipet. Assumethat the density of water is 0.99707 g/cm3 and that the densityof the weights is 8.40 g/cm3. (b) What are the absolute andrelative errors introduced by failing to account for the effectof buoyancy? Is this a significant source of determinate errorfor the calibration of a pipet? Explain.2. Repeat the questions in problem 1 for the case when amass of 0.2500 g is measured for a solid that has a densityof 2.50 g/cm3.3.
Is the failure to correct for buoyancy a constant orproportional source of determinate error?4. What is the minimum density of a substance necessary tokeep the buoyancy correction to less than 0.01% when usingbrass calibration weights with a density of 8.40 g/cm3?5. Describe how you would use a serial dilution to prepare 100mL each of a series of standards with concentrations of1.000 × 10–5, 1.000 × 10–4, 1.000 × 10–3, and 1.000 × 10–2 Mfrom a 0.1000 M stock solution.
Calculate the uncertainty foreach solution using a propagation of uncertainty, andcompare to the uncertainty if each solution was prepared by asingle dilution of the stock solution. Tolerances for differenttypes of volumetric glassware and digital pipets are found inTables 4.2 and 4.4. Assume that the uncertainty in themolarity of the stock solution is ±0.0002.6. Three replicate determinations of the signal for a standardsolution of an analyte at a concentration of 10.0 ppm give valuesof 0.163, 0.157, and 0.161 (arbitrary units), respectively.
Thesignal for a method blank was found to be 0.002. Calculate theconcentration of analyte in a sample that gives a signal of 0.118.7. A 10.00-g sample containing an analyte was transferred to a250-mL volumetric flask and diluted to volume. When a10.00-mL aliquot of the resulting solution was diluted to 25.00mL it was found to give a signal of 0.235 (arbitrary units).
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