D. Harvey - Modern Analytical Chemistry (794078), страница 2
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. . in ChapterRepresentative Methods246Annotated methods of typicalanalytical procedures link theory withpractice. The format encouragesstudents to think about the design ofthe procedure and why it works.Modern Analytical ChemistryAn additional problem is encountered when the isolated solid is nonstoichiometric. For example, precipitating Mn2+ as Mn(OH)2, followed by heatingto produce the oxide, frequently produces a solid with a stoichiometry of MnOx ,where x varies between 1 and 2. In this case the nonstoichiometric product resultsfrom the formation of a mixture of several oxides that differ in the oxidation stateof manganese.
Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure.6Margin NotesMargin notes direct studentsto colorplates located towardthe middle of the book110Modern Analytical Chemistryeither case, the calibration curve provides a means for relating Ssamp to the analyte’s concentration.Representative MethodsRepresentative Method The best way to appreciate the importance of the theoretical and practical details discussed in the previous section is to carefully examine theprocedure for a typical precipitation gravimetric method.
Although each methodhas its own unique considerations, the determination of Mg2+ in water and wastewater by precipitating MgNH4PO4 ⋅ 6H2O and isolating Mg2P2O7 provides an instructive example of a typical procedure.EXAMPLE 5.3Color plate 1 shows an example of a set ofexternal standards and their correspondingnormal calibration curve.A second spectrophotometric method for the quantitative determination ofPb2+ levels in blood gives a linear normal calibration curve for whichSstand = (0.296 ppb–1) × CS + 0.003What is the Pb2+ level (in ppb) in a sample of blood if Ssamp is 0.397?SOLUTIONCA =0.296 ppb –1(NH4)2HPO4 as the precipitant.
The precipitate’s solubility in neutral solutions(0.0065 g/100 mL in pure water at 10 °C) is relatively high, but it is much less solublein the presence of dilute ammonia (0.0003 g/100 mL in 0.6 M NH3). The precipitant isnot very selective, so a preliminary separation of Mg2+ from potential interferents isnecessary.
Calcium, which is the most significant interferent, is usually removed byits prior precipitation as the oxalate. The presence of excess ammonium salts fromthe precipitant or the addition of too much ammonia can lead to the formation ofMg(NH4)4(PO4)2, which is subsequently isolated as Mg(PO3)2 after drying. Theprecipitate is isolated by filtration using a rinse solution of dilute ammonia. Afterfiltering, the precipitate is converted to Mg2P2O7 and weighed.Procedure. Transfer a sample containing no more than 60 mg of Mg2+ into a600-mL beaker. Add 2–3 drops of methyl red indicator, and, if necessary, adjust thevolume to 150 mL.
Acidify the solution with 6 M HCl, and add 10 mL of 30% w/v(NH4)2HPO4. After cooling, add concentrated NH3 dropwise, and while constantlystirring, until the methyl red indicator turns yellow (pH > 6.3). After stirring for5 min, add 5 mL of concentrated NH3, and continue stirring for an additional 10 min.Allow the resulting solution and precipitate to stand overnight.
Isolate theprecipitate by filtration, rinsing with 5% v/v NH3. Dissolve the precipitate in 50 mLof 10% v/v HCl, and precipitate a second time following the same procedure. Afterfiltering, carefully remove the filter paper by charring. Heat the precipitate at 500 °Cuntil the residue is white, and then bring the precipitate to constant weight at1100 °C.1. Why does the procedure call for a sample containing no more than 60 mg of0.397 – 0.003== 1.33 ppb0.296 ppb –1It is worth noting that the calibration equation in this problem includes anextra term that is not in equation 5.3.
Ideally, we expect the calibration curve togive a signal of zero when CS is zero. This is the purpose of using a reagentblank to correct the measured signal. The extra term of +0.003 in ourcalibration equation results from uncertainty in measuring the signal for thereagent blank and the standards.An external standardization allows a related series of samples to be analyzedusing a single calibration curve. This is an important advantage in laboratorieswhere many samples are to be analyzed or when the need for a rapid throughput ofl iiti ltii lf thtlt dExamples of Typical ProblemsEach example problem includes adetailed solution that helps students inapplying the chapter’s material topractical problems.Determination of Mg2+ in Water and Wastewater7Description of Method.
Magnesium is precipitated as MgNH4PO4 ⋅ 6H2O usingQuestionsTo determine the concentration of Pb2+ in the sample of blood, we replaceSstand in the calibration equation with Ssamp and solve for CASsamp – 0.003Method 8.1matrix matchingAdjusting the matrix of an externalstandard so that it is the same as thematrix of the samples to be analyzed.method of standard additionsA standardization in which aliquots of astandard solution are added to thesample.qyThere is a serious limitation, however, to an external standardization. Therelationship between Sstand and CS in equation 5.3 is determined when the analyte is present in the external standard’s matrix.
In using an external standardization, we assume that any difference between the matrix of the standards and thesample’s matrix has no effect on the value of k. A proportional determinate erroris introduced when differences between the two matrices cannot be ignored. Thisis shown in Figure 5.4, where the relationship between the signal and the amountof analyte is shown for both the sample’s matrix and the standard’s matrix. Inthis example, using a normal calibration curve results in a negative determinateerror. When matrix problems are expected, an effort is made to match the matrixof the standards to that of the sample.
This is known as matrix matching. Whenthe sample’s matrix is unknown, the matrix effect must be shown to be negligible, or an alternative method of standardization must be used. Both approachesare discussed in the following sections.5B.4 Standard AdditionsThe complication of matching the matrix of the standards to that of the samplecan be avoided by conducting the standardization in the sample. This is knownas the method of standard additions. The simplest version of a standard addition is shown in Figure 5.5.
A volume, Vo, of sample is diluted to a final volume,Vf, and the signal, Ssamp is measured. A second identical aliquot of sample isBold-faced Key Terms with Margin DefinitionsKey words appear in boldface when they are introduced within the text.The term and its definition appear in the margin for quick review by thestudent. All key words are also defined in the glossary.x1400-Fm 9/9/99 7:38 AM Page xi. . .
End of ChapteryyList of Key Terms5E 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)The key terms introduced within the chapter arelisted at the end of each chapter. Page referencesdirect the student to the definitions in the text.(p. 110)Summary5F 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.The summary provides the student with a briefreview of the important concepts within the chapter.Suggested ExperimentsAn annotated list of representative experiments isprovided from the Journal of Chemical Education.Suggested ReadingsExperiments5G Suggested EXPERIMENTSSuggested readings give the studentaccess to more comprehensivediscussion of the topics introducedwithin the chapter.The 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.ReferencesThe references cited in thechapter are provided so thestudent can access them forfurther information.3J PROBLEMS1. When working with a solid sample, it often is necessary tobring the analyte into solution by dissolving the sample in asuitable solvent.
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