D. Harvey - Modern Analytical Chemistry (794078), страница 82
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The following data are reported for a series ofthiourea standards.[thiourea] (M)∆f (Hz)3.00 × 10–75.00 × 10–77.00 × 10–79.00 × 10–715.00 × 10–725.00 × 10–735.00 × 10–750.00 × 10–774.61201592053275437891089(a) Characterize this method with respect to the scale ofoperation shown in Figure 3.6 of Chapter 3. (b) Using aregression analysis, determine the relationship between thecrystal’s frequency shift and the concentration of thiourea.(c) A sample containing an unknown amount of thiourea istaken through the procedure and gives a ∆f of 176 Hz. Whatis the molar concentration of thiourea in the sample?(d) What is the 95% confidence interval for theconcentration of thiourea in this sample assuming onereplicate?8I SUGGESTED READINGSThe following resources provide a general history of gravimetry.Beck, C.
M. “Classical Analysis: A Look at the Past, Present, andFuture,” Anal. Chem. 1991, 63, 993A–1003A.Laitinen, H. A.; Ewing, G. W., eds. A History of AnalyticalChemistry. The Division of Analytical Chemistry of theAmerican Chemical Society: Washington, DC, 1977,pp. 10–24.Sources providing additional examples of inorganic and organicgravimetric methods include the following texts.Bassett, J.; Denney, R.
C.; Jeffery, G. H.; et al. Vogel’s Textbook ofQuantitative Inorganic Analysis, 4th ed. Longman: London,1981.Erdey, L. Gravimetric Analysis, Pergamon: Oxford, 1965.Steymark, A. Quantitative Organic Microanalysis, The BlakistonCo.: New York, 1951.The following text provides more information onthermogravimetry.Wendlandt, W. W. Thermal Methods of Analysis, 2nd ed. Wiley:New York, 1986.For a review of isotope dilution mass spectrometry see thefollowing article.Fassett, J. D.; Paulsen, P.
J. “Isotope Dilution Mass Spectrometryfor Accurate Elemental Analysis,” Anal. Chem. 1989, 61,643A–649A.1400-CH08 9/9/99 2:18 PM Page 272272Modern Analytical Chemistry8J REFERENCES1. Valcárcel, M.; Rios, A. Analyst 1995, 120, 2291–2297.2. (a) Moody, J. R.; Epstein, M. S. Spectrochim. Acta 1991, 46B,1571–1575. (b) Epstein, M. S. Spectrochim.
Acta 1991, 46B, 1583–1591.3. Von Weimarn, P. P. Chem. Revs. 1925, 2, 217.4. Bassett, J.; Denney, R. C.; Jeffery, G. H.; et al. Vogel’s Textbook ofQuantitative Inorganic Analysis, 4th ed. Longman: London, 1981,p. 408.5. Gordon, L; Salutsky, M. L.; Willard, H. H. Precipitation fromHomogeneous Solution, Wiley: New York, 1959.6. Ward, R., ed. Non-Stoichiometric Compounds (Ad. Chem. Ser. 39);American Chemical Society: Washington, DC, 1963.7. Method 3500-Mg D as published in Standard Methods for theExamination of Water and Wastewater, 18th ed. American PublicHealth Association: Washington, DC, 1992, pp. 3–73 to 3–74.8.
Jungreis, E. Spot Test Analysis, 2nd ed. Wiley: New York, 1997.9. Young, R. S. Chemical Analysis in Extractive Metallurgy, Griffen:London, 1971, pp. 302–304.10. (a) Ward, M. D.; Buttry, D. A. Science 1990, 249, 1000–1007;(b) Grate, J. W.; Martin, S. J.; White, R. M. Anal. Chem. 1993, 65,940A–948A; (c) Grate, J.
W.; Martin, S. J.; White, R. M. Anal. Chem.1993, 65, 987A–996A.11. Muratsugu, M.; Ohta, F.; Miya, Y. et al. Anal. Chem. 1993, 65,2933–2937.12. Sinha, S. K.; Shome, S. C. Anal. Chim. Acta 1960, 24, 33–36.13. Adapted from Sorum, C. H.; Lagowski, J. J. Introduction to SemimicroQualitative Analysis, 5th ed.
Prentice-Hall: Englewood Cliffs, N. J.,1977, p. 285.14. Grote, Z. Anal. Chem. 1941, 122, 395.15. Nawrocki, J.; Carr, P. W.; Annen, M. J.; et al. Anal. Chim. Acta 1996,327, 261–266.16. Data taken from the pamphlet Fat Determination by SFE, ISCO, Inc.:Lincoln, NE.17.
Delumyea, R. D.; McCleary, D. L. J. Chem. Educ. 1993, 70, 172–173.18. Yao, S. F.; He, F. J.; Nie, L. H. Anal. Chim. Acta 1992, 268, 311–314.\1400-CH09 9/9/99 2:12 PM Page 2739ChapterTitrimetric Methods of AnalysisTitrimetry, in which we measure the volume of a reagent reactingstoichiometrically with the analyte, first appeared as an analyticalmethod in the early eighteenth century. Unlike gravimetry, titrimetryinitially did not receive wide acceptance as an analytical technique.Many prominent late-nineteenth century analytical chemists preferredgravimetry over titrimetry and few of the standard texts from that erainclude titrimetric methods.
By the early twentieth century, however,titrimetry began to replace gravimetry as the most commonly usedanalytical method.Interestingly, precipitation gravimetry developed in the absence ofa theory of precipitation. The relationship between the precipitate’smass and the mass of analyte, called a gravimetric factor, wasdetermined experimentally by taking known masses of analyte (anexternal standardization). Gravimetric factors could not be calculatedusing the precipitation reaction’s stoichiometry because chemicalformulas and atomic weights were not yet available! Unlike gravimetry,the growth and acceptance of titrimetry required a deeperunderstanding of stoichiometry, thermodynamics, and chemicalequilibria.
By the early twentieth century the accuracy and precision oftitrimetric methods were comparable to that of gravimetry,establishing titrimetry as an accepted analytical technique.2731400-CH09 9/9/99 2:12 PM Page 274274Modern Analytical Chemistry9A Overview of TitrimetrytitrimetryAny method in which volume is thesignal.titrantThe reagent added to a solutioncontaining the analyte and whosevolume is the signal.Titrimetric methods are classified into four groups based on the type of reaction involved. These groups are acid–base titrations, in which an acidic or basic titrant reacts with an analyte that is a base or an acid; complexometric titrations involving ametal–ligand complexation reaction; redox titrations, where the titrant is an oxidizing or reducing agent; and precipitation titrations, in which the analyte and titrantreact to form a precipitate. Despite the difference in chemistry, all titrations shareseveral common features, providing the focus for this section.9A.1 Equivalence Points and End Pointsequivalence pointThe point in a titration wherestoichiometrically equivalent amounts ofanalyte and titrant react.For a titration to be accurate we must add a stoichiometrically equivalent amountof titrant to a solution containing the analyte.
We call this stoichiometric mixturethe equivalence point. Unlike precipitation gravimetry, where the precipitant isadded in excess, determining the exact volume of titrant needed to reach the equivalence point is essential. The product of the equivalence point volume, Veq, and thetitrant’s concentration, CT, gives the moles of titrant reacting with the analyte.Moles titrant = Veq × CTend pointThe point in a titration where we stopadding titrant.indicatorA colored compound whose change incolor signals the end point of a titration.titration errorThe determinate error in a titration dueto the difference between the end pointand the equivalence point.Knowing the stoichiometry of the titration reaction(s), we can calculate the molesof analyte.Unfortunately, in most titrations we usually have no obvious indication thatthe equivalence point has been reached.
Instead, we stop adding titrant when wereach an end point of our choosing. Often this end point is indicated by a change inthe color of a substance added to the solution containing the analyte. Such substances are known as indicators. The difference between the end point volume andthe equivalence point volume is a determinate method error, often called the titration error. If the end point and equivalence point volumes coincide closely, thenthe titration error is insignificant and can be safely ignored.
Clearly, selecting an appropriate end point is critical if a titrimetric method is to give accurate results.9A.2 Volume as a Signal*Almost any chemical reaction can serve as a titrimetric method provided thatthree conditions are met. The first condition is that all reactions involving thetitrant and analyte must be of known stoichiometry. If this is not the case, thenthe moles of titrant used in reaching the end point cannot tell us how much analyte is in our sample. Second, the titration reaction must occur rapidly. If we addtitrant at a rate that is faster than the reaction’s rate, then the end point will exceed the equivalence point by a significant amount.
Finally, a suitable methodmust be available for determining the end point with an acceptable level of accuracy. These are significant limitations and, for this reason, several titration strategies are commonly used.A simple example of a titration is an analysis for Ag+ using thiocyanate, SCN–,as a titrant.Ag+(aq) + SCN–(aq)t AgSCN(s)*Instead of measuring the titrant’s volume we also can measure its mass. Since the titrant’s density is a measure of itsmass per unit volume, the mass of titrant and volume of titrant are proportional.1400-CH09 9/9/99 2:12 PM Page 275Chapter 9 Titrimetric Methods of Analysis275This reaction occurs quickly and is of known stoichiometry.
A titrant of SCN– iseasily prepared using KSCN. To indicate the titration’s end point we add a smallamount of Fe3+ to the solution containing the analyte. The formation of the redcolored Fe(SCN)2+ complex signals the end point. This is an example of a directtitration since the titrant reacts with the analyte.If the titration reaction is too slow, a suitable indicator is not available, or thereis no useful direct titration reaction, then an indirect analysis may be possible.
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