D. Harvey - Modern Analytical Chemistry (794078), страница 70
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Imagine how you would determine a food’s moisture content bya direct analysis. One possibility is to heat a sample of the food to a temperatureat which the water in the sample vaporizes. If we capture the vapor in apreweighed absorbent trap, then the change in the absorbent’s mass provides a direct determination of the amount of water in the sample.
An easier approach,however, is to weigh the sample of food before and after heating, using the changein its mass as an indication of the amount of water originally present. We call thisan indirect analysis since we determine the analyte by a signal representing itsdisappearance.The indirect determination of moisture content in foods is done by difference.The sample’s initial mass includes the water, whereas the final mass is measuredafter removing the water.
We can also determine an analyte indirectly without itsever being weighed. Again, as with the determination of Pb2+ as PbO2(s), we takeadvantage of the analyte’s chemistry. For example, phosphite, PO33–, reduces Hg2+to Hg22+. In the presence of Cl– a solid precipitate of Hg2Cl2 forms.2HgCl2(aq) + PO33–(aq) + 3H2O(l)t Hg2Cl2(s) + 2H3O+(aq) + 2Cl–(aq)+ PO43–(aq)gravimetryAny method in which the signal is a massor change in mass.1400-CH08 9/9/99 2:17 PM Page 234234Modern Analytical ChemistryIf HgCl2 is added in excess, each mole of PO33– produces one mole of Hg2Cl2. Theprecipitate’s mass, therefore, provides an indirect measurement of the mass ofPO33– present in the original sample.Summarizing, we can determine an analyte gravimetrically by directly determining its mass, or the mass of a compound containing the analyte.
Alternatively,we can determine an analyte indirectly by measuring a change in mass due to itsloss, or the mass of a compound formed as the result of a reaction involving theanalyte.8A.2precipitation gravimetryA gravimetric method in which thesignal is the mass of a precipitate.electrogravimetryA gravimetric method in which thesignal is the mass of an electrodeposit onthe cathode or anode in anelectrochemical cell.volatilization gravimetryA gravimetric method in which the lossof a volatile species gives rise to thesignal.particulate gravimetryA gravimetric method in which the massof a particulate analyte is determinedfollowing its separation from its matrix.Types of Gravimetric MethodsIn the previous section we used four examples to illustrate the different ways thatmass can serve as an analytical signal.
These examples also illustrate the four gravimetric methods of analysis. When the signal is the mass of a precipitate, we call themethod precipitation gravimetry. The indirect determination of PO33– by precipitating Hg2Cl2 is a representative example, as is the direct determination of Cl– byprecipitating AgCl.In electrogravimetry the analyte is deposited as a solid film on one electrode inan electrochemical cell. The oxidation of Pb2+, and its deposition as PbO2 on a Ptanode is one example of electrogravimetry. Reduction also may be used in electrogravimetry.
The electrodeposition of Cu on a Pt cathode, for example, provides adirect analysis for Cu2+.When thermal or chemical energy is used to remove a volatile species, we callthe method volatilization gravimetry. In determining the moisture content offood, thermal energy vaporizes the H2O. The amount of carbon in an organic compound may be determined by using the chemical energy of combustion to convertC to CO2.Finally, in particulate gravimetry the analyte is determined following its removal from the sample matrix by filtration or extraction.
The determination of suspended solids is one example of particulate gravimetry.8A.3 Conservation of MassAn accurate gravimetric analysis requires that the mass of analyte present in a sample be proportional to the mass or change in mass serving as the analytical signal.For all gravimetric methods this proportionality involves a conservation of mass.For gravimetric methods involving a chemical reaction, the analyte should participate in only one set of reactions, the stoichiometry of which indicates how the precipitate’s mass relates to the analyte’s mass.
Thus, for the analysis of Pb2+ and PO33–described earlier, we can write the following conservation equationsMoles Pb2+ = moles PbO2Moles PO33– = moles Hg2Cl2Removing the analyte from its matrix by filtration or extraction must be complete.When true, the analyte’s mass can always be found from the analytical signal; thus,for the determination of suspended solids we know thatFilter’s final mass – filter’s initial mass = g suspended solidwhereas for the determination of the moisture content we haveSample’s initial mass – sample’s final mass = g H2O1400-CH08 9/9/99 2:17 PM Page 235Chapter 8 Gravimetric Methods of Analysis235Specific details, including worked examples, are found in the sections of this chaptercovering individual gravimetric methods.8A.4 Why Gravimetry Is ImportantExcept for particulate gravimetry, which is the most trivial form of gravimetry, it isentirely possible that you will never use gravimetry after you are finished with thiscourse.
Why, then, is familiarity with gravimetry still important? The answer is thatgravimetry is one of only a small number of techniques whose measurements require only base SI units, such as mass and moles, and defined constants, such asAvogadro’s number and the mass of 12C.* The result of an analysis must ultimatelybe traceable to methods, such as gravimetry, that can be related to fundamentalphysical properties.1 Most analysts never use gravimetry to validate their methods.Verifying a method by analyzing a standard reference material, however, is common.
Estimating the composition of these materials often involves a gravimetricanalysis.28B Precipitation GravimetryPrecipitation gravimetry is based on the formation of an insoluble compound following the addition of a precipitating reagent, or precipitant, to a solution of theanalyte. In most methods the precipitate is the product of a simple metathesis reaction between the analyte and precipitant; however, any reaction generating a precipitate can potentially serve as a gravimetric method. Most precipitation gravimetric methods were developed in the nineteenth century as a means for analyzing ores.Many of these methods continue to serve as standard methods of analysis.8B.1 Theory and PracticeA precipitation gravimetric analysis must have several important attributes. First,the precipitate must be of low solubility, high purity, and of known composition ifits mass is to accurately reflect the analyte’s mass.
Second, the precipitate must be ina form that is easy to separate from the reaction mixture. The theoretical and experimental details of precipitation gravimetry are reviewed in this section.Solubility Considerations An accurate precipitation gravimetric method requiresthat the precipitate’s solubility be minimal. Many total analysis techniques can routinely be performed with an accuracy of better than ±0.1%.
To obtain this level ofaccuracy, the isolated precipitate must account for at least 99.9% of the analyte. Byextending this requirement to 99.99% we ensure that accuracy is not limited by theprecipitate’s solubility.Solubility losses are minimized by carefully controlling the composition of thesolution in which the precipitate forms. This, in turn, requires an understanding ofthe relevant equilibrium reactions affecting the precipitate’s solubility. For example,Ag+ can be determined gravimetrically by adding Cl– as a precipitant, forming aprecipitate of AgCl.Ag+(aq) + Cl–(aq)t AgCl(s)8.1*Two other techniques that depend only on base SI units are coulometry and isotope-dilution mass spectrometry.Coulometry is discussed in Chapter 11.
Isotope-dilution mass spectroscopy is beyond the scope of an introductory text,however, the list of suggested readings includes a useful reference.precipitantA reagent that causes the precipitation ofa soluble species.1400-CH08 9/9/99 2:17 PM Page 236236Modern Analytical Chemistry0.00Figure 8.1Solubility of AgCl as a function of pCl. Thedashed line shows the predicted SAgCl,assuming that only reaction 8.1 andequation 8.2 affect the solubility of AgCl.The solid line is calculated using equation8.7, and includes the effect of reactions8.3–8.5.
A ladder diagram for the AgClcomplexation equilibria is superimposed onthe pCl axis.log (Solubility)–1.00–2.00–3.00–4.00–5.00–6.00Ag+ (aq)AgCl2– (aq)AgCl (aq)–7.006534210pClIf this is the only reaction considered, we would falsely conclude that the precipitate’s solubility, SAgCl, is given byS AgCl = [Ag + ] =Ksp[Cl − ]8.2and that solubility losses may be minimized by adding a large excess of Cl–. In fact,as shown in Figure 8.1, adding a large excess of Cl– eventually increases the precipitate’s solubility.To understand why AgCl shows a more complex solubility relationship thanthat suggested by equation 8.2, we must recognize that Ag+ also forms a series ofsoluble chloro-complexestK AgCl(aq)βAg+(aq) +2Cl–(aq) t AgCl2–(aq)βAg+(aq) + 3Cl–(aq) t AgCl32–(aq)1Ag+(aq) + Cl–(aq)8.328.438.5The solubility of AgCl, therefore, is the sum of the equilibrium concentrations forall soluble forms of Ag+.SAgCl = [Ag+] + [AgCl(aq)] + [AgCl2–] + [AgCl32–]8.6Substituting the equilibrium constant expressions for reactions 8.3–8.5 into equation8.6 defines the solubility of AgCl in terms of the equilibrium concentration of Cl–.S AgCl =Ksp[Cl − ]+ K1Ksp + β2 Ksp[Cl − ] + β3 Ksp[Cl − ]28.7Equation 8.7 explains the solubility curve for AgCl shown in Figure 8.1.
As Cl–is added to a solution of Ag+, the solubility of AgCl initially decreases because of reaction 8.1. Note that under these conditions, the final three terms in equation 8.7are small, and that equation 8.1 is sufficient to describe the solubility of AgCl. Increasing the concentration of chloride, however, leads to an increase in the solubility of AgCl due to the soluble chloro-complexes formed in reactions 8.3–8.5.**Also shown in Figure 8.1 is a ladder diagram for this system. Note that the increase in solubility begins when thehigher-order soluble complexes, AgCl2– and AgCl32–, become the dominant species.1400-CH08 9/9/99 2:17 PM Page 237Chapter 8 Gravimetric Methods of Analysis237pHHPO42– 12pKa3 = 12.3510HPO42–8H2PO4–6H2PO4–H3PO4pKa2 = 7.20H3PO4log(solubility)Ca3(PO4)2PO43 –14H2PO4–HPO42–2Figure 8.2pKa1 = 2.15020(a)PO43–44681012pH(b)Clearly the equilibrium concentration of chloride is an important parameter if theconcentration of silver is to be determined gravimetrically by precipitating AgCl.
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