Modern Analytical Cheymistry - Chapter 8

Chapter 8 Gravimetric Methods of Analysis Gravimetry encompasses all techniques in which we measure mass or a change in mass. When you step on a scale after exercising you are making, in a sense, a gravimetric determination of your mass. Measuring mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably the oldest analytical technique. 232 Chapter 8 Gravimetric Methods of Analysis 233 8A Overview of Gravimetry Before we look more closely at specific gravimetric methods and their applications, let’s take a moment to develop a broad survey of gravimetry. Later, as you read through the sections of this chapter discussing different gravimetric methods, this survey will help you focus on their similarities. It is usually easier to understand a new method of analysis when you can see its relationship to other similar methods. gravimetry Any method in which the signal is a mass or change in mass. 8A.1 Using Mass as a Signal At the beginning of this chapter we indicated that in gravimetry we measure mass or a change in mass. This suggests that there are at least two ways to use mass as an analytical signal. We can, of course, measure an analyte’s mass directly by placing it on a balance and recording its mass. For example, suppose you are to determine the total suspended solids in water released from a sewage-treatment facility. Sus-pended solids are just that; solid matter that has yet to settle out of its solution ma-trix. The analysis is easy. You collect a sample and pass it through a preweighed fil-ter that retains the suspended solids. After drying to remove any residual moisture, you weigh the filter. The difference between the filter’s original mass and final mass gives the mass of suspended solids. We call this a direct analysis because the analyte itself is the object being weighed. What if the analyte is an aqueous ion, such as Pb2+? In this case we cannot iso-late the analyte by filtration because the Pb2+ is dissolved in the solution’s matrix. We can still measure the analyte’s mass, however, by chemically converting it to a solid form. If we suspend a pair of Pt electrodes in our solution and apply a suffi-ciently positive potential between them for a long enough time, we can force the reaction Pb2+(aq) + 4H2O(l) tPbO2(s) + H2(g) + 2H3O+(aq) to go to completion. The Pb2+ ion in solution oxidizes to PbO2 and deposits on the Pt electrode serving as the anode. If we weigh the Pt anode before and after applying the potential, the difference in the two measurements gives the mass of PbO2 and, from the reaction’s stoichiometry, the mass of Pb2+. This also is a direct analysis be-cause the material being weighed contains the analyte. Sometimes it is easier to remove the analyte and use a change in mass as the analytical signal. Imagine how you would determine a food’s moisture content by a direct analysis. One possibility is to heat a sample of the food to a temperature at which the water in the sample vaporizes. If we capture the vapor in a preweighed absorbent trap, then the change in the absorbent’s mass provides a di-rect 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 change in its mass as an indication of the amount of water originally present. We call this an indirect analysis since we determine the analyte by a signal representing its disappearance. 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 measured after removing the water. We can also determine an analyte indirectly without its ever being weighed. Again, as with the determination of Pb2+ as PbO2(s), we take advantage 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) tHg2Cl2(s) + 2H3O+(aq) + 2Cl–(aq)+ PO43–(aq) 234 Modern Analytical Chemistry If HgCl2 is added in excess, each mole of PO33– produces one mole of Hg2Cl2. The precipitate’s mass, therefore, provides an indirect measurement of the mass of PO33– present in the original sample. Summarizing, we can determine an analyte gravimetrically by directly deter-mining 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 its loss, or the mass of a compound formed as the result of a reaction involving the analyte. precipitation gravimetry A gravimetric method in which the signal is the mass of a precipitate. electrogravimetry A gravimetric method in which the signal is the mass of an electrodeposit on the cathode or anode in an electrochemical cell. volatilization gravimetry A gravimetric method in which the loss of a volatile species gives rise to the signal. particulate gravimetry A gravimetric method in which the mass of a particulate analyte is determined following its separation from its matrix. 8A.2 Types of Gravimetric Methods In the previous section we used four examples to illustrate the different ways that mass can serve as an analytical signal. These examples also illustrate the four gravi-metric methods of analysis. When the signal is the mass of a precipitate, we call the method precipitation gravimetry. The indirect determination of PO33– by precipi-tating Hg2Cl2 is a representative example, as is the direct determination of Cl– by precipitating AgCl. In electrogravimetry the analyte is deposited as a solid film on one electrode in an electrochemical cell. The oxidation of Pb2+, and its deposition as PbO2 on a Pt anode is one example of electrogravimetry. Reduction also may be used in electro-gravimetry. The electrodeposition of Cu on a Pt cathode, for example, provides a direct analysis for Cu2+. When thermal or chemical energy is used to remove a volatile species, we call the method volatilization gravimetry. In determining the moisture content of food, thermal energy vaporizes the H2O. The amount of carbon in an organic com-pound may be determined by using the chemical energy of combustion to convert C to CO2. Finally, in particulate gravimetry the analyte is determined following its re-moval from the sample matrix by filtration or extraction. The determination of sus-pended solids is one example of particulate gravimetry. 8A.3 Conservation of Mass An accurate gravimetric analysis requires that the mass of analyte present in a sam-ple 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 partici- pate in only one set of reactions, the stoichiometry of which indicates how the pre-cipitate’s mass relates to the analyte’s mass. Thus, for the analysis of Pb2+ and PO33– described earlier, we can write the following conservation equations Moles Pb2+ = moles PbO2 Moles PO33– = moles Hg2Cl2 Removing 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 that Filter’s final mass – filter’s initial mass = g suspended solid whereas for the determination of the moisture content we have Sample’s initial mass – sample’s final mass = g H2O Chapter 8 Gravimetric Methods of Analysis 235 Specific details, including worked examples, are found in the sections of this chapter covering individual gravimetric methods. 8A.4 Why Gravimetry Is Important Except for particulate gravimetry, which is the most trivial form of gravimetry, it is entirely possible that you will never use gravimetry after you are finished with this course. Why, then, is familiarity with gravimetry still important? The answer is that gravimetry is one of only a small number of techniques whose measurements re- quire only base SI units, such as mass and moles, and defined constants, such as Avogadro’s number and the mass of 12C.* The result of an analysis must ultimately be traceable to methods, such as gravimetry, that can be related to fundamental physical properties.1 Most analysts never use gravimetry to validate their methods. Verifying a method by analyzing a standard reference material, however, is com-mon. Estimating the composition of these materials often involves a gravimetric analysis.2 8B Precipitation Gravimetry Precipitation gravimetry is based on the formation of an insoluble compound fol-lowing the addition of a precipitating reagent, or precipitant, to a solution of the analyte. In most methods the precipitate is the product of a simple metathesis reac-tion between the analyte and precipitant; however, any reaction generating a pre-cipitate can potentially serve as a gravimetric method. Most precipitation gravimet-ric 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. precipitant A reagent that causes the precipitation of a soluble species. 8B.1 Theory and Practice A precipitation gravimetric analysis must have several important attributes. First, the precipitate must be of low solubility, high purity, and of known composition if its mass is to accurately reflect the analyte’s mass. Second, the precipitate must be in a form that is easy to separate from the reaction mixture. The theoretical and exper-imental details of precipitation gravimetry are reviewed in this section. Solubility Considerations An accurate precipitation gravimetric method requires that the precipitate’s solubility be minimal. Many total analysis techniques can rou-tinely be performed with an accuracy of better than ±0.1%. To obtain this level of accuracy, the isolated precipitate must account for at least 99.9% of the analyte. By extending this requirement to 99.99% we ensure that accuracy is not limited by the precipitate’s solubility. Solubility losses are minimized by carefully controlling the composition of the solution in which the precipitate forms. This, in turn, requires an understanding of the relevant equilibrium reactions affecting the precipitate’s solubility. For example, Ag+ can be determined gravimetrically by adding Cl– as a precipitant, forming a precipitate of AgCl. Ag+(aq) + Cl–(aq) tAgCl(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. 236 Modern Analytical Chemistry 0.00 –1.00 –2.00 Figure 8.1 Solubility of AgCl as a function of pCl. The dashed line shows the predicted SAgCl, assuming that only reaction 8.1 and equation 8.2 affect the solubility of AgCl. The solid line is calculated using equation 8.7, and includes the effect of reactions 8.3–8.5. A ladder diagram for the AgCl complexation equilibria is superimposed on the pCl axis. –3.00 –4.00 –5.00 –6.00 Ag+ (aq) –7.00 6 5 AgCl (aq) AgCl2– (aq) 4 3 2 1 0 pCl If this is the only reaction considered, we would falsely conclude that the precipi-tate’s solubility, SAgCl, is given by SAgCl = [Ag+] = [Clp] 8.2 and 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 precipi-tate’s solubility. To understand why AgCl shows a more complex solubility relationship than that suggested by equation 8.2, we must recognize that Ag+ also forms a series of soluble chloro-complexes Ag+(aq) + Cl–(aq) K1 AgCl(aq) 8.3 Ag+(aq) +2Cl–(aq) b2 AgCl2–(aq) 8.4 Ag+(aq) + 3Cl–(aq) b3 AgCl32–(aq) 8.5 The solubility of AgCl, therefore, is the sum of the equilibrium concentrations for all soluble forms of Ag+. SAgCl = [Ag+] + [AgCl(aq)] + [AgCl2–] + [AgCl32–] 8.6 Substituting the equilibrium constant expressions for reactions 8.3–8.5 into equation 8.6 defines the solubility of AgCl in terms of the equilibrium concentration of Cl–. SAgCl = [Clp] + K1Ksp + b2Ksp[Cl ] + b3Ksp[Cl ] 8.7 Equation 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 re-action 8.1. Note that under these conditions, the final three terms in equation 8.7 are small, and that equation 8.1 is sufficient to describe the solubility of AgCl. In-creasing the concentration of chloride, however, leads to an increase in the solubil-ity 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 the higher-order soluble complexes, AgCl2– and AgCl32–, become the dominant species. ... - tailieumienphi.vn