Modern Analytical Cheymistry - Chapter 8 pot

232 CChhaapptteerr 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. 1400-CH08 9/9/99 2:17 PM Page 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. 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 Pb 2+ ? In this case we cannot iso- late the analyte by filtration because the Pb 2+ 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 Pb 2+ (aq)+4H 2 O(l) t PbO 2 (s)+H 2 (g)+2H 3 O + (aq) to go to completion. The Pb 2+ ion in solution oxidizes to PbO 2 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 PbO 2 and, from the reaction’s stoichiometry, the mass of Pb 2+ . 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 Pb 2+ as PbO 2 (s), we take advantage of the analyte’s chemistry. For example, phosphite, PO 3 3– , reduces Hg 2+ to Hg 2 2+ . In the presence of Cl – a solid precipitate of Hg 2 Cl 2 forms. 2HgCl 2 (aq)+PO 3 3– (aq)+3H 2 O(l) t Hg 2 Cl 2 (s)+2H 3 O + (aq) + 2Cl – (aq)+ PO 4 3– (aq) gravimetry Any method in which the signal is a mass or change in mass. 1400-CH08 9/9/99 2:17 PM Page 233 If HgCl 2 is added in excess, each mole of PO 3 3– produces one mole of Hg 2 Cl 2 . The precipitate’s mass, therefore, provides an indirect measurement of the mass of PO 3 3– 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. 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 PO 3 3– by precipi- tating Hg 2 Cl 2 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 Pb 2+ , and its deposition as PbO 2 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 Cu 2+ . 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 H 2 O. The amount of carbon in an organic com- pound may be determined by using the chemical energy of combustion to convert C to CO 2 . 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 Pb 2+ and PO 3 3– described earlier, we can write the following conservation equations Moles Pb 2+ = moles PbO 2 Moles PO 3 3– = moles Hg 2 Cl 2 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 H 2 O 234 Modern Analytical Chemistry 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. 1400-CH08 9/9/99 2:17 PM Page 234 Chapter 8 Gravimetric Methods of Analysis 235 precipitant A reagent that causes the precipitation of a soluble species. 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 12 C.* 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. 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) 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. 1400-CH08 9/9/99 2:17 PM Page 235 Figure 8.1 Solubility of AgCl as a function of pCl. The dashed line shows the predicted S AgCl , 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. If this is the only reaction considered, we would falsely conclude that the precipi- tate’s solubility, S AgCl , is given by 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) t K 1 AgCl(aq) 8.3 Ag + (aq) +2Cl – (aq) t β 2 AgCl 2 – (aq) 8.4 Ag + (aq) + 3Cl – (aq) t β 3 AgCl 3 2– (aq) 8.5 The solubility of AgCl, therefore, is the sum of the equilibrium concentrations for all soluble forms of Ag + . S AgCl = [Ag + ] + [AgCl(aq)] + [AgCl 2 – ] + [AgCl 3 2– ] 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 – . 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.* S K KK K K AgCl sp sp sp sp Cl Cl Cl=+ + + − −− [] [] [] 12 3 2 ββ S K AgCl + sp Ag Cl == − [] [] 236 Modern Analytical Chemistry 654 –7.00 –6.00 –5.00 –4.00 –3.00 –2.00 –1.00 0.00 3 pCl log (Solubility) 210 Ag + ( aq ) AgCl ( aq ) AgCl 2 – ( aq ) *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, AgCl 2 – and AgCl 3 2– , become the dominant species. 1400-CH08 9/9/99 2:17 PM Page 236 Chapter 8 Gravimetric Methods of Analysis 237 Figure 8.2 (a) Ladder diagram for phosphate; (b) Solubility diagram for Ca 3 (PO 4 ) 2 showing the predominate form of phosphate for each segment of the solubility curve. Clearly the equilibrium concentration of chloride is an important parameter if the concentration of silver is to be determined gravimetrically by precipitating AgCl. In particular, a large excess of chloride must be avoided. Another important parameter that may affect a precipitate’s solubility is the pH of the solution in which the precipitate forms. For example, hydroxide precipitates, such as Fe(OH) 3 , are more soluble at lower pH levels at which the concentration of OH – is small. The effect of pH on solubility is not limited to hydroxide precipitates, but also affects precipitates containing basic or acidic ions. The solubility of Ca 3 (PO 4 ) 2 is pH-dependent because phosphate is a weak base. The following four reactions, therefore, govern the solubility of Ca 3 (PO 4 ) 2 . Ca 3 (PO 4 ) 2 (s) t K sp 3Ca 2+ (aq) + 2PO 4 3– (aq) 8.8 PO 4 3– (aq)+H 2 O(l) t K b1 HPO 4 2– (aq)+OH – (aq) 8.9 HPO 4 2– (aq)+H 2 O(l) t K b2 H 2 PO 4 – (aq)+OH – (aq) 8.10 H 2 PO 4 – (aq)+H 2 O(l) t K b3 H 3 PO 4 (aq)+OH – (aq) 8.11 Depending on the solution’s pH, the predominate phosphate species is either PO 4 3– , HPO 4 2– , H 2 PO 4 – , or H 3 PO 4 . The ladder diagram for phosphate, shown in Figure 8.2a, provides a convenient way to evaluate the pH-dependent solubility of phos- phate precipitates. When the pH is greater than 12.4, the predominate phosphate species is PO 4 3– , and the solubility of Ca 3 (PO 4 ) 2 will be at its minimum because only reaction 8.8 occurs to an appreciable extent (see Figure 8.2b). As the solution becomes more acidic, the solubility of Ca 3 (PO 4 ) 2 increases due to the contributions of reactions 8.9–8.11. Solubility can often be decreased by using a nonaqueous solvent. A precip- itate’s solubility is generally greater in aqueous solutions because of the ability of water molecules to stabilize ions through solvation. The poorer solvating ability of nonaqueous solvents, even those that are polar, leads to a smaller solu- bility product. For example, PbSO 4 has a K sp of 1.6 × 10 –8 in H 2 O, whereas in a 50:50 mixture of H 2 O/ethanol the K sp at 2.6 × 10 –12 is four orders of magnitude smaller. pH H 3 PO 4 H 2 PO 4 – H 2 PO 4 – HPO 4 2– HPO 4 2– p K a3 = 12.35 p K a2 = 7.20 p K a1 = 2.15 PO 4 3– 14 12 10 8 6 4 2 0 246 pH 8 1012140 H 3 PO 4 H 2 PO 4 – log(solubility) Ca 3 (PO 4 ) 2 HPO 4 2– PO 4 3– (a) (b) 1400-CH08 9/9/99 2:17 PM Page 237 Figure 8.3 Schematic model of AgCl showing difference between bulk and surface atoms of silver. Silver and chloride ions are not shown to scale. Avoiding Impurities Precipitation gravimetry is based on a known stoichiometry between the analyte’s mass and the mass of a precipitate. It follows, therefore, that the precipitate must be free from impurities. Since precipitation typically occurs in a solution rich in dissolved solids, the initial precipitate is often impure. Any impu- rities present in the precipitate’s matrix must be removed before obtaining its weight. The greatest source of impurities results from chemical and physical interac- tions occurring at the precipitate’s surface. A precipitate is generally crystalline, even if only on a microscopic scale, with a well-defined lattice structure of cations and anions. Those cations and anions at the surface of the precipitate carry, respec- tively, a positive or a negative charge as a result of their incomplete coordination spheres. In a precipitate of AgCl, for example, each Ag + ion in the bulk of the pre- cipitate is bound to six Cl – ions. Silver ions at the surface, however, are bound to no more than five Cl – ions, and carry a partial positive charge (Figure 8.3). Precipitate particles grow in size because of the electrostatic attraction between charged ions on the surface of the precipitate and oppositely charged ions in solu- tion. Ions common to the precipitate are chemically adsorbed, extending the crystal lattice. Other ions may be physically adsorbed and, unless displaced, are incorpo- rated into the crystal lattice as a coprecipitated impurity. Physically adsorbed ions are less strongly attracted to the surface and can be displaced by chemically ad- sorbed ions. One common type of impurity is an inclusion. Potential interfering ions whose size and charge are similar to a lattice ion may substitute into the lattice structure by chemical adsorption, provided that the interferent precipitates with the same crystal structure (Figure 8.4a). The probability of forming an inclusion is greatest when the interfering ion is present at substantially higher concentrations than the dissolved lattice ion. The presence of an inclusion does not decrease the amount of analyte that precipitates, provided that the precipitant is added in sufficient excess. Thus, the precipitate’s mass is always larger than expected. Inclusions are difficult to remove since the included material is chemically part of the crystal lattice. The only way to remove included material is through reprecip- itation. After isolating the precipitate from the supernatant solution, it is dissolved 238 Modern Analytical Chemistry Cl – Ag + Bulk silver ion surrounded by 6 chloride ions Surface silver ion surrounded by 4 chloride ions inclusion A coprecipitated impurity in which the interfering ion occupies a lattice site in the precipitate. 1400-CH08 9/9/99 2:17 PM Page 238 in a small portion of a suitable solvent at an elevated temperature. The solution is then cooled to re-form the precipitate. Since the concentration ratio of interferent to analyte is lower in the new solution than in the original supernatant solution, the mass percent of included material in the precipitate decreases. This process of re- precipitation is repeated as needed to completely remove the inclusion. Potential solubility losses of the analyte, however, cannot be ignored. Thus, reprecipitation requires a precipitate of low solubility, and a solvent for which there is a significant difference in the precipitate’s solubility as a function of temperature. Occlusions, which are a second type of coprecipitated impurity, occur when physically adsorbed interfering ions become trapped within the growing precipitate. Occlusions form in two ways. The most common mechanism occurs when physically adsorbed ions are surrounded by additional precipitate before they can be desorbed or displaced (see Figure 8.4a). In this case the precipitate’s mass is always greater than expected. Occlusions also form when rapid precipitation traps a pocket of solution within the growing precipitate (Figure 8.4b). Since the trapped solution contains dis- solved solids, the precipitate’s mass normally increases. The mass of the precipitate may be less than expected, however, if the occluded material consists primarily of the analyte in a lower-molecular-weight form from that of the precipitate. Occlusions are minimized by maintaining the precipitate in equilibrium with its supernatant solution for an extended time. This process is called digestion and may be carried out at room temperature or at an elevated temperature. During di- gestion, the dynamic nature of the solubility–precipitation equilibrium, in which the precipitate dissolves and re-forms, ensures that occluded material is eventually exposed to the supernatant solution. Since the rate of dissolution and reprecipita- tion are slow, the chance of forming new occlusions is minimal. After precipitation is complete the surface continues to attract ions from solu- tion (Figure 8.4c). These surface adsorbates, which may be chemically or physically adsorbed, constitute a third type of coprecipitated impurity. Surface adsorption is minimized by decreasing the precipitate’s available surface area. One benefit of di- gestion is that it also increases the average size of precipitate particles. This is not surprising since the probability that a particle will dissolve is inversely proportional to its size. During digestion larger particles of precipitate increase in size at the ex- pense of smaller particles. One consequence of forming fewer particles of larger size is an overall decrease in the precipitate’s surface area. Surface adsorbates also may be removed by washing the precipitate. Potential solubility losses, however, cannot be ignored. Inclusions, occlusions, and surface adsorbates are called coprecipitates because they represent soluble species that are brought into solid form along with the de- sired precipitate. Another source of impurities occurs when other species in solu- tion precipitate under the conditions of the analysis. Solution conditions necessary to minimize the solubility of a desired precipitate may lead to the formation of an additional precipitate that interferes in the analysis. For example, the precipitation of nickel dimethylgloxime requires a pH that is slightly basic. Under these condi- tions, however, any Fe 3+ that might be present precipitates as Fe(OH) 3 . Finally, since most precipitants are not selective toward a single analyte, there is always a risk that the precipitant will react, sequentially, with more than one species. The formation of these additional precipitates can usually be minimized by carefully controlling solution conditions. Interferents forming precipitates that are less soluble than the analyte may be precipitated and removed by filtration, leaving the analyte behind in solution. Alternatively, either the analyte or the interferent can be masked using a suitable complexing agent, preventing its precipitation. Chapter 8 Gravimetric Methods of Analysis 239 Figure 8.4 Example of coprecipitation: (a) schematic of a chemically adsorbed inclusion or a physically adsorbed occlusion in a crystal lattice, where C and A represent the cation–anion pair comprising the analyte and the precipitant, and is the impurity; (b) schematic of an occlusion by entrapment of supernatant solution; (c) surface adsorption of excess C. CACACACACACACACACACA ACACACACACACACACACAC CACACACAMACACACACACA ACACACACACACAMACACAC CACACACACACACACACACA AMACACACACACACACACAC CACACACACACACACACACA (a) CACACACACACACACACACA ACACACACACACACACACAC CACACACACACACACACACA ACACACACACACACACACAC CACACACACACACACACACA ACACACACACACACACACAC CACACACACACACACACACA (b) CA ACC CC C C CACACACAC C C ACACACACACACAC CACACACACACACACACACAC (c) occlusion A coprecipitated impurity trapped within a precipitate as it forms. digestion The process by which a precipitate is given time to form larger, purer particles. adsorbate A coprecipitated impurity that adsorbs to the surface of a precipitate. M 1400-CH08 9/9/99 2:17 PM Page 239 Both of the above-mentioned approaches are illustrated in Fresenius’s analyti- cal method for determining Ni and Co in ores containing Pb 2+ , Cu 2+ , and Fe 3+ as potential interfering ions (see Figure 1.1 in Chapter 1). The ore is dissolved in a so- lution containing H 2 SO 4 , selectively precipitating Pb 2+ as PbSO 4 . After filtering, the supernatant solution is treated with H 2 S. Because the solution is strongly acidic, however, only CuS precipitates. After removing the CuS by filtration, the solution is made basic with ammonia until Fe(OH) 3 precipitates. Cobalt and nickel, which form soluble amine complexes, remain in solution. In some situations the rate at which a precipitate forms can be used to separate an analyte from a potential interferent. For example, due to similarities in their chemistry, a gravimetric analysis for Ca 2+ may be adversely affected by the presence of Mg 2+ . Precipitates of Ca(OH) 2 , however, form more rapidly than precipitates of Mg(OH) 2 . If Ca(OH) 2 is filtered before Mg(OH) 2 begins to precipitate, then a quantitative analysis for Ca 2+ is feasible. Finally, in some cases it is easier to isolate and weigh both the analyte and the interferent. After recording its weight, the mixed precipitate is treated to convert at least one of the two precipitates to a new chemical form. This new mixed precipitate is also isolated and weighed. For example, a mixture containing Ca 2+ and Mg 2+ can be analyzed for both cations by first isolating a mixed precipitate of CaCO 3 and MgCO 3 . After weighing, the mixed precipitate is heated, converting it to a mixture of CaO and MgO. Thus Grams of mixed precipitate 1 = grams CaCO 3 + grams MgCO 3 Grams of mixed precipitate 2 = grams CaO + grams MgO Although these equations contain four unknowns (grams CaCO 3 , grams MgCO 3 , grams CaO, and grams MgO), the stoichiometric relationships between CaCO 3 and CaO Moles CaCO 3 = moles CaO and between MgCO 3 and MgO Moles MgCO 3 = moles MgO provide enough additional information to determine the amounts of both Ca 2+ and Mg 2+ in the sample.* Controlling Particle Size Following precipitation and digestion, the precipitate must be separated from the supernatant solution and freed of any remaining impu- rities, including residual solvent. These tasks are accomplished by filtering, rinsing, and drying the precipitate. The size of the precipitate’s particles determines the ease and success of filtration. Smaller, colloidal particles are difficult to filter because they may readily pass through the pores of the filtering device. Large, crystalline particles, however, are easily filtered. By carefully controlling the precipitation reaction we can significantly increase a precipitate’s average particle size. Precipitation consists of two distinct events: nu- cleation, or the initial formation of smaller stable particles of precipitate, and the subsequent growth of these particles. Larger particles form when the rate of particle growth exceeds the rate of nucleation. 240 Modern Analytical Chemistry *Example 8.2 shows how to solve this type of problem. 1400-CH08 9/9/99 2:17 PM Page 240 Chapter 8 Gravimetric Methods of Analysis 241 A solute’s relative supersaturation, RSS, can be expressed as 8.12 where Q is the solute’s actual concentration, S is the solute’s expected concentra- tion at equilibrium, and Q – S is a measure of the solute’s supersaturation when precipitation begins. 3 A large, positive value of RSS indicates that a solution is highly supersaturated. Such solutions are unstable and show high rates of nucle- ation, producing a precipitate consisting of numerous small particles. When RSS is small, precipitation is more likely to occur by particle growth than by nucleation. Examining equation 8.12 shows that we can minimize RSS by either decreasing the solute’s concentration or increasing the precipitate’s solubility. A precipitate’s solubility usually increases at higher temperatures, and adjusting pH may affect a precipitate’s solubility if it contains an acidic or basic anion. Temperature and pH, therefore, are useful ways to increase the value of S. Conducting the precipitation in a dilute solution of analyte, or adding the precipitant slowly and with vigorous stir- ring are ways to decrease the value of Q. There are, however, practical limitations to minimizing RSS. Precipitates that are extremely insoluble, such as Fe(OH) 3 and PbS, have such small solubilities that a large RSS cannot be avoided. Such solutes inevitably form small particles. In addi- tion, conditions that yield a small RSS may lead to a relatively stable supersaturated solution that requires a long time to fully precipitate. For example, almost a month is required to form a visible precipitate of BaSO 4 under conditions in which the ini- tial RSS is 5. 4 An increase in the time required to form a visible precipitate under conditions of low RSS is a consequence of both a slow rate of nucleation and a steady decrease in RSS as the precipitate forms. One solution to the latter problem is to chemically generate the precipitant in solution as the product of a slow chemical reaction. This maintains the RSS at an effectively constant level. The precipitate initially forms under conditions of low RSS, leading to the nucleation of a limited number of parti- cles. As additional precipitant is created, nucleation is eventually superseded by par- ticle growth. This process is called homogeneous precipitation. 5 Two general methods are used for homogeneous precipitation. If the precipi- tate’s solubility is pH-dependent, then the analyte and precipitant can be mixed under conditions in which precipitation does not occur. The pH is then raised or lowered as needed by chemically generating OH – or H 3 O + . For example, the hydrol- ysis of urea can be used as a source of OH – . CO(NH 2 ) 2 (aq)+H 2 O(l) t CO 2 (g) + 2NH 3 (aq) NH 3 (aq)+H 2 O(l) t NH 4 + (aq)+OH – (aq) The hydrolysis of urea is strongly temperature-dependent, with the rate being negli- gible at room temperature. The rate of hydrolysis, and thus the rate of precipitate formation, can be controlled by adjusting the solution’s temperature. Precipitates of BaCrO 4 , for example, have been produced in this manner. In the second method of homogeneous precipitation, the precipitant itself is generated by a chemical reaction. For example, Ba 2+ can be homogeneously precipi- tated as BaSO 4 by hydrolyzing sulphamic acid to produce SO 4 2– . NH 2 SO 3 H(aq)+2H 2 O(l) t NH 4 + (aq)+H 3 O + (aq)+SO 4 2– (aq) RSS QS S = − relative supersaturation A measure of the extent to which a solution, or a localized region of solution, contains more dissolved solute than that expected at equilibrium (RSS). homogeneous precipitation A precipitation in which the precipitant is generated in situ by a chemical reaction. Color Plate 5 shows the difference between a precipitate formed by direct precipitation and a precipitate formed by a homogeneous precipitation. 1400-CH08 9/9/99 2:17 PM Page 241 [...]... Co2+ NO 1-nitroso-2-naphthol OH K+ sodium tetraphenylborate NO3– nitron Na[B(C6H5)4] NC6H5 –N N C6H5 N+ C6H5 1400-CH 08 9/9/99 2: 18 PM Page 250 250 Modern Analytical Chemistry Table 8. 5 Selected Gravimetric Methods for the Analysis of Organic Functional Groups and Heteroatoms Based on Precipitation Analyte Treatment Precipitant Precipitate Organic halides R-X X = Cl, Br, I Organic Halides R-X X = Cl,... AgCl, the determination of SO42– as BaSO4, and the determination of Ca2+ as CaC2O4 H2O ⋅ 1400-CH 08 9/9/99 2: 18 PM Page 267 Chapter 8 Gravimetric Methods of Analysis 267 8H PROBLEMS 1 Starting with the equilibrium constant expressions for reactions 8. 1, and 8. 3 8. 5, verify that equation 8. 7 is correct 2 Equation 8. 7 shows how the solubility of AgCl varies as a function of the equilibrium concentration... × 1.0 08 g/mol × 1000 mg/g = FW H2O 18. 015 g/mol = 1.533 mg H mg H 1.533 mg × 100 = × 100 = 1.51% w/w H mg sample 101.3 mg 1400-CH 08 9/9/99 2: 18 PM Page 261 Chapter 8 Gravimetric Methods of Analysis and for chlorine Moles Cl = moles AgCl g AgCl × AW Cl × 1000 mg/g 0.2627 g × 35.453 g/mol × 1000 mg/g = FW AgCl 143.32 g/mol = 64. 98 mg Cl mg Cl 64. 98 mg × 100 = × 100 = 53.35% w/w Cl mg sample 121 .8 mg Adding... appropriate units, of the amount of analyte to the amount of sample 1400-CH 08 9/9/99 2: 18 PM Page 265 Chapter 8 Gravimetric Methods of Analysis EXAMPLE 8. 8 A 200.0-mL sample of water was filtered through a preweighed glass fiber filter After drying to constant weight at 105 °C, the filter was found to have increased in mass by 48. 2 mg Determine the total suspended solids for the sample in parts per... hydroxide, oxalate, sulfate, sulfide, and phosphate A summary of selected methods, grouped by precipitant, is shown in Table 8. 1 Many inorganic anions can be determined using the same reactions by reversing the analyte 247 1400-CH 08 9/9/99 2: 18 PM Page 2 48 2 48 Modern Analytical Chemistry Table 8. 1 Selected Gravimetric Method for Inorganic Cations Based on Precipitation Analyte Precipitant Precipitate Formed... calculated using the known combined mass of the two original precipitates 7 .81 54 g – g Mg(C9H6NO)2 = 7 .81 54 g – 7.5125 g = 0.3029 g Al(C9H6NO)3 Using the conservation of Mg and Al, the %w/w Mg and %w/w Al in the sample can now be determined as in Example 8. 1, where AW is an atomic weight 1400-CH 08 9/9/99 2: 18 PM Page 253 Chapter 8 Gravimetric Methods of Analysis Moles Mg = moles Mg(C9H6NO)2 Moles Al =... sample contained 0.1414 g – 0.0 183 g = 0.1231 g SiO2 The %w/w SiO2, therefore, is 0.1231 g g SiO2 × 100 = × 100 = 24.61% w/w SiO2 0.5003 g g sample Finally, in some quantitative applications it is necessary to compare the result for a sample with a similar result obtained using a standard 261 1400-CH 08 9/9/99 2: 18 PM Page 262 262 Modern Analytical Chemistry EXAMPLE 8. 7 A 26.23-mg sample of MgC2O4 • H2O... briefly considered 1400-CH 08 9/9/99 2: 18 PM Page 263 Chapter 8 Gravimetric Methods of Analysis 263 8D.1 Theory and Practice Two approaches have been used to separate the analyte from its matrix in particulate gravimetry The most common approach is filtration, in which solid particulates are separated from their gas, liquid, or solid matrix A second approach uses a liquid-phase or solid-phase extraction... outlined in Tables 8. 1, 8. 2, 8. 4, and 8. 5 Since this does not require quantitative measurements, the analytical signal is simply the observation that a precipitate has formed Although qualitative applications of precipitation gravimetry have been largely replaced by spectroscopic methods of analysis, they continue to find application in spot testing for the presence of specific analytes .8 8B.4 Evaluating... indirect method for the determination of Si in ores and alloys by formation of volatile SiF4 provides an instructive example of a typical procedure 257 1400-CH 08 9/9/99 2: 18 PM Page 2 58 Modern Analytical Chemistry Representative Methods 2 58 Method 8. 2 Determination of Si in Ores and Alloys9 Description of Method Silicon is determined by dissolving the sample in acid Dehydration of the resulting solution . fundamental of all analytical measurements, and gravimetry is unquestionably the oldest analytical technique. 1400-CH 08 9/9/99 2:17 PM Page 232 Chapter 8 Gravimetric Methods of Analysis 233 8A Overview. exceeds the rate of nucleation. 240 Modern Analytical Chemistry *Example 8. 2 shows how to solve this type of problem. 1400-CH 08 9/9/99 2:17 PM Page 240 Chapter 8 Gravimetric Methods of Analysis 241 A. AgCl SCN – SO 2 /CuSO 4 CuSCN CuSCN SO 4 2– BaCl 2 BaSO 4 BaSO 4 1400-CH 08 9/9/99 2: 18 PM Page 2 48 Chapter 8 Gravimetric Methods of Analysis 249 Table 8. 3 Reactions for the Homogeneous Preparation of Selected Inorganic