A Guide to Using This Text .. in Chapter Representative Methods Annotated methods of typical analytical procedures link theory with when the isolated solid is Do practice. The format encourages students to think about the design of the procedure and why it works. precipitating MgNH, PO, 6H,O and isolating Ms P, O, provides a Margin Notes Margin Determination of Mga in Water and t note to colorplates located t the middle of the book fltering, the precipitate is converted to Maj P O,and weighed r case, the calibration curve provides for relating Sung to EXAMLE5.3 Celar plah Ithow时 =(0396pb-)xCs+0.03 出的,贴钟m of Pb* in the sample of bood, we replace 1.33 Ppb nation results from uncertainty in measuring the signal for 把 e many peace Nbzedgben Examples of Typical Problems Each example problem includes a eireann detailed solution that helps students in complication of matching the matrix of the standards to that of the sample applying the chapter's material to practical problems. whc1 da secoed identical aliquot of sam中 Bold-faced Key Terms with Margin Definitions Key words appear in boldface when they are introduced within the text The term and its definition appear in the margin for quick review by the student. All key words are also defined in the glossarx Modern Analytical Chemistry A Guide to Using This Text . . . in Chapter Representative Methods Annotated methods of typical analytical procedures link theory with practice. The format encourages students to think about the design of the procedure and why it works. 246 Modern Analytical Chemistry Representative Methods An additional problem is encountered when the isolated solid is non￾stoichiometric. For example, precipitating Mn2+ as Mn(OH)2, followed by heating to 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 results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice de￾fects in the crystal structure.6 Representative Method The best way to appreciate the importance of the theoreti￾cal and practical details discussed in the previous section is to carefully examine the procedure for a typical precipitation gravimetric method. Although each method has its own unique considerations, the determination of Mg2+ in water and waste￾water by precipitating MgNH4PO4 ⋅ 6H2O and isolating Mg2P2O7 provides an in￾structive example of a typical procedure. Method 8.1 Determination of Mg2+ in Water and Wastewater7 Description of Method. Magnesium is precipitated as MgNH4PO4 ⋅ 6H2O using (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 soluble in the presence of dilute ammonia (0.0003 g/100 mL in 0.6 M NH3). The precipitant is not very selective, so a preliminary separation of Mg2+ from potential interferents is necessary. Calcium, which is the most significant interferent, is usually removed by its prior precipitation as the oxalate. The presence of excess ammonium salts from the precipitant or the addition of too much ammonia can lead to the formation of Mg(NH4)4(PO4)2, which is subsequently isolated as Mg(PO3)2 after drying. The precipitate is isolated by filtration using a rinse solution of dilute ammonia. After filtering, the precipitate is converted to Mg2P2O7 and weighed. Procedure. Transfer a sample containing no more than 60 mg of Mg2+ into a 600-mL beaker. Add 2–3 drops of methyl red indicator, and, if necessary, adjust the volume 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 constantly stirring, until the methyl red indicator turns yellow (pH > 6.3). After stirring for 5 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 the precipitate by filtration, rinsing with 5% v/v NH3. Dissolve the precipitate in 50 mL of 10% v/v HCl, and precipitate a second time following the same procedure. After filtering, carefully remove the filter paper by charring. Heat the precipitate at 500 °C until the residue is white, and then bring the precipitate to constant weight at 1100 °C. Questions 1. Why does the procedure call for a sample containing no more than 60 mg of q y There is a serious limitation, however, to an external standardization. The relationship between Sstand and CS in equation 5.3 is determined when the ana￾lyte is present in the external standard’s matrix. In using an external standardiza￾tion, we assume that any difference between the matrix of the standards and the sample’s matrix has no effect on the value of k. A proportional determinate error is introduced when differences between the two matrices cannot be ignored. This is shown in Figure 5.4, where the relationship between the signal and the amount of analyte is shown for both the sample’s matrix and the standard’s matrix. In this example, using a normal calibration curve results in a negative determinate error. When matrix problems are expected, an effort is made to match the matrix of the standards to that of the sample. This is known as matrix matching. When the sample’s matrix is unknown, the matrix effect must be shown to be negligi￾ble, or an alternative method of standardization must be used. Both approaches are discussed in the following sections. 5B.4 Standard Additions The complication of matching the matrix of the standards to that of the sample can be avoided by conducting the standardization in the sample. This is known as the method of standard additions. The simplest version of a standard addi￾tion 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 is matrix matching Adjusting the matrix of an external standard so that it is the same as the matrix of the samples to be analyzed. method of standard additions A standardization in which aliquots of a standard solution are added to the sample. Examples of Typical Problems Each example problem includes a detailed solution that helps students in applying the chapter’s material to practical problems. Margin Notes Margin notes direct students to colorplates located toward the middle of the book Bold-faced Key Terms with Margin Definitions Key words appear in boldface when they are introduced within the text. The term and its definition appear in the margin for quick review by the student. All key words are also defined in the glossary. 110 Modern Analytical Chemistry either case, the calibration curve provides a means for relating Ssamp to the ana￾lyte’s concentration. EXAMPLE 5.3 A second spectrophotometric method for the quantitative determination of Pb2+ levels in blood gives a linear normal calibration curve for which Sstand = (0.296 ppb–1) × CS + 0.003 What is the Pb2+ level (in ppb) in a sample of blood if Ssamp is 0.397? SOLUTION To determine the concentration of Pb2+ in the sample of blood, we replace Sstand in the calibration equation with Ssamp and solve for CA It is worth noting that the calibration equation in this problem includes an extra term that is not in equation 5.3. Ideally, we expect the calibration curve to give a signal of zero when CS is zero. This is the purpose of using a reagent blank to correct the measured signal. The extra term of +0.003 in our calibration equation results from uncertainty in measuring the signal for the reagent blank and the standards. An external standardization allows a related series of samples to be analyzed using a single calibration curve. This is an important advantage in laboratories where many samples are to be analyzed or when the need for a rapid throughput of l i iti l t i i l f th t l t d C S A samp ppb === – . . . –. . . – 0 003 0 296 0 397 0 003 0 296 1 33 1 ppb ppb –1 Color plate 1 shows an example of a set of external standards and their corresponding normal calibration curve. x 1400-Fm 9/9/99 7:38 AM Page x