D. Harvey - Modern Analytical Chemistry (794078), страница 92
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Note that this equation assumes that a blank has been analyzedto correct the signal for the volume of titrant reacting with the reagents.Consider, for example, the determination of sulfurous acid, H2SO3, by titratingwith NaOH to the first equivalence point. Using the conservation of protons, we writeMoles NaOH = moles H2SO31400-CH09 9/9/99 2:13 PM Page 313Chapter 9 Titrimetric Methods of AnalysisSubstituting the molarity and volume of titrant for moles, and rearranging givesVb =1× moles H2 SO3Mb9.10where k is equivalent tok =1MbThere are two ways in which the sensitivity can be increased.
The first, and most obvious, is to decrease the concentration of the titrant, since it is inversely proportional to the sensitivity, k. The second method, which only applies if the analyte ismultiprotic, is to titrate to a later equivalence point. When H2SO3 is titrated to thesecond equivalence point, for instance, equation 9.10 becomesVb = 2 ×1× moles H2 SO3Mbwhere k is now equal tok =2MbIn practice, however, any improvement in the sensitivity of an acid–base titrationdue to an increase in k is offset by a decrease in the precision of the equivalencepoint volume when the buret needs to be refilled.
Consequently, standard analyticalprocedures for acid–base titrimetry are usually written to ensure that titrations require 60–100% of the buret’s volume.Selectivity Acid–base titrants are not selective. A strong base titrant, for example,will neutralize any acid, regardless of strength.
Selectivity, therefore, is determinedby the relative acid or base strengths of the analyte and the interferent. Two limitingsituations must be considered. First, if the analyte is the stronger acid or base, thenthe titrant will begin reacting with the analyte before reacting with the interferent.The feasibility of the analysis depends on whether the titrant’s reaction with the interferent affects the accurate location of the analyte’s equivalence point. If the aciddissociation constants are substantially different, the end point for the analyte canbe accurately determined (Figure 9.24a).
Conversely, if the acid dissociation constants for the analyte and interferent are similar, then an accurate end point for theanalyte may not be found (Figure 9.24b). In the latter case, a quantitative analysisfor the analyte is not possible.In the second limiting situation the analyte is a weaker acid or base than the interferent. In this case the volume of titrant needed to reach the analyte’s equivalencepoint is determined by the concentration of both the analyte and the interferent. Toaccount for the contribution from the interferent, an equivalence point for the interferent must be present. Again, if the acid dissociation constants for the analyteand interferent are significantly different, the analyte’s determination is possible. If,however, the acid dissociation constants are similar, only a single equivalence pointis found, and the analyte’s and interferent’s contributions to the equivalence pointvolume cannot be separated.Time, Cost, and Equipment Acid–base titrations require less time than most gravimetric procedures, but more time than many instrumental methods of analysis,particularly when analyzing many samples.
With the availability of instruments for3131400-CH09 9/9/99 2:13 PM Page 314314Modern Analytical Chemistry14.012.0pH10.08.06.04.02.00.00.0020.0040.0060.00 80.00 100.00 120.00 140.00Volume of titrant20.0040.0060.00 80.00 100.00 120.00 140.00Volume of titrant(a)14.012.0pH10.06.04.0Figure 9.24Titration curves for a 50.00 mL mixture of0.100 M HA and 0.100 M HB with 0.100 MNaOH, where (a) pKa,HA = 3 and pKa,HB = 8;and (b) pKa,HA = 5 and pKa,HB = 6.
Thedashed lines indicate the location of the twoequivalence points.8.02.00.00.00(b)performing automated titrations, however, concerns about analysis time are less ofa problem. When performing a titration manually the equipment needs are few (aburet and possibly a pH meter), inexpensive, routinely available in most laboratories, and easy to maintain. Instrumentation for automatic titrations can be purchased for around $3000.9C Titrations Based on Complexation Reactionscomplexation titrationA titration in which the reaction betweenthe analyte and titrant is a complexationreaction.The earliest titrimetric applications involving metal–ligand complexation were thedeterminations of cyanide and chloride using, respectively, Ag+ and Hg2+ as titrants.Both methods were developed by Justus Liebig (1803–1873) in the 1850s.
The use ofa monodentate ligand, such as Cl– and CN–, however, limited the utility of complexation titrations to those metals that formed only a single stable complex, suchas Ag(CN)2– and HgCl2. Other potential metal–ligand complexes, such as CdI42–,were not analytically useful because the stepwise formation of a series of metal–ligand complexes (CdI+, CdI2, CdI3–, and CdI42–) resulted in a poorly defined endpoint.The utility of complexation titrations improved following the introduction bySchwarzenbach, in 1945, of aminocarboxylic acids as multidentate ligands capableof forming stable 1:1 complexes with metal ions.
The most widely used of thesenew ligands was ethylenediaminetetraacetic acid, EDTA, which forms strong 1:1complexes with many metal ions. The first use of EDTA as a titrant occurred in1400-CH09 9/9/99 2:13 PM Page 3151946, when Schwarzenbach introduced metallochromic dyesas visual indicators for signaling the end point of a complexation titration.–Chapter 9 Titrimetric Methods of Analysis315CH2COO–CH2COO–OOCH2CN::N9C.1 Chemistry and Properties of EDTAEthylenediaminetetraacetic acid, or EDTA, is an aminocar–OOCH2Cboxylic acid.
The structure of EDTA is shown in Figure 9.25a.(a)EDTA, which is a Lewis acid, has six binding sites (the four carboxylate groups and the two amino groups), providing six pairsof electrons. The resulting metal–ligand complex, in which EDTA forms a cage-likestructure around the metal ion (Figure 9.25b), is very stable. The actual number ofcoordination sites depends on the size of the metal ion; however, all metal–EDTAcomplexes have a 1:1 stoichiometry.OOONOMNOOOMetal–EDTA Formation Constants To illustrate the formation of a metal–EDTAcomplex consider the reaction between Cd2+ and EDTACd2+(aq) + Y4–(aq)t CdY2–(aq)where Y4– is a shorthand notation for the chemical form of EDTA shown in Figure9.25. The formation constant for this reactionKf =O(b)[CdY 2 − ]= 2.9 × 1016[Cd2 + ][Y 4 − ]Figure 9.25Structures of (a) EDTA, and (b) a sixcoordinate metal–EDTA complex.9.11is quite large, suggesting that the reaction’s equilibrium position lies far to the right.Formation constants for other metal–EDTA complexes are found in Appendix 3C.Y4–10.17EDTA Is a Weak Acid Besides its properties as a ligand, EDTA is also a weak acid.The fully protonated form of EDTA, H6Y2+, is a hexaprotic weak acid with successive pKa values ofpKa1 = 0.0pKa2 = 1.5pKa3 = 2.0pKa4 = 2.68pKa5 = 6.11pKa6 = 10.17The first four values are for the carboxyl protons, and the remaining two values arefor the ammonium protons.
A ladder diagram for EDTA is shown in Figure 9.26.The species Y4– becomes the predominate form of EDTA at pH levels greater than10.17. It is only for pH levels greater than 12 that Y4– becomes the only significantform of EDTA.Conditional Metal–Ligand Formation Constants Recognizing EDTA’s acid–baseproperties is important. The formation constant for CdY2– in equation 9.11 assumes that EDTA is present as Y4–. If we restrict the pH to levels greater than 12,then equation 9.11 provides an adequate description of the formation of CdY2–. ForpH levels less than 12, however, Kf overestimates the stability of the CdY2– complex.At any pH a mass balance requires that the total concentration of unboundEDTA equal the combined concentrations of each of its forms.CEDTA = [H6Y2+] + [H5Y+] + [H4Y] + [H3Y–] + [H2Y2–] + [HY3–] + [Y4–]To correct the formation constant for EDTA’s acid–base properties, we must account for the fraction, αY 4–, of EDTA present as Y4–.α Y 4− =[Y 4 − ]CEDTAHY3–9.126.11pHH2Y2–H3Y–H4Y2.682.01.5H5Y+H6Y2+Figure 9.26Ladder diagram for EDTA.0.01400-CH09 9/9/99 2:13 PM Page 316316Modern Analytical ChemistryTable 9.12Values of αY4– for Selected pHspHαY4-pHαY4-2345673.7 × 10–142.5 × 10–113.6 × 10–93.5 × 10–72.2 × 10–54.8 × 10–489101112135.4 × 10–35.2 × 10–20.350.850.981.00Table 9.13Conditional Formation Constantsfor CdY2–pHKf’pHKf’2345671.1 × 1037.3 × 1051.0 × 1081.0 × 10106.4 × 10111.4 × 101389101112131.6 × 10141.5 × 10151.0 × 10162.5 × 10162.8 × 10162.9 × 1016Values of αY 4– are shown in Table 9.12.
Solving equation 9.12 for [Y4–] and substituting into the equation for the formation constant givesKf =[CdY 2 − ][Cd2 + ]α Y 4 − CEDTAIf we fix the pH using a buffer, then αY4– is a constant. Combining αY 4– with KfgivesK f′ = α Y 4 − × K f =conditional formation constantThe equilibrium formation constant fora metal–ligand complex for a specific setof solution conditions, such as pH.auxiliary complexing agentA second ligand in a complexationtitration that initially binds with theanalyte but is displaced by the titrant.[CdY 2 − ][Cd 2 + ]CEDTA9.13where Kf´ is a conditional formation constant whose value depends on the pH.
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