D. Harvey - Modern Analytical Chemistry (794078), страница 91
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If the weak acid is diprotic, then the FW may beeither 58.78 g/mol or 117.6 g/mol, depending on whether the titration was tothe first or second equivalence point. Succinic acid, with a formula weight of118.1 g/mol is a possibility, but malonic acid is not. If the analyte is a triproticweak acid, then its FW must be 58.78 g/mol, 117.6 g/mol, or 176.3 g/mol. Noneof these values is close to the formula weight for citric acid, eliminating it as apossibility. Only succinic acid provides a possible match.Equilibrium Constants Another application of acid–base titrimetry is the determination of equilibrium constants. Consider, for example, the titration of a weak acid,HA, with a strong base. The dissociation constant for the weak acid isKa =[A − ][H 3O + ][HA]9.9When the concentrations of HA and A – are equal, equation 9.9 reduces toKa = [H3O+], or pH = pKa.
Thus, the pKa for a weak acid can be determined bymeasuring the pH for a solution in which half of the weak acid has been neutralized.On a titration curve, the point of half-neutralization is approximated by the volumeof titrant that is half of that needed to reach the equivalence point. As shown in Figure 9.20, an estimate of the weak acid’s pKa can be obtained directly from the titration curve.This method provides a reasonable estimate of the pKa, provided that the weakacid is neither too strong nor too weak.
These limitations are easily appreciated byconsidering two limiting cases. For the first case let’s assume that the acid is strongenough that it is more than 50% dissociated before the titration begins. As a resultthe concentration of HA before the equivalence point is always less than the concentration of A–, and there is no point along the titration curve where [HA] = [A–].At the other extreme, if the acid is too weak, the equilibrium constant for the titration reactionHA(aq) + OH–(aq)t H2O(l) + A–(aq)pHmay be so small that less than 50% of HA will have reacted at the equivalence point.In this case the concentration of HA before the equivalence point is always greaterFigure 9.20Estimating the pKa for a weak acid from itstitration curve with a strong base.14.012.010.08.0pKa6.04.02.00.00.0010.00Veq pt2 × Veq pt20.0030.00 40.00 50.00Volume of titrant60.0070.001400-CH09 9/9/99 2:13 PM Page 311311Chapter 9 Titrimetric Methods of Analysisthan that of A–.
Determining the pKa by the half-equivalence point method overestimates its value if the acid is too strong and underestimates its value if the acid istoo weak.A second approach for determining the pKa of an acid is to replot the titrationcurve in a linear form as a Gran plot. For example, earlier we learned that the titration of a weak acid with a strong base can be plotted in a linear form using the following equationVb × [H3O+] = Ka × Veq – Ka × VbPlotting Vb × [H3O+] versus Vb, for volumes less than the equivalence point volumeyields a straight line with a slope of –Ka.
Other linearizations have been developedthat use all the points on a titration curve7 or require no assumptions.8 This approach to determining acidity constants has been used to study the acid–base properties of humic acids, which are naturally occurring, large-molecular-weight organicacids with multiple acidic sites. In one study, a sample of humic acid was found tohave six titratable sites, three of which were identified as carboxylic acids, two ofwhich were believed to be secondary or tertiary amines, and one of which was identified as a phenolic group.9Scale of Operation In an acid–base titration the volume of titrant needed toreach the equivalence point is proportional to the absolute amount of analytepresent in the analytical solution. Nevertheless, the change in pH at the equivalence point, and thus the utility of an acid–base titration, is a function of theanalyte’s concentration in the solution being titrated.When the sample is available as a solution, the smallest concentration ofanalyte that can be readily analyzed is approximately 10–3 M (Figure 9.21).
If,for example, the analyte has a gram formula weight of 120 g/mol, then thelower concentration limit is 120 ppm. When the analyte is a solid, it must firstbe placed into solution, the volume of which must be sufficient to allow thetitration’s end point to be monitored using a visual indicator or a suitableprobe.
If we assume a minimum volume of 25 mL, and a lower concentrationlimit of 120 ppm, then a sample containing at least 3 mg of analyte is required. Acid–base titrations involving solid or solution samples, therefore, aregenerally limited to major and minor analytes (see Figure 3.6 in Chapter 3).The analysis of gases can be extended to trace analytes by pulling a large volume of the gas through a suitable collection solution.Efforts have been made to develop methods for conducting acid–basetitrations on a much smaller scale.
In one experimental design, samples of20–100 µL were held by capillary action between a flat-surface pH electrodeand a stainless steel rod.10 The titrant was added by using the oscillations ofa piezoelectric ceramic device to move an angled glass rod in and out of atube connected to a reservoir containing the titrant (see Figure 9.22).
Eachtime the glass tube was withdrawn an approximately 2-nL microdroplet oftitrant was released. The microdroplets were allowed to fall onto the steelrod containing the sample, with mixing accomplished by spinning the rodat 120 rpm. A total of 450 microdroplets, with a combined volume of0.81–0.84 µL, was dispensed between each pH measurement.
In this fashiona titration curve was constructed. This method was used to titrate solutionsof 0.1 M HCl and 0.1 M CH3COOH with 0.1 M NaOH. Absolute errorsranged from a minimum of +0.1% to a maximum of –4.1%, with relativepH9B.8 Evaluation of Acid–Base Titrimetry14.0012.0010.008.006.004.002.000.00(a)(b)(c)(d)(d)(c)(b)(a)020406080Volume of NaOH (mL)100Figure 9.21Titration curves for (a) 10–1 M HCl,(b) 10–2 M HCl, (c) 10–3 M HCl, and(d) 10–4 M HCl. In each case the titrantis an equimolar solution of NaOH.PiezoelectricceramicTitrantpHmeterSampleFigure 9.22Experimental design for a microdroplettitration apparatus.1400-CH09 9/9/99 2:13 PM Page 312312Modern Analytical ChemistryDiffusionalmicroburetAgar gelmembraneSampleHeptane(a)(b)Figure 9.23(a) Experimental set-up for a diffusionalmicrotitration; (b) close-up showing the tipof the diffusional microburet in contact withthe drop of sample.standard deviations from 0.15% to 4.7%.
The smallest volume of sample that wassuccessfully titrated was 20 µL.More recently, a method has been described in which the acid–base titration isconducted within a single drop of solution.11 The titrant is added using a microburet fashioned from a glass capillary micropipet (Figure 9.23). The microburet has a1–2 µm tip filled with an agar gel membrane.
The tip of the microburet is placedwithin a drop of the sample solution, which is suspended in heptane, and the titrantis allowed to diffuse into the sample. The titration is followed visually using a colored indicator, and the time needed to reach the end point is measured. The rate ofthe titrant’s diffusion from the microburet must be determined by calibration.Once calibrated, the end point time can be converted to an end point volume.
Samples usually consisted of picoliter volumes (10–12 L), with the smallest sample being0.7 pL. The precision of the titrations was usually about 2%.Titrations conducted with microliter or picoliter sample volumes require asmaller absolute amount of analyte. For example, diffusional titrations have beensuccessfully conducted on as little as 29 femtomoles (10–15 mol) of nitric acid. Nevertheless, the analyte must still be present in the sample at a major or minor levelfor the titration to be performed accurately and precisely.Accuracy When working with macro–major and macro–minor samples,acid–base titrations can be accomplished with relative errors of 0.1–0.2%.
The principal limitation to accuracy is the difference between the end point and the equivalence point.Precision The relative precision of an acid–base titration depends primarily on theprecision with which the end point volume can be measured and the precision ofthe end point signal. Under optimum conditions, an acid–base titration can be accomplished with a relative precision of 0.1–0.2%.
The relative precision can be improved by using the largest volume buret that is feasible and ensuring that most ofits capacity is used to reach the end point. Smaller volume burets are used when thecost of reagents or waste disposal is of concern or when the titration must be completed quickly to avoid competing chemical reactions.
Automatic titrators are particularly useful for titrations requiring small volumes of titrant, since the precisionwith which the volume can be measured is significantly better (typically about±0.05% of the buret’s volume).The precision of the end point signal depends on the method used to locate theend point and the shape of the titration curve. With a visual indicator, the precisionof the end point signal is usually between ±0.03 mL and 0.10 mL. End points determined by direct monitoring often can be determined with a greater precision.Sensitivity For an acid–base titration we can write the following general analyticalequationVolume of titrant = k × moles of analytewhere k, the sensitivity, is determined by the stoichiometric relationship betweenanalyte and titrant.
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