D. Harvey - Modern Analytical Chemistry (794078), страница 83
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Suppose you wish to determine the concentration of formaldehyde, H2CO, in an aqueous solution. The oxidation of H2CO by I3–H2CO(aq) + 3OH–(aq) + I3–(aq)t HCO2–(aq) + 3I–(aq) + 2H2O(l)is a useful reaction, except that it is too slow for a direct titration. If we add a knownamount of I3–, such that it is in excess, we can allow the reaction to go to completion. The I3– remaining can then be titrated with thiosulfate, S2O32–.I3–(aq) + 2S2O32–(aq)t S4O62–(aq) + 3I–(aq)This type of titration is called a back titration.Calcium ion plays an important role in many aqueous environmental systems.A useful direct analysis takes advantage of its reaction with the ligand ethylenediaminetetraacetic acid (EDTA), which we will represent as Y4–.Ca2+(aq) + Y4–(aq)t CaY2–(aq)back titrationA titration in which a reagent is added toa solution containing the analyte, andthe excess reagent remaining after itsreaction with the analyte is determinedby a titration.Unfortunately, it often happens that there is no suitable indicator for this directtitration.
Reacting Ca2+ with an excess of the Mg2+–EDTA complexCa2+(aq) + MgY2–(aq)t CaY2–(aq) + Mg2+(aq)releases an equivalent amount of Mg2+. Titrating the released Mg2+ with EDTAMg2+(aq) + Y4–(aq)t MgY2–(aq)gives a suitable end point. The amount of Mg2+ titrated provides an indirect measure of the amount of Ca2+ in the original sample. Since the analyte displaces aspecies that is then titrated, we call this a displacement titration.When a suitable reaction involving the analyte does not exist it may be possibleto generate a species that is easily titrated. For example, the sulfur content of coal canbe determined by using a combustion reaction to convert sulfur to sulfur dioxide.S(s) + O2(g) → SO2(g)Passing the SO2 through an aqueous solution of hydrogen peroxide, H2O2,SO2(g) + H2O2(aq) → H2SO4(aq)produces sulfuric acid, which we can titrate with NaOH,H2SO4(aq) + 2OH–(aq)t SO42–(aq) + 2H2O(l)providing an indirect determination of sulfur.9A.3 Titration CurvesTo find the end point we monitor some property of the titration reaction that has awell-defined value at the equivalence point.
For example, the equivalence point fora titration of HCl with NaOH occurs at a pH of 7.0. We can find the end point,displacement titrationA titration in which the analyte displacesa species, usually from a complex, andthe amount of the displaced species isdetermined by a titration.1400-CH09 9/9/99 2:12 PM Page 276276Modern Analytical Chemistry14.0012.0010.00pH8.00Equivalence point6.004.002.00Figure 9.1Acid–base titration curve for 25.0 mL of0.100 M HCl with 0.100 M NaOH.titration curveA graph showing the progress of atitration as a function of the volume oftitrant added.0.000.0010.0020.0030.00Volume NaOH (mL)40.0050.00therefore, by monitoring the pH with a pH electrode or by adding an indicator thatchanges color at a pH of 7.0.Suppose that the only available indicator changes color at a pH of 6.8.
Is thisend point close enough to the equivalence point that the titration error may besafely ignored? To answer this question we need to know how the pH changes during the titration.A titration curve provides us with a visual picture of how a property, such aspH, changes as we add titrant (Figure 9.1). We can measure this titration curve experimentally by suspending a pH electrode in the solution containing the analyte,monitoring the pH as titrant is added.
As we will see later, we can also calculate theexpected titration curve by considering the reactions responsible for the change inpH. However we arrive at the titration curve, we may use it to evaluate an indicator’s likely titration error. For example, the titration curve in Figure 9.1 shows usthat an end point pH of 6.8 produces a small titration error. Stopping the titrationat an end point pH of 11.6, on the other hand, gives an unacceptably large titrationerror.The titration curve in Figure 9.1 is not unique to an acid–base titration.Any titration curve that follows the change in concentration of a species in thetitration reaction (plotted logarithmically) as a function of the volume of titranthas the same general sigmoidal shape. Several additional examples are shown inFigure 9.2.Concentration is not the only property that may be used to construct a titrationcurve.
Other parameters, such as temperature or the absorbance of light, may beused if they show a significant change in value at the equivalence point. Many titration reactions, for example, are exothermic. As the titrant and analyte react, thetemperature of the system steadily increases. Once the titration is complete, furtheradditions of titrant do not produce as exothermic a response, and the change intemperature levels off. A typical titration curve of temperature versus volume oftitrant is shown in Figure 9.3. The titration curve contains two linear segments, theintersection of which marks the equivalence point.1400-CH09 9/9/99 2:12 PM Page 277pCdChapter 9 Titrimetric Methods of Analysis27718.016.014.012.010.08.06.04.02.00.00.0010.00 20.00 30.00 40.00Volume of titrant (mL)50.0080204060Volume of titrant (mL)100Potential (V)(a)1.8001.6001.4001.2001.0000.8000.6000.4000.2000.0000(b)Temperature (°C)8.0pCl6.04.02.0Figure 9.2Examples of titration curves for (a) acomplexation titration, (b) a redoxtitration, and (c) a precipitationtitration.Equivalence point0.00.0010.00 20.00 30.00 40.00Volume of titrant (mL)50.00(c)Volume of titrant (mL)Figure 9.3Example of a thermometric titration curve.9A.4 The BuretThe only essential piece of equipment for an acid–base titration is a means for delivering the titrant to the solution containing the analyte.
The most common methodfor delivering the titrant is a buret (Figure 9.4). A buret is a long, narrow tube withgraduated markings, and a stopcock for dispensing the titrant. Using a buret with asmall internal diameter provides a better defined meniscus, making it easier to readthe buret’s volume precisely. Burets are available in a variety of sizes and tolerancesburetVolumetric glassware used to delivervariable, but known volumes of solution.1400-CH09 9/9/99 2:12 PM Page 278278Modern Analytical Chemistry012Table 9.1Volume(mL)5102550100Specifications for VolumetricBuretsClassaSubdivision(mL)Tolerance(mL)ABABABABAB0.010.010.020.020.10.10.10.10.20.2±0.01±0.02±0.02±0.04±0.03±0.06±0.05±0.10±0.10±0.20aSpecificationsfor class A and class B glassware are taken from AmericanSociety for Testing Materials (ASTM) E288, E542, and E694 standards.Figure 9.4Volumetric buret showing a portion of itsgraduated scale.(Table 9.1), with the choice of buret determined by the demands of the analysis.The accuracy obtainable with a buret can be improved by calibrating it over severalintermediate ranges of volumes using the same method described in Chapter 5 forcalibrating pipets.
In this manner, the volume of titrant delivered can be correctedfor any variations in the buret’s internal diameter.Titrations may be automated using a pump to deliver the titrant at a constantflow rate, and a solenoid valve to control the flow (Figure 9.5). The volume oftitrant delivered is determined by multiplying the flow rate by the elapsed time. Automated titrations offer the additional advantage of using a microcomputer for datastorage and analysis.9B Titrations Based on Acid–Base Reactionsacid–base titrationA titration in which the reaction betweenthe analyte and titrant is an acid–basereaction.The earliest acid–base titrations involved the determination of the acidity or alkalinity of solutions, and the purity of carbonates and alkaline earth oxides.
Before1800, acid–base titrations were conducted using H2SO4, HCl, and HNO3 as acidictitrants, and K2CO3 and Na2CO3 as basic titrants. End points were determinedusing visual indicators such as litmus, which is red in acidic solutions and blue inbasic solutions, or by observing the cessation of CO2 effervescence when neutralizing CO32–. The accuracy of an acid–base titration was limited by the usefulness ofthe indicator and by the lack of a strong base titrant for the analysis of weak acids.The utility of acid–base titrimetry improved when NaOH was first introducedas a strong base titrant in 1846.
In addition, progress in synthesizing organic dyesled to the development of many new indicators. Phenolphthalein was first synthesized by Bayer in 1871 and used as a visual indicator for acid–base titrations in1877. Other indicators, such as methyl orange, soon followed. Despite the increasing availability of indicators, the absence of a theory of acid–base reactivity made selecting a proper indicator difficult.Developments in equilibrium theory in the late nineteenth century led to significant improvements in the theoretical understanding of acid–base chemistry and,1400-CH09 9/9/99 2:12 PM Page 279Chapter 9 Titrimetric Methods of Analysis279Figure 9.5Typical instrumentation for performing anautomatic titration.Courtesy of Fisher Scientific.in turn, of acid–base titrimetry.
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