D. Harvey - Modern Analytical Chemistry (794078), страница 86
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The color ofa solution containing an indicator, therefore, continuously changes as the concentration of HIn decreases and the concentration of In– increases. If we assume thatboth HIn and In– can be detected with equal ease, then the transition between thetwo colors reaches its midpoint when their concentrations are identical or when thepH is equal to the indicator’s pKa. The equivalence point and the end point coincide, therefore, if an indicator is selected whose pKa is equal to the pH at the equivalence point, and the titration is continued until the indicator’s color is exactlyhalfway between that for HIn and In–. Unfortunately, the exact pH at the equivalence point is rarely known. In addition, detecting the point where the concentrations of HIn and In– are equal may be difficult if the change in color is subtle.We can establish a range of pHs over which the average analyst will observe achange in color if we assume that a solution of the indicator is the color of HInwhenever its concentration is ten times more than that of In–, and the color of In–1400-CH09 9/9/99 2:12 PM Page 289Chapter 9 Titrimetric Methods of Analysiswhenever the concentration of HIn is ten times less than that of In–.
Substituting these inequalities into equation 9.6pH = pKa + logpHIn–1= pKa − 110pH = pKa,HIn + 1pH = pKa,HInpH = pKa + log10= pKa + 11Indicator’scolor transitionregionpH = pKa,HIn – 1shows that an indicator changes color over a pH range of ±1 units on eitherside of its pKa (Figure 9.11).
Thus, the indicator will be the color of HIn whenthe pH is less than pKa – 1, and the color of In– for pHs greater than pKa + 1.The pH range of an indicator does not have to be equally distributed on eitherside of the indicator’s pKa. For some indicators only the weak acid or weak base is colored. For other indicators both the weak acid and weak base are colored, but oneform may be easier to see. In either case, the pH range is skewed toward those pH levels for which the less colored form of the indicator is present in higher concentration.A list of several common acid–base indicators, along with their pKas, colorchanges, and pH ranges, is provided in the top portion of Table 9.4.
In some cases,Table 9.4289Properties of Selected Indicators, Mixed Indicators,and Screened Indicators for Acid–Base TitrationsIndicatorAcid ColorBase ColorpH RangepKacresol redthymol bluebromophenol bluemethyl orangeCongo redbromocresol greenmethyl redbromocresol purplelitmusbromothymol bluephenol redcresol redthymol bluephenolphthaleinalizarin yellow Rredredyellowredblueyellowredyellowredyellowyellowyellowyellowcolorlessyellowyellowyellowblueorangeredblueyellowpurpleblueblueredredblueredorange/red0.2–1.81.2–2.83.0–4.63.1–4.43.0–5.03.8–5.44.2–6.35.2–6.85.0–8.06.0–7.66.8–8.47.2–8.88.0–9.68.3–10.010.1–12.0—1.74.13.7—4.75.06.1—7.17.88.28.99.6—Mixed IndicatorAcid ColorBase ColorpH Rangebromocresol green and methyl orangebromocresol green and chlorophenol redbromothymol blue and phenol redorangeyellow-greenyellowblue-greenblue-violetviolet3.5–4.35.4–6.27.2–7.6Screened IndicatorAcid ColorBase ColorpH Rangedimethyl yellow and methylene bluemethyl red and methylene blueneutral red and methylene blueblue-violetred-violetviolet-bluegreengreengreen3.2–3.45.2–5.66.8–7.3HInFigure 9.11Ladder diagram showing the range of pHlevels over which a typical acid–baseindicator changes color.1400-CH09 9/9/99 2:12 PM Page 290290Modern Analytical Chemistry14.012.0pH10.0Figure 9.12Titration curve for 50.00 mL of 0.100 MCH3COOH with 0.100 M NaOH showing therange of pHs and volumes of titrant overwhich the indicators bromothymol blue andphenolphthalein are expected to changecolor.Phenolphthalein8.0Bromothymol blue6.04.02.00.00.0010.0020.0030.0040.00Volume of titrant50.0060.0070.00mixed indicators, which are a mixture of two or more acid–base indicators, providea narrower range of pHs over which the color change occurs.
A few examples ofsuch mixed indicators are included in the middle portion of Table 9.4. Adding aneutral screening dye, such as methylene blue, also has been found to narrow thepH range over which an indicator changes color (lower portion of Table 9.4). Inthis case, the neutral dye provides a gray color at the midpoint of the indicator’scolor transition.The relatively broad range of pHs over which any indicator changes colorplaces additional limitations on the feasibility of a titration.
To minimize a determinate titration error, an indicator’s entire color transition must lie within the sharptransition in pH occurring near the equivalence point. Thus, in Figure 9.12 we seethat phenolphthalein is an appropriate indicator for the titration of 0.1 M aceticacid with 0.1 M NaOH. Bromothymol blue, on the other hand, is an inappropriateindicator since its change in color begins before the initial sharp rise in pH and, as aresult, spans a relatively large range of volumes.
The early change in color increasesthe probability of obtaining inaccurate results, and the range of possible end pointvolumes increases the probability of obtaining imprecise results.The need for the indicator’s color transition to occur in the sharply rising portion of the titration curve justifies our earlier statement that not every equivalencepoint has an end point. For example, trying to use a visual indicator to find the firstequivalence point in the titration of succinic acid (see Figure 9.10c) is pointlesssince any difference between the equivalence point and the end point leads to alarge titration error.Finding the End Point by Monitoring pH An alternative approach to finding atitration’s end point is to monitor the titration reaction with a suitable sensorwhose signal changes as a function of the analyte’s concentration.
Plotting the datagives us the resulting titration curve. The end point may then be determined fromthe titration curve with only a minimal error.The most obvious sensor for an acid–base titration is a pH electrode.* For example, Table 9.5 lists values for the pH and volume of titrant obtained during thetitration of a weak acid with NaOH. The resulting titration curve, which is called apotentiometric titration curve, is shown in Figure 9.13a. The simplest method forfinding the end point is to visually locate the inflection point of the titration curve.This is also the least accurate method, particularly if the titration curve’s slope at theequivalence point is small.*See Chapter 11 for more details about pH electrodes.1400-CH09 9/9/99 2:12 PM Page 291Chapter 9 Titrimetric Methods of AnalysisTable 9.5Data for the Titration of a Weak Acid with0.100 M NaOHNormal TitrationVolume(mL)pH0.002.892.004.524.0010.0012.0014.0015.0015.5015.6015.7015.8016.0017.0018.0020.0024.00First DerivativeVolume(mL)∆pH∆V1.000.8153.000.2707.000.13811.000.13013.000.24014.500.45015.251.3415.556.5015.658.9015.757.8015.902.9016.500.69017.500.29019.000.18522.000.1035.065.896.156.637.087.758.409.2910.0710.6511.3411.6312.00Second DerivativeVolume(mL)∆2pH∆V 22.00–0.2735.00–0.0339.00–0.00212.000.05513.750.14014.881.1915.4017.215.6024.015.70–11.015.83–32.816.20–3.6817.00–0.40018.25–0.07020.50–0.02712.41Another method for finding the end point is to plot the first or second derivative of the titration curve.
The slope of a titration curve reaches its maximum valueat the inflection point. The first derivative of a titration curve, therefore, shows aseparate peak for each end point. The first derivative is approximated as ∆pH/∆V,where ∆pH is the change in pH between successive additions of titrant. For example, the initial point in the first derivative titration curve for the data in Table 9.5 is∆pH4.52 − 2.89== 0.815∆V2.00 − 0.00and is plotted at the average of the two volumes (1.00 mL).
The remaining data forthe first derivative titration curve are shown in Table 9.5 and plotted in Figure 9.13b.2911400-CH09 9/9/99 2:12 PM Page 292Modern Analytical Chemistry1412108642010∆pH/∆V801051520Volume of titrant (mL)25∆2pH/∆V 2(a)Titration curves for a weak acid with0.100 M NaOH—(a) normal titrationcurve; (b) first derivative titration curve;(c) second derivative titration curve;(d) Gran plot.420Figure 9.136025(b)403020100–10 2–20–30–40461401201008060402008 10 12 14 16 18 20 2210Volume of titrant (mL)(c)5101520Volume of titrant (mL)Vb[H+] × 107pH2921113141512Volume of titrant (mL)16(d)The second derivative of a titration curve may be more useful than the first derivative, since the end point is indicated by its intersection with the volume axis.The second derivative is approximated as ∆(∆pH/∆V)/∆V, or ∆2pH/∆V 2.
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