D. Harvey - Modern Analytical Chemistry (794078), страница 85
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This is the same titration for which we previouslycalculated the titration curve (Table 9.3 and Figure 9.6).SOLUTIONWe begin by drawing the axes for the titration curve (Figure 9.7a). We have alreadyshown that the volume of NaOH needed to reach the equivalence point is 50 mL,so we draw a vertical line intersecting the x-axis at this volume (Figure 9.7b).*Question 4 in the end-of-chapter problems asks you to consider why these pH limits correspond to approximately10% and 90% of the equivalence point volume.1400-CH09 9/9/99 2:12 PM Page 285Chapter 9 Titrimetric Methods of AnalysisPercent titrated50100Percent titrated150200014.014.012.012.010.010.08.08.0pHpH06.06.04.04.02.02.00.00.0050.00Volume of titrant500.00.00100.0015050.00Volume of titrantPercent titrated050100200100.00Percent titrated150200014.014.012.012.010.010.08.08.0pHpH100(b)(a)6.06.04.04.02.02.00.00.0050.00Volume of titrant500.00.00100.00(c)10015050.00Volume of titrant200100.00(d)Percent titrated050100Percent titrated150200014.014.012.012.010.010.08.08.0pHpH2856.06.04.04.02.02.00.00.0050.00Volume of titrant0.00.00100.00(e)Figure 9.7How to sketch an acid–base titration curve; see text for explanation.(f)5010050.00Volume of titrant150200100.001400-CH09 9/9/99 2:12 PM Page 286286Modern Analytical ChemistryBefore the equivalence point the titrant is the limiting reagent, and the pHis controlled by a buffer consisting of unreacted acetic acid and its conjugateweak base, acetate.
The pH limits for the buffer region are plotted bysuperimposing the ladder diagram for acetic acid on the y-axis (Figure 9.7c)and adding the appropriate points at 10% (5.0 mL) and 90% (45.0 mL) of theequivalence point volume.After the equivalence point the pH is controlled by the concentration ofexcess NaOH. Again, we have already done this calculation.
Using values fromTable 9.3, we plot two additional points.An approximate sketch of the titration curve is completed by drawingseparate straight lines through the two points in the buffer region and the twopoints in the excess titrant region (Figure 9.7e). Finally, a smooth curve isdrawn connecting the three straight-line segments (Figure 9.7f).This approach can be used to sketch titration curves for other acid–base titrations including those involving polyprotic weak acids and bases or mixtures of weakacids and bases (Figure 9.8).
Figure 9.8a, for example, shows the titration curvewhen titrating a diprotic weak acid, H2A, with a strong base. Since the analyte isPercent titrated05010015020014.012.0pH10.08.06.04.02.00.00.0050.00Volume of titrant100.00(a)Percent titrated05010015020014.012.0Figure 9.8Sketches of titration curves for (a) 50.00 mLof 0.0500 M diprotic weak acid (pKa1 = 3,pKa2 = 7) with 0.100 M strong base; and(b) 50.00 mL of a mixture of weak acidsconsisting of 0.075 M HA (pKa,HA = 3) and0.025 M HB (pKa,HB = 7) with 0.100 Mstrong base. The points used to sketch thetitration curves are indicated by the dots (•).Equivalence points are indicated by thearrows.pH10.08.06.04.02.00.00.00(b)50.00Volume of titrant100.001400-CH09 9/9/99 2:12 PM Page 287Chapter 9 Titrimetric Methods of Analysis287diprotic there are two equivalence points, each requiring the same volume oftitrant.
Before the first equivalence point the pH is controlled by a buffer consistingof H2A and HA–, and the HA–/A2– buffer determines the pH between the two equivalence points. After the second equivalence point, the pH reflects the concentrationof the excess strong base titrant.Figure 9.8b shows a titration curve for a mixture consisting of two weak acids:HA and HB. Again, there are two equivalence points. In this case, however, theequivalence points do not require the same volume of titrant because the concentration of HA is greater than that for HB. Since HA is the stronger of the two weakacids, it reacts first; thus, the pH before the first equivalence point is controlled bythe HA/A– buffer.
Between the two equivalence points the pH reflects the titrationof HB and is determined by the HB/B– buffer. Finally, after the second equivalencepoint, the excess strong base titrant is responsible for the pH.9B.2 Selecting and Evaluating the End PointWhere Is the Equivalence Point? We have already learned how to calculate theequivalence point for the titration of a strong acid with a strong base, and for thetitration of a weak acid with a strong base. We also have learned to sketch a titration curve with a minimum of calculations. Can we also locate the equivalencepoint without performing any calculations? The answer, as you may have guessed,is often yes!It has been shown3 that for most acid–base titrations the inflection point,which corresponds to the greatest slope in the titration curve, very nearly coincideswith the equivalence point.
The inflection point actually precedes the equivalencepoint, with the error approaching 0.1% for weak acids or weak bases with dissociation constants smaller than 10–9, or for very dilute solutions. Equivalence points determined in this fashion are indicated on the titration curves in Figure 9.8.The principal limitation to using a titration curve to locate the equivalencepoint is that an inflection point must be present. Sometimes, however, an inflectionpoint may be missing or difficult to detect. Figure 9.9, for example, demonstratesthe influence of the acid dissociation constant, Ka, on the titration curve for a weakacid with a strong base titrant. The inflection point is visible, even if barely so, foracid dissociation constants larger than 10–9, but is missing when Ka is 10–11.Another situation in which an inflection point may be missing or difficult todetect occurs when the analyte is a multiprotic weak acid or base whose successivedissociation constants are similar in magnitude.
To see why this is true let’s consider the titration of a diprotic weak acid, H2A, with NaOH. During the titration thefollowing two reactions occur.pHEarlier we made an important distinction between an end point and an equivalencepoint. The difference between these two terms is important and deserves repeating.The equivalence point occurs when stoichiometrically equal amounts of analyte andtitrant react. For example, if the analyte is a triprotic weak acid, a titration withNaOH will have three equivalence points corresponding to the addition of one, two,and three moles of OH– for each mole of the weak acid.
An equivalence point,therefore, is a theoretical not an experimental value.An end point for a titration is determined experimentally and represents theanalyst’s best estimate of the corresponding equivalence point. Any difference between an equivalence point and its end point is a source of determinate error. As weshall see, it is even possible that an equivalence point will not have an associated endpoint.14.012.0(f)10.0(e)(d)8.0(c)6.0(b)4.0(a)2.00.00.0020.00 40.00 60.00Volume of titrantFigure 9.9Titration curves for 50.00 mL of 0.100 Mweak acid with 0.100 M strong base. ThepKas of the weak acids are (a) 1, (b) 3, (c) 5,(d) 7, (e) 9, (f) 11.1400-CH09 9/9/99 2:12 PM Page 288pH288Modern Analytical Chemistry14.012.0 Maleic acid10.08.06.04.02.00.00.00 20.00 40.00 60.00Volume of titrant80.00pH(a)14.012.0 Malonic acid10.08.06.04.02.00.00.00 20.00 40.00 60.00Volume of titrant80.00pH(b)14.012.0 Succinic acid10.08.06.04.02.00.00.00 20.00 40.00 60.00Volume of titrantH2A(aq) + OH–(aq) → HA–(aq) + H2O(l)9.3HA–(aq) + OH–(aq) → A2–(aq) + H2O(l)9.4Two distinct inflection points are seen if reaction 9.3 is essentially completebefore reaction 9.4 begins.Figure 9.10 shows titration curves for three diprotic weak acids.
The titration curve for maleic acid, for which Ka1 is approximately 20,000 times largerthan Ka2, shows two very distinct inflection points. Malonic acid, on the otherhand, has acid dissociation constants that differ by a factor of approximately690. Although malonic acid’s titration curve shows two inflection points, thefirst is not as distinct as that for maleic acid. Finally, the titration curve for succinic acid, for which the two Ka values differ by a factor of only 27, has only asingle inflection point corresponding to the neutralization of HC4H4O4– toC4H4O42–.
In general, separate inflection points are seen when successive aciddissociation constants differ by a factor of at least 500 (a ∆pKa of at least 2.7).Finding the End Point with a Visual Indicator One interesting group ofweak acids and bases are derivatives of organic dyes. Because such compounds have at least one conjugate acid–base species that is highly colored,their titration results in a change in both pH and color. This change in colorcan serve as a useful means for determining the end point of a titration, provided that it occurs at the titration’s equivalence point.The pH at which an acid–base indicator changes color is determined byits acid dissociation constant.
For an indicator that is a monoprotic weakacid, HIn, the following dissociation reaction occursHIn(aq) + H2O(l)80.00(c)Figure 9.10Titration curves for (a) maleic acid,pKa1 = 1.91, pKa2 = 6.33; (b) malonic acid,pKa1 = 2.85, pKa2 = 5.70; (c) succinic acid,pKa1 = 4.21, pKa2 = 5.64. Titration curves arefor 50.00 mL of 0.0500 M acid with 0.100 Mstrong base. Equivalence points for all threetitrations occur at 25.00 and 50.00 mL oftitrant.t H3O+(aq) + In–(aq)for which the equilibrium constant isKa =[In − ][H 3O + ][HIn]9.5Taking the negative log of each side of equation 9.5, and rearranging to solve for pHgives a familiar equation.pH = pKa + log[In − ][HIn]9.6The two forms of the indicator, HIn and In–, have different colors.
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