Analytical Chem istry - DePauw University

428 Analytical Chemistry 2.0141210Maleic AcidpK a1 = 1.91pK a2 = 6.33141210Malonic AcidpK a1 = 2.85pK a2 = 5.70141210Succinic AcidpK a1 = 4.21pK a2 = 5.64pH86pH86pH8644422200 20 40 60 80Volume of NaOH (mL)00 20 40 60 80Volume of NaOH (mL)Figure 9.11 Titration curves for the diprotic weak acids maleic acid, malonic acid, and succinic acid. Each titrationcurve is for 50.0 mL of 0.0500 M weak acid using 0.100 M NaOH. Although each titration curve has equivalencepoints at 25.0 mL and 50.0 mL of NaOH, the titration curve for succinic acid shows only one inflection point.00 20 40 60 80Volume of NaOH (mL)−−HA( aq) + OH ( aq) → HA ( aq) + HO()l2 29.3− − 2−HA ( aq) + OH ( aq) → A ( aq) + H O()lTo see two distinct inflection points, reaction 9.3 must be essentially completebefore reaction 9.4 begins.Figure 9.11 shows titration curves for three diprotic weak acids. Thetitration curve for maleic acid, for which K a1 is approximately 20,000larger than K a2 , has two distinct inflection points. Malonic acid, on theother hand, has acid dissociation constants that differ by a factor of approximately690. Although malonic acid’s titration curve shows two inflectionpoints, the first is not as distinct as that for maleic acid. Finally, the titrationcurve for succinic acid, for which the two K a values differ by a factor of only27, has only a single inflection point corresponding to the neutralizationof HC 4 H 4 O 4 – to C 4 H 4 O 4 2– . In general, we can detect separate inflectionpoints when successive acid dissociation constants differ by a factor of atleast 500 (a DpK a of at least 2.7).Fi n d i n g t h e En d p o i n t w it h a n In d i c a t o rOne interesting group of weak acids and weak bases are organic dyes. Becausean organic dye has at least one highly colored conjugate acid–basespecies, its titration results in a change in both pH and color. We can usethis change in color to indicate the end point of a titration, provided thatit occurs at or near the titration’s equivalence point.Let’s use an indicator, HIn, to illustrate how an acid–base indicatorworks. Because the indicator’s acid and base forms have different colors—the weak acid, HIn, is yellow and the weak base, In – , is red—the color of asolution containing the indicator depends on their relative concentrations.The indicator’s acid dissociation reaction+ −HIn( aq) + H O() l H O ( aq) + In ( aq )2 329.4