Analytical Chem istry - DePauw University

Chapter 9 Titrimetric Methods429has an equilibrium constant of+ −[ HO ][ In ]=[ HIn]K a3Taking the negative log of each side of equation 9.5, and rearranging tosolve for pH leaves with a equation−InpH = pK + log [ ]a[ HIn]relating the solution’s pH to the relative concentrations of HIn and In – .If we can detect HIn and In – with equal ease, then the transition fromyellow to red (or from red to yellow) reaches its midpoint, which is orange,when their concentrations are equal, or when the pH is equal to the indicator’spK a . If the indicator’s pK a and the pH at the equivalence point areidentical, then titrating until the indicator turns orange is a suitable endpoint. Unfortunately, we rarely know the exact pH at the equivalence point.In addition, determining when the concentrations of HIn and In – are equalmay be difficult if the indicator’s change in color is subtle.We can establish the range of pHs over which the average analyst observesa change in the indicator’s color by making the following assumptions—theindicator’s color is yellow if the concentration of HIn is 10 greater thanthat of In – , and its color is red if the concentration of HIn is 10 smallerthan that of In – . Substituting these inequalities into equation 9.6pH = pK+ log 1 = pK−1aa109.59.6pH = pK+ log 10 = pK+ 1aa1shows that the indicator changes color over a pH range extending ±1 uniton either side of its pK a . As shown in Figure 9.12, the indicator is yellowwhen the pH is less than pK a – 1, and it is red for pHs greater than pK a + 1.pHIn –indicatoris color of In –pH = pK a,HInHInindicator’scolor transitionrangeindicatoris color of HInFigure 9.12 Diagram showing the relationship between pHand an indicator’s color. The ladder diagram defines pH valueswhere HIn and In – are the predominate species. Theindicator changes color when the pH is between pK a – 1 andpK a + 1.