Analytical Chem istry - DePauw University

Chapter 10 Spectroscopic Methods593systems in which only a single complex is formed and for which Beer’s lawis obeyed.De t e r m i n a t i o n o f Equilibrium Co n s t a n t sAnother important application of molecular absorption spectroscopy is thedetermination of equilibrium constants. Let’s consider, as a simple example,an acid–base reaction of the general form+ −HIn( aq) + H O() l H O ( aq) + In ( aq )2 3where HIn and In – are the conjugate weak acid and weak base forms of anacid–base indicator. The equilibrium constant for this reaction is+ −[ HO ][ In ]=[ HIn]K a3To determine the equilibrium constant’s value, we prepare a solution inwhich the reaction is in a state of equilibrium and determine the equilibriumconcentration of H 3 O + , HIn, and In – . The concentration of H 3 O + iseasy to determine by simply measuring the solution’s pH. To determine theconcentration of HIn and In – we can measure the solution’s absorbance.If both HIn and In – absorb at the selected wavelength, then, from equation10.6, we know that−A= ε b[ HIn] + ε b[ In ] 10.15HInwhere e HIn and e In are the molar absorptivities for HIn and In – . The totalconcentration of indicator, C, is given by a mass balance equationInC = [ HIn] + [ In − ]10.16Solving equation 10.16 for [HIn] and substituting into equation 10.15giveswhich we simplify toA= b C − −−ε ( [ In ]) + ε b[ In ]HInA= bC − b −−ε ε [ In ] + ε b[ In ]InHIn HIn In−A= A + b[ In ]( ε − ε )10.17HIn In HInwhere A HIn , which is equal to e HIn bC, is the absorbance when the pH isacidic enough that essentially all the indicator is present as HIn. Solvingequation 10.17 for the concentration of In – gives[ In ]− =A−AHIn=b( ε − ε )InHIn10.18