Spectrophotometric Determination of an Equilibrium Constant

Spectrophotometric Determination of an Equilibrium Constant...

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Spectrophotometric Determination of an Equilibrium Constant 1,2 Authors: B. K. Kramer, B. D. Lamp, D. L. McCurdy* and J. M. McCormick Last Update: December 29, 2006 Introduction Typically acid-base indicators are themselves weak acids or bases whose acid and base forms have different colors in solution. As the result of the reaction with excess titrant, we convert one form to the other causing a color change that indicated the endpoint of a titration. If we represent the indicator's acid form as HIn and its basic form as In - , then the following equilibrium describes the chemical reaction that occurs as the [H + ] is changed. If HIn and In - have different colors, then the solution's color will change as a function of [H + ] depending on which of the compounds is present in the greater amount. The acid dissociation equilibrium constant (K a ) for the indicator that describes this reaction is given by Eqn. 1, in terms of the concentrations of the hydrogen ion, In - and HIn. Because we are working in aqueous solution, it is convenient to rearrange Eqn. 1 to Eqn. 2 by taking the negative logarithm of both sides, and then recognizing the definitions of pK a and pH, rewriting Eqn. 2 as Eqn. 3, which is simply another version of the Henderson-Hasselbach equation ( More Info ). Note that Eqn. 3 predicts that the indicator's pK a corresponds to the pH of an indicator solution when the logarithmic term equals zero (i. e., when [In - ] equals [HIn]). (1) (2)
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(3) A convenient way to determine the equilibrium constant of a reaction involving colored species and H + is to use absorbance spectroscopy. If we monitor a wavelength at which either one of the two species strongly absorbs we will see the absorbance as a function of pH change as that species' concentration in solution changes. From the equilibrium between HIn and In - , given above, and considering Le Chatelier's principle, we can see that when the [H + ] is large (low pH ), ( Help Me ) the equilibrium will shift completely to the left and the indicator will be completely in the HIn form. Consider the experiment whose results are shown in Fig. 1. In this experiment, the absorbance of an indicator solution is measured at two wavelengths as the solution's pH is varied. The acidic form of the indicator, HIn, absorbs strongly at wavelength λ 1 and the basic form, In - , absorbs strongly at λ 2 . So when the solution is very acidic, as on the left side of Fig. 1, all of the indicator is in the HIn form, resulting in a large absorbance at λ 1 (labeled A max, λ 1 ) but a small absorbance at λ 2 (since [In - ] is small). At high pH, all of the indicator is in the In - form giving a strong absorbance at λ 2 (labeled A max, λ 2 ) and minimal absorbance at λ 1 . As the pH changes from acidic to basic, HIn is converted to In - in accordance with Eqn. 3. This conversion results in a decrease in [HIn] and a corresponding increase in [In - ]. Since the absorbance at each wavelength is directly proportional to concentration, we observe a decrease in the absorbance at
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Spectrophotometric Determination of an Equilibrium Constant...

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