Acid Dissociation Constant

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Using spectrophotometric method:
determine the wavelengths at which the acid and base forms of the dye in aqueous medium exhibit maximum absorption; determine the molar absorptivities of the acid and base forms of the dye and estimate an unknown concentration of the dye in solution using the Beer-Lambert’s Law; and determine the acid dissociation constant of the indicator dye. THEORY

The absorption or reflection of certain wavelengths of light account for observed colors such as the rainbow or the blue sky. Color intensity can be associated with increasing concentration of a substance responsible for absorbing or reflecting light. Thus, if a substance appears colored when dissolved in solution, colorimetric methods (techniques used to determine concentration of a substance by analysis of its inherent color), such as spectrophotometry, can be used to determine quantitatively the amount of the substance dissolved in solution. It is found empirically that the amount of light absorbed by a specific sample depends on three items: (1) the concentration of the solution; (2) the distance travelled by the light through the sample; and (3) the natural ability of the specific substance to absorb light. The previous statement is also known as the Beer’s Law: A = Є b c(6-1)

where A is the absorbance, Є is the molar absorptivity (how well the material absorbs light), b is the path length (through which the light passes), and c is the solution concentration. In typical spectrophotometric techniques, it is generally perceived that the value of b remains the same by using the same sample cell holder (cuvette). Accordingly, the value for Є is constant for a specific chemical species at a given wavelength. In this experiment, indicator dyes are good candidates for analysis, in that, these substances give varied colors when subjected to different pH environments. Indicators dyes are compounds that are essentially weak acids (or bases) that exhibit different colors at various pH levels. The color exhibited by the aqueous solution of the dye is dependent simply whether the dye is present largely in its acidic form (HIn) or its basic form (In–). Such property of dyes in aqueous media affords the use of spectrophotometric methods to relate absorbance data to the relative amounts of the acid and base forms of the dye in buffered solutions.

The dissociation of an acid dye in aqueous solution can be represented as

HIn + H2O H3O+ + In– (6-2)
(color 1) (color 2)

where HIn and In– are the acid and conjugate forms of the dye, respectively. If the pH of the solution containing the indicator dye changes, the equilibrium shown in equation (6 – 1) will be driven either towards more reactants (more HIn) or more products (more In–). This results in a color change that depends on the concentration of each dye form present.

For instance, in a strongly acidic solution, the equilibrium is shifted to the left and thus the indicator will be present in the HIn form, exhibiting a color that corresponds to that of HIn. Conversely, in a strongly basic solution, the equilibrium is shifted to the right resulting in a color characteristic of the In– form. Appropriately, at an intermediate pH value, a color which is primarily a combination of colors 1 and 2 results, where the tinge depends largely on the relative amounts of the dye forms present.

Considering the mass action expression for the reaction depicted in (6-2)

Ka=H3O+In-HIn (6-3)

The previous equation can be transformed in such a way that introduces pH in the equation

pKa=pH-logIn-HIn (6-4)

Equation (6-4) is commonly known as the Henderson-Hasselbalch equation.

Employing both Beer’s Law and the Henderson-Hasselbalch equation allows the analysis of a solution that contains two colored species, in this case, the acid and base...