Acid Dissociation Constant

EXPERIMENT 2
ACID DISSOCIATION CONSTANT OF AN INDICATOR DYE

OBJECTIVES

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 forms of the indicator dye.

The ratio [In–]/[HIn] at different pH values and at constant total dye concentration may be investigated using spectrophotometric methods through absorbance measurements. This technique involves the following:

(a) Determination of the wavelengths λHIn and λIn- at which the acid and base forms of the dye exhibit maximum absorption. (b) Determination of the absorptivities of both acid and base forms of the dye at λHIn and λIn- using Beer’s Law. (c) Measurement of the absorbances of buffered solutions of the dye at λHIn and λIn-.

The buffered solutions can be taken to be mixtures of two independently absorbing species, HIn and In–, and hence, the absorbances are simply additive sums of the absorbances due to HIn and In–. This relationship is an extension of the Beer’s Law known as the Beer-Lambert’s Law, which can be interpreted in the subsequent equations:

A=AλHIn+AλIn- (6-5)

AλHIn=aλHIn,HIn*HIn+aλHIn,In-*In- (6-6) AλIn-=aλIn-,HIn*HIn+aλIn-,In-*In- (6-7)

where AλHIn and AλIn- are the absorbances of the dye solution at λHIn and λIn-, respectively; and aλHIn,HIn , aλHIn,In- , aλIn-,HIn , aλIn-,In- are the absorptivities of HIn and In– at the wavelengths, λHIn and λIn-, correspondingly.

MATERIALS

spectrophotometer indicator dyes (0.08 g/L in 20% ethanol) pH meter 0.05 M and 0.01 M HCl analytical balance 0.05 M and 0.01 M borax (Na2B4O7•10H2O) solution
100 mL volumetric flasks buffers solutions pipettes unknown sample

PROCEDURE

I. Spectra of the Acid and Base Forms of the Dye A. Preparation of Dye Solutions 1. Obtain the assigned dye solution from your laboratory instructor. 2. Prepare the acidic solution of your dye: a. Place 10 mL of 0.05M HCl in a 100-mL volumetric flask. b. Add 10 mL of the dye to the HCl in the volumetric flask. c. Dilute to volume with distilled water. d. Mix well and set aside. 3. Prepare the basic solution of your dye using 0.05M borax solution.

B. Determination of the Wavelength of Maximum Absorbance (λmax) 1. Measure the absorbances of the solutions prepared in Part A at 20-nm intervals within the 340 – 625 nm wavelength range. 2. Make measurements at smaller intervals within the vicinity of the wavelength of maximum absorption. 3. Record all data properly. 4. Identify the λHIn and the λIn-.

Important reminders: a. Zero (100% transmittance) the spectrophotometer against the blank every time a new wavelength of incident light is set. b. The blank should consist of the solvent including all the reagents other than the specific absorbant being analyzed. c. Wash the sample cuvette very thoroughly. Make sure to wash it with small portions of the test liquid prior to every measurement. d. Ensure that the optically clear faces of the cuvette are free from finger marks, stains ore drops of liquids. e. Strive to keep the cuvette on the same position each time it is used.

II. Determination of Molar Absorptivities A. Preparation of Dilute Solutions 1. Take 10, 25, and 40 mL aliquots of the acidic solution prepared in Part IA and put into separate 50 mL volumetric flasks. 2. Dilute each solution to mark using 0.01M HCl. 3. Repeat step 1 with the basic solution this time using 0.01M borax solution for dilution. 4. Label the flasks. B. Absorbance Measurements at the (λmax) 1. Measure the absorbances of the six solutions at the wavelengths of maximum absorption, λHIn and the λIn-, which were determined in Part 1B. 2. Record all data properly.

III. Determination of the pKa A. Preparation of Solutions at Various pH Levels 1. Prepare five solutions at various pH values but with constant total dye concentration by following the succeeding steps. 2. For each solution to be prepared, obtain 10 mL of the original dye solution and place into a 100 mL volumetric flask. 3. Dilute to the mark with the buffer solution.
NOTES:
e. The buffer system to be used should consist of a weak acid or weak base whose pKa value is within ± 0.10 unit of the desired pH value. f. The four pH values chosen should fall within the transformation range of the dye. g. Select the appropriate buffer for this range of pH values.

B. Absorbance and pH Measurements 1. Measure the absorbances (at λHIn and the λIn-) of each of the buffered solutions prepared in Part IIIA. 2. Determine the actual pH of the five solutions using a pH meter. 3. Record all data.

Figure 6.1. Sample absorption spectra of an indicator dye in (A) acidic solution, (B) basic solution, and (C) solution at intermediate pH.

DATA ANALYSIS 4. Prepare a plot of the absorbance of the acid solutions against the wavelengths of maximum absorption, λHIn and the λIn-. (See Figure 6.1) Do the same for the basic solutions. 5. Overlay the plots and locate the isosbestic point. (Refer to Figure 6.2) 6. Plot the absorbance against concentration of the dye in the basic and acidic solutions at λHIn and the λIn-. 7. Using Beer-Lambert’s Law, derive the values of the absorptivities of the acid and base forms at the two wavelengths from the graphs obtained in #3. You should be able to derive four values: aλHIn,HIn (absorptivity of the acid form, HIn, at the λHIn) aλHIn,In- (absorptivity of the base form, In–, at the λHIn) aλIn-,HIn (absorptivity of the acid form, HIn, at the λIn-) aλIn-,In- (absorptivity of the base form, In–, at the λIn-)

8. Calculate the concentrations of the acid and base forms of the dye in the various buffered solutions using equations (6-6) and (6-7). 9. Use Henderson-Hasselbalch equation (6-4) to calculate the pKa of the dye. Determine the average pKa value. You might need to do regression analysis.

Figure 6.2. Plot of absorbance as a function of pH for an indicator dye. The isosbestic point is where the absorbance plot of the measurements made at λHIn (I) crosses that of absorbance plot of the measurements made at λIn-(II).

POSTLAB QUESTIONS 5. Discuss the principle behind the operation of a simple spectrophotometer. Use diagrams when deemed appropriate. 6. What are the assumptions and limitations of Beer’s Law? 7. What is the significance of the isosbestic point?

REFERENCES

BRAUN, R. D. 1982. Introduction to Chemical Analysis, New York: McGraw-Hill Book Co.

BASSETT, J. et al. 1981. Vogels’s Textbook of Quantitative Inorganic Analysis, 4th ed. New York: Longman.

DANIELS, F. et al. 1970. Experimental Physical Chemistry, New York: McGraw-Hill Book Co.

ALBERTY, R.A. and R.J. Silbey. 1992. Physical Chemistry, New York: John Wiley & Sons, Inc.

APPENDIX

If bromothymol blue (3,3- dibromo-thymolsulfonephthalein) is the dye to be used in the experiment, the following information is important: * At pH less than 6, the indicator is yellow and at pH greater than 7.6, the indicator is blue. At an intermediate pH, the blue and yellow combine to yield a green solution. * The absorbance of a pH 6.85 bromothymol blue solution was 0.7333 at 430 nm and 0.5690 at 555 nm. * The minimum absorbance at 430 nm was 0.1320, and the minimum absorbance at 555 nm was 0.0210. * The absorbance of a pH 1 solution of the same concentration of bromothymol blue was 1.097 at 430 nm and the absorbance of a pH 13 solution of the same concentration of bromothymol blue was 1.4280 at 555 nm.

References: BRAUN, R. D. 1982. Introduction to Chemical Analysis, New York: McGraw-Hill Book Co. BASSETT, J. et al. 1981. Vogels’s Textbook of Quantitative Inorganic Analysis, 4th ed. New York: Longman. DANIELS, F. et al. 1970. Experimental Physical Chemistry, New York: McGraw-Hill Book Co. ALBERTY, R.A. and R.J. Silbey. 1992. Physical Chemistry, New York: John Wiley & Sons, Inc. APPENDIX If bromothymol blue (3,3- dibromo-thymolsulfonephthalein) is the dye to be used in the experiment, the following information is important: * At pH less than 6, the indicator is yellow and at pH greater than 7.6, the indicator is blue. At an intermediate pH, the blue and yellow combine to yield a green solution. * The absorbance of a pH 6.85 bromothymol blue solution was 0.7333 at 430 nm and 0.5690 at 555 nm. * The minimum absorbance at 430 nm was 0.1320, and the minimum absorbance at 555 nm was 0.0210. * The absorbance of a pH 1 solution of the same concentration of bromothymol blue was 1.097 at 430 nm and the absorbance of a pH 13 solution of the same concentration of bromothymol blue was 1.4280 at 555 nm.