Spectrophotometric Determination of pK_a of Phenol Red

This procedure uses instrumentation to accomplish quantitative analysis. You will get far more experience in this during CH427. In this experiment, the pKa of phenol red is determined spectrophotometrically. In lecture we will learn that the advantage of a spectrophotometric titration over a potentiometric titration (and especially over indicator-based titrations) is that more of the titration curve contains information. In fact, you can determine an endpoint without ever sampling that point in the titration.

In a sense, we are doing a titration in this experiment in an odd way, by constructing solutions of varying pH from the ground up, rather than by sequentially adding titrant. Phenol red (phenolsulphonephthalein, C₁₉H₁₅O₅S) is a commonly used pH indicator. It is a diprotic acid, H₂In, whose dissociations can be described by the following equations:

H₂In à HIn^- + H⁺ (1)

HIn^- à In^2- + H⁺ (2)

(3)

It is the color change during the second dissociation that is usually used for indicator based titrations. HIn^- has a yellow color and In^2- has a red color. (This means their absorption spectra are different.) When both HIn^- and In^2- are present, the solution has an orange color. (Note 1) Equation (3) can be rearranged to give

(4)

The ratio, [In^2-]/[HIn^-] can be determined by spectrophotometry. If the log of this ratio is plotted vs. pH, the slope is 1 and the intercept is -pKa.

{The line should cross the pH axis at pH = pKa, because when [In^2-] = [HIn^-] the log term is zero, making pH = pKa.}

PROCEDURE

Again, due to the scarcity of the equipment, you will have to pair up for this experiment. Prepare the solutions independently, then come together for the absorbance measurements. As always, take turns doing the “hands-on” parts so that both partners will get the experience.

There are two major steps in the determination of the ratio [In^2-]/[HIn^-]:

(1) Preparation of solutions with different pH values. An acidic solution of phenol red is prepared in which essentially all the indicator is in the HIn^- form. A basic solution is prepared in which essentially all the indicator is in the form of In^2-. Buffered solutions (containing the indicator) with different pH values are prepared, in which both In^2- and HIn^- are present but their ratios vary with pH. In all solutions the total concentration of indicator ([In^2-] + [Hln^-]) remains the same.

(2) Measurement of absorbances. In this part of the experiment, the absorbance will be measured at 550 nm (the peak wavelength of the In^2- absorption band) and used in the calculation of pKa.

By defining the following absorbances at the selected wavelength:

A_a = absorbance of HIn^- (i.e., indicator prepared in the acidic solution)

A_b = absorbance of In2- (i.e., indicator prepared in the basic solution)

A = absorbance of mixture (i.e., indicator prepared in the buffered solutions)

the ratio of concentrations can be calculated from the absorbances as follows:

(5)

Solution Available

1. Phenol red solution: 0.0500 g phenol red dissolved in 50.00 mL of 95% ethanol and diluted to 250.0 mL with distilled water.

Solutions to Prepare

2. 0.1 M NaOH solution (prepare from 1 M NaOH).

3. 0.25 M KH₂PO₄ : Weigh 0.85 g (to 0.1 mg) of KH₂PO₄ into a 25-mL volumetric flask, dissolve in distilled water, dilute to the mark, and mix thoroughly.

4. 0.25 M Na₂HPO₄ : Weigh 0.89 g (to 0.1 mg) of Na2HPO4 into a 25-mL volumetric flask, dissolve in distilled water, dilute to the mark, and mix thoroughly.

5. Solutions for spectrophotometric measurements: To each of six 25-mL volumetric flasks pipet 1.00 mL of the phenol red solution. Then pipet the volumes of phosphate solutions according to the table below:

flask	KH2PO4 (mL)	Na2HPO4 (mL)	Composition
1	10	0	acidic
2	4	2	buffered
3	2.5	2.5	buffered
4	1	3	buffered
5	0.4	3.2	buffered

Dilute all 5 solutions with distilled water to the mark, then fill flask 6 to the mark with 0.1 M NaOH solution, and mix all flasks thoroughly. The solution in flask 1 is the acidic solution; the pH of this solution is sufficiently low that essentially all the indicator is in the HIn^- form. The solution in flask 6 is the basic solution (0.1 M NaOH) in which all the indicator is in the In^2- form.

Measure the temperature of the solutions. The K_a2 of phosphoric acid is 6.149 x10^-8 at 20 ºC and 6.303 x 10^-8 at 25 ºC. Calculate the pK_a2 at the measured temperature by interpolation, if necessary. Next calculate the pH of flasks 2 through 5 using the value of pK_a2 you just determined.

Note: since the phosphate solutions are so much more concentrated than the indicator, you may neglect the influence of the latter in the calculation of pH. Otherwise this would be much harder.

pH Measurements

Use the Fisher Accumet pH meter to measure the pH of the six solutions.

Absorbance Measurements

Measure the absorbance at 550 nm for all the solutions using the cuvettes in your drawer. Be wary of carryover! Ask the TA for help if you don’t know how to use the Beckman DU-250. Make sure that you are measuring against (i.e., doing a blank or baseline measurement) a suitable reference; for example, the same cuvette with water in it.

REQUIRED MEASUREMENTS

As usual, prelabs are due before you start work on this experiment.

Report the pH and absorbance of the six solutions and the derived and measured values of log([In^2-]/[HIn^-]) for the buffered solutions. Plot log([In^2-]/[HIn^-]) vs. pH for the derived and measured pH and derive the linear least-squares fit through the data. Note the value of pKa for phenol red on the graph. This value should be between 7.5 and 8.0. If not, try to identify possible errors. The graphs should be presented as part of the results. If there is a difference between the measured and calculated pH values, suggest its origin.

NOTES

1) The absorbance, which imparts color to the solution, of each of the compounds present acts independently and we see the sum of the absorbances of the two compounds present.

Mathematically: A = A_(HIn-) + A_(In2-) = ε_(HIn-) b c_(HIn-) + ε_(In2-) b c_(In2-).