A Simplified Method for Finding the Pka of an Acid–Base Indicator by Spectrophotometry

In the Laboratory

A Simplified Method for Finding the pKa of an Acid–Base Indicator by Spectrophotometry

George S. Patterson* Suffolk University, 41 Temple Street, Boston, MA 02114

λ General chemistry textbooks devote much space to the max at a different wavelength. If the cell path length is kept important concept of equilibrium. To illustrate one aspect constant and all solutions contain the same total molarity of λ of equilibrium, a new laboratory experiment on the measure- indicator, the acid–base ratio at the max of either the acid or ment of an equilibrium constant was desired. Ideally, the ex- base form is given by (3, 10, 11) periment would ᎑ 1. result in a reasonably accurate value of the equilibrium HIn A – AIn constant, ᎑ = (2) [In ] AHIn – A 2. use a small number of solutions that are safe to handle—or at least be familiar to students—and simple to dispose, where A is the absorbance of the solution containing a certain total concentration of the acid–base mixture, A ᎑ is the 3. use equipment commonly found in a general chemistry In laboratory, and absorbance of the base form at the same concentration, and AHIn is the absorbance of the acid form at the same concentration. 4. not exceed the skills of a typical general chemistry Substituting the expression for the HIn–In᎑ ratio from student. eq 2 into eq 1, A well-known experiment in analytical and physical ᎑ chemistry laboratory courses is the spectrophotometric A – AIn pK = pH + log (3) determination of the pK of an acid–base indicator (1–9). a 10 a AHIn – A Following published procedures, this experiment yields accurate results using equipment found in most general chemistry labs or (pH meters and single-wavelength spectrophotometers, such A – A ᎑ as the Spectronic 20). The acidic and basic solutions generated In log10 =pKa –pH (4) during the experiment are probably familiar to students and can AHIn – A be disposed by neutralizing them then pouring them down the drain. In most published procedures, however, several The pK a of an indicator can be determined by either of two buffer solutions must be prepared by technicians before the equivalent methods, an algebraic method or a graphical lab or by students during the lab. Also, the procedures would method. In the algebraic method, sets of pH and absorbance be difficult for most general chemistry students to complete in values are substituted into eq 3 and the pKa is calculated for a three-hour laboratory period. We have developed a simpler each set. The pKa reported is the average of the calculated ᎑ method that uses fewer solutions; pKa results for this method pKa’s. In the graphical method, log10[(A – AIn )/(AHIn – A)] using eight common indicators are reported here. vs pH from eq 4 is plotted, and pKa is obtained as the x- For the simple method outlined here to work well, there intercept. The line should have a slope of ᎑1. must be only one acid form of the indicator (HIn) and one base form (In᎑) in equilibrium: Experimental Procedure HIn H+ + In᎑ A 1% solution of phenolphthalein in isopropanol, pHydrion buffer capsules (pH 4, 7, and 10), and 50% sodium If we use concentrations rather than activities, the expression hydroxide solution were purchased from Fisher Scientific Co. for the equilibrium constant for the reaction is Aqueous solutions containing 0.04% bromocresol green, + ᎑ 0.04% bromocresol purple, 0.04% bromophenol blue, 0.04% [H ][In ] bromothymol blue, 0.10% methyl orange, 0.10% sodium salt Ka = HIn of methyl red, and 0.04% phenol red were obtained from Aldrich Chemical Co. The logarithmic form of the equation is The procedure for determining the pKa for bromophenol blue is described in detail. Conditions for determining the HIn pK values for the other indicators are tabulated. pKa = pH + log10 ᎑ (1) a [In ] A bromophenol blue solution in its base form was prepared by dissolving 6 drops of the 0.04% dye solution and 2 drops The acid form of the indicator has a color, such as yellow, of 1 M NaOH in 10 mL of distilled water. To obtain an esti- λ λ with its corresponding max at one wavelength, and the base mate of max, the absorbances of the solution were measured form has another color, such as blue, with its corresponding on a Bausch & Lomb Spectronic 20D spectrophotometer at *Email: [email protected]. 20-nm intervals from 560 to 640 nm (Table 1). The absorbance

JChemEd.chem.wisc.edu • Vol. 76 No. 3 March 1999 • Journal of Chemical Education 395 In the Laboratory

Table 1. Absorbance Values λ Table 2. Conditions for Obtaining max for Indicators for Bromophenol Blue Nmo. of Drops Wavelength/n Weavelength/nm Absorbanc Indicator Dye Base λ λ Range max max 5360 0.55 Soln or Acid Lit (12) Exptl 5280 0.81 B92romocresol green a 5780–660 651 61 6600 0.79 B92romocresol purple a 5140–620 509 59 6120 0.28 B62romophenol blue a 5260–640 509 59 6740 0.07 B92romothymol blue a 5780–660 651 61 5490 0.91 M12ethyl orange b 4260–540 502 505–51 M12ethyl red b 4080–560 553 520–52 P12henolphthalein a 5300–580 505 55 λ a at 590 nm was measured to determine the value of max more P42henol red 5820–600 505 56 λ precisely. Conditions for determining max for all indicators NOTE: For sulphonphthalein indicators such as bromocresol green and are listed in Table 2. bromothymol blue and for phenolphthalein, the best choice of wave- λ The solution for determining the pKa of bromophenol blue length is the max of the base form of the indicator because the base form λ λ was prepared by dissolving 5.0 mL of 0.04% bromophenol blue has a higher absorbance at its max than the acid form has at its max. λ 1 Also, the acid form generally absorbs very little at the max of the base, solution and the contents of one pH 4 buffer capsule in water λ whereas the base form absorbs significantly at the max of the acid. The in a 250-mL volumetric flask. Fifty milliliters of the solu- azo dyes methyl orange and methyl red have the opposite behavior, and λ tion was poured into each of five 100-mL beakers. Using a the best wavelength for measuring their pK a is the max of the acid form. pH meter accurate to 0.01 pH unit, two of the solutions were a1 M NaOH; b1 M HCl. adjusted to about pH 3.4 and pH 3.7 by dropwise addition of 1 M HCl. Two other solutions were adjusted to approximately pH 4.3 and pH 4.6 by dropwise addition of 1 M NaOH. Table 3. Solutions Used To Measure pK of Indicators The solution in the fifth beaker had a pH of about 4.0. The a approximate pH values used for all the indicators are listed Vol of Buffer in Table 3. In each case, solutions were adjusted to pH values Indicator Indicator/ Capsule Approximate pH Values lower than that of the buffer capsule with 1 M HCl and to pH mL a (pH) values higher than that of the buffer capsule with 1 M NaOH. B0romocresol green 94,. 4,.0 4,.3 4,.6 42.9 5. The absorbances of the five bromophenol blue solutions B0romocresol purple 77,. 5,.4 5,.7 6,.0 66.3 6. were measured with a Bausch & Lomb Spectronic 20D B0romophenol blue 54,. 3,.4 3,.7 4,.0 46.3 4. spectrophotometer. The pH 3.4 solution was then adjusted B0romothymol blue 97,. 6,.4 6,.7 7,.0 76.3 7. to about pH 2 with two drops of concentrated HCl solution to produce pure HIn, and the absorbance of the resulting M5ethyl orange 14,. 3,.1 3,.4 3,.7 43.0 4. Methyl red b 14,.5 4,.4 4,.7 5,.0 56.3 5. solution was measured to determine AHIn. Similarly, the pH 4.6 solution was adjusted to about pH 12 with two drops of P2henolphthalein 00. 1 c 8,.8, 9,.1 9,.4 90.7 10. ᎑ 50% NaOH solution to produce pure In , and the absorbance P0henol red 37,. 7,.2 7,.5 7,.8 84.1 8. ᎑ of the resulting solution was measured to determine AIn . The aVolumes of indicator solutions were chosen such that the highest results for bromophenol blue are displayed in Table 4. The absorbance value for each indicator was between 0.7 and 1.0. Results ᎑ x-intercept from the plot of log10[(A – AIn )/(AHIn – A)] vs were not as satisfactory when the highest absorbance value was sig- ᎑ pH (Fig. 1) was 3.95, and the slope was 0.96. The pK results nificantly below or above this range. a b for all the indicators investigated are listed in Table 5. Some methyl red precipitated from solution. The solution was filtered before use. c2.0 g of glycerin was added to prevent borax in the buffer from Discussion of Results causing the color to fade.

The average pKa values for the majority of the indicators obtained using eq 3 have small standard deviations, and the slopes of the plots of eq 4 for the indicators are generally close ᎑ to 1. However, the pKa values of phenolphthalein determined Table 4. pKa Determination for Bromophenol Blue by both methods show a much greater uncertainty. Phenol- ᎑ A – AIn phthalein is a dibasic indicator, whose pKa values are so similar log peH Apbsorbanc 10 Ka from eq 3 that the spectrophotometric method does not produce accurate AHIn – A results (15). Methyl red is also a dibasic indicator with a small 30.35 00.17 05.6 3.9 difference between pKa values (16 ), but the standard deviation 37.65 08.28 03.2 3.9 of the average pK a value using eq 3 and the slope of the line from eq 4 have only slightly larger deviations than most of the 31.94 00.41 04.0 3.9 other indicators. Other investigators have also found that 42.30 0.56 ᎑ 0.34 3.96 methyl red produces reasonably accurate results (1, 7, 8). 40.64 0.67 ᎑ 0.65 3.99 The pK values determined by the algebraic method, using a a5v 3.9 ± 0.02 eq 3, and the graphical method, using eq 4, are essentially 12 A 0.818 the same, even for phenolphthalein. Most of these values In¯ 2 A 0.006 are within about 0.1 pH unit of the pKa values found in the HIn

396 Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu In the Laboratory

0.800 the lab period. 0.600 Ð A)] Ð Note

0.400 HIn

0.200 1. The contents of a pH 4 buffer capsule can be replaced by 1.0 g

) / (A / ) of potassium acid phthalate. A mixture of 0.37 g KH PO and 0.60 g

- 2 4 0.000 In anhydrous Na2HPO4 can be substituted for the contents of a pH 7 –0.200 buffer capsule. 3.50 4.00 4.50 5.00 –0.400 [(A Ð A Ð [(A Literature Cited

10 10 –0.600

log –0.800 pH 1. Brown, W. E.; Campbell, J. A. J. Chem. Educ. 1968, 45, 674– 675. Several indicators were studied by the methods of Ramette ᎑ (4) and Tobey (7). Figure 1. Plot of log10[( A – AIn )/(A HIn – A )] vs pH for bromophenol blue. 2. Lai, S. T. F.; Burkhart, R. D. J. Chem. Educ. 1976, 53, 500. The authors assume that, for a number of indicators, the absorbances λ ᎑ ᎑ λ of HIn at the max of In and In at the max of HIn are negligible. Several solutions of an indicator are prepared with different pH λ literature at the same ionic strength. The greatest difference values, and absorbances of the solutions at each max are measured. was found for the pKa of phenolphthalein, which was about The pKa of the indicator is obtained from the equation pK = pH + ᎑∆ ᎑ ∆ ᎑ log( AIn AHIn/ AHIn AIn ), where AHIn is the absorbance of a solu- 0.3–0.4 pH unit lower than the literature value. λ tion at the max of HIn, AIn᎑ is the absorbance of the solution at the This procedure uses fewer solutions than other published ᎑ λ of In , ∆A ᎑ is the range of A ᎑ values, and ∆A is the range methods for finding the pK of an indicator. Solutions required max In In HIn a of AHIn values. (Note that this is the correct equation. The equation prior to the lab can be prepared easily or purchased inexpen- given in ref 2 is incorrect.) Data are presented for thymol blue. sively. Students in the lab prepare just two solutions, the one 3. Ramette, R. W. Chemical Equilibrium and Analysis; Addison- λ used to determine the max of the acid or base form of the Wesley: Reading, MA, 1981; pp 676–681. In a general procedure, indicator and the stock solution used to measure the pKa of students measure the absorption spectra of two solutions containing the indicator. The strong acids and bases used are somewhat the acidic and basic forms of an indicator to determine its ana- λ λ lytical wavelength, max, or the instructor tells them max. The ab- dangerous to handle, but students would probably be familiar λ sorbances of the acid and base forms of the indicator at max, AHIn with their use from previous experiments. At the end of ᎑ ᎑ and AIn , respectively, are used in eq 2 to calculate [HIn]/[In ]. the experiment, the students themselves or technicians can Three solutions of the indicator with different pH’s around its neutralize the solutions generated during the experiment and pK a value are prepared by students using an acid–conjugate base pour them down the drain. buffer, where the pKa of the acid is near the pK a of the indicator. They measure the absorbances and calculate the ionic strengths Conclusions of these solutions. Everyone determines the pKa value for each buffered solution using concentration and absorbance data and This procedure for the spectrophotometric determination activity coefficients, then averages the values. of pK a values of indicators is a good general chemistry lab 4. Ramette, R. W. J. Chem. Educ. 1963, 40, 252–254. Each student is experiment. It leads to accurate results using Spectronic 20’s assigned a different ionic strength at which to prepare solutions and pH meters found in most general chemistry labs. The of bromcresol green at different pH’s to determine the concentration quotient, Q, of the indicator. First, he or she prepares a lab procedure can conveniently be completed within three solution of the indicator in sodium acetate solution, using KCl hours, because there are few solutions to prepare and other to achieve the ionic strength, and measures the absorption spectrum manipulations are kept to a minimum. In addition, students of the solution. The student then adds several aliquots of acetic are probably familiar with the types of reagents used and acid solution and finally an aliquot of hydrochloric acid solution could even dispose their own waste solutions at the end of to the indicator solution. After each aliquot is added, the absorbance

Table 5. Results of Measurement of pKa Values of Indicators

Lit Value (13) of pKa pK Ionic Strength pK a Slope of Indicator at Ionic Strength a from Range Used from Eq 3 Eq 4 Plot 05.01 00.0 0.1 Eq 4 B0romocresol green 40.8 46.7 44.6 02.02–0.0 4.6 ± 02.02 4.6 ᎑1.04 B8romocresol purple 61.2 62.2 65.1 08.02–0.0 6.1 ± 09.03 6.1 ᎑0.94 B6romophenol blue 40.0 45.0 33.8 05.02–0.0 3.9 ± 05.02 3.9 ᎑0.96 B9romothymol blue 73.1 70.1 78.1 00.04–0.0 7.0 ± 00.02 7.0 ᎑1.00 M6ethyl orange 36.4 36.4 32.4 02.0 3.4 ± 03.02 3.4 ᎑1.04 M0ethyl red 50.0 50.0 56.0 01.03–0.0 4.9 ± 00.05 4.9 ᎑0.91 P––7henolphthalein 9. a ~40.1 9.3 ± 07.20 9.3 ᎑1.36 P2henol red 74.9 71.8 79.8 05.07–0.0 7.6 ± 06.02 7.6 ᎑1.03

NOTE: The volumes of acid and base solutions added to the buffered indicator solutions were small compared to that of the indicator solution itself. Calculations do not need to take this dilution into account, because it does not affect the values of the pK a. aReference 14.

JChemEd.chem.wisc.edu • Vol. 76 No. 3 March 1999 • Journal of Chemical Education 397 In the Laboratory

λ of the resulting solution is measured at max, except that the entire 7. Tobey, S. W. J. Chem. Educ. 1958, 35, 514–515. The absorption spectra of the solutions containing 1:1 acetate:acetic acid and spectra of the acidic and basic forms of methyl red were mea- λ hydrochloric acid are recorded. Absorption readings are corrected sured to determine their respective max values. The absorbancies λ for dilution. Each student calculates the hydrogen ion concentra- of both the acidic and basic forms at both max values were de- tion of each solution using the dissociation quotient of acetic acid termined using Beer’s law plots. Four solutions of methyl red with at his or her assigned ionic strength. They calculate pQ values for the same ionic strength but different pH’s were prepared using each solution using eq 3, then determine an average value. The class the same concentration of sodium acetate and different concen- pools their average pQ values at different ionic strengths, then each trations of acetic acid. The pH of each solution was measured λ person plots pQ vs log f, using the equation pQ = pKa + log f. In with a pH meter, and the absorbance was measured at the max the equation, f is the ratio of activity coefficients and Ka is the value of both the acidic and basic forms. Hydrogen ion concen- acid dissociation constant for the indicator using activities. The trations from pH values and concentrations of the acidic and ba- y-intercept of the graph is pKa. sic forms of methyl red in the four solutions from the absorbance 5. Salzberg, H. W.; Morrow, J. I.; Cohen, S. R.; Green, M. E. Physical and absorbancy data were used to calculate pKa values for each Chemistry Laboratory: Principles and Experiments; Macmillan: New solution. The values were averaged. York, 1978; pp 402–405. Students measure the absorption spectra 8. Walters, D.; Birk, J. P. J. Chem. Educ. 1990, 67, A252–A258. of two solutions containing the acidic and basic forms of bromo- Methyl orange, methyl red, and phenolphthalein were studied. A λ phenol blue to determine its analytical wavelength, max. Next, number of solutions of each indicator were prepared using buffers they dilute solutions containing the indicator until one of the so- that produced a range of pH values such that the solution with low- λ lutions has an absorbance of 0.9–1.0 at max. They further dilute est pH contained the pure acid form of the indicator and the solu- this solution to 0.2, 0.4, 0.6, and 0.8 times its original strength. tion with highest pH contained the pure base form. The absorbance λ ᎑ They measure the absorbance of the diluted solutions at max and of each solution was measured, and plots of (AHIn – AIn )/(A – AHIn) + ᎑1 ᎑ + ᎑1 prepare a Beer’s law plot from the absorbances of the five solutions. vs [H ] from the equation (AHIn – AIn )/(A – AHIn) = 1 + Ka[H ] Each person prepares several solutions with pHs between 3.4 and produced straight lines with slopes equal to Ka. This equation can 4.6 that have the same total concentration of bromophenol blue be derived from eq 3. as the solution with an absorbance of 0.9–1.0. The solutions are 9. Willard, H. H.; Merritt, Jr., L. L.; Dean, J. A. Instrumental Meth- prepared in buffers in this pH range, or the pH is adjusted with hydro- ods of Analysis, 4th ed; Van Nostrand: New York, 1965; pp 108– chloric acid or ammonia solution. Students measure the absor- λ 109. Students obtain the experimental data for bromcresol green bance of these solutions at max. They obtain the pKa of bromophenol by the method of Ramette (4), except that they measure pH with blue from eq 1 using absorbancies from the Beer’s law data and a pH meter and everyone uses the same ionic strength. They de- the absorbances of the pH 3.4–4.6 solutions or from a plot of eq 3, termine values for pKa by both methods described by Sawyer et similar to the method described here. al. (6 ). 6. Sawyer, D. T.; Heineman, W. R.; Beebe, J. M. Chemistry Experiments 10. Ramette, R. W. Chemical Equilibrium and Analysis; Addison- for Instrumental Methods; Wiley: New York, 1984; pp 193–198. Wesley: Reading, MA, 1981; Chapter 13. Students measure the absorption spectra of solutions of bromothymol blue at pH 1, 7, and 13 and choose two wavelengths to the left 11. Ramette, R. W. J. Chem. Educ. 1967, 44, 647–654. and right of the isosbestic point that have maximum differences 12. Lange’s Handbook of Chemistry; Dean, J. A., Ed.; McGraw-Hill: between the absorbances of the acid and base forms of the indicator. New York, 1992; pp 8.115–8.116. They prepare solutions of the indicator at seven other pH values us- 13. Handbook of Analytical Chemistry; Meites, L., Ed.; McGraw-Hill: ing phosphate buffers and measure the absorbances of the solutions New York, 1963; Sec. 3 p 36. at the two wavelengths. For each wavelength, students plot A vs 14. Skoog, D. A.; West, D. M. Analytical Chemistry: An Introduction, pH using the data from the nine solutions. The pK is equal to the a 4th ed.; Saunders: Philadelphia, 1986; p 164. pH at the inflection point of each curve. Also, they determine the ratios of [In2᎑]/[[HIn᎑] for each solution from one of the curves 15. Kolthoff, I. M. Acid–Base Indicators; Rosenblum, C., Translator; 2᎑ ᎑ Macmillan: New York, 1937; pp 112 and 221–224. and plot log10[In ]/[[HIn ] vs pH, using an equation derived from eq 1. The pKa is the y-intercept of the graph. 16. Ramette, R. W.; Dratz, E. A.; Kelly, P. W. J. Phys. Chem. 1962, 66, 527–532.

398 Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu