In the Laboratory

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

A Simplified Method for Finding the pKa of an AcidBaseIndicator by Spectrophotometry

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

General chemistry textbooks devote much space to theimportant concept of equilibrium. To illustrate one aspectof equilibrium, a new laboratory experiment on the measure-ment of an equilibrium constant was desired. Ideally, the ex-periment would

1. result in a reasonably accurate value of the equilibriumconstant,

2. use a small number of solutions that are safe tohandleor at least be familiar to studentsand simpleto dispose,

3. use equipment commonly found in a general chemistrylaboratory, and

4. not exceed the skills of a typical general chemistrystudent.

A well-known experiment in analytical and physicalchemistry laboratory courses is the spectrophotometricdetermination of the pKa of an acidbase indicator (19).Following published procedures, this experiment yields accurateresults using equipment found in most general chemistry labs(pH meters and single-wavelength spectrophotometers, suchas the Spectronic 20). The acidic and basic solutions generatedduring the experiment are probably familiar to students and canbe disposed by neutralizing them then pouring them downthe drain. In most published procedures, however, severalbuffer solutions must be prepared by technicians before thelab or by students during the lab. Also, the procedures wouldbe difficult for most general chemistry students to complete ina three-hour laboratory period. We have developed a simplermethod that uses fewer solutions; pKa results for this methodusing eight common indicators are reported here.

For the simple method outlined here to work well, theremust be only one acid form of the indicator (HIn) and onebase form (In{) in equilibrium:

HIn H+ + In{

If we use concentrations rather than activities, the expressionfor the equilibrium constant for the reaction is

Ka =

[H+][In{ ]

HIn

The logarithmic form of the equation is

pKa = pH + log10

HIn

[In{ ](1)

The acid form of the indicator has a color, such as yellow,with its corresponding max at one wavelength, and the baseform has another color, such as blue, with its corresponding

max at a different wavelength. If the cell path length is keptconstant and all solutions contain the same total molarity ofindicator, the acidbase ratio at the max of either the acid orbase form is given by (3, 10, 11)

HIn

[In{ ]=

A A In{

AHIn A(2)

where A is the absorbance of the solution containing a certaintotal concentration of the acidbase mixture, AIn{ is theabsorbance of the base form at the same concentration, and AHInis the absorbance of the acid form at the same concentration.

Substituting the expression for the HInIn{ ratio fromeq 2 into eq 1,

pKa = pH + log10

A A In{

AHIn A(3)

or

log10

A A In{

AHIn A= pKa pH (4)

The pK a of an indicator can be determined by either of twoequivalent methods, an algebraic method or a graphicalmethod. In the algebraic method, sets of pH and absorbancevalues are substituted into eq 3 and the pKa is calculated foreach set. The pKa reported is the average of the calculatedpKas. In the graphical method, log10[(A AIn{)/(AHIn A)]vs pH from eq 4 is plotted, and pKa is obtained as the x-intercept. The line should have a slope of {1.

Experimental Procedure

A 1% solution of phenolphthalein in isopropanol,pHydrion buffer capsules (pH 4, 7, and 10), and 50% sodiumhydroxide solution were purchased from Fisher Scientific Co.Aqueous solutions containing 0.04% bromocresol green,0.04% bromocresol purple, 0.04% bromophenol blue, 0.04%bromothymol blue, 0.10% methyl orange, 0.10% sodium saltof methyl red, and 0.04% phenol red were obtained fromAldrich Chemical Co.

The procedure for determining the pKa for bromophenolblue is described in detail. Conditions for determining thepKa values for the other indicators are tabulated.

A bromophenol blue solution in its base form was preparedby dissolving 6 drops of the 0.04% dye solution and 2 dropsof 1 M NaOH in 10 mL of distilled water. To obtain an esti-mate of max, the absorbances of the solution were measuredon a Bausch & Lomb Spectronic 20D spectrophotometer at20-nm intervals from 560 to 640 nm (Table 1). The absorbance*Email: spatters@acad.suffolk.edu.

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

at 590 nm was measured to determine the value of max moreprecisely. Conditions for determining max for all indicatorsare listed in Table 2.

The solution for determining the pKa of bromophenol bluewas prepared by dissolving 5.0 mL of 0.04% bromophenol bluesolution and the contents of one pH 4 buffer capsule1 in waterin a 250-mL volumetric flask. Fifty milliliters of the solu-tion was poured into each of five 100-mL beakers. Using apH meter accurate to 0.01 pH unit, two of the solutions wereadjusted to about pH 3.4 and pH 3.7 by dropwise addition of1 M HCl. Two other solutions were adjusted to approximatelypH 4.3 and pH 4.6 by dropwise addition of 1 M NaOH.The solution in the fifth beaker had a pH of about 4.0. Theapproximate pH values used for all the indicators are listedin Table 3. In each case, solutions were adjusted to pH valueslower than that of the buffer capsule with 1 M HCl and to pHvalues higher than that of the buffer capsule with 1 M NaOH.

The absorbances of the five bromophenol blue solutionswere measured with a Bausch & Lomb Spectronic 20Dspectrophotometer. The pH 3.4 solution was then adjustedto about pH 2 with two drops of concentrated HCl solutionto produce pure HIn, and the absorbance of the resultingsolution was measured to determine AHIn. Similarly, the pH4.6 solution was adjusted to about pH 12 with two drops of50% NaOH solution to produce pure In{, and the absorbanceof the resulting solution was measured to determine AIn{. Theresults for bromophenol blue are displayed in Table 4. Thex-intercept from the plot of log10[(A AIn{)/(AHIn A)] vspH (Fig. 1) was 3.95, and the slope was { 0.96. The pKa resultsfor all the indicators investigated are listed in Table 5.

Discussion of Results

The average pKa values for the majority of the indicatorsobtained using eq 3 have small standard deviations, and theslopes of the plots of eq 4 for the indicators are generally closeto {1. However, the pKa values of phenolphthalein determinedby both methods show a much greater uncertainty. Phenol-phthalein is a dibasic indicator, whose pKa values are so similarthat the spectrophotometric method does not produce accurateresults (15). Methyl red is also a dibasic indicator with a smalldifference between pKa values (16 ), but the standard deviationof the average pK a value using eq 3 and the slope of the linefrom eq 4 have only slightly larger deviations than most of theother indicators. Other investigators have also found thatmethyl red produces reasonably accurate results (1, 7, 8).

The pKa values determined by the algebraic method, usingeq 3, and the graphical method, using eq 4, are essentiallythe same, even for phenolphthalein. Most of these valuesare within about 0.1 pH unit of the pKa values found in the

seulaVecnabrosbA.1elbaTeulBlonehpomorBrof

mn/htgnelevaW ecnabrosbA065 355.0085 218.0006 697.0026 182.0046 770.0095 419.0

gniniatbOrofsnoitidnoC.2elbaT xam srotacidnIrof

rotacidnIsporDfo.oN mn/htgnelevaW

eyDnloS

esaBdicAro egnaR

xam(tiL 21 )

xamltpxE

neerglosercomorB 9 2a 066085 716 516elpruplosercomorB 9 2a 026045 195 095

eulblonehpomorB 6 2a 046065 295 095eulblomyhtomorB 9 2a 066085 716 516

egnarolyhteM 1 2b 045064 225 015505derlyhteM 1 2b 065084 035 525025

nielahthplonehP 1 2a 085005 355 055derlonehP 4 2a 006025 855 065

NOTE: For sulphonphthalein indicators such as bromocresol green andbromothymol blue and for phenolphthalein, the best choice of wave-length is the max of the base form of the indicator because the base formhas a higher absorbance at its max than the acid form has at its max.Also, the acid form generally absorbs very little at the max of the base,whereas the base form absorbs significantly at the max of the acid. Theazo dyes methyl orange and methyl red have the opposite behavior, andthe best wavelength for measuring their pKa is the max of the acid form.

a1 M NaOH; b1 M HCl.

perusaeMoTdesUsnoituloS.3elbaT Ka srotacidnIfo

rotacidnIfoloV

/rotacidnILm a

reffuBeluspaC

)Hp(seulaVHpetamixorppA

neerglosercomorB 0.9 4 ,0.4 ,3.4 ,6.4 ,9.4 2.5elpruplosercomorB 0.7 7 ,4.5 ,7.5 ,0.6 ,3.6 6.6

eulblonehpomorB 0.5 4 ,4.3 ,7.3 ,0.4 ,3.4 6.4eulblomyhtomorB 0.9 7 ,4.6 ,7.6 ,0.7 ,3.7 6.7

egnarolyhteM 5.1 4 ,1.3 ,4.3 ,7.3 ,0.4 3.4derlyhteM b 5.1 4 ,4.4 ,7.4 ,0.5 ,3.5 6.5

nielahthplonehP 2.0 01 c ,8.8 ,1.9 ,4.9 ,7.9 0.01derlonehP 0.3 7 ,2.7 ,5.7 ,8.7 ,1.8 4.8

aVolumes of indicator solutions were chosen such that the highestabsorbance value for each indicator was between 0.7 and 1.0. Resultswere not as satisfactory when the highest absorbance value was sig-nificantly below or above this range.

bSome methyl red precipitated from solution. The solution was filteredbefore use.

c2.0 g of glycerin was added to prevent borax in the buffer fromcausing the color to fade.

p.4elbaT Ka eulBlonehpomorBrofnoitanimreteD

Hp ecnabrosbA pKa 3qemorf

53.3 071.0 06.0 59.356.3 782.0 82.0 39.349.3 114.0 00.0 49.303.4 265.0 { 43.0 69.346.4 076.0 { 56.0 99.3

va 59.3 20.021 A nI 818.02 A nIH 600.0

log10A AIn{

AHIn A

In the Laboratory

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

literature at the same ionic strength. The greatest differencewas found for the pKa of phenolphthalein, which was about0.30.4 pH unit lower than the literature value.

This procedure uses fewer solutions than other publishedmethods for finding the pKa of an indicator. Solutions requiredprior to the lab can be prepared easily or purchased inexpen-sively. Students in the lab prepare just two solutions, the oneused to determine the max of the acid or base form of theindicator and the stock solution used to measure the pKa ofthe indicator. The strong acids and bases used are somewhatdangerous to handle, but students would probably be familiarwith their use from previous experiments. At the end ofthe experiment, the students themselves or technicians canneutralize the solutions generated during the experiment andpour them down the drain.

Conclusions

This procedure for the spectrophotometric determinationof pK a values of indicators is a good general chemistry labexperiment. It leads to accurate results using Spectronic 20sand pH meters found in most general chemistry labs. Thelab procedure can conveniently be completed within threehours, because there are few solutions to prepare and othermanipulations are kept to a minimum. In addition, studentsare probably familiar with the types of reagents used andcould even dispose their own waste solutions at the end of

the lab period.

Note

1. The contents of a pH 4 buffer capsule can be replaced by 1.0 gof potassium acid phthalate. A mixture of 0.37 g KH2PO4 and 0.60 ganhydrous Na2HPO4 can be substituted for the contents of a pH 7buffer capsule.

Literature Cited

1. Brown, W. E.; Campbell, J. A. J. Chem. Educ. 1968, 45, 674675. Several indicators were studied by the methods of Ramette(4) and Tobey (7).

2. Lai, S. T. F.; Burkhart, R. D. J. Chem. Educ. 1976, 53, 500. Theauthors assume that, for a number of indicators, the absorbancesof HIn at the max of In{ and In{ at the max of HIn are negligible.Several solutions of an indicator are prepared with different pHvalues, and absorbances of the solutions at each max are measured.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-tion at the max of HIn, AIn{ is the absorbance of the solution at themax of In{, AIn{ is the range of AIn{ values, and AHIn is the rangeof AHIn values. (Note that this is the correct equation. The equationgiven in ref 2 is incorrect.) Data are presented for thymol blue.

3. Ramette, R. W. Chemical Equilibrium and Analysis; Addison-Wesley: Reading, MA, 1981; pp 676681. In a general procedure,students measure the absorption spectra of two solutions containingthe acidic and basic forms of an indicator to determine its ana-lytical wavelength, max, or the instructor tells them max. The ab-sorbances of the acid and base forms of the indicator at max, AHInand AIn{, respectively, are used in eq 2 to calculate [HIn]/[In{].Three solutions of the indicator with different pHs around itspK a value are prepared by students using an acidconjugate basebuffer, where the pKa of the acid is near the pK a of the indicator.They measure the absorbances and calculate the ionic strengthsof these solutions. Everyone determines the pKa value for eachbuffered solution using concentration and absorbance data andactivity coefficients, then averages the values.

4. Ramette, R. W. J. Chem. Educ. 1963, 40, 252254. Each student isassigned a different ionic strength at which to prepare solutionsof bromcresol green at different pHs to determine the concen-tration quotient, Q, of the indicator. First, he or she prepares asolution of the indicator in sodium acetate solution, using KClto achieve the ionic strength, and measures the absorption spectrumof the solution. The student then adds several aliquots of aceticacid solution and finally an aliquot of hydrochloric acid solutionto the indicator solution. After each aliquot is added, the absorbance

log 1

0 [(A

A I

n-) /

(AH

In A)

] 0.8000.600

0.400

0.200

0.000

0.200

0.400

0.600

0.800

3.50 4.00 4.50 5.00

pH

Figure 1. Plot of log10[( A AIn { )/(AHIn A )] vs pH for bromo-phenol blue.

pfotnemerusaeMfostluseR.5elbaT Ka srotacidnIfoseulaV

rotacidnI(eulaVtiL 31 pfo) Ka

htgnertScinoIta htgnertScinoIdesUegnaR

pKa3qEmorf

pKamorf4qE

foepolStolP4qE

10.0 50.0 01.0neerglosercomorB 08.4 07.4 66.4 40.020.0 26.4 20.0 26.4 { 40.1

elpruplosercomorB 82.6 12.6 21.6 50.020.0 81.6 30.0 91.6 { 49.0

eulblonehpomorB 60.4 00.4 58.3 30.020.0 59.3 20.0 59.3 { 69.0

eulblomyhtomorB 91.7 31.7 01.7 80.040.0 00.7 20.0 00.7 { 00.1

egnarolyhteM 64.3 64.3 64.3 20.0 24.3 20.0 34.3 { 40.1

derlyhteM 00.5 00.5 00.5 60.030.0 19.4 50.0 09.4 { 19.0

nielahthplonehP 7.9 a 1.0~ 43.9 02.0 73.9 { 63.1

derlonehP 29.7 48.7 18.7 90.070.0 56.7 20.0 66.7 { 30.1NOTE: 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 pKa.

aReference 14.

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

of the resulting solution is measured at max, except that the entirespectra of the solutions containing 1:1 acetate:acetic acid andhydrochloric acid are recorded. Absorption readings are correctedfor dilution. Each student calculates the hydrogen ion concentra-tion of each solution using the dissociation quotient of acetic acidat his or her assigned ionic strength. They calculate pQ values foreach solution using eq 3, then determine an average value. The classpools their average pQ values at different ionic strengths, then eachperson plots pQ vs log f, using the equation pQ = pKa + log f. Inthe equation, f is the ratio of activity coefficients and Ka is theacid dissociation constant for the indicator using activities. They-intercept of the graph is pKa.

5. Salzberg, H. W.; Morrow, J. I.; Cohen, S. R.; Green, M. E. PhysicalChemistry Laboratory: Principles and Experiments; Macmillan: NewYork, 1978; pp 402405. Students measure the absorption spectraof two solutions containing the acidic and basic forms of bromo-phenol blue to determine its analytical wavelength, max. Next,they dilute solutions containing the indicator until one of the so-lutions has an absorbance of 0.91.0 at max. They further dilutethis solution to 0.2, 0.4, 0.6, and 0.8 times its original strength.They measure the absorbance of the diluted solutions at max andprepare a Beers law plot from the absorbances of the five solutions.Each person prepares several solutions with pHs between 3.4 and4.6 that have the same total concentration of bromophenol blueas the solution with an absorbance of 0.91.0. The solutions areprepared in buffers in this pH range, or the pH is adjusted with hydro-chloric acid or ammonia solution. Students measure the absor-bance of these solutions at max. They obtain the pKa of bromophenolblue from eq 1 using absorbancies from the Beers law data andthe absorbances of the pH 3.44.6 solutions or from a plot of eq 3,similar to the method described here.

6. Sawyer, D. T.; Heineman, W. R.; Beebe, J. M. Chemistry Experimentsfor Instrumental Methods; Wiley: New York, 1984; pp 193198.Students measure the absorption spectra of solutions of bromothy-mol blue at pH 1, 7, and 13 and choose two wavelengths to the leftand right of the isosbestic point that have maximum differencesbetween the absorbances of the acid and base forms of the indicator.They prepare solutions of the indicator at seven other pH values us-ing phosphate buffers and measure the absorbances of the solutionsat the two wavelengths. For each wavelength, students plot A vspH using the data from the nine solutions. The pKa is equal to thepH at the inflection point of each curve. Also, they determinethe ratios of [In2{]/[[HIn{] for each solution from one of the curvesand plot log10[In2{]/[[HIn{] vs pH, using an equation derivedfrom eq 1. The pKa is the y-intercept of the graph.

7. Tobey, S. W. J. Chem. Educ. 1958, 35, 514515. The absorptionspectra of the acidic and basic forms of methyl red were mea-sured to determine their respective max values. The absorbanciesof both the acidic and basic forms at both max values were de-termined using Beers law plots. Four solutions of methyl red withthe same ionic strength but different pHs were prepared usingthe same concentration of sodium acetate and different concen-trations of acetic acid. The pH of each solution was measuredwith a pH meter, and the absorbance was measured at the maxvalue of both the acidic and basic forms. Hydrogen ion concen-trations from pH values and concentrations of the acidic and ba-sic forms of methyl red in the four solutions from the absorbanceand absorbancy data were used to calculate pKa values for eachsolution. The values were averaged.

8. Walters, D.; Birk, J. P. J. Chem. Educ. 1990, 67, A252A258.Methyl orange, methyl red, and phenolphthalein were studied. Anumber of solutions of each indicator were prepared using buffersthat produced a range of pH values such that the solution with low-est pH contained the pure acid form of the indicator and the solu-tion with highest pH contained the pure base form. The absorbanceof each solution was measured, and plots of (AHIn AIn{)/(A AHIn)vs [H+]{1 from the equation (AHIn AIn{)/(A AHIn) = 1 + Ka[H+]{1

produced straight lines with slopes equal to Ka. This equation canbe derived from eq 3.

9. Willard, H. H.; Merritt, Jr., L. L.; Dean, J. A. Instrumental Meth-ods of Analysis, 4th ed; Van Nostrand: New York, 1965; pp 108109. Students obtain the experimental data for bromcresol greenby the method of Ramette (4), except that they measure pH witha pH meter and everyone uses the same ionic strength. They de-termine values for pKa by both methods described by Sawyer etal. (6 ).

10. Ramette, R. W. Chemical Equilibrium and Analysis; Addison-Wesley: Reading, MA, 1981; Chapter 13.

11. Ramette, R. W. J. Chem. Educ. 1967, 44, 647654.12. Langes Handbook of Chemistry; Dean, J. A., Ed.; McGraw-Hill:

New York, 1992; pp 8.1158.116.

13. Handbook of Analytical Chemistry; Meites, L., Ed.; McGraw-Hill:New York, 1963; Sec. 3 p 36.

14. Skoog, D. A.; West, D. M. Analytical Chemistry: An Introduction,4th ed.; Saunders: Philadelphia, 1986; p 164.

15. Kolthoff, I. M. AcidBase Indicators; Rosenblum, C., Translator;Macmillan: New York, 1937; pp 112 and 221224.

16. Ramette, R. W.; Dratz, E. A.; Kelly, P. W. J. Phys. Chem. 1962,66, 527532.