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

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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).
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