EXPERIMET 14. ACID DISSOCIATIO COSTAT OF METHYL RED 1 The acid dissociation constant, Ka, of a dye is determined using spectrophotometry. Introduction In aqueous solution, methyl red is a zwitterion and has a resonance structure somewhere between the two extreme forms shown in Figure 1. In acidic solutions, the red form (HMR) is more stable. When base is added, a proton is lost and the yellow anion (MR ) of methyl red is favored. The basic form is yellow because it absorbs blue and violet light. The equilibrium constant for the ionization of methyl red is K a = [H+ ][MR ] [HMR] (1) It is convenient to use this equation in the form pk a = ph log [MR ] [HMR] (2) We can determine the acid-dissociation constant, pk a, by varying the ph and measuring the ratio [MR ]/[HMR]. We will use acetic acid-acetate buffers to control the ph, since the K a value for acetic acid is in the same range as the K a value for methyl red. The ph of these buffers force methyl red to distribute itself somewhat evenly between the two colored forms. O2C O2C H H Acid form (HMR) red H + OH - O 2C Basic form (MR - ) yellow Figure 1. HMR and MR forms of methyl red. 1 Based on an experiment in R. J. Sime, Physical Chemistry, Saunders, Philadelphia, PA, 1990; and CH341 Lab Manual, Colby College, Waterville, ME., 2011 1 Last updated: September 18, 17
Since both forms of methyl red absorb strongly in the visible range, the ratio [MR ] to [HMR] may be determined spectrophotometrically. The absorption of light is governed by Beer s Law: A = ε [ X] (3) where A is the absorbance, ε is the molar absorption coefficient, l is the path length of the cell in centimeters, and [X] is the molar concentration of the absorbing species. The absorbance of mixtures is the sum of the separate absorbencies. In mixtures of the acid and base forms of methyl red the total absorbance is A = A MR + A HMR (4) The absorption spectra of MR and HMR are given schematically in Figure 2. For two components in solution, the absorbance must be measured at two different wavelengths. The best wavelengths to choose for the analysis are where one form absorbs strongly and the absorbance of the other form is negligible. Examination of Figure 2 reveals that there are no wavelengths where one form, MR or HMR, absorbs exclusively. For this case, we need to set up two equations in two unknowns, one equation for each wavelength. Call the two wavelengths λ 1 and λ 2. The absorbance at λ 1 is A 1 and at λ 2 is A 2. The two measurements then provide two simultaneous equations with two unknowns: A 1 = ε 1,MR [MR ]+ε 1,HMR [HMR] (5) A 2 = ε 2,MR [MR ]+ε 2,HMR [HMR] (6) The molar absorbance coefficients are illustrated in Figure 2. The molar absorbance coefficients are determined from standard solutions that contain one component alone. Eqs. (5) and (6) provide two equations in two unknowns. For an unknown solution, the absorbances at the two wavelengths, A 1 and A 2, are determined and then eqs. (5) and (6) are solved for the unknown concentrations [MR ] and [HMR] at each given ph. Figure 2. Absorbance of a solution is the sum of the absorbances of the constituents. Measurements at two wavelengths are necessary to determine the composition of a two-constituent solution if the absorbance bands overlap. The first subscript indexes the wavelength and the second subscript indexes the constituent. 2 Last updated: September 18, 17
An isosbestic point is a wavelength where two species have the same molar absorptivity. At an isosbestic point the absorbance is proportional to the total concentration of the two species, and is independent of their relative concentrations. Apparatus Hewlett Packard 8453A Diode Array UV/Visible Spectrophotometer ph meter Methyl red Sodium acetate Acetic acid Hydrochloric acid 95 % ethanol (denatured) Volumetric flasks and pipettes for preparing solutions. Procedure A stock solution of methyl red has been previously prepared for you by dissolving 1 g of crystalline methyl red in 300 ml of 95 percent ethanol and diluting to 500 ml with distilled water. In this experiment, you will need to prepare a standard solution of methyl red by adding 5 ml of the stock solution to 50 ml of 95 percent ethanol and diluting to 100 ml with water. You may need to prepare this solution more than once. Be sure to use a volumetric pipet for the stock solution, however a 100-mL cylinder may be used for the ethanol. In order to determine the wavelength of maximum absorption for the fully deprotonated form of methyl red (MR ) and the fully protonated form of methyl red (HMR), it is necessary to work at a ph much higher or much lower than methyl red s pk a. At high ph, the fully deprotonated form will be the dominant (ca. 100%) species in solution. At low ph, the fully protonated form will dominate. The spectrum of fully deprotonated methyl red is determined by dissolving it in sodium acetate. The absorption spectrum of fully protonated methyl red is determined by dissolving it in hydrochloric acid. The high ph solution is conveniently prepared by diluting a mixture of 10 ml of the standard methyl red solution and 25 ml of 0.04 M sodium acetate to 100 ml in a volumetric flask. Prepare the low ph solution by diluting a mixture of 10 ml of the standard methyl red solution and 10 ml of a 0.1 M hydrochloric acid to 100 ml in a volumetric flask. Use volumetric pipettes to deliver all these solutions into 100 ml volumetric flasks. Both solutions should be brought up to volume using distilled or deionized water. Measure the UV-VIS spectrum of the high-ph and low-ph sample. Use a range of 400 800 nm. Distilled or deionized water should be used as a blank. The procedure to use the spectrophotometer is given in Appendix A. You should save all your spectra to a disk, or to a properly named folder on the hard-drive. You may export each of your spectra as CSV 3 Last updated: September 18, 17
(comma separated values) from ChemStation for easy import into a spreadsheet, such as Microsoft Excel. If you click slightly to the left of each sample row in the result table, this will select the individual spectrum. Click on the File menu, and Export Selected Spectrum As CSV. These files can be imported into Excel for data analysis and/or re-plotting. To open the files in Excel, launch Excel, and then open the file. Make sure you import it as a comma delimited file. From your two UV-VIS spectra, determine l max for MR (l 1 ) and HMR (l 2 ). Prepare four more solutions of each type: acidic and basic, by varying the volume of the standard methyl red solution in 2 ml increments, from 2 to 8 ml. 2 Use a volumetric pipet for all of these volumes. Measure UV-VIS spectra for all ten solutions, being sure to record both the absorbance at l 1 and at l 2 for each solution. Beer s law states that A = el[x], so a plot of A vs. [X] for each compound at each of the two chosen wavelength should give a straight line whose slope is equal to el. Since l = 1 cm for our cuvettes, the numerical value of e is exactly equal to the slope. You should perform the analysis of you data using a spreadsheet. Make sure you set the intercept to be equal to zero when you do your least-mean-squares fit. At this point, you should have four plots of A vs. [X], and hence four values of e. You should tabulate these values, and their standard errors, in your results section of the lab report. When methyl red is dissolved in a solution with a ph close to its pk a, both forms of the dye (HMR and MR ) will be present in substantial amounts. By measuring the absorbance at the pair of wavelengths selected, you can calculate the amount of each form in solution. From the absorbance of the solution at each wavelength, and by using the value of e for each compound at each wavelength, you can use simultaneously solve equations (5) and (6) to determine [MR ] and [HMR]. The ratio of [MR ] to [HMR] is 1:10 at a ph equal to one unit below the pk a of the dye. Conversely, the ratio of [MR ] to [HMR] is 10:1 at a ph equal to one unit above the pk a. It is imperative to have as many of your solutions as possible in this ph = pk a ±1 range! Since the two forms of the dye have different colors (red and yellow), at the point where the ph pk a, the solution should have an orange color. Obtain a ph meter, and calibrate it using ph 4 and 7 buffer solutions. Follow the procedure on the yellow laminated card next to the ph meter (or see the procedure from the manual after this paragraph). Be sure to rinse the ph electrode with deionized water when changing solutions. The manual for the ph meter is located on the class website if you need more details. 2 You will now have five sets of data for each dye: HMR and MR, since you used 10 ml of dye in the previous step. 4 Last updated: September 18, 17
Figure 3. ph calibration procedure. Prepare 10 (at a very minimum) solutions of methyl red at phs in the range of 3.5 to 6.5. Your solutions should be 0.01 M in sodium acetate, contain a constant total concentration of the dye, and various concentrations of acetic acid. 3 This can be done by using 10 ml of standard dye solution (using a volumetric pipet), 25 ml of 0.04 M sodium acetate, and varying amounts of 0.10 M acetic acid. You should prepare and measure the ph of these solutions one at a time. 4 Start by adding acetic acid to the first flask until the solution appears orange. ote: when the ph approaches the pk a the color will appear to be halfway between the fully protonated (red) and deprotonated (yellow) forms. Once you have your first orange solution, add deionized water until the total volume is about 90 ml, then measure and record its ph. You can then remove the ph probe and add deionized water until it is at volume. To make your other solutions, carefully add acetic acid until the solution appear orange. Add deionized water until the total volume is about 90 ml, then measure the ph of each solution. Add a few drops of aoh or HCl (0.1 M) to raise or lower the ph by a small amount. You need to make sure that no two solutions have a ph within 0.10 units. ote: because we have a buffer, its ph should not change appreciably upon the addition of H 2 O. Make sure the majority of your solutions have a color intermediate between the acidic red and basic yellow form. By measuring the absorbance of each one of these solutions at l 1 and l 2, it is possible to calculate the actual concentrations of HMR and MR for each solution ph. 3 Acetic acid has a pk a of 4.76 at 25 ºC. Hence a mixture of acetic acid and acetate ion will produce a buffer 4 If you prepare the solutions one at a time, you can be sure to obtain enough phs close to the pk a (estimated by the orange solution color). 5 Last updated: September 18, 17
If your ph is more than one unit away from the pk a of methyl red, then there will be more than a ten fold excess of the one methyl red form over the other. This will make determining the concentrations using their UV-VIS absorbance very difficult. Be sure to save your spectra, and export each one as a csv file. Finishing Up Once you are finished, be sure to rinse clean all cuvettes with distilled water. Let drip dry on a kim-wipe before putting the cuvette away. Press the UV-VIS power switch to turn it off, and dispose of all the methyl-red solutions in the appropriate waste container. Do not dispose of the provided stock solution! All volumetric flasks can be rinsed clean with tap water, followed by a small amount of distilled water. They should be drip dried before returning to the supply cupboard. Warning Chemstation can be temperamental in exporting csv files. If the csv files do not contain the full spectrum, try re-exporting the spectra one by one after you click on each curve (it will highlight with diamonds). Calculations Graph absorbance versus dye concentration in acidic and basic solutions at l 1 and l 2 on a single plot. Calculate and tabulate the four molar absorptivity coefficients. Be sure to include appropriate units. Using the CSV exported spectra, you should graph A vs. l for all ten of your highand low-ph solutions on a single plot. In addition, you should graph A vs. l for the ten intermediate ph solutions on a second plot. The raw spectra you printed out from Chemstation should be included in an appendix to your lab report. Calculate and tabulate the concentrations of the acidic (HMR) and basic (MR ) forms of the dye in the various buffer solutions using eqs. (5), and (6). Show all work for at least one of your solutions, or include your Excel worksheet with formulas visible. Use eq. (2) to calculate and tabulate the pk a value for the dye at each ph. Show your work for at least one of your calculations. Be sure to perform a propagation of errors for each pk a value you calculate. You may assume a nominal error of ±0.005 for each absorbance measurement, and a nominal error of ±0.03 for each ph measurement. As a means of testing and averaging the data, plot log {[MR ]/[HMR]} versus ph, and perform a least-mean-squares fit using a spreadsheet. Explain how this plot allows you to determine pk a. An average value from the literature 5 is 5.05 ± 0.05 for the 25 to 30 ºC temperature range. 5 Kolthoff, I. M.; Acid-Base Indicators, The Macmillan Company, ew York, 1953. 6 Last updated: September 18, 17
Questions 1. Derive equation (2) from equation (1). 2. Explain why the pk a of an acid-base indicator establishes its suitability in determining the equivalence point of an acid-base titration. 3. Why do you not need to calculate the molar concentration of the dye solutions to determine the pk a? (If you used concentrations in units of g/l for the HMR and MR the value of pk a would be unchanged.) 4. Why do we expect to see an isosbestic point in this experiment? What would it mean if the isosbestic point were not present? Pre-Lab Questions Calculate the ratio of deprotonated methyl-red (MR ) to methyl-red (HMR) when the ph is 1.00 greater than the pk a. Calculate the ratio of deprotonated methyl-red (MR ) to methyl-red (HMR) when the ph is 1.00 smaller than the pk a. Calculate the ratio of deprotonated methyl-red (MR ) to methyl-red (HMR) when the ph is equal to the pk a. Imagine you have two substances, A and B. The molar absorptivity coefficient of A is 122 M 1 cm 1 at 425 nm. The molar absorptivity coefficient of B is 751 M 1 cm 1 at the same wavelength. Calculate the absorption of light at 425 nm in a 1-cm cell if it is filled with a solution containing [A] = 8.5 x 10 3 M and [B] = 1.2 x 10 3 M. Imagine substances A and B have molar absorptivity coefficients of 544 M 1 cm 1 and 84 M 1 cm 1 at a wavelength of 532 nm. Calculate the absorption of light at 425 nm and 532 nm if the concentrations of A and B are 1.9 x 10 3 M and 3.1 x 10 3 M respectively. If a mixture of A and B has an absorption of 1.044 at 425 nm and an absorption of 0.544 at 532 nm, then calculate the molar concentration of A and B. 7 Last updated: September 18, 17