EXPERIMENT 14. ACID DISSOCIATION CONSTANT OF METHYL RED1
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
Ka =
[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, pKa, by varying the pH and measuring the
ratio [MR–]/[HMR]. We will use acetic acid-acetate buffers to control the pH, since the Ka
value for acetic acid is in the same range as the Ka value for methyl red. The pH of these
buffers force methyl red to distribute itself somewhat evenly between the two colored forms.
O2C
N
N
O2C
N
N
H
N
N
H
Acid form (HMR) red
H+
OHO2C
N
N
N
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
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Last updated: October 18, 2015
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 = !! [ X ]
(3)
where A is the absorbance, ! 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 = AMR – + AHMR
(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 !1 and !2. The absorbance at !1 is A1 and at !2 is A2. The two measurements
then provide two simultaneous equations with two unknowns:
A1 = !1,MR! ![MR ! ]+ !1,HMR ![HMR]
(5)
A2 = ! 2,MR! ![MR ! ]+ ! 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, A1 and A2, 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.
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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.
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 pKa. 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 pipettes to deliver the solutions into 100 mL volumetric flasks. Both solutions should
be brought up to volume using distilled water.
Measure the UV-VIS spectrum of the high-pH and low-pH sample. Use a range of 400 –
800 nm. Distilled 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 (comma separated values) from ChemStation for easy import into a spreadsheet, such as Microsoft Excel.
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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 !max for MR– (!1) and HMR (!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
Measure UV-VIS spectra for all ten solutions, being sure to record both the absorbance at !1
and at !2 for each solution.
Beer’s law states that A = !l[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 "l. Since l = 1 cm
for our cuvettes, the numerical value of ! 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 !. 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 pKa, 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 ! 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 pKa of the dye. Conversely, the ratio of [MR–] to [HMR] is 10:1 at a pH equal to
one unit above the pKa. It is imperative to have as many of your solutions as possible in this
pH = pKa ±1 range! Since the two forms of the dye have different colors (red and yellow), at
the point where the pH ! pKa, 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.
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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, 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. Note: when the
pH approaches the pKa 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 NaOH 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.
Note: because we have a buffer, its pH should not change appreciably upon the addition of
H2O.
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 !1 and !2,
it is possible to calculate the actual concentrations of HMR and MR– for each solution pH.
3
4
Acetic acid has a pKa of 4.76 at 25 ºC. Hence a mixture of acetic acid and acetate ion will produce a buffer
If you prepare the solutions one at a time, you can be sure to obtain enough pHs close to the pKa (estimated
by the orange solution color).
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If your pH is more than one unit away from the pKa 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
5
•
Graph absorbance versus dye concentration in acidic and basic solutions at !1 and !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. ! for all ten of your highand low-pH solutions on a single plot. In addition, you should graph A vs. ! 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 pKa 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 pKa 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 pKa. An average value from the literature5 is 5.05 ± 0.05 for
the 25 to 30 ºC temperature range.
Kolthoff, I. M.; “Acid-Base Indicators,” The Macmillan Company, New York, 1953.
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Questions
1. Derive equation (2) from equation (1).
2. Explain why the pKa 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 pKa? (If you used concentrations in units of g/L for the HMR and MR– the
value of pKa 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
1. Calculate the ratio of deprotonated methyl-red (MR–) to methyl-red (HMR) when the
pH is 1.00 greater than the pKa.
2. Calculate the ratio of deprotonated methyl-red (MR–) to methyl-red (HMR) when the
pH is 1.00 smaller than the pKa.
3. Calculate the ratio of deprotonated methyl-red (MR–) to methyl-red (HMR) when the
pH is equal to the pKa.
4. Imagine you have two substances, A and B. The molar absorptivity coefficient of A is
122 M–1cm–1 at 425 nm. The molar absorptivity coefficient of B is 751 M–1cm–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–1cm–1 and
84 M–1cm–1 at a wavelength of 532 nm.
5. 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.
6. 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.
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Last updated: October 18, 2015