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Spectrometric Determination of the Acid Dissociation Constant of an Acid-base Indicator
Learning Goals
- Gain appreciation of the dynamics of perturbing a chemical equilibrium
- Gain an understanding of how to use Beerās Law, especially in conjunction with a two- component mixture.
- Practice preparing standard solutions for producing Beerās law plots.
- Gain a deep appreciation for how acid-base indicators work.
- Distinguish between directional error and random uncertainty.
Introduction In this experiment you will determine the acid dissociation constant, Ka, of an acid-base indicator system. An acid base indicator is generally a weak acid-base system, HIn/In-, where the HIn form is a different color than the In-^ form in aqueous solutions. As a result an aqueous solution of an indicator goes through a color transition with in a fairly narrow pH range, ph =2. As an example, the illustration below represents a solution of the indicator, as the pH increases from pKa -1 to pKa+1. In this illustration the acidic form (HIn) is blue and basic form (In-) is yellow.
The Ka for an indicator system is the equilibrium constant for the following reaction. HIn ( aq ) + H 2 O ( l ) ļ Inā^ ( aq ) + H 3 O+^ ( aq ) (rxn 1)
[HIn]
Ka [^ In ][H^3 O ]
In this experiment you will begin with a dilute solution of an indicator buffered at a pH near its pKa. You will measure the concentrations of [In-], [HIn] and [H 3 O+] and use these concentrations to calculate a
Each of these beakers contains a solution of the same four substances at a different pH. You will study a similar set of solutions in this experiment. Your set of solutions will contain different substances and will be different colors from those shown here.
p. 2
value for Ka. Details of these measurements are discussed below. Then you will add a little HCl to the solution. The HCl will drive the reaction to the left (according to Le Chatelierās Principle). You will remeasure the concentrations of [In-], [HIn] and [H 3 O+] and use these concentrations to calculate another value for Ka. You will repeat this process until you have several measurements of Ka. Next, you will add a little NaOH to the solution. The NaOH will consume some H 3 O+^ and drive rxn 1 to the right (according to Le Chatelierās Principle). You will remeasure the concentrations of [In-], [HIn] and [H 3 O+] and use these concentrations to calculate another value for Ka. You will repeat this process until you have made several additional measurements of Ka. In the end you should have about twelve measurements in a pH range of 1.4 bracketing the expected pKa of the indicator.
Measuring [H 3 O+] For each solution the [H 3 O+] will be determined by measuring the pH using a pH meter. We will then use the pH to calculate [H 3 O+]. We will learn how to properly use a pH meter, including how to use buffers to calibrate, the importance of thoroughly rinsing and blot drying the probe between measurements and the importance of periodically recalibrating to avoid drift issues.
Spectroscopic measurement of [HIn] and [In-] HIn (^) ( aq ) is a different color than InĖ (^) (aq) , while water and the hydronium ion, H 3 O+ ( aq ), are colorless. So the color of the solution in which this reaction is happening depends on the ratio HIn (aq) /InĖ (aq). For example, if HIn (aq) is yellow and InĖ (aq) is blue, then a solution that is yellow must
contain far more HIn (^) (aq) than InĖ (aq). On the other hand, a blue solution contains a lot more InĖ (aq) than
HIn (^) (aq). And a green solution would contain a nearly equal mixture of HIn (^) (aq) and InĖ (^) (aq) , because green is the color that results when yellow and blue are mixed equally (this is the situation when the pH = pKa of the indicator). So, it is possible to estimate the relative amount of HIn (aq) and InĖ (aq) just by looking at
the solution. However, part of this experiment involves measuring the amount of HIn (aq) and InĖ (aq) more precisely than is possible using just your eyes. The instrument that we will use to measure the color of the solution is a spectrophotometer. White light, the light that we are all familiar with, is a blend of all colors of light in the visible spectrum. When the colors of light are separated they can form a rainbow. A spectrophotometer separates light into its separate colors. It is able to separate the light into colors because each color of light has a different wavelength than the other colors. The spectrophotometer can shine a narrow band of
Color wheel needed for pre-lab question 2(c).
Beerās Law Plots In a mixture of HIn and In-^ the absorbance at a particular wavelength is the sum of the absorbances of HIn and In-^ at that wavelength.
A( 1 ) = A( 1 )HIn + A( 1 )In-
In this experiment we will be measuring the absorbance of each solution at two different wavelength; one where HIn absorbs strongly and another where In- absorbs strongly. But, as seen below from some of the spectra shown below, the visible absorption spectra of HIn and In- are quite broad. As a result, absorbances from both components tend to be significant at all wavelengths. In general, we can determine the concentration of two absorbing species in a mixture by measuring the absorbance of the mixture at two different wavelengths and by obtaining calibration curves for both components at both wavelengths. With this in hand one can construct and solve a system of two independent equations that contain the two unknown concentrations, [HIn] and [In-], in the mixture.
A( 1 ) = A( 1 )HIn + A( 1 )In- = eHIn@ 1 b[HIn] + eIn-@ 1 b[In-]
A( 2 ) = A( 2 )HIn + A( 2 )In- = eHIn@ 2 b[HIn] + eIn-@ 2 b[In-]
Here, eHIn@ 1 b represents the slope of the Beerās law plot for the HIn species at 1 and eHIn@ 1 b represents the slope of the Beerās law plot for the HIn species at 2. These Beerās Law plots will be produced by using standard solutions prepared at a pH that is three pH units less than the pKa of the indicator, so that 99.9% of the indicator is in the HIn form. Likewise, eIn-@ 1 b represents the slope of the
Beerās law plot for the In-^ species at 1 and eIn-@ 2 b represents the slope of the Beerās law plot for the In- species at 2. These Beerās Law plots will be produced by using standard solutions prepared at a pH that is three pH units higher than the pKa of the indicator, so that 99.9% of the indicator is in the In-^ form.
The concentrations of [HIn] and [In-] can be calculated by solving the system of equations, where s is used to represents the slopes of the four Beerās Law plots:
A( 1 ) = sHIn@ 1 [HIn] + sIn-@ 1 [In-]
A( 2 ) = sHIn@ 2 b[HIn] + sIn-@ 2 [In-]
Solving this system of equations is not difficult, and you can earn extra credit for turning in a step by step solution of the problem, separately from your report, to Professor Evans, during the next discussion section. Below are the final solutions.
[In-] = (sHIn@ 2 A( 1 )- sHIn@ 1 A( 2 )) / (sHIn@ 2 sIn-@ 1 -sHIn@ 1 sIn-@ 2 )
[HIn] = (A( 1 ) ā {slope}In-@ 1 [In-])/{slope}HIn@ 1
One final note: Generally, the wavelengths are chosen so that the ratios between the absorbances of the two species, AHIn / AIn-, are maximized and minimized. The wavelength chosen in this write-up reflect the limitations of some fix wavelength spectrometers that were used previously in this course.
Procedure
Instructions and Overview
You will be assigned to study one indicator, either bromophenol blue or phenol red. You are going to make an aqueous solution of this acid-base indicator. You will calibrate the equipment, a pH meter and a spectrophotometer, that you need to use for the experiment. Next you will prepare a series of HIn standards and a series of In- standards that will be used to produce the four beerās law plots. Finally, you will prepare an indicator solution near the pKa of the indicator, measure its pH and its absorbance at both wavelengths. Using dilute solutions of NaOH and HCl you will adjust the pH and remeasure the absorbances to several times. You will use the excel template associated with this experiment to process your data.
Table 1 -- pH and wavelength settings for different indicators Assigned indicator pH values (adjust one trial to each pH value)
Absorbance ratio maximum for HIn (Ī» 1 )
Absorbance ratio maximum for InĖ (Ī» 2 )
Bromophenol blue 3. 3 - 4. 7 430 565
Phenol red 7.0-8. 4 430 565
Make a solution and adjust it to a different pH value for each trial
Trial 1 Trial 2 Trial 3 Trial 4 Trial 5
Measure pH Measure absorbance at 1
Measure absorbance at 2
Calculate [H 3 O=]
Use calibration curves to calculate [Inā] and [HIn]
for each solution
Calculate Keq
Procedure and Calculations Flow Chart
Preparing the standards
Bromophenol Blue Master HIn standard: std 1 has been prepared for you. Its concentration is 2.985ā10-5^ M. Take about 10 mL of std 1. Prepare std 2 by mixing 3.00 mL of std 1 and 1.00 mL of 0.10 M HCl using a micropipette. Prepare std 3 by mixing 2.00 mL of std 1 and 2.00 mL of 0.10 M HCl using a micropipette. Prepare std 4 by mixing 1.00 mL of std 1 and 3. mL of 0.10 M HCl using a micropipette. Prepare std 5 by mixing 1.00 mL of std 3 and 3.00 mL of 0.10 M HCl using a micropipette.
Master In-^ standard: std 1 has been prepared for you. Its concentration is 2.985ā10-5^ M. Take about 10 mL of std 1. Prepare std 2 by mixing 3.00 mL of std 1 and 1.00 mL of diluted buffer 7 using a micropipette. Prepare std 3 by mixing 2.00 mL of std 1 and 2. mL of diluted buffer 7 using a micropipette. Prepare std 4 by mixing 1.00 mL of std 1 and 3.00 mL of diluted buffer 7 using a micropipette. Prepare std 5 by mixing 1.00 mL of std 3 and 3.00 mL of diluted buffer 7 using a micropipette.
Phenol Red Master HIn standard: std 1 has been prepared for you. Its concentration is 2.882ā10-5^ M. Take about 10 mL of std 1. Prepare std 2 by mixing 3.00 mL of std 1 and 1.00 mL of diluted buffer 4 using a micropipette. Prepare std 3 by mixing 2.00 mL of std 1 and 2. mL of diluted buffer 4 using a micropipette. Prepare std 4 by mixing 1.00 mL of std 1 and 3.00 mL of diluted buffer 4 using a micropipette. Prepare std 5 by mixing 1.00 mL of std 3 and 3.00 mL of diluted buffer 4 using a micropipette.
Master In-^ standard: std 1 has been prepared for you. Its concentration is 2.882ā10-5^ M. Take about 10 mL of std 1. Prepare std 2 by mixing 3.00 mL of std 1 and 1.00 mL of diluted buffer 10 using a micropipette. Prepare std 3 by mixing 2.00 mL of std 1 and 2.00 mL of diluted buffer 10 using a micropipette. Prepare std 4 by mixing 1.00 mL of std 1 and 3.00 mL of diluted buffer 10 using a micropipette. Prepare std 5 by mixing 1.00 mL of std 3 and 3.00 mL of diluted buffer 10 using a micropipette.
- Go to step 4 and repeat the process until you have twelve different sets of measurements of pH and the absorbances at both wavelengths at pH values roughly equally spaced between 3.3 and 4.7 for bromophenol blue or between 7.0 and 8.4 for phenol red.
Data Section of Lab Report ; {to be included in your lab report (word file)}
- Show the four Beerās Law Plots (3 pt each) on a single graph and produce a table that reports the slopes of these plots. (5 pts) Are the intercepts near zero, as expected? If not, how should you proceed?
- Show a table of [HIn], [In-], [H 3 O+], Ka and pKa values determined for each of your test solutions. (5 pts) These values of [HIn] and [In-] are calculated on your spreadsheet, using the slopes of the Beerās Law Plots and the solution to the set of equations. The [H 3 O]+^ is calculated from the measured pH.
- Calculate the alpha fractions of HIn and In- from [HIn] and [In-] for each of you twelve test solutions and plot these alpha fractions as a function of pH on the same plot. (5 pts) Estimate the pKa of your indicator from this plot. (3 pts)
- Plot the calculated pKa values as a function of the measured pH value for your twelve measurements. (5 pts) This plot will be used to address #3 in the discussion section.
- Calculate your mean value of Ka and report the Ka as mean Ā± 95 % CI. (5 pts) Calculate your mean value of p Ka and report the pKa as mean Ā± 95 % CI. (5 pts)
- The literature value of Ka for bromophenol blue is 1.15 10 Ė^4. The literature value of Ka for phenol red is 2 10 Ė^8. Calculate the percent error of your mean Ka value using this equation: ( pts)
% error literaturevalueliteratureexperimentvalue alvalue 100 %
Discussion Section
Analyze the plot in #3 carefully. Discuss if [HIn] and [In-] changed as a function of pH in a predictable way, according to Le Chatelierās principle. (5 pts)
Why did we need four Beerās Law Plots in this experiment? (5 pts)
Discuss the possible factors that are contributing to the uncertainty in Ka. Does the
variation in the calculated pKa values appear to be random or is it a function of pH? If it
appears to be a function of pH, discuss the possible reasons and the implications. (5 pts)
Discuss the possible factors contributing to the % error in the measurement. (5 pts)
Lab Report
SPREADSHEET 10 ABSTRACT 10 PROCEDURE 10 DATA 50 DISCUSSION 20
