Expt B: Determining the Equilibrium Constant of Bromothymol Blue. Keywords: Equilibrium Constant, ph, indicator, spectroscopy

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1 Objectives: Keywords: Equilibrium Constant, ph, indicator, spectroscopy Prepare all solutions needed for measurement of the equilibrium constant for bromothymol Make the required spectroscopic measurements on the solutions and from this data, determine the equilibrium constant for bromothymol. Bromothymol is a chemical indicator used to detect weak acids and bases. It works as an indicator by displaying a change in color from the protonated form (HBB) to the non-protonated form (BB - ). This is illustrated below in the ph dependent equilibrium between the two forms. HO OH O OH Br O S Br Br + H 2 O Br + H O + O O SO - Figure One: Equilibrium of bromothymol ( and forms) Obviously, this equilibrium is ph dependent and under acidic conditions, the bromothymol will be protonated and as a result, the solution will be. Under basic conditions, the deprotonated form results in a solution. But these are the two extreme cases and it is found that between ph 6 to 8, the solution appears green, a color resulting from the presence of both protonated and deprotonated forms of bromothymol. Towards ph 6, the solution is a more greenish while towards ph 8, the solution is more of a bluish green. Hence the color of the solution can be used as a visual guide to the relative amounts of protonated and deprotonated forms of bromothymol. The absorbance spectra of each of these are thus shown below: B-1

2 Figure Two: bsorbance Spectra of Bromothymol Blue ( and forms) The form, BB -, has an absorbance maximum at about 616 nm. The form, HBB, has its maximum absorbance at 42 nm. In this experiment, we will measure the absorbance of the form at 45 nm, where the absorbance is still strong and the absorbance of the BB - is minimal NOTE: s can be seen in the spectra in Figure Two at 42 nm, BB - (the form) also absorbs a small fix is included later to cancel this out in the experimental but for the purposes of the calculation below, we are assuming there is no absorbance here and the only species absorbing at 42 nm is the form HBB). In this experiment, we will consider the equilibrium between the two forms HBB () H 2 O H O + + BB - () (1) The equilibrium expression, K c, for the HBB/BB - equilibrium (Eq. 1) is: K c [ + H O [ BB [ HBB (2) The value of K c should be independent of all factors except a change in temperature. t high ph, the concentration of the form, [BB -, is large and [HBB is small, and at low ph, [HBB is large and [BB - is small. B-2

3 In this experiment, you will be working with a solution that is green in color, so that contains both [HBB and [BB - in comparable quantities. Both the and forms of bromothymol have Beer s law expressions that relate absorbance () to concentration ([, in molarity) at their respective wavelengths: For the form, HBB: b [ HBB and for the form, BB - : b [ BB () (4) where is the molar absorptivity (L mol -1 cm -1 ) and b is the pathlength in cm. Solving Equations and 4 for [HBB and [BB -, respectively, gives: [ HBB [ BB b b (5) (6) These two equations can be substituted into the K c expression (Eq. 2) and the b s cancel: K c [ H + O + H O b [ b (7) Note that it is not necessary to know the concentrations of [HBB or [BB - in the green solution, only the ratio 616 nm / 45 nm. There are five values from Eq. 7 that you must obtain to determine K c for bromothymol. These are summarized in Table 1. You will determine three of these values for a solution that is green in color, meaning that both HBB and BB - are present in reasonable quantities (not almost zero as would be the case in either the or solutions at high and low ph values, respectively). B-

4 Table 1: Quantities measured for the determination of K c Quantity [H O + green How we measure it: Use a ph meter to determine the ph of the green solution and calculate this from that value Measure the absorbance of the green solution at 616 nm Discussed below green Measure the absorbance of the green solution at 45 nm (this also needs a small experimental tweak to cancel out the contribution see experimental section for more details) Discussed below The K c expression given above (Eq. 7) is now re-written with green labels indicating that you will determine absorbance values at two wavelengths for the green form of your bromothymol solution: K c [ H O + green green 45 nm (8) The value for ~100% HBB and negligible BB - ) and the value for will be determined when the solution is completely (low ph; will be determined when the solution is completely (high ph; ~100% BB - ). This is because we need to relate the values to concentration via the Beer s law equation ( x b x M) and unless the equilibrium is shifted almost 100% one way or the other, we will not know the concentration exactly. The experiment is designed so that we will prepare three solutions, each with the identical concentration of bromothymol. We will measure out equivalent amounts of bromothymol solution into three beakers. Into one beaker you will add an exact volume of an acid, HCl(aq); into another, you will add the same volume of a base, NaOH(aq); into the third solution, you will add the same volume of a buffer solution with a ph of approximately 6.5. The first solution will be, the second solution will be and the third solution will be green. B-4

5 NOTE: ll three solutions have the same total concentration of bromothymol This is present either as 100% HBB ( solution), 100% BB - ( solution), or a combination of HBB and BB - (green solution). The absorbance at 45 nm of the solution is due entirely to the form (HBB); while the absorbance at 616 nm is due entirely to the form (BB - ). We can write a Beer s law expression for the absorbance of each solution at each wavelength: b [ HBB( ) (9) b [ BB ( ) (10) Since we have designed the experiment such that all HBB and BB - originates from the same source, the concentration of bromothymol in the solution equals the concentration of bromothymol in the solution: [ HBB( ) [ BB ( ) which, upon substitution of Eq. 9 and 10 into Eq. 11, gives: (11) b 616 nm b (12) The b values cancel and Eq. 12 is rearranged: 45 nm (1) The labels and on and denote that these are the absorbance values of the and solutions, at their respective wavelengths. The above ratio of values can be substituted into the K c expression (Eq. 8): K c [ H O + green green 45 nm [ H O + green green 45 nm (14) From Eq. 14, you should see how we can determine K c from only absorbance values and the [H O +, obtained from a ph measurement on the green solution. B-5

6 Experimental Prepare a buffer solution by dissolving approximately 0.4 g of sodium phosphate monobasic, NaH 2 PO 4 and 0.4 g of sodium phosphate dibasic, Na 2 HPO 4 in approximately 50 ml water. Stir to completely dissolve both salts. (Note: a buffer is a solution which can maintain a constant ph unless significant amounts of acid or base are added) If the 1 M solutions are not available, using the acids and bases available, prepare approximately 10 ml of 1 M HCl and 10 ml of 1 M NaOH solutions. dd 2 ml (this value may be changed dependent on freshness of the bromothymol solution check the board first) of bromothymol indicator to the buffer solution and stir to mix the indicator uniformly through the solution. The solution should appear green in color. If the solution is green, you can skip this step. If the solution is, add 1 M HCl(aq), a drop at a time, with thorough mixing, until you obtain a shade of green. If the solution is, add 1 M NaOH (aq), a drop at a time, again with thorough mixing, until you obtain a shade of green. Determine the ph of buffer solution. the buffer solution using a calibrated ph meter. Record the ph and temperature of this solution. Use a volumetric pipet to transfer ml of the green, buffered solution to each of three clean and dry 100 ml beakers. Using a 2.00 ml volumetric pipet, transfer 2.00 ml of 1.0 M HCl into one of the three beakers. The solution should turn. This solution will be referred to as Yellow. Clean and rinse the 2.00 ml volumetric pipet and then use it to transfer 2.00 ml of 1.0 M NaOH into one of other beakers. The green solution should turn. This solution will be referred to as Blue. Clean and rinse the 2.00 ml volumetric pipet and then use it to transfer 2.00 ml of distilled water into the remaining beaker. The green solution should remain green. This solution will be referred to as Green. Note: Even though you prepared your solutions in beakers rather than volumetric flasks, they all contain the same final volume of solution (12.00 ml) and the same number of total moles of bromothymol (delivered with the ml pipet). This gives an equivalent total concentration of bromothymol in each beaker. On the Ocean Optics spectrometer, measure the spectra for the green, and solutions and save copies of the spectra you will replot these in Excel and use them to extract the data needed to determine the equilibrium constant (instructions for saving spectra are in the ppendix of this manual) B-6

7 Safety / Waste Disposal The materials used in this reaction should be collected in the waste container in the hood at the end of the experiment. Data nalysis You should now have all of the measurements you need to calculate the equilibrium constant for bromothymol. Fixing the absorbance of the green solution at 45 nm: Before we determine the equilibrium constant, we have to fix the value of the absorbance of the green solution at 45 nm so the only absorbance here is from the HBB i.e. we remove the BB - contribution. It s actually reasonably simple to do and requires a few simple calculations. First, understand that in the spectrum of a colored species, the relative absorbance at two wavelengths to each other does not change as concentration changes. For example, for a colored species, absorbance at 00 nm is 1.2 and absorbance at 400 nm is 1.5. If we dilute the solution by a half, absorbance at 00 nm is now 0.6 and absorbance at 400 nm is But the ratio of absorbance at 00 nm / absorbance at 400 nm is the same in both cases. (1.2/1.5 is the same as 0.6/0.75) 1) So for the solution which is 100% BB -, let s calculate the ratio of the absorbance at the two wavelengths 45 and 616 nm. Get these values from your saved spectra and calculate the ratio of absorbance at 45 nm/616 nm for the pure solution. 2) Now measure the absorbance of the green spectrum at 45 nm. The problem we have is that the absorbance is from both the and species present. ) Now since there is no absorbance of the species (HBB) at 616 nm (see Figure Two), in the green solution, we know the absorbance at 616 nm is only from the species (BB - ). So find this from your green spectrum and using the ratio you calculated in step 1) above for the pure, what is the contribution to the absorbance at 45 nm. If you have done this right, it should be less than the value you listed in step 2) above 4) Subtract the value calculated in step from that found in step 2 to obtain the corrected value of green absorbance at 45 nm and it is this value you will use in the following steps. B-7

8 Obtaining the Equilibrium Constant: Equations 1, 2 and 14 are rewritten below. HBB() + H 2 O H 2 O + + BB - () K c [H O+ [BB () [HBB() K c [H O + green green You can simply plug values from the table into the K c expression as long as you use the corrected value of the green absorbance at 45 nm (see previous page) and assuming the contribution at 616 nm is negligible which figure two shows it is. Perform the calculation of K c in your laboratory notebook and report your pk c value (remember pk c -logk c ) to two decimal places. Grading of Experiment B This experiment will be graded by an entrance (0 pts) and exit quiz (40 pts). You are also asked to hand-in a copy of your spectral overlay (0 pts) which has all three spectra plotted on the same graph by the end of the lab (it should look like Figure Two with the addition of the green solution). You may work on the graph with your group but the quiz will be individual. Wiki Component of Experiment B Values for the equilibrium constant should be shared on the wiki on the page for experiment B. separate table is provided for each lab section though all data will be visible. You should obtain the average value for your section and the class to date and see how your value for the equilibrium constant compares to this. Reference: The Equilibrium Constant for Bromothymol Blue: General Chemistry Laboratory Experiment Using Spectroscopy. Elsbeth Klotz, Robert Doyle, Erin Gross, and Bruce Mattson, Journal of Chemical Education (5), B-8

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