Determination of an Equilibrium Constant

Transcription

1 Last updated 1/29/ GES Learning Objectives Students will be able to: Determine the numerical value of an equilibrium constant from measured concentrations of all reaction species. Use an absorption spectrum to determine the wavelength of maximum absorbance and predict the color of the material absorbing light. Explain how absorbance, concentration, and molar absorptivity are related. Create a standard curve by making solutions of known dye concentration and measuring their absorbances. Use a Vernier, SpectroVis Plus spectrometer to collect a visible absorption spectrum of an aqueous solution. Use volumetric glassware to prepare solutions of known dye concentration. Use a standard curve to determine unknown concentrations. Interpret a graph in order to extract physical information from a linear equation. Use equations for ph and pk a to convert between ph and [H + ] or pk a and K a. Background Chemical Equilibrium In a chemical reaction, products begin to form when reactants are mixed and if the reaction is irreversible (only proceeds in the forward direction), the reaction will be complete when one of the reactants is completely consumed. If the reaction is reversible, however, the situation is quite different. Reactants form products as before, but now the products can react to reform reactants. The reaction is never complete but continues in both directions. Eventually the rate of the forward reaction is exactly the same as the rate of the reaction in the reverse direction, so that product is formed and consumed in equal amounts. The reaction is said to have reached equilibrium at this point. When a reaction mixture is at equilibrium the concentrations of all reactants and all products remain constant. A classic example of a reversible reaction is the formation of ammonia from its elements:! " #$%+&' " #$%! "!' & #$% (1) When equilibrium is achieved, ammonia forms and decomposes at the same rate, so the concentrations of nitrogen, hydrogen, and ammonia all remain constant. An important mathematical relationship exists at equilibrium. The product of the concentration of each product raised to the power equal to its coefficient in the balanced equation, divided by the product of each reactant raised to the power equal to its coefficient in the balanced equation is equal to a constant,

2 called the equilibrium constant, and given the symbol K, often with various subscripts for different types of reactions. The equilibrium constant for the above reaction is! " =! #$% "! #& " & # $ % #! $ $ # " & $ (2) Equilibrium constant summary: All products are in the numerator. All reactants are in the denominator. Coefficients in the balanced equation become exponents in the K expression. Concentrations in mol L 1 are used for ions. Concentrations in mol L 1 are used for weak electrolytes and nonelectrolytes. Liquids and solids are set equal to 1 Gases may be expressed in mol L 1 in which case K is called K c, or Gases may be expressed in atm in which case K is called K p. K for a reaction is constant for changes in all variables except temperature. When reactants and products are at equilibrium, it does not mean that they are present in equal amounts, but only that the amounts stay constant. When there are more products than reactants at equilibrium, the equilibrium constant is greater than one. An equilibrium constant smaller than one will be obtained when there are more reactants than products at equilibrium. In today s experiment the equilibrium constant will be determined for the reaction of a weak acid, specifically the acid- base indicator, bromothymol blue. Bromothymol blue is a complicated organic molecule, HC 27 H 27 Br 2 O 5 S, and may be represented as HInd. When dissolved into water the following reversible reaction occurs and equilibrium is reached very rapidly.!"#$%&'(!! + %&'(+"#$! %&'( )*++,-.+/* (3) The equilibrium constant for weak acids establishing this equilibrium is called K a and is given by:! #! # "! " = #+ $ " $%&% $! " #$%& # $ (4) To find K a, the concentrations of H +, Ind and Hind will be found for three solutions, A, B, and C, each containing bromothymol blue and various amounts of other reagents. Since the temperature will not be changed, each solution will produce the same value for K a if the experiment is a success. Ind has an intense blue color. Solutions of known concentration of Ind will be prepared and labeled blue(1) blue(4). The absorbance spectrum of Ind will be obtained using one of these blue solutions and the wavelength of maximum absorbance (λ blue,max ) chosen. The absorbance of each blue solution at λ blue,max will be measured and recorded. A best- fit straight- line calibration curve of absorbance versus concentration will be prepared. The absorbance of solutions A, B, and C will be measured at λ blue,max. The concentration of Ind in each of these solutions will be found by substituting the absorbance into the best- fit equation and solving for x, the concentration of Ind.

3 HInd has a less intense yellow color. Solutions of known concentration of HInd will be prepared and labeled yellow(1)- yellow(4). A calibration curve of Absorbance vs concentration will be prepared after finding λ yellow,max from an examination of the absorbance spectrum. The absorbance of solutions A, B, and C at λ yellow,max will be measured and converted into concentrations of HInd. [H + ] of solutions A, B, and C will be determined using a calibrated ph meter. The ph will be measured, and [H + ] will be found using ph = log[h + ]. When looking at equation (3) it seems as if [H + ] must be equal to [Ind ]. This is true if there are no other sources of either of those two ions. Solutions A, and B and C will each have various amounts of H 2 PO 4, which can supply H +, and they will also have HPO 4 2, which can consume H +. The [H + ] will therefore be different than [Ind ]. The solutions blue(1)- blue(4) and yellow(1)- yellow(4) need to have known concentrations of Ind and HInd. Blue(1) is prepared by combining a known amount of indicator with some NaOH. The base reacts with H + and shifts the equilibrium of reaction (3) to the right such that to many significant figures all of the indicator will be Ind and none will be HInd:! + "#$%+&!! "#$%!! ' &""% (5) This can easily by seen by rearranging the equilibrium constant expression (4)! #! " " = $%&% $! " # + #! $ " #$%& # $ (6) Decreasing H + by many orders of magnitude results in a corresponding large increase in [Ind ]/ [Hind] Yellow(1) is prepared by combining a known amount of indicator with some HCl. The acid reacts with Ind and shifts the equilibrium of reaction (3) to the left such that to many significant figures the indicator is all Hind with no Ind. Solutions yellow(2) yellow(4) and blue(2) blue(4) are prepared by dilution and the concentration of the important species in each will be found using M 1 V 1 = M 2 V 2. When [H + ], [Ind ], and [HInd] are all determined for solutions A, B, and C, the equilibrium constant may be determined in triplicate. If the values happen not to agree, there is one way to check for errors. Each solution has the same total amount of indicator which can be determined using M 1 V 1 = M 2 V 2. The total amount of indicator is also obtained by adding the experimental concentrations of Ind and HInd. [Ind ] + [HInd] = [Ind] total (7) Finally, since M 1 V 1 = M 2 V 2 is such an important part of the calculations in this and many other experiments, it may be worthwhile to review. First, its ONLY use is to calculate concentrations that result from diluting solutions. It is not used for stoichiometric calculations of reactants forming products. Here M 1 is the molarity of some more concentrated solution, V 1 is the volume of the same concentrated solution used to prepare a more dilute solution, V 2 is the TOTAL volume of a more dilute solution prepared from the concentrated one and M 2 is the molarity of the more dilute solution.

4 Procedure Part I Safety Wear goggles and gloves. Avoid contact with sodium hydroxide. Waste Disposal Once neutralized, solutions can be poured down the large sinks with running water. Calibrating the spectrometer. 1. Start Logger Pro with the SpectroVis Plus attached by USB. The SpectroVis Plus will not operate correctly if there is a GoLink adapter connected to the USB port. Ensure that you disconnect the GoLink adapter from the computer to avoid problems collecting spectra. 2. Click the button in the upper- left corner with the picture of the spectrum on it. 3. A pop- up window appears. On the right in the popup is a spectrum picture. This will be referred to as the Spectrometer menu in these instructions. Click on it and select Absorbance. If you cannot click the button, click the stop button on the toolbar for the data collection. 4. Set Wavelength Smoothing to 1, and Samples to Average to Click on the Spectrometer menu again and choose Calibrate. The Sample Time is how long the detector collects light before recording the spectrum. The calibration sets this value automatically to maximize the signal without saturating the detector. 6. Place a cuvette filled about 2/3 full with deionized water into the spectrometer. Make sure the outside of the cuvette is dry and that the clear windows face the white arrow and the white lamp symbol. Press Finish Calibration. This subtracts the background spectrum of the lamp and the solvent so that the absorbances reported are for nothing but the solute. 7. Write down your values for Sample Time Wavelength Smoothing and Samples to Average. Standard Curve Standard Ind - Solutions: 1. Under the File Menu, start a new Experiment. Fill your cuvette with deionized water and ensure that you still have zero absorbance at all wavelengths when you press Collect. If you do not, you can re- calibrate the spectrometer. 2. Number four test tubes Blue- 1 through Blue Using a 5.00mL graduated pipet, pipet the volume of standard 4.0 x 10 4 M (0.025%) HInd stock solution as indicated in the Table below into a 25.00mL volumetric flask. 4. Using a 10mL graduated cylinder, measure between 4 5mL of 0.5M NaOH and add it to the flask to convert all HInd to the blue Ind form. 5. Dilute the solution to the mark with deionized water and invert and mix a number of times. 6. Rinse a test tube with two small portions of the diluted standard and transfer the remaining solution to the tube for measurement later. Seal the tube with Parafilm. Std. Soln Vol. HInd Stock (ml) Vol. 0.5M NaOH (ml) Blue Blue Blue Blue

5 Standard HInd Solutions: 1. Under the File Menu, start a new Experiment. Fill your cuvette with deionized water and ensure that you still have zero absorbance at all wavelengths when you press Collect. If you do not, you can re- calibrate the spectrometer. 2. Number four test tubes Yellow- 1 through Yellow Using a 5.00mL graduated pipet, pipet the volume of standard 4.0 x 10 4 M (0.025%) HInd stock solution as indicated in the Table below into a 25.00mL volumetric flask. 4. Using a 10mL graduated cylinder, measure between 4 5mL of 0.5M HCl and add it to the flask to convert all Ind - to the yellow HInd form. 5. Dilute the solution to the mark with deionized water and invert and mix a number of times. 6. Rinse a test tube with two small portions of the diluted standard and transfer the remaining solution to the tube for measurement later. Seal the tube with Parafilm. Std. Soln Vol. HInd Stock (ml) Vol. 0.5M HCl (ml) Yellow Yellow Yellow Yellow

6 Procedure Part II Safety Wear goggles and gloves. Avoid contact with sodium hydroxide. Waste Disposal Once neutralized, solutions can be poured down the large sinks with running water. Preparation of Solutions for determination of K a : 1. Use a 10mL graduated pipet to measure the volumes of 0.100M Na 2 HPO 4 and another 10mL graduated pipet to measure the volumes of 0.100M NaH 2 PO 4 into a 25.00mL volumetric flask as indicated in the Table below. 2. Using a 5.00mL graduated pipet, measure 1.00mL of the standard 4.0 x 10 4 M (0.025%) HInd stock solution into the flask. 3. Dilute the buffered solutions to the mark and invert and mix a number of times. 4. Rinse a test tube with two small portions of the solutions and transfer the remaining solution to the tube for storage. Seal each tube with Parafilm. Soln. Vol. HInd Stock (ml) Vol. (Na 2 HPO 4 ) (ml) Vol. (NaH 2 PO 4 ) (ml) A B C Measurement of Solutions for determination of K a : 1. Use the instructions from Part I to ensure that your spectrometer is properly calibrated. 2. Measure the spectra for solutions A, B, and C and record the absorbance at the same wavelengths used to build your calibration curve. 3. Disconnect the SpectroVis Plus from the computer and attach the GoLink with the ph probe attached. If you have problems with Logger Pro recognizing the ph probe, restart Logger Pro. 4. Note that the ph probe is stored in an electrolyte solution (this is not just water). Remove the ph probe from the storage solution, rinse it with DI water from your wash bottle into a beaker, and gently pat the probe dry with a KimWipe. 5. Insert the ph probe into each solution and record the ph, rinsing the probe with DI water between solutions.

7 Report Form Computer Number Name Name DATA In the table below, record the absorbances of the standard solutions. λ max = nm Solution λ blue, max [Ind ] Blank M Blue- 1 Blue- 2 Blue- 3 Blue- 4 Using Excel, construct a plot of Absorbance vs. Concentration of Ind (Standard curve plot). Include the Blank as one of the data points. Attach the graph to your report. In the table below, record the absorbances of the standard solutions. λ max = nm Solution λ yellow,max [HInd] Blank M Yellow- 1 Yellow- 2 Yellow- 3 Yellow- 4 Using Excel, construct a plot of Absorbance vs. Concentration of HInd (Standard curve plot). Include the Blank as one of the data points. Attach the graph to your report.

8 In the table below, record the absorbance and ph values of the solutions for the determination of K a. Solution λ blue, max λ yellow,max ph [Ind ] [HInd] [H + ] A B C Calculate the concentration of Ind and HInd in Solutions A, B, and C using the best- fit straight- line equation from your standard curves and the absorbance measurements. Enter them into the table. Calculate the H + ion concentration for Solutions A, B, and C. Given that [H + ] = 10 ph Use your results for [HInd], [Ind ], and [H + ] to calculate the numerical value of the equilibrium constant, K a. Since K a is a constant, if the experiment worked perfectly all three values would be the same. List your values in the Table below. Show your calculation of K a for Solution A. Solution K a pk a A B C Average pk a Calculate pk a for each solution then calculate the average value. Given: pk a = logk a