The Determination of an Equilibrium Constant

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1 The Determination of an Equilibrium Constant Chemical reactions occur to reach a state of equilibrium. The equilibrium state can be characterized by quantitatively defining its equilibrium constant, K eq. See Vernier # 10 BACKGROUND Think of the simple reaction between reactants A & B creating product C: A + B C A snapshot of the reaction, where x & y are the concentration of A (Fe + ) and B (SCN ) and z is the concentration of C (FeSCN + ), the product, and can be represented as: xa + yb <----> zc + (x-z)a + (y-z)b In this experiment the initial concentration of A is held constant, while the concentration of B is changed, as per. At the beginning of the reaction (time, t=0) there is only A & B, because no C has been formed. At equilibrium (time=t eq ), some of the reactants A & B have been consumed to form the product C. The amount of A & B remaining at equilibrium can be determined based upon the mole ratios between A, B, and C. For this simple example, the mole ratio between A:B:C is 1:1:1 thus, for every mole of product formed one mole of A is consumed and one mole of B is consumed. At t=0 at t=t equil # moles of A = A init # moles of A equil = A init - # moles of C equil # moles of B = B init # moles of B equil = B init - # moles of C equil # moles of C = 0 # moles of C equil = C equil which can be measured. The equilibrium constant, K eq = [products] / [reactants], so in this simple model: K eq = [C equil ] / ([A equil ] * [B equil ]) EXPERIMENT In this experiment, you will determine the value of K eq for the reaction between iron (III) ions and thiocyanate ions, SCN. Fe(NO ) (aq) + KSCN (aq) FeSCN + (aq) From simple model: A B C The equilibrium constant, K eq, is defined by the equation shown below. [FeSCN + ] K eq = (equation 1) ( [Fe(NO ) ] equil [KSCN] equil ) To find the value of K eq, it is necessary to determine the molar concentration [mol/l] of each of 1

2 the three species in solution at equilibrium (at constant temperature). You will use a spectrophotometer to help you measure the concentrations. The amount of light absorbed by a colored solution is proportional to its concentration. In part I of this experiment, you will first prepare a series of standard solutions of FeSCN + from solutions of varying concentrations of SCN and constant concentrations of H + and Fe + that are in stoichiometric excess. The excess of H + ions will ensure that Fe + engages in no side reactions (to form FeOH +, for example). The excess of Fe + ions will make the SCN ions the limiting reagent, thus all of the SCN used will form FeSCN + ions. The FeSCN + complex forms slowly, taking at least one minute for the color to develop. It is best to take absorbance readings after a specific amount of time has elapsed, between two and four minutes after preparing the equilibrium mixture. Unless instructed otherwise, take all readings for ABSORBANCE at 10 seconds. Do not wait much longer than four minutes to take readings, however, because the mixture is light sensitive and the FeSCN + ions will slowly decompose. From this data, you will create a calibration curve of Absorbance vs. [FeSCN + ] (the product) and determine the equation for the line y=mx+b. In part II, you will prepare a new series of solutions that have varied concentrations of the Fe + ions and the SCN ions, with a constant concentration of H + ions. Using the calibration curve generated in Part I, you will use the results of this part to calculate the reaction equilibrium constant. DILUTION CALCULATIONS: Based on M 1 V 1 = M V (M= Molarity, V = Volume) M solution = (M Reactant * V Reactant ) / V Solution (equation ) where V solution = V Reactant + V water PROCEDURE Part I - Prepare and Test Standard Solutions 1. ALWAYS wear glasses when working in the chemistry laboratory.. Label five 100 ml beakers 1-. Obtain small volumes of 0.00 M Fe(NO ), M SCN, and distilled water. CAUTION: Fe(NO ) solutions in this experiment are prepared in 1.0 M HNO and should be handled with care. Prepare four Fe solutions according to the dilution chart in DATA TABLE PART I (adding the desired amount of water). Use a 10.0 ml graduated (1/10mL) to transfer each solution to a 0mL graduate cylinder. Mix each dilution thoroughly. DO NOT MIX THE Fe (III) solution with the SCN until you are ready to measure the absorbance with the spectrometer. DO NOT PREMIX THE CHEMICALS TOGETHER AS THEY WILL REACT! b. Calculate the [Fe(NO ) ] and [KSCN]. Because the Fe + ion is 100 times as concentrated, assume that all of the SCN ions react. From the 1:1:1 stoichiometric relationship of the reactants and product mol of FeSCN + = mol of KSCN = (0.00 mol/l) * (# ml KSCN)/1000

3 [FeSCN + ] = (moles FeSCN + )/Volume of solution [FeSCN + ] = (0.00 mol/l) * (# ml KSCN-)/0 ml (equation ) DATA TABLE - PART I DATA TABLE Prepare Prepare Prepare Total Fe(NO ) Trial 0. M Units ml ml ml ml M Calculate (equation ) Measure and Record KSCN 0.00 M H O [FeSCN + ] ABS Connect a Spectrophotometer to the computer with the USB cable.. Start the Logger Pro program on your computer.. Calibrate the Spectrophotometer. Note: always use the same cuvette! a) Prepare a blank by filling an empty cuvette ¾ full with distilled water. Place the blank in the cuvette slot of the Spectrophotometer and calibrate the instrument. 6. You are now ready to collect absorbance data for the standard solutions. Click COLLECT to begin data collection. a) Empty the water from the cuvette. Create the mixture of Fe (III) and SCN and fill the cuvette ¾ full. Wipe the outside with a tissue, place it in the Spectrophotometer, and close the lid. Wait for the absorbance value displayed in the Meter window to stabilize. In Logger Pro, click the Configure Spectrometer button. Click Abs vs. Concentration as the Collection Mode. Select the wavelength of about nm. Click OK. Note: Take readings at 10 seconds unless directed otherwise. Click KEEP, type the concentration of FeSCN + (from your pre-lab calculations) in the edit box, and press the ENTER key. b) Discard the cuvette contents as directed. Repeat the procedure in Part a of this step to measure the absorbance and record the concentration of each solution for Beakers,, and. c) Click STOP when you have finished collecting data to view a graph of absorbance vs. concentration. 7. Click the Linear Fit button. This line should pass near or through the data points and the origin of the graph. Another option is to choose Curve Fit from the Analyze menu, and then select Proportional. The Proportional fit has a y-intercept value equal to 0; therefore, this regression line will always pass through the origin of the graph). Record the equation of the

4 line y=mx+b for future calculations. (RECORD EQUATION OF THE LINE y=mx+b) Part II YOU WILL USE THE CALIBRATION CURVE YOU CREATED IN PART I TO MEASURE THE CONCENTRATIONS BASED UPON MEASURED ABSORBANCES 8. Prepare five test tubes of solutions, according to the chart below. Follow the necessary steps from Part I to test the absorbance values of each mixture. Record the test results in your data table. Note: You are using M Fe(NO ) in this test. 9. Calculate the concentration of Fe(NO ) and KSCN for each test tube using equation. Record the ABS of each solution in DATA TABLE PART II. DATA TABLE - PART II Record ABS DATA ANALYSIS You must determine the NET ABSORBANCE of the solutions in Test Tubes - to test only the color created by the reaction. Subtract the ABS for Test Tube 1 (containing only Fe and water) from the ABS of Test Tubes -. Use the NET ABSORBANCE values, along with the best fit line equation in Part I to calculate the [FeSCN+] at equilibrium for each of the mixtures that you prepared in Part II. Note: for y = mx + b you will solve for x, thus: [FeSCN + ] = (NET ABS b)/m (Equation ) ANALYSIS TABLE 1 DATA TABLE Measure Measure Measure Total (equation ) (equation ) Fe(NO ) KSCN Initial Initial Trial 0.00 M 0.00 M H O [Fe(NO ) ] [KSCN] Units ml ml ml ml M M ANALYSIS Table From Data Table II Calculate Trial [Fe(NO ) ] inital [KSCN] initial ABS NET ABS Units M M 1 n/a [C equil ] (Equation ) [FeSCN + ]

5 Note the last column is the numerator of equation (1) ANALYSIS TABLE To compute the K eq, you must determine the moles of each REACTANT (A equil, B equil ) that remain when the system is at equilibrium. This is done by computing the number of moles of product created, C equil, and subtracting that from the initial number of moles of each reactant (A init, B init ). Note that all reactant and product ions are dissolved in the same volume of solution (10 ml), so the change in the # moles is the same as the change in the concentrations (Mol/L) for each ion. ANALYSIS Table Table II [C equil ] Product [A equil ] Reactant [B equil ] Reactant Trial [Fe(NO ) ] initial [KSCN] initial [FeSCN + ] [Fe(NO ) ] equil [KSCN] equil Units M M M M M 1 Note the last columns are the denominator of equation (1) Compute Keq using the values computed in ANALYSIS TABLE 1 and ANALYSIS TABLE in Equation 1. ANALYSIS TABLE ANALYSIS (Equation 1) Trial Compute K eq 1 n/a Avg Keq: Conclusion: Compose a final paragraph to discuss the results. Include the equation of the line from the calibration curve: y=mx+b with m and b determined from your data. Complete all remaining portions of the standard lab report.

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