EXP. 5 DETERMINATION OF AN EQUILIBRIUM CONSTANT

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1 University of Puget Sound Department of Chemistry Chem 230 EXP. 5 DETERMINATION OF AN EQUILIBRIUM CONSTANT LABORATORY OBJECTIVES AND ASSESSMENTS 1. Understand the relationship between equilibrium constant and concentration. a. Recognize the characteristics of chemical equilibrium. b. Demonstrate that reaction mixtures with differing concentrations of reactant and product are at equilibrium. c. Calculate the initial concentration of reactants and products of a chemical reaction. d. Write the equilibrium equation for any balanced chemical equation. e. Describe and demonstrate the use of a calibration curve and Beer s Law to measure the concentration of Fe(SCN) 2+. f. Calculate the equilibrium constant, K c, from the equilibrium concentrations of products and reactants. g. Calculate the equilibrium concentrations of reactants and/or products from K c and initial concentrations of reactants and/or products using ICE tables. 2. Understand how to use Le Châtelier s principle to manipulate equilibria. a. State Le Châtelier s Principle. b. Describe and demonstrate on specified chemical reactions how Le Châtelier s Principle is applied to equilibrium systems to shift the equilibrium of a chemical system. INTRODUCTION This experiment will give you an opportunity to determine the equilibrium constant for a reaction and use Le Châtelier s principle. Formation of Fe(SCN) 2+ When chemical substances react, the reaction typically does not go to completion. Rather, the system goes to some intermediate state in which both the reactants and products have concentrations which do not change with time. Such a system is said to be in dynamic chemical equilibrium. When the reaction between Fe 3+ and SCN - (thiocyanate) ions in an aqueous solution comes to equilibrium, the solution contains reactants and the product, Fe(SCN) 2+. The chemical equation for this reaction is Fe 3+ (aq) + SCN - (aq) Fe(SCN) 2+ (aq) (1) The product is a complex ion that has a coordinate covalent bond between the iron cation and an atom (probably the S atom) from the thiocyanate anion. The color of this complex ion is so intense that thiocyanate ions can be used to detect very small quantities of Fe 3+. Interestingly, Fe(SCN) 2+ appears to exist solely in solution; solid compounds containing this cation and some anion have never been isolated. At equilibrium a reaction mixture obeys the Law of Mass Action, which imposes a condition on the concentrations of reactants and products. This condition is expressed in the equilibrium constant K c. The object of this experiment is to determine the value for the equilibrium constant for reaction (1). The equilibrium constant is given by the expression K c = (2) c230 Exp. 5 - Determination of an Equilibrium Constant 1

2 where the concentrations of the substances are those at equilibrium. If these concentrations can be determined, K c can be calculated easily. SPECTROPHOTOMETRY Both reactants, Fe 3+ and SCN -, are essentially colorless, whereas the complex ion product is highly colored. Therefore, you can use a spectrophotometer to monitor the concentration of Fe(SCN) 2+ by measuring the absorbance due to the complex ion according to Beer s law. A = εbc (3) LE CHÂTELIER S PRINCIPLE To determine the relationship between Fe(SCN) 2+ and absorbance, the absorbance of a series of solutions of known concentrations of complex ion must be measured. But there is a problem. How can solutions of known concentrations of Fe(SCN) 2+ be obtained? After all, this substance is a participant in the equilibrium with Fe 3+ and SCN - ions. Stoichiometric quantities of reactants yield a specific concentration of product which can be calculated if the equilibrium constant, K c, is known. But K c is the term that is trying to be determined! The difficulty of making solutions with known concentrations of Fe(SCN) 2+ can be overcome by using Le Châtelier s principle. This principle suggests that an equilibrium position can be shifted to the right, that is, in the forward direction, when more of a given reactant is added. As more reactant is added, more product will form. It is possible to add so much of one reactant that essentially all of the other reactant is converted to product. In this experiment you will use overwhelming amounts of Fe 3+ and limited quantities of SCN- to achieve this result. The concentration of Fe(SCN) 2+ that is formed will be essentially identical to the starting concentration of the limiting reactant, SCN -. THE STANDARD OR CALIBRATION CURVE In Part 1 of this experiment you will prepare a series of solutions having known, limited initial concentrations of SCN - and an excess of Fe 3+ which allows you to know the concentrations of Fe(SCN) 2+. You will plot absorbances versus concentrations of Fe(SCN) 2+ (at the λ max of Fe(SCN) 2+ ) which should give a straight line (the calibration curve). DETERMINATION OF K C As noted above, when solutions containing Fe 3+ ion and thiocyanate ion are mixed, reaction (1) occurs forming the Fe(SCN) 2+ complex ion which has a deep red color. As a result of the reaction, the equilibrium amounts of Fe 3+ and SCN - are less than they would have been if no reaction occurred; for every mole of Fe(SCN) 2+ that is formed, one mole of Fe 3+ and one mole of SCN - have reacted. The value of K c in equation (2) is constant at a given temperature. This means that solutions containing Fe 3+ and SCN - will react until the concentrations of remaining reactants and formed products satisfy the value of K c. The same value of the K c will be obtained no matter what initial amounts of Fe 3+ and SCN - are used. Our purpose in this experiment will be to determine the value of K c for this reaction using several solutions made up in different ways, and to show that K c indeed has the same value in each circumstance. The reaction is a good one to study because K c is a convenient c230 Exp. 5 - Determination of an Equilibrium Constant 2

3 magnitude and the color of the Fe(SCN) 2+ ion makes the analysis of the equilibrium mixture amenable to spectrophotometric analysis. In Part 2 of this experiment you will combine solutions of known initial concentrations of iron(iii) nitrate, Fe(NO 3 ) 3, and potassium (or sodium) thiocyanate, KSCN (or NaSCN.) Then you will determine the absorbance at λ max of these new solutions. The absorbance can be used to determine the equilibrium concentration of Fe(SCN) 2+. Knowing the initial concentrations of the reactants and the equilibrium concentration of Fe(SCN) 2+, you can calculate the equilibrium concentrations of the remaining reactants. You can then determine the value of K c. CALCULATIONS Since the calculations required in this experiment may not be apparent, we will go through a specific example. Let us assume that we prepare a solution by mixing 10.0 ml of 2.00 x 10-3 M Fe(NO 3 ) 3 with 10.0 ml of 2.00 x 10-3 M KSCN. As a result of reaction (1) some red Fe(SCN) 2+ ion forms. The concentration of the Fe(SCN) 2+ in this solution can be determined by finding the absorbance of the solution at the λ max and using a standard curve to determine its concentration. Let's say the concentration at equilibrium is found to be 1.50 x 10-4 M. Our problem is to determine K c for the reaction from this information. To do this we can carry out the following steps and summarize the information on a reaction (or ICE) table. 1. Write a balanced equation for the reaction. 2. Calculate the initial concentrations of the reactants and/or products. 3. Using stoichiometry, find the change during the reaction. 4. Calculate the equilibrium (final) concentrations. 5. Write the equilibrium constant and calculate Kc for the reaction. Here are the steps for solving K c for reaction (1) from the information given above. Fe 3+ (aq) + SCN - (aq) Fe(SCN) 2+ (aq) Calculate the initial [Fe 3+ ], [SCN - ] and [Fe(SCN) 2+ ]: [Fe 3+ ] init = [SCN - ] init = = M = M and of course, [Fe(SCN) 2+ ] init = 0 Set up the reaction table, Table 1, with x = [FeSCN 2+ ], the concentration of Fe(SCN) 2+ at equilibrium. Table 1. Reaction Table or Ice Table for equilibrium of Fe(SCN) 2+. Concentration (M) Fe 3+ + SCN - Fe(SCN) 2+ Initial Change -x -x +x Equilibrium x x x To calculate the equilibrium concentration of all the components we must solve for x. From the reaction table, x is the equilibrium concentration of FeSCN 2+ which you c230 Exp. 5 - Determination of an Equilibrium Constant 3

4 will determine from the absorbance versus [Fe(SCN) 2+ ] standard curve. In the above problem it is given as the following: x = [Fe(SCN) 2+ ] = M Therefore, the equilibrium concentrations are: [Fe 3+ ] = 8.5 x 10-4 M [SCN - ] = 8.5 x 10-4 M and [Fe(SCN) 2+ ] = 1.50 x 10-4 M Substituting into the mass-action expression: K c = = = 2.1 x 10 2 In this experiment you will determine the absorbance of different solutions at the wavelength of maximum absorbance (λ max ). That data will be transformed into concentrations similar to those shown in the example above. The calculations involved in processing the concentration terms are completely analogous to those illustrated. (Your value for K c will differ from the one we obtained, since the data in our example were obtained at a different temperature and thus relate to a different value of K c. EXPERIMENTAL PROCEDURE ALL SOLUTIONS IN THIS EXPERIMENT CAN BE DISPOSED IN THE SINK WITH PLENTY OF WATER. COLLECT IN A WASTE CONTAINER AT YOU DESK AND DISPOSE AS NEEDED. WORK IN PAIRS All stock solutions are prepared in 0.10 M HNO 3 and all dilutions are done using 0.10 M HNO 3, therefore the H + concentration is maintained at a constant concentration. The hydrogen ion does not participate directly in the reaction you are studying, but its presence is necessary to avoid the formation of brown-colored species such as Fe(OH) 2+, which would interfere with the analysis of [Fe(SCN) 2+ ]. You will be using volumetric and graduated pipets and volumetric flasks to prepare all solutions, and measuring absorbances for various solutions. We will not be providing detailed instructions since you have done these types of manipulations and used the spectrometer for the past two weeks. Part 1. THE STANDARD CURVE PREPARATION OF SOLUTIONS of varying known Fe(SCN) 2+ concentration. Using the techniques from last week, and the volumes given in Table 1, prepare the series of solutions. Place each solution into another clean, dry, labeled container and thoroughly rinse the volumetric flask before making the next solution. These solutions are used to establish a standard curve of absorbance at λ max for Fe(SCN) 2+ versus Fe(SCN) 2+ concentration. (See Table 1 in What-to-Do.) c230 Exp. 5 - Determination of an Equilibrium Constant 4

5 Table 1. Composition of Solutions for Standard Curve Solution M Fe(NO 3 ) 3 (in 0.10 M HNO 3 ), ml M NaSCN (in 0.10 M HNO 3 ), ml 0.10 M HNO 3, ml add to total add to total add to total add to total add to total DETERMINING λ max, for Fe(SCN) 2+. Rinse (x3) cuvette with Solution 1. Calibrate the Spectrophotometer with a cuvette containing Solution 1. Rinse (x3) cuvette with Solution 3 to prepare a cuvette with solution 3 and record an Absorbance vs. λ plot. Save your plot and select absorbance vs. concentration (mol/l). Select the appropriate λ. STANDARD CURVE. Collect absorbance-concentration data of solutions 1 through 5 at λ max after switching to Absorbance vs. Concentration in LoggerPro. Record each solution's absorbance in both the computer and in your laboratory notebook (Table 1). Make sure to enter the concentrations determined for Prelab in Table 1. Use the application to find the best-fit line linear fit through your data and use the equation for this line as your standard curve. Record the calculated equation for the line in your notebook. LEAVE THE Application OPEN with the data and proceed to Part 2. Part 2. Determination of Equilibrium Constant (K c ) BEFORE PROCEEDING YOU MUST Prepare M Fe(NO 3 ) 3. A solution of M Fe(NO 3 ) 3 is not available. To make this solution, dilute 0.50 ml of M Fe(NO 3 ) 3, measured with a 1.00-mL pipet, to 50 ml with 0.1 M HNO 3 in a volumetric flask. PREPARATION OF TEST SOLUTIONS (Table 2). Dry and label 5 medium size test tubes as suitable containers for these solutions. Stir each test solution for approximately one minute until the color does not change. With the Spectrophotometer set at λ max for the complex, measure and record absorbance of solutions 6 through 10. Table 2. Test Solutions for K c Determination Solution M Fe(NO 3 ) 3 * (in 0.10 M HNO 3 ), ml M NaSCN (in 0.10 M HNO 3 ), ml 0.10 M HNO 3, ml add to total add to total add to total add to total add to total c230 Exp. 5 - Determination of an Equilibrium Constant 5

6 DETERMINATION OF FE(SCN) 2+ EQUILIBRIUM CONCENTRATION. From the absorbance value of each solution and the equation for the standard curve determine the Fe(SCN) 2+ equilibrium concentration for each solution. Calculate K c for each solution. Determine the average K c, its range and 95% confidence interval of the mean and report with appropriate significant figures. ALL SOLUTIONS IN THIS EXPERIMENT CAN BE DISPOSED IN THE SINK WITH PLENTY OF WATER. QUESTIONS Q.1. When Fe 3+ and SCN - react to reach an equilibrium with Fe(SCN) 2+, what happens to the initial conc. of Fe3+ in part 2? How are the number of moles Fe(SCN) 2+ produced and the number of moles Fe 3+ used up related to each other? Q.2. A student mixes 5.0 ml of 2.00 x 10-3 M Fe(NO 3 ) 3 with 5.0 ml of 2.00 x 10-3 M NaSCN. She finds that in the equilibrium mixture the concentration of Fe(SCN) 2+ is 1.4 x 10-4 M. Use the data to put together a reaction table and calculate K c. Show all work. Q.3. Q.4. Q.5. After calibration of your spectrometer with the blank, you inadvertently put a fingerprint on the cuvette which affects the absorbance reading for a Fe(SCN) 2+ solution. Will the absorbance read higher or lower than it should in this case? Briefly explain. If the absorbance of a solution reads greater than 2.0 on the spectrophotometer, how could the preparation of the solution be modified to obtain a more accurate reading? Why can you calculate [Fe(SCN) 2+ ] from the amounts of reactants mixed in Part 1, but you can not calculate [Fe(SCN) 2+ ] from the amounts of reactants mixed in Part 2? c230 Exp. 5 - Determination of an Equilibrium Constant 6

7 WHAT TO DO To Be Turned in From Exp. 4- Determination of Red#40 and Blue#1 dyes in Koolaid : 1) Please hand in the following items in a packet STAPLED: a) A formal Results and Discussion for this lab. (The Appendix can be copy pages from notebook). See the Guidelines and Exp. 4 Handout for additional information. You are collecting data in pairs BUT the written report is individual. You may work on the figures with your partner but make sure that when it comes to writing you are working alone. 2) Upload a copy of the report to Turnitin electronically. (Without Appendix if copy pages were turned in.) Please Note: Your Absorbance Spectra for the dyes may be in two separate figures. As well, the Calibration Curves may also be in two separate figures. For Experiment 5 Before Lab: Read this experiment. Fill in the Title bar to include the experiment #, title, your name, partner's name, date, lab section, and TA's name. This information should be included on each page in your laboratory notebook for every experiment. All prelab material should be written in your laboratory notebook; your TA at the start of the lab will grade the pre-lab assignment. For this week s experiment your Prelab write-up should include, in addition to the completed title bars, the following sections. 1. Purpose After carefully reading the experiment, briefly state what you understand to be the purpose of this lab exercise. 2 Table of Reagents for Fe(NO 3 ) 3, KSCN, and HNO 3. BE SURE TO NOTE THE DISPOSAL PROCEDURES. Your lab book should also have the following information and tables ready for use: 3. Prepare the following two full page tables in your notebook before coming to lab (please note that these tables are extended versions of Tables 1 and 2 in the experiment). Each of these tables should be one full page and should be oriented sideways in your notebook ( landscape ). Before lab you should have calculated all initial concentrations and entered them in the appropriate tables in your notebook. c230 Exp. 5 - Determination of an Equilibrium Constant 7

8 During the Lab: Carry out the procedure as written. Modify your procedure if you find it necessary, but be sure to record the modifications. Record all observations and in Part 1 and Part 2. Put the data in the appropriate tables which you have prepared in your laboratory notebook. Plot the standard curve in LoggerPro and find the best-fit line for your calibration curve. To Be Turned In NEXT WEEK NOTE: Specific pages and order of assignment to be turned in will be state on the Moodle page for the next experiment. The report for this experiment includes: Part 1. The Standard Curve A printed copy of Table 1 (prepared in a Word document). Include a title. Sample calculations with all units for Table 1. Printed copy of Absorbance Spectrum copied from LoggerPro and pasted into a Word doc. Include appropriate caption. Printed copy of Standard Curve copied from LoggerPro and pasted into a Word doc. Include appropriate caption. Part 2. Determination of Equilibrium Constant (K c ) Printed copy of a Completed Table 2 (prepared in a Word Document). Don t forget to include your Mean K c and 95% confidence interval of the mean. All sample calculations with all units for Part 2. Questions and Sample Calculations Your responses to questions and sample calculations should be found on clearly labeled summary pages (from your notebook). Report answers to the questions in complete sentences. c230 Exp. 5 - Determination of an Equilibrium Constant 8