Determination of K c for a Complex Ion Formation

Transcription

1 Determination of K c for a Complex Ion Formation Objectives Find the value of the equilibrium constant for formation of FeSCN 2+ by using the visible light absorption of the complex ion. Confirm the stoichiometry of the reaction. Background In the study of chemical reactions, chemistry students first study reactions that go to completion. Inherent in these familiar problems such as calculation of theoretical yield, limiting reactant, and percent yield is the assumption that the reaction can consume all of one or more reactants to produce products. In fact, most reactions do not behave this way. Instead, reactions reach a state where, after mixing the reactants, a stable mixture of reactants and products is produced. This mixture is called the equilibrium state; at this point, chemical reaction occurs in both directions at equal rates. Therefore, once the equilibrium state has been reached, no further change occurs in the concentrations of reactants and products. The equilibrium constant, K, is used to quantify the equilibrium state. The expression for the equilibrium constant for a reaction is determined by examining the balanced chemical equation. For a reaction involving aqueous reactants and products, the equilibrium constant is expressed as a ratio between reactant and product concentrations, where each term is raised to the power of its reaction coefficient: aa (aq) + bb (aq)! cc (aq) + dd (aq) K c = [ C]c D A [ ] d [ ] a [ B] b (1) When an equilibrium constant is expressed in terms of molar concentrations, the equilibrium constant is referred to as K c. The value of this constant at equilibrium is always the same at a given temperature, regardless of the initial reaction concentrations. Whether the reactants are mixed in their exact stoichiometric ratios or one reactant is initially present in large excess, the ratio described by the equilibrium constant expression will be achieved once the reaction composition stops changing. We will be studying the reaction that forms the reddish-orange iron(iii) thiocyanate complex ion, Fe(H 2 O) 5 SCN 2+ (aq). The chemical equation describing the formation of this complex ion is Fe(H 2 O) 6 3+ (aq) + SCN (aq)! Fe(H 2 O) 5 SCN 2+ (aq) + H 2 O(l) (2) Notice that the reaction involves the displacement of a water ligand by a thiocyanate ligand, SCN. However, for simplicity, and because water ligands do not change the net charge of the species, water can be omitted from the formulas of Fe(H 2 O) 6 3+ (aq) and Fe(H 2 O) 5 SCN 2+ (aq) in our chemical equation. Thus, the chemical formula Fe(H 2 O) 6 3+ (aq) may be simplified as Fe 3+ (aq) and Fe(H 2 O) 5 SCN 2+ (aq) as FeSCN 2+ (aq). Making these changes, we can rewrite the simplified chemical equation for the reaction and its corresponding equilibrium constants expression as: Determination of K c Page 1 of 6

2 Fe 3+ (aq) + SCN (aq)! FeSCN 2+ (aq) K c = [ FeSCN 2+ ] [ Fe 3+ ] SCN " [ ] (3) In this experiment you will create several different aqueous mixtures of Fe 3+ and SCN. Because this reaction reaches equilibrium nearly instantly, these mixtures turn reddish-orange very quickly due to the formation of the product FeSCN 2+ (aq). The intensity of the color of the mixtures is proportional to the concentration of product formed at equilibrium. As long as all mixtures are measured at the same temperature, the ratio described in Equation (3) will be the same because the value of K c is a constant. Measurement of [FeSCN 2+ ]: Because the complex ion product is the only strongly colored species in the system, its concentration can be determined by measuring the intensity of the orange color in equilibrium systems of these ions. This method relies on Beer's Law, which is given by the equation: A = "!c (4) where A is the absorbance of light by the solution; c is the molar concentration of the solution;! is the path length, or the distance that the light travels through the solution; and! is the molar absorptivity, which is a constant that expresses the absorbing ability of a chemical species at a particular wavelength. The absorbance, A, is roughly correlated with the color intensity observed visually; the more intense the color, the greater the absorbance. By using a spectrophotometer, the absorbance, A, of a solution can be measured directly. Solutions containing FeSCN 2+ are placed into the spectrophotometer and their absorbances at 447 nm are measured. The path length,!, is the same for all measurements and has a value of 1.00 cm. Rearrangement of Equation (4) allows for calculation of the molar concentration, c, from the known value of the constant " #!. The value of this constant is determined by plotting the absorbances, A, vs. molar concentrations, c, for several solutions with known concentration of FeSCN 2+ (aq) as shown in Figure 1. The slope of this calibration curve is then used to find unknown concentrations of FeSCN 2+ (aq) in the experiment from their measured absorbances. x Absorbance x x light x Slope =! x l Molar Concentration l Figure 1: Plots of A vs. c for solutions with known concentrations of FeSCN 2+ (aq) can be used as a calibration curve. This plot is used to determine the FeSCN 2+ (aq) concentration in solutions where that value is not known. The path length, l, is demonstrated in the diagram of a cuvet and is taken to be 1.00 cm in this experiment. Determination of K c Page 2 of 6

3 Calculations In order to determine the value of K c given by Equation (3), the equilibrium values of [Fe 3+ ], [SCN ], and [FeSCN 2+ ] must be found. These values can be determined from a reaction table ('ICE' table), as shown in Table 1: Table 1: Reaction ICE Table Fe 3+ (aq) + SCN (aq)! FeSCN 2+ (aq) Initial Concentration [Fe 3+ ] i [SCN ] i 0 Change in Concentration x x + x Equilibrium Concentration [Fe 3+ ] i x [SCN ] i x x = [FeSCN 2+ ] The reaction "ICE" table demonstrates the method used in order to find the equilibrium concentrations of each species. The values that come directly from the experimental procedure are found in the shaded regions. From these values, the remainder of the table can be completed. The initial concentrations of the reactants in Table 1 that is, [Fe 3+ ] and [SCN ] prior to any reaction can be found by a dilution calculation based on the values from Table 2 found in the procedure. Once the reaction reaches equilibrium, we assume that the reaction has shifted forward by an amount, x. Notice from Table 1 that the value of x is simply equal to the equilibrium concentration of FeSCN 2+ (aq), or that x = [FeSCN 2+ ] at equilibrium. The equilibrium value of [FeSCN 2+ ] is determined spectroscopically using Beer s Law. Its initial value in the table is zero because no FeSCN 2+ (aq) is added to the initial solution. Finally, the equilibrium concentrations of the reactants, Fe 3+ (aq) and SCN (aq), are found by subtracting the equilibrium concentration of FeSCN 2+ (aq) from the initial concentrations of Fe 3+ (aq) and SCN (aq), as shown in the table above. Once all the equilibrium values are known, they can be applied to the equilibrium constant expression in Equation (3) to determine the value of K c. Standard Solutions of FeSCN 2+ (aq) In order to find the equilibrium concentration of FeSCN 2+ in our solutions we require the preparation of standard solutions with known [FeSCN 2+ ]. These are prepared by mixing a small amount of dilute KSCN solution with a more concentrated solution of Fe(NO 3 ) 3. The solution has overwhelming amount of the excess reagent (Fe 3+ ), driving the equilibrium position far towards products. So at equilibrium the concentration of Fe 3+ (aq) is very high due to its large excess, and therefore the equilibrium concentration of SCN (aq) must be very small. In other words, we assume that essentially all of the SCN (aq) present becomes FeSCN 2+ (aq) product. Examine the K c equilibrium-constant expression to prove this to yourself. Determination of K c Page 3 of 6

4 Procedure Safety GENERAL SAFETY: Students must wear safety goggles at all times. CHEMICAL HANDLING: The iron(iii) nitrate solutions contain nitric acid. Avoid contact with skin and eyes; wash hands frequently during the lab and wash hands and all glassware thoroughly after the experiment. WASTE DISPOSAL: All chemicals used must go in the proper waste container for disposal. Materials and Equipment You will need the following additional items for this experiment: 5-mL volumetric pipet 10-mL graduated pipet rubber pipet bulb Spectrometer 5 cuvets Part A. Solution Preparation Your instructor will demonstrate the proper use of the volumetric glassware used in this experiment. Label two clean, dry 50-mL beakers, and pour ml of 2.00 x 10 3 M Fe(NO 3 ) 3 (already dissolved by the stockroom in 1 M HNO 3 ) into one beaker. Then pour ml of 2.00 x 10 3 M KSCN into the other beaker. There are two Fe(NO 3 ) 3 solutions used for this experiment, be certain to use the 2.00 x 10 3 M Fe(NO 3 ) 3 solution for this step. At your work area, label five clean and dry medium test tubes to be used for the five test mixtures you will make. Using your volumetric pipet, add 5.00 ml of your 2.00 x 10 3 M Fe(NO 3 ) 3 solution into each of the five test tubes. Using your graduated pipet, add the correct amount of KSCN solution to each of the labeled test tubes, according to Table 2 below. Rinse out your graduated pipet with deionized water, and then use it to add the appropriate amount of deionized water into each of the labeled test tubes, according to Table 2 below. Stir each solution thoroughly with your stirring rod until a uniform orange color is obtained. To avoid contaminating the solutions, rinse and dry your stirring rod after stirring each solution. Determination of K c Page 4 of 6

5 Table 2: Test mixtures Mixture Fe(NO 3 ) 3 solution KSCN solution water ml 5.00 ml 0 ml ml 4.00 ml 1.00 ml ml 3.00 ml 2.00 ml ml 2.00 ml 3.00 ml ml 1.00 ml 4.00 ml Five solutions will be prepared from 2.00 x 10 3 M KSCN and 2.00 x 10 3 M Fe(NO 3 ) 3 according to this table. Note that the total volume for each mixture is ml, assuming volumes are additive. If the mixtures are prepared properly, the solutions will gradually become lighter in color from the first to the fifth mixture. Use this table to perform dilution calculations to find the initial reactant concentrations to use in Table 1. Part B. Preparation of a Stock Solution of FeSCN 2+ Before examining the five test mixtures, prepare a stock solution with known concentration of FeSCN 2+ (aq). Obtain 15 ml of M Fe(NO 3 ) 3 (aq). Rinse your volumetric pipet with a few milliliters of this solution, and add ml of this solution into cleaned and dried large test tube labeled stock solution. There are two Fe(NO 3 ) 3 solutions used for this experiment, be certain to use the M Fe(NO 3 ) 3 solution for this step. Using your graduated pipet, add 8.00 ml deionized water to the large test tube. Rinse your graduated pipet with a few milliliters of 2.00 x 10 3 M KSCN. Then add 2.00 ml of the KSCN solution to the large test tube. Mix the solution with a clean and dry stirring rod until a uniform dark-orange solution is obtained. This stock solution should be darker than any of the other five solutions prepared previously. Part C. Creating a Calibration Curve To determine the concentrations of your equilibrium mixtures of FeSCN 2+ (aq) prepared in Part A you will measure the absorbance of each mixture using a spectrophotometer. To do so you will need to create a calibration curve. A calibration curve is a plot of the absorbance at 447 nm vs. molar concentration for a series of standard solutions of known FeSCN 2+ (aq) concentration. From this curve, you can determine the value of [FeSCN 2+ ] in each equilibrium mixture from its absorbance at 447 nm. A few dilutions of the stock solution prepared in Part B will be used to prepare four standard solutions for your calibration curve. In addition, one blank solution containing only Fe(NO 3 ) 3 will be used to zero the spectrophotometer. Table 3 shows the preparation method for each of the standards. You should prepare each of these solutions accordingly using your volumetric glassware as in the previous parts of the experiment. Use clean dry large test tubes for this step. Swirl each of these standard solutions well to mix the contents before continuing. Determination of K c Page 5 of 6

6 Tube Table 3: Standard Solutions Composition Blank M Fe(NO 3 ) 3 in 1 M HNO 3 1 Stock Solution (Part B) ml Stock ml H 2 O ml Stock ml H 2 O ml Stock ml H 2 O Four standard solutions and one blank solution will be prepared for the calibration curve. Once each of these standard solutions has been prepared have your instructor come over and show you how to operate the spectrometer. Fill a cuvet to just below the label with the blank solution. If your instructor has assigned your group a temperature then heat or cool the cuvet until its contents are at the desired temperature and record this value on your data sheet. Carefully wipe off the outside with a tissue. Insert the cuvet into the spectrometer and make sure it is oriented correctly by aligning the mark on cuvet towards the front. Close the lid. Use this solution to zero your spectrometer. For each standard solution in Table 3, rinse your cuvet twice with a small amount (~0.5 ml) of the standard solution to be measured, disposing of the rinse solution each time. Then fill the cuvet with the standard, heat or cool (if required) and record the temperature, insert the cuvet into the spectrometer as before, and record the absorbance reading on your data sheet. You will use these absorbance values to plot your calibration curve. Calculate the concentration of FeSCN 2+ (aq) in each of these standard solutions using the dilution equation, M 1 V 1 = M 2 V 2. Now plot your measured absorbance for each of these solutions versus their respective concentration value using Excel. A computer is available in the balance room or you may do so down in the Science Computer Lab. Add a best-fit line to this plot using the Excel trendline function. Select Display Equation on Chart from the trendline function options menu. In addition, because you used your blank solution to zero your spectrometer you should also select the option, set intercept = 0, from this menu. This will cause your plot to pass through the origin. Your plot should be a perfectly straight line and your best-fit line should pass directly through each of your data points. If any of your data points fall off of your best-fit line, you should remake that particular solution, measure its absorbance again, and replot your data using this new value until a perfectly straight line through all of your data points is obtained. Part D. Spectrophotometric Determination of [FeSCN 2+ ] Use your spectrometer to measure the absorbance of each of the five equilibrium mixtures of unknown FeSCN 2+ (aq) concentration you prepared in Part A according to Table 1. Be sure to heat or cool each cuvet if your group was assigned a temperature. Record the temperature and absorbance of each solution on your data sheet. The value of [FeSCN 2+ ] for each of these solutions is determined using your calibration curve. Determination of K c Page 6 of 6

7 Name: Lab Partner: Date: Lab Section: Lab Report: Determination of the Equilibrium Constant For a Reaction Experimental Data Part A. Initial Concentrations of Fe 3+ and SCN in Unknown Mixtures Tube Reagent Volumes / ml 2.00 x 10-3 M 2.00 x 10-3 M Fe(NO 3 ) 3 KSCN Initial Concentrations / M Water [Fe 3+ ] i [SCN ] i Show a sample dilution calculation below for determining the value of [Fe 3+ ] i for Tube 1: Part C. Creating a Calibration Curve Tube Absorbance [FeSCN 2+ ] / M Temp / ºC Blank 1 2 Note that since [Fe 3+ ] >> [SCN ] in the Standard Solutions, the reaction is forced to completion, thus causing essentially all the added SCN (aq) to be converted to FeSCN 2+ (aq). 3 4 Show sample dilution calculations below for determining the values of [FeSCN 2+ ] for Tubes 1 and 2: Determination of K c Page 1 of 4

8 Use Excel to create a plot of absorbance versus concentration for the data from your standard solution. Your graph should have an appropriate title and labeled axes with an appropriate scale. Add a trendline to the data points. Select Display Equation on Chart and set intercept = 0 in the trendline function options menu. As described in the procedure, your plot should be a perfectly straight line and your best-fit line should pass directly through each of your data points. Submit this graph with your report. Record the equation of the best-fit line obtained from this graph here: Using the equation of your best-fit line and taking the value of the path length,!, to be 1.00 cm, determine the value of the molar absorptivity,!, of these solutions at 447 nm as described by Beer s Law given by Equation (4). What are the units of!? Hint: The value of the absorbance, A, is unitless. Value and units of! : Part D. Spectrophotometric Determination of [FeSCN 2+ ] Use your measured absorbances and the value of! you determined above for Equation (3) to determine the concentration of FeSCN 2+ (aq) in each of the equilibrium mixtures you prepared in Part A. Enter these values in the table below. Equilibrium Mixture Measured Absorbance [FeSCN 2+ ] / M Temp / ºC Show a sample calculation below for [FeSCN 2+ ] in equilibrium mixture 1: Determination of K c Page 2 of 4

9 Analysis The chemical equation describing the reaction that is assumed to occur in this experiment is: Fe 3+ (aq) + SCN (aq)! FeSCN 2+ (aq) Write the equilibrium constant expression for this equation below: Using your data from the previous pages of this report, write out a complete Reaction Table (or ICE table) below for the reaction occurring in Equilibrium Mixture 1 (see Table 2): Determine the value of K c for Equilibrium Mixture 1 from these data. Show your calculations below: Using the same method, complete the table below for all the equilibrium concentrations and values of K c for each of the five equilibrium mixtures prepared in Part A. Determine the average value of K c. Mixture 1 Equilibrium Concentrations / M [Fe 3+ ] [SCN ] [FeSCN 2+ ] K c Average value of K c : Determination of K c Page 3 of 4

10 Additional Analysis: Is an Alternative Reaction Stoichiometry Supported? Suppose that instead of forming the FeSCN 2+ complex ion, the reaction between Fe 3+ (aq) and SCN (aq) resulted in the formation of a complex ion with a chemical formula of Fe(SCN) 2 + according to, Fe +3 (aq) + 2 SCN (aq)! Fe(SCN) 2 + (aq) Write the corresponding equilibrium-constant expression for K c for this chemical equation: Create a new Reaction Table (or ICE Table) for Equilibrium Mixture 1 below using the stoichiometry of the alternative chemical equation above as the basis for your calculations: Determine the value of K c for Equilibrium Mixture 1 from these data. Show your calculations below: Using the same method, complete the table below for all the equilibrium concentrations and values of K c for each of the five equilibrium mixtures based on the alternative chemical equation above. Mixture 1 Equilibrium Concentrations / M [Fe 3+ ] [SCN ] [FeSCN 2+ ] K c Based on the calculated values of K c in this table and those in the table at the bottom of the previous page, can you tell which, if either, reaction equation best describes the equilibrium reaction occurring in your mixtures? Justify your response (continue your answer on the back of this sheet if needed): Determination of K c Page 4 of 4