DETERMINATION OF K c FOR AN EQUILIBRIUM SYSTEM

DETERMINATION OF K c FOR AN EQUILIBRIUM SYSTEM 1 Purpose: To determine the equilibrium constant K c for an equilibrium system using spectrophotometry to measure the concentration of a colored complex ion. Introduction: The Reaction To Be Studied When an aqueous solution containing iron (III) ions, Fe +3, is combined with another solution containing thiocyanate ions, SCN -, the following reaction occurs: Fe +3 (aq) + SCN - (aq) FeSCN +2 (aq) (rxn. 1) The FeSCN +2 product is an example of a complex ion. In the course of this reaction, a new covalent bond has formed between the Fe +3 ion and a lone pair of electrons on the thiocyanate ion. This new bond can easily be broken at room temperature, thus resulting in the re-forming of iron (III) and thiocyanate: FeSCN +2 (aq) Fe +3 (aq) + SCN - (aq) (rxn. 2) Note that rxn. 2 is the reverse of rxn. 1. In the reaction container, both reactions will easily occur at room temperature. Fe 3+ (aq) + SCN - (aq) FeSCN +2 (aq) (rxn. 3) Once the rate of the reverse reaction is equal to the rate of the forward reaction, a state of dynamic equilibrium will be established. Every time one Fe +3 and SCN - come together to form one FeSCN +2, another FeSCN +2 dissociates to become Fe +3 and SCN -. While individual ions continue to change in this way, there is no net change in the amount of any reactant or product. At equilibrium the concentration of each substance remains constant. Therefore, the value of K c in this expression also remains constant: [FeSCN +2 ] K c = (eq. 1) [Fe +3 ] [SCN - ] The goal of this lab is to determine the value of K c for the equilibrium system described in rxn. 3.

2 Determining The Equilibrium Concentration of FeSCN +2 To find K c using Eq. 1, the concentration of three different ions must be known at equilibrium. In this experiment, we will measure the equilibrium [FeSCN +2 ] indirectly using a spectrophotometer (see below). Then, from knowledge of the original [Fe +3 ] and [SCN - ], their equilibrium concentrations can be calculated. Once all equilibrium concentrations are determined, eq. 1 can be used to calculate K c. The reason that we focus on [FeSCN +2 ] is because it has a red color when dissolved in water; neither Fe +3 (aq) nor SCN - (aq) has a color. We observe the color red when photons with wavelengths in the red region of the electromagnetic spectrum bounce off an object (in this case the FeSCN +2 ion) and strike the retina of our eyes. Photons in other color regions are absorbed by the object. When in solution, the intensity of the red color you observe from FeSCN +2 is related to its concentration, a value you need to know. The more intense the red solution is, the higher its FeSCN +2 concentration. Using your eyes, you could probably classify a FeSCN +2 (aq) solution as concentrated or dilute. For this experiment, that is not good enough. You need to know the specific molarity of FeSCN +2 (aq). Unfortunately, your eyes cannot determine that. However, there is an instrument that can give a quantitative measurement about the behavior of photons that are aimed at some sample solution: a spectrophotometer. A spectrophotometer is an instrument which has a light source and an "observer" (an electronic detector) all combined in one box. The light source does not, however, emit all colors of light. Instead, the source emits just a single wavelength of visible light at a time. The light source can be set to one particular wavelength for an experiment. Then, a sample solution is placed in the path of that light. The electronic detector measures how much of the original light was able to pass through the solution, in terms of percent transmittance, %T (see Figure 1). Light Source Only ONE λ Some light passes through Detector Object (usually a solution) FIGURE 1. Operation of a spectrophotometer: Light of one wavelength is emitted from the source and aimed at a solution. Some of the light is absorbed; some passes through (is transmitted ). The detector measures the amount of light transmitted and displays this as a percentage.

3 There are two ways to think about the original light that was emitted from the spectrophotometer's light source. You could focus on how much passed through the solution (as in percent transmittance) or you could focus on how much was absorbed by the solution. Most mathematical applications of spectrophotometry use absorbance, A, instead of %T. In this experiment we will be measuring percent transmittance rather than absorbance, then mathematically converting to absorbance. Greater precision can be obtained this way since the transmittance scale on the Spectronic 20 s is linear, whereas the absorbance scale is logarithmic. In essence, this means that at very high absorbances there is a significant sacrifice of precision of the measurements. There are two important relationships to know about A: A c (where c = concentration) (eq. 2) A = log 100 %T (eq. 3) The first of these, eq. 2, is referred to as Beer's Law. It states simply that absorbance is directly proportional to concentration. The greater the concentration of a solution, the more light will be absorbed. The second, eq. 3, is the mathematical definition of A: it is the common logarithm of 100 divided by the percent transmittance. As with all proportionalities, eq. 2 can be made into a useful equation when the proportionality sign is replaced with an equal sign and a proportionality constant. For practical applications involving Beer's Law, eq. 4 is most useful. In this equation, A is the absorbance, β is the Beer's Law constant (the proportionality constant), and, c is the concentration of the solution (for our purposes, the molarity). A = βc (eq. 4) In order to determine the equilibrium molarity of FeSCN +2, you will measure %T directly. That can be converted to A using eq. 3. Then, using eq. 4, the molarity of the FeSCN +2 can be calculated, if and only if the value of β is known. Therefore, the first part of today's lab will be to determine the value of β for the system you are studying. Determination of B for Beer's Law In order to find β, three tests will be run with solutions of known concentrations of FeSCN +2. After the %T values are converted to A values, a graph of [FeSCN +2 ] vs. A can determine β. Note that eq. 4, A = βc, is in y = mx form. Therefore, the slope of the graph will be the value of β. (To decide which quantity goes on the x-axis, answer the question "what depends on what?" Does concentration depend on absorbance, or, does absorbance depend on concentration? Remember that the independent quantity should be placed on the x-axis.) Did you find anything troubling in the last paragraph? Perhaps the idea that a solution of known concentration of FeSCN +2 might seem a contradiction, since you already know that once

4 in solution, it dissociates into Fe +3 and SCN - ions, and reaches an equilibrium as in rxn. 3. This trouble with trying to make a solution with a known concentration of FeSCN +2 can be resolved when you apply LeChatelier s principle to the system. Here is rxn. 3 again: Fe +3 (aq) + SCN - (aq) FeSCN +2 (aq) (rxn. 3) According to LeChatelier's principle, addition of one reactant should force an equilibrium to the right (formation of more products). As more and more of this reactant is added, more and more of the product will be formed. If enough of this reactant is added, essentially all of the other reactant will be converted to product. If you knew the amount of the other reactant (the limiting reactant), you could determine the amount of product. In this part of the lab you will use extremely large amounts of SCN - (aq) with a limited amount of Fe +3 (aq). Since so much SCN - will be used, it can safely be assumed (by LeChatelier's principle) that all of the Fe +3 has been converted to FeSCN +2. If the amount of Fe +3 is known, then the amount, and thus concentration, of FeSCN +2 can be known as well. Three solutions with known [FeSCN +2 ] will placed individually in the spectrophotometer and their %T determined using 450 nm as the single wavelength (λ) emitted from the light source. Determining The Equilibrium Concentrations of Fe +3 and SCN - Once you have found β, you are ready to begin working on the second part of the lab, in which you will determine K c for rxn. 3. Recall that the K c expression is: [FeSCN +2 ] K c = (eq. 1) [Fe +3 ] [SCN - ] In this part of the lab, you will not have any one reactant present in tremendous excess. All three species, Fe +3, SCN - and FeSCN +2 will be present in various concentrations. You already know that [FeSCN +2 ] will be found using Beer's Law and eq. 4, A = βc. First you will measure %T for a given solution; then %T is converted to A using eq. 3. Then c (which in this case is [FeSCN +2 ]) can be calculated. However, what about the concentrations of Fe +3 and SCN - at equilibrium? They must be determined in order to find K c. These values will be calculated, after the concentration of FeSCN 2+ has been determined. Since the stoichiometry of rxn. 3 is 1:1:1, once you know the molarity of FeSCN 2+ produced, that molarity must also be the amount of both Fe +2 and SCN - that have been consumed in reaching equilibrium. Thus that amount must be subtracted from the initial concentrations of Fe +2 and SCN - in order to obtain the equilibrium concentrations of these species. (See eqs. 5 and 6.)

[Fe +3 ] equil = [Fe +3 ] initial - [FeSCN +2 ] equil (eq. 5) 5 [SCN - ] equil = [SCN - ] initial - [FeSCN +2 ] equil (eq. 6) Once equilibrium concentrations of all species are known, K c can then easily be calculated. Procedure A. Determination of β for Beer's Law 1. Using a buret, add 4.00 ml of 0.0025 M Fe(NO 3 ) 3 (which is in 0.1 M HNO 3 ) to a 100- ml volumetric flask. Add enough deionized water to bring the total volume to the mark on the neck of the flask. Stopper and shake the flask. Label this flask Diluted Fe +3. 2. Obtain three 16 x 150 mm test tubes and number them 1-3. DO NOT use the spectrophotometer tubes (cuvettes), they are too small to use at this point. 3. Properly prepare two burets, and fill them with the solutions required: diluted Fe +3 and 0.1 M HNO 3. You will use a 5.00 ml volumetric pipet to measure the 1.0 M KSCN. Your instructor will show you the correct use of the pipet. 4. Into each test tube, place the specified amount of each solution as listed on Table 1. TABLE 1 TEST ml of ml of ml of TUBE DILUTED Fe +3 1 M KSCN 0.1 M HNO 3 1 1.00 5.00 4.00 2 2.00 5.00 3.00 3 3.00 5.00 2.00 5. Once all the contents of a test tube have been added, use a vortex mixer to mix thoroughly. 6. Following the instructions on the sheet next to the Spectronic 20, prepare a blank and use it to adjust the 100% transmittance. 7. Pour the reaction mixture for test tube 1 into a spectrophotometer tube (cuvette) so that it is two-thirds full. Wipe the outside of the cuvette with a Kimwipe. 8. Place the cuvette into the spectrophotometer, the light source of which is already pre-set to 450 nm. (Do not adjust the wavelength setting! If you have questions, see your instructor.) Record the percent transmittance (%T) for the sample to the nearest 0.1%.

6 9. Repeat steps 6-7 for all the test tube mixtures. 10. Properly discard your Diluted Fe +3 solution; you are done with it. 11. Perform the calculations to determine the value of β: find [FeSCN +2 ] and A for each trial. Graph the values and find the slope of the graph using the Microsoft Excel graphing software in the Science Learning Center. B. Determination of K c 1. Using burets, add the appropriate amounts of 0.0025 M Fe(NO 3 ) 3, 0.0025 M KSCN, and 0.1 M HNO 3 to three clean, numbered (4-6) test tubes as listed in Table 2. NOTE: BE SURE YOU ARE USING THE CORRECT SOLUTIONS. DO NOT USE THE DILUTED Fe +3 OR THE 1 M KSCN SOLUTIONS FROM PART A! TABLE 2 TEST ml of ml of ml of TUBE 0.0025 M Fe(NO 3 ) 3 0.0025 M KSCN 0.1 M HNO 3 4 1.00 1.00 5.00 5 1.00 1.50 4.50 6 1.00 2.00 4.00 2. Once all the contents of a test tube have been added, use the vortex mixer to mix thoroughly. 3. Pour the reaction mixture from test tube 4 into a clean, dry cuvette so that it is two-thirds full. 4. Place the cuvette into the spectrophotometer, and record the %T at 450 nm. 5. Repeat steps 3-4 for all the test tube mixtures. Record %T for each. 6. Properly discard your solutions as directed by your lab instructor.

7 Calculations Your main goal in this lab is to find the value of the equilibrium constant, K c, for this reaction system: Fe +3 (aq) + SCN - (aq) FeSCN +2 (aq) (rxn. 3) In order to do so, you must know equilibrium concentrations of all three species in rxn. 3. None of them can be found directly. Therefore, your strategy for calculations is as follows: Part A Determination of Beer s Law constant β 1. From the % transmittances obtained for tubes 1-3, calculate the corresponding absorbances using eq. 3. 2. Calculate the equilibrium concentration of FeSCN +2. This will equal the initial concentration of Fe +3 since, for Part A, all the Fe +3 was converted into FeSCN +2. Note that you will need to do two dilution calculations to obtain [Fe +3 ] initial, first diluting 4.00 ml of original stock solution to 100.00 ml in a volumetric flask, then diluting some (either 1.00, 2.00, or 3.00 ml) of that solution to 10.00 ml for use in tubes 1-3. 3. Using the Microsoft Excel graphing software, plot [FeSCN +2 ] on the x-axis versus absorbance, A, on the y-axis. The slope of this graph will equal the Beer s Law constant β. Include your data table and graph with your lab report. Part B Determination of K c 4. From the % transmittances obtained for tubes 4-6, calculate the corresponding absorbances using eq. 3. 5 Using eq. 4, calculate c, which represents the equilibrium concentration of FeSCN +2. Use the value for β that you obtained in Part A. 6. Calculate [Fe +3 ] initial and [SCN - ] initial for tubes 4-6. These are dilution calculations, and thus you can use the equation M 1 V 1 = M 2 V 2. Refer to Table 2 for concentrations and volumes of reagents. 7. The change in the concentrations of both Fe +3 and SCN - will be equal to the equilibrium concentration of FeSCN +2 which was produced. 8. Calculate [Fe +3 ] equil and [SCN - ] equil using eqns. 5 and 6. 9. Calculate K c, using eq. 1. After finding K c for several trials (tubes 4 through 6), calculate your average K c.

8 Determination of K c for an Equilibrium System Data and Calculations Sheet Name Partner A. Determination of β for Beer's Law I. Data Test Tube %T A [FeSCN +2 ] 1 2 3 Show your work here for determination of [FeSCN +2 ] for tube 1. (You do not need to show your work for tubes 2and 3.) II. Finding β by graphing, linear regression Graph the values of A and [FeSCN +2 ] appropriately. Then find the slope of the best line by linear regression. Include your graph and any print-out from computer linear regression. Equation of the best line: Value of β (include units):

9 B Determination of K c I. Data (NOTE - Space has been left on pages 10-11 for you to show all your calculations for test tube 4.) Test Tube %T A [FeSCN +2 ] EQUIL 4 5 6 Fill in the ICE chart here for test tube 4 (show all calculations on pages 10-11). Fe 3+ (aq) + SCN - (aq) FeSCN +2 (aq) Initial, M Change, M Equilibrium, M Fill in the ICE chart here for test tube 5. Fe 3+ (aq) + SCN - (aq) FeSCN +2 (aq) Initial, M Change, M Equilibrium, M Fill in the ICE chart here for test tube 6. Fe 3+ (aq) + SCN - (aq) FeSCN +2 (aq) Initial, M Change, M Equilibrium, M

10 Test Tube Kc 4 5 6 Show your work here for all values from test tube 4. 1. A 2. [FeSCN +2 ] equil 3. [Fe +3 ] initial (refer to Table 2 and use M 1 V 1 = M 2 V 2 ) 4. [SCN - ] initial (refer to Table 2 and use M 1 V 1 = M 2 V 2 ) 5. [Fe +3 ] change 6. [SCN - ] change

7. [Fe +3 ] equil 11 8. [SCN - ] equil 9. K c II. Average K c Find the average of your three experimental values for K c. Average K c =

12 Determination of K c for an Equilibrium System Post-lab Questions 1. A sample of 15.00 ml of 0.0500 M (NH 4 ) 2 SO 4 is diluted to 100.00 ml in a volumetric flask. Then 6.00 ml of this solution is removed and diluted further to a total volume of 17.00 ml. What is the molarity of NH 4 + in the final solution? 2. 1.25 mole of ethanol and 1.85 mole of acetic acid are dissolved in water and kept at 100 o C. The volume of the solution is 250.0 ml. At equilibrium, 0.25 mole of acetic acid has been consumed in producing ethyl acetate. Calculate K c at 100 o C for the reaction C 2 H 5 OH (aq) + CH 3 COOH (aq) CH 3 COOC 2 H 5(aq) + H 2 O (l) ethanol acetic acid ethyl acetate

Determination of K c for an Equilibrium System 13 Pre-laboratory Assignment Name Section 1. Calculate [Fe +3 ] initial for test tubes 1-3. Show your work here for one of the tubes. 2. A student performed a lab similar to this one in an attempt to find K eq for the equilibrium system X + (aq) + Y - (aq) Z (blue, aq). In one trial, the student combined 5.00 ml of 0.10 M X + with 10.00 ml of 0.20 M Y - in a test tube. When the resulting solution was analyzed with a spectrophotometer set at λ= 600 nm, 4.00% of the light passed through the solution. For this equilibrium system, the Beer s law constant, β, is known to be 92.4 L mol -1. A. Calculate the initial molarity of each reactant added to the test tube at the moment of mixing, [X + ] init and [Y - ] init. (HINT: these are dilution calculations.) B. Calculate the value of A, then find [Z] equil. C. Set up an I.C.E. table to find [X + ] equil and [Y - ] equil. D. Find the value of K c for this equilibrium system. Last revised 4/6/2016 DN