# Experiment 3 Measurement of an Equilibrium Constant

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1 3-1 Experiment 3 Measurement of an Equilibrium Constant Introduction: Most chemical reactions (e.g., the generic A + B 2C) are reversible, meaning they have a forward reaction (A + B forming 2C) and a backward reaction (2C forming A+ B). Initially, when the concentrations of A and B are much higher than the concentration of C, the forward reaction rate is much faster than the reverse reaction rate. However, when enough C is formed and A and B consumed, the rate at which A and B are disappearing slows down and becomes the same as the rate at which A and B are being formed by the reverse reaction. When this happens, the concentrations of reactants (A and B) become constant, and the same is true of the product, (C). The reaction system is then said to be at equilibrium. The ratio of the product of the product concentrations to the product of the reactant concentrations at chemical equilibrium (each concentration raised to a power equal to the coefficients in the balanced reaction) is called the equilibrium constant, K eq, for the reaction. Thus for the generic example, 2 [ C] K eq = [ A][ B] K eq for the Formation of FeSCN 2+ : In some reversible reactions, the forward and reverse reaction rates are fast, so that equilibrium is rapidly reached. One such reaction is that of iron(iii) ion, Fe 3+, with the thiocyanate ion, SCN -, that forms a complex ion, iron thiocyanate, or thiocyanatoiron(iii), FeSCN 2+. (We ll stick with iron thiocyanate!): Fe 3+ (aq) + SCN (aq) FeSCN 2+ (aq) (1) The double-headed arrow shows that the reaction is reversible. The equilibrium constant in terms of molar concentrations can be expressed as [FeSCN 2+ ] eq K eq = (2) [Fe 3+ ] eq [SCN ] eq In order to determine K eq, it is necessary to determine the equilibrium concentrations of the reactants and products in solutions, which are prepared by mixing carefully measured volumes of Fe 3+ and SCN solutions of known initial concentrations. The equilibrium concentration of the FeSCN 2+ ion, [FeSCN 2+ ] eq, formed in such a solution can be determined from the measured absorbance of the solution using a colorimeter. This is possible because FeSCN 2+ absorbs blue and green light, producing a solution that is reddish orange in color while the Fe 3+ and SCN ions do not absorb visible light. The amount of light absorbed is thus proportional to [FeSCN 2+ ] in accordance with Beers Law. It is therefore necessary to first prepare solutions of known [FeSCN 2+ ] (called standard solutions) and obtain a calibration plot of absorbance vs. [FeSCN 2+ ]. The same kind of process was done to determine crystal violet concentrations in Experiment 2.

2 3-2 Preparation of Standard Solutions: To get solutions with known [FeSCN 2+ ], the following process will be used. You will prepare standard solutions by mixing carefully measured volumes of solutions of Fe 3+ (using FeNO 3 stock solution) and SCN (using KSCN stock solution) of known concentrations. These volumes for standard solutions A-F are listed in the Standard Solutions Table in Part A step 7. The key to getting a known concentration of FeSCN 2+ in each of these solutions is that the initial concentration of Fe 3+ is much greater than the initial concentration of SCN ion. When the Fe 3+ concentration is in large excess, the equilibrium will shift (according to LeChatelier s Principle) to the product side until virtually all the SCN is converted to FeSCN 2+. Thus the equilibrium concentration of FeSCN 2+ in a standard solution will be virtually the same as the initial concentration of SCN in the solution. This initial value, [SCN ] initial, which equals [FeSCN 2+ ] in the mixed standard solution, can be calculated from the volume and molarity of the SCN stock solution (mol SCN = MxV) and the final total volume (in L) of the mixed standard solution. With these calculated values for [FeSCN 2+ ] and the measured absorbances of these standard solutions, a Beers Law plot can be obtained. Calculation of K eq from [FeSCN 2+ ] eq, [Fe 3+ ] eq and [SCN ] eq : A series of sample solutions can then be made up from varying combinations of the reactant solutions as shown in the Sample Solutions Table in Part B, Step 5. Once the equilibrium concentration of FeSCN 2+ is determined in these solutions using the measured absorbances and the Beers Law plot, it is an easy matter to determine the equilibrium concentrations of the other reactant species. This is because as equation (1) shows, for every one FeSCN 2+ produced, one Fe 3+ ion is used up. Thus the concentration of Fe 3+ that remains at equilibrium is the initial concentration of Fe 3+ minus the concentration of Fe 3+ that formed product, which is the same as [FeSCN 2+ ] eq. The equilibrium concentrations of Fe 3+ and for the same reasons, SCN can thus be expressed as [Fe 3+ ] eq = [Fe 3+ ] initial [FeSCN 2+ ] eq (3) [SCN ] eq = [SCN ] initial [FeSCN 2+ ] eq (4) These concentrations are then used to determine K eq from equation (2). An ICE (Initial, Change, Equilibrium) table can also be used to relate [FeSCN 2+ ] eq to the equilibrium concentrations of the reactants. For example, given [Fe 3+ ] initial = M, and [SCN ] initial = M, and an equilibrium concentration, [FeSCN 2+ ] eq = M, the ICE table will be: Fe 3+ + SCN FeSCN 2+ Initial Change Equilibrium The initial concentration of FeSCN 2+ is zero because the reaction has not yet started, but at equilibrium its concentration, as measured from the absorbance, is M. This equates to a change of M in the FeSCN 2+. From the balanced reaction, if M is gained on the product side, it must have been lost from the reactants.

3 3-3 Therefore, the equilibrium concentrations of the reactants are their initial concentrations less the equilibrium concentration of the FeSCN 2+. For this example, the equilibrium constant would be as shown in the following calculation. K [ ] [ ][ ] 2 eq = = Consult your textbook to see why K eq does not have units. In this experiment you will determine K eq for reaction (1) by obtaining a Beers Law plot for FeSCN 2+ and using the plot to calculate [FeSCN 2+ ] eq in sample solutions from absorbance measurements. Pre-Lab Notebook: Provide a title, purpose, reaction(s), summary of the procedure, and a table of reagents, Fe(NO 3 ) 3, KSCN, and HNO 3. Create the Part A and Part B Data Tables shown below. Use the values in the Standard Solutions Table in Part A and the Sample Solutions Table in Part B to calculate the values of concentration in the shaded areas of the Data Tables. Then enter these values into the tables before coming to lab. Recall that the molarity of an ion in the mixed solutions is given by (MxV of stock solution / total mixed solution volume in L). Also note that the [FeSCN 2+ ] in the Part A Data Table is obtained by calculating the [SCN ] initial as discussed in the section above on Preparation of Standard Solutions. To avoid a common student error, note that the concentration of Fe(NO 3 ) 3 in Part A is M, while in Part B, it is 2.00 x 10 3 M. Part A: Data Table (Standards) Part B: Data Table (Samples) Flask [FeSCN 2+ ] Abs Beaker [Fe 3+ ] initial [SCN ] initial Abs [FeSCN 2+ ] eq A 1 B 2 C 3 D 4 E 5 F Equipment: Stock Solutions: 100 ml (or 150 ml) Beakers (5) M Fe(NO 3 ) 3 50 ml Volumetric flasks (6) 2.00 x 10-3 M Fe(NO 3 ) 3 50 ml Beakers (2) 2.00 x 10-3 M KSCN Buret 0.5 M HNO 3 Ring stand, buret clamp 10.0 ml Graduated pipets (2) and pipet bulb 400 ml Beaker (for waste) Vernier equipment and colorimeter In-Lab Experimental Procedure: Note: Work in pairs. Volumetric measurements must be accurate, so measure all of the solutions carefully and rinse the pipets and buret with the appropriate stock solutions before use.

6 3-6 Lab Report Outline for Equilibrium Constant Graded Sections of Report Percent of Grade Pre-Lab 10 In-Lab Part A table: 10 Part B table: 10 Post-Lab (You will save considerable time and effort by using Excel to carry out your calculations and plotting. But in your lab notebook post-lab section, show required sample calculations, being sure to number each step.) Part A: Calibration Curve: 1. Show a sample calculation of [FeSCN 2+ ] for standard solution A Attach an Excel spreadsheet giving the table of data from LoggerPro and the clearly labeled chart of the Beers Law plot showing the equation of the line and a trendline. 10 Part B: Equilibrium Solutions (Show sample calculations for Sample 1.) 1. Calculate the [FeSCN 2+ ] eq using the equation of the line from the Beers Law plot Calculate [Fe 3+ ] eq and [SCN ] eq using equations (3) and (4) Calculate K eq using equation (2) Attach a table (preferably from Excel) showing the calculation of the average of the K eq values for sample solutions 1-5 and state, The mean value of K eq is. 20 Discussion: Summarize what you accomplished. Problems with experimental procedure? Sources of error? 10

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