Determination of an Equilibrium Constant

Introduction

A state of chemical equilibrium exists when the rate of the forward reaction is equal to the rate of the reverse reaction. Once equilibrium has established itself, the amounts of products and reactants are constant. Furthermore, if one of the product or reactant concentrations can be measured, it can be used to determine the remaining concentrations and the equilibrium constant.

In this experiment, we will begin by combining aqueous solutions of iron(III) ion (Fe³⁺) and thiocyanate ion (SCN^-). The reaction that occurs produces the thiocyanoiron(III) complex ion responsible for the equilibrium mixture's deep red color.

iron(III)            thiocyanate                       thiocyanoiron(III)   

The final state of the equilibrium (i.e., the final concentrations of products and reactants) depends on the relative amounts of reactants before the reaction occurs. However, regardless of the initial concentrations, the final equilibrium concentrations must satisfy the following relationship:

where the bracketed terms are molar equilibrium concentrations of the different species, and K_c is the temperature-dependent equilibrium constant.

In today's experiment, we will study the chemical equilibrium described above by varying the initial concentrations of each reactant. After equilibrium is achieved, the colorimeter will be used to determine the concentration of thiocyanoiron(III) complex ion. This is then used to determine the concentrations of iron(III) ion and thiocyanate ion . These concentrations are then substituted into the expression for K_c to check and determine whether the equilibrium constant is really constant from one case to the next.

The molar absorptivity, ε, will be used to convert measured absorbances (via the colorimeter) to FeSCN²⁺ concentrations. The molar absorptivity of FeSCN²⁺ will be obtained by using a standard solution that contains an initial 100x excess of Fe³⁺ ion in comparison to SCN^-. According to Le Châtelier's principle, this high concentration shifts the reaction far to the right in favor of the product, using up approximately 100% of the SCN^- ions. Consequently, the [FeSCN²⁺] in the equilibrium mixture is approximately equal to the original [SCN^-].  The [FeSCN²⁺] for each of the equilibrium mixtures (vials) may then be determined from their absorbances and the molar absorptivity.

Knowing the equilibrium concentration of the product FeSCN²⁺ species, it is possible to determine the equilibrium concentrations of reactants. First calculate the concentration of each original reactant before equilibrium was achieved using initial volume and concentration information. Next calculate the concentration of FeSCN²⁺ formed. Since products and reactants are in a 1:1 mole ratio and any product formed reduces the amount of reactant remaining in the reaction mixture, the concentration of remaining reactant is determined by:

equilibrium concentration _reactant = initial concentration _reactant - equilibrium concentration _product

Calculate the concentration of each reactant by dividing the number of moles of reactant by the mixture's total volume. Use these concentrations to calculate the equilibrium constant for each of the mixtures.

The colorimeter used in today's experiment will be set to a wavelength of 470 nm. This wavelength is used since it is readily absorbed by the FeSCN²⁺ complex ion. As the concentration of the sample increases, the amount of light that passes through the sample decreases, and the absorbance increases.

Procedure

1. Obtain a pair of goggles. You will be working in pairs or individually today.
2. Obtain six vials with screw-on lids and prepare the following solutions using two burets (Use the 0.00200 M Fe(NO₃)₃ and 0.00200 M KSCN solutions). Be sure to thoroughly mix the contents of each of the six vials before proceeding.

3. Preparation of the standard: Use your 10 mL graduated cylinder to measure 9.0 mL of 0.200 M Fe(NO₃)₃ (read carefully) into a seventh vial. Next, add 1.0 mL of 0.0020 M KSCN from the buret. Mix well.
4. In the "Experiments" folder of Logger Pro, you will find another folder called "Probes & Sensors". Open the "colorimeter" file from the list of probes and sensors.
5. Prepare a blank cuvette by filling a cuvette 3/4 full with deionizes water.  Then calibrate the colorimeter at a wavelength of 470 nm.
   • HANDLING CUVETTES:  Cuvettes should be wiped clean and dry on the outside with a Kimwipe^®.  Do not use a paper towel!  Handle the cuvettes near the top of the ribbed sides.  Solutions should be free of bubbles.  If a cuvette is not dry on the inside, a small amount of the solution to be used should be used to rinse the cuvette before filling.  Always align the reference mark on the cuvette (typically the non-ribbed side) with the reference mark on the colorimeter.
   • CALIBRATION of SQUARE COLORIMETERS:  Click the icon on the toolbar used to calibrate the probes.  (Alternatively, select "Calibrate" from the "Experiments" menu.)  Place the blank cuvette in the cuvette slot of the colorimeter and close the lid.  Turn the wavelength knob of the colorimeter to the 0% T position.  In this position, the light source is turned off, so no light is received by the photocell.  Type "0" in the % edit box.  When the voltage stabilizes, click "Keep."  Turn the knob of the colorimeter to the desired wavelength.  In this position, the sample transmits 100% of the light.  Type "100" in the % edit box.  When the voltage stabilizes, click "Keep."  Then click "OK."
   • CALIBRATION of ROUNDED COLORIMETERS:  Use the arrow buttons to select the desired wavelength.  With the blank cuvette correctly positioned in the colorimeter, press the blue "Cal" button on top of the colorimeter.  When the red light stops blinking, the colorimeter is calibrated and may be used.
6. Rinse the cuvette twice with ~1 mL portions of the vial #1 contents. Fill the cuvette ~3/4 full. Now, insert the cuvette into the colorimeter, close the lid and record the absorbance reading. Repeat this step for each of the six remaining numbered vials, including the standard.
7. Place your used solutions in the designated waste container(s). 
8. Remove your cuvette from the colorimeter since it may severely damage the sensor if left in the sample compartment! Clean all vials and cuvettes before returning them to their appropriate location.

Data Analysis and Questions

1. Determine the [FeSCN²⁺] for the standard solution, as described in the Introduction. Then calculate the molar absorptivity, ε.
2. Use the molar absorptivity, ε, to determine the [FeSCN²⁺] in each of the 6 unknown equilibrium mixtures  (writing formulas in Excel will simplify these calculations... don't be afraid to ask for help). 
3. Calculate the initial molarity for Fe³⁺ and SCN^- in each of the 6 vials. Using the molarity of FeSCN²⁺ at equilibrium in each of the six trials, determine the molarity of each reactant when equilibrium is reached (see the Introduction). Once again, you are encouraged to use formulas in Excel to simplify these calculations.
4. Use the equilibrium concentrations to calculate equilibrium constants for each of the six trials. 
5. Calculate the average K_c.
6. How constant were your K_c values at room temperature? Explain any variation.
7. See if you can find literature and/or internet references for the equilibrium constant for this equilibrium. Please cite the reference(s). How does your result compare with the one(s) you cited? Perhaps you will even find a similar experiment, with sample results, posted out on the Web.

Data Table
Use Excel to create a data table that includes six columns—one for each of the six vials. The following information should be included as rows for each trial :

• volume Fe³⁺ solution used
• volume SCN^- solution used
• Absorbance
• [Fe³⁺]_initial (after dilution, before reaction)
• [SCN^-]_init (after dilution, before reaction)
• [FeSCN²⁺]_eq
• [Fe³⁺]_eq
• [SCN^-]_eq
• K_c calculated

Also include the absorbance for the standard solution and the average values of K_c at the bottom of the table.

Lab Report
You may choose to submit an individual or group report for this lab. Follow the guidelines for Laboratory Reports located at http://webs.anokaramsey.edu/chemistry/Chem1062. For this lab report, you will need to include a title, abstract, procedure, results, discussion, and references. You may use the above questions to guide your discussion, but the discussion should be more than just answering the questions and should flow logically as you discuss the lab and the results.

Follow your instructor’s directions for submitting this lab report. Remember to name the file as specified (Lastname_Equilibrium or Lastname1_LastName2_Equilibrium). If you are emailing your report, use the subject line “Chem 1062: Equilibrium”. Also, embed the Excel table in the Word document so that the professor may view the formulas in each cell.  If you submit a paper copy of your report, include one set of sample calculations for one of the trials, either handwritten or typed.  If you worked in pairs and are submitting this assignment on an individual basis, please underline your own name and include your lab partner’s name on the assignment.

Portions of this lab courtesy of Kirk Boraas, Minneapolis Community and Technical College, and Vernier Software, "Chemistry With Computers". Edited by Lance S. Lund, Anoka-Ramsey Community College. Updated April, 2011.