Equilibrium Constant for a Metal-complex Ion

The Goal of the Experiment

In this experiment you will determine the numerical value of the equilibrium constant for the reaction:

This will be accomplished by measuring the equilibrium concentration of the blood-red metal-complex ion iron(Ⅲ) thiocyanate (FeSCN²⁺) with five different initial concentrations of iron(Ⅲ) (Fe³⁺) and thiocyanate (SCN^–) ions. The value of the equilibrium constant is calculated using the equilibrium constant expression:

The value calculated for K_eq will be the same, within experimental error, for a variety of different concentrations of the reactants and product.

The technique used to measure concentrations in this experiment is spectrophotometry. Since iron(Ⅲ) thiocyante is blood red in color (though its solutions at low concentration appear orange) it absorbs light strongly at the blue end of the visible spectrum. Specifically, its wavelength of maximum absorption is 450 nm. You will use absorption at this wavelength to find the equilibrium concentration of FeSCN²⁺. By subtraction you will calculate the concentration, at equilibrium, of Fe³⁺ and SCN^–. Because the stoichiometric ratios are 1:1 the concentration of the product is the exact amount by which the concentration of each reactant will be reduced. For example, if the measured concentration of FeSCN²⁺ is 9.00 × 10^–5 M and the initial concentrations of

Vernier SpectroVis Instrument diagram

The value or 139 is similar to typical values usually found in carrying out this experiment. Note that although the value of K_eq will be about the same (a typical result is about a 15% variation) the concentrations of reactants and products can be different. Each different set of equilibrium concentrations is called an equilibrium position.

Measuring [FeSCN²⁺]_eq

This experiment depends on careful measurements of the concentration of the colored complex ion’s concentration. The initial concentrations of the reactants are determined by the dilutions that take place when they are mixed. If the concentration of FeSCN²⁺ is known, then stoichiometry (see calculations above) can easily find the equilibrium concentrations of the reactants. The question then is, how do we measure the concentration of FeSCN²⁺?

The answer is spectrophotometry. A spectrophotometer is an instrument that measures the intensity of light after it is passed through a colored solution. In order to use it the intensity of the light source in the instrument is measured with a colorless solution. The intensity of the light after passing through the colored solution is then compared with this ‘blank’ measurement to calculate the amount of light absorbed, known as the absorbance. A diagram of the instrument used in your lab is at right.

FeSCN2+ ion spectrum

A spectrophotometer can be used in a variety of ways. One way to use it is to generate an absorbance spectrum. This graphs the strength of light absorbance as a function of wavelength. The image at right shows the absorbance spectrum of the The graph shows a region of the spectrum with strong light absorbance centered on about 450 nm. The spectrum shows almost no absorption above about 650 nm. Since blue is absorbed and red is transmitted, the material has a red appearance to our eyes. Because it is the blue light that is absorbed, and because it is specifically the light at 450 nm that is most strongly absorbed, this is the wavelength of light that you will use to measure the concentration of FeSCN²⁺.

The absorption of light at a wavelength of maximum absorption (λ_max) is directly proportional to the concentration of the colored substance. This proportion is known at Beer’s Law: A = εbc

In this equation A represents absorbance (which has no units). The concentration in mol/L is c, the path length in centimeters is b (usually 1 cm), and ε (the Greek letter epsilon) represents the molar absorptivity constant in inverse molarity and inverse cm (M^–1cm^–1). This constant relates the

Sample Results for Part I

Reference Solution Concentrations: Before Equilibrium Fe3+   +   SCN–   ⇌          After Equilibrium Fe3+   +   SCN–   ⇌   FeSCN2+ Schematic showing how the big difference in initial conc. of reactants leads to a predictable concentration of the product

The problem remains, however, of how to establish the concentration of a solution of FeSCN²⁺ independent of spectrophotometric measurements. It turns out to be quite straightforward. The idea is to arrange the concentrations of the reactants in such a way that regardless of the value of the equilibrium constant we can make a valid assumption about the concentration of FeSCN²⁺. This is done by putting Le Châtelier’s Principle into practice. Le Châtelier’s Principle is the idea that a system at equilibrium will respond to stresses placed on that equilibrium by changing reactant and product concentrations in such a way as to minimize the stress. For example, if the concentration of one reactant is increased then when a new equilibrium position is established the concentrations of both reactans will decrease while the concentration of products will increase. This uses up the added reactant and minimizes the stress on the equilibrium. In this experiment the series of five solutions with a known concentration of FeSCN²⁺ will be made by using a huge excess of Fe³⁺ ions and a very small concentration of SCN^– ions. In this way the initial concentration of SCN^– ([SCN^–]₀) is reduced effectively to zero at equilibrium and is stoichiometrically converted into FeSCN²⁺. This is illustrated schematically at right. The main idea can be expressed symbolically like this: [SCN^–]₀ = [FeSCN²⁺]_eq

In summary: In Part I you will measure volumes of high-concentration iron(III) (Fe³⁺) and low-concentration thiocyanate (SCN^–) and mix them to make five reference solutions. In the reference solutions the equilibrium concentration of the complex ion will be assumed to be equal to the initial concentration of the thiocyanate ion. The initial concentration of SCN^– was so low that it is stoichiometrically converted. There is a difference of a factor of about a thousand between the concentration of the Fe³⁺ and the SCN^– in order to guartantee this assumption will be true. These five reference solutions will be used to establish a direct proportion between absorption of light at 450 nm and molar concentration of the complex ion (FeSCN²⁺). By doing so you will make it possible to measure the equilibrium concentration of the complex ion in the trials designed to be used to measure the value of the equilibrium constant.

In Part II you will mix iron(III) and thiocyanate solutions with roughly similar concentrations. Neither reactant will be completely converted into the product in these solutions so that both reactants and the product will have significant and comparable concentrations at equilibrium. By measuring the absorbance of these solutions at 450 nm you will measure the molar concentration of the complex ion. Then, by using stoichiometry, you will calculate the concentration of the two reactants at equilibrium based on the fact that all of the product molecules exist due to the consumption of some of the reactant molecules.

Objectives

1. Determine the Beer’s Law constant for FeSCN²⁺
2. Measure the value of K_eq for five different sets of initial concentrations of Fe³⁺ and SCN^– for the reaction:
   Fe³⁺ + SCN^– ⇌ FeSCN²⁺.

Materials

The following list does not cover all possible hazards, just the ones that can be anticipated. Move slowly and carefully in the lab: haste and impatience have caused more than one accident.

Always leave stock solution bottles tightly closed when not in immediate use!

• As always, wash hands before leaving the lab, eating, or drinking, or going to the bathroom.
• Wear chemical splash goggles, gloves, and a chemical-resistant apron.
• Iron(III) nitrate is a skin and tissue irritant; it is corrosive and toxic, and causes stains. Use care in handling the solution.
• Nitric acid (HNO₃) is corrosive and toxic. This chemical is used in making the iron(III) nitrate solutions and adds to their toxicity and corrosiveness.
• Potassium thiocyanate (KSCN) is toxic by ingestion. Avoid contact with eyes and skin.
• All solutions used in this lab must be collected for hazardous waste disposal. None of the reactants or products may be dumped into the sewer system.

Collect all waste in the designated bottle by pouring the solution out of the cuvet, rinsing the cuvet by filling it once with tap water and pouring it into the bottle, and the closing the bottle again. Use the funnel provided to make splashing outside the bottle less likely.

Procedure

The most time-consuming part of the lab is mixing the ten solutions you need. Part I requires 5, with 10 volume measurements. Part II requires 5, with 14 volume measurements. Since precision is desirable you may want to make all of the solutions at once, even though the procedure splits them into their own respective sections. The spectroscopic measurements can be accomplished relatively quickly.

Part I

In this part of the lab you will collect absorbance vs. concentration data for the complex ion (FeSCN²⁺) in order to establish a relationship between absorbance and concentration at equilibrium. You will use the data to make a Beer’s Law plot; the slope of the best-fit straight line for this plot is the constant of the proportion between absorption and concentration.

1. Obtain two small beakers. Label one “0.2 M Fe(NO₃)₃” and label the other “2 x 10^–4 M KSCN”. These are the Reference solutions.
2. Into the Fe(NO₃) ₃ beaker collect about 50 mL of the reference stock solution (0.2 M).
3. Into the KSCN beaker collect about 30 mL of the reference stock solution (2 x 10^–4 M).
4. You will need 5 50-mL beakers into which you can measure out the amounts of each solution required. Label them Ref. 1 - 5.
5. Mix the solutions to make the reference solutions according to the information in the table. Using a separate syringe or pipet for each solution, measure the amounts of each one needed into the labeled beakers. Do the necessary calculations to fill in the rest of the table.

6. When you are done with the syringes or pipets, take them apart and rinse very well to clean them for re-use and set aside to dry.
7. Each reference solution will need to be measured in the spectrophotometer. Stir each one carefully so that no cross-contamination occurs. Then fill a cuvet with each solution using a disposable pipet, capping them after they are full. They have a capacity of about 3 mL. Be careful to keep track of which cuvet has which reference solution in it!
8. Fill a cuvet with a blank solution consisting of about 3 mL of the 0.200 M Fe(NO₃)₃ solution. Place it into the spectrophotometer with the flat, smooth sides facing the white circle and triangle.
9. Plug the SpectroVis Plus unit into the USB port of the computer and start the Logger Lite or Logger Pro software. Or if you are using a Chromebook, use the search function to find “Vernier Spectral Analysis”.
10. Calibrate the Spectrometer by finding this function in your software. This step is critical because it provides the baseline for brightness measurements to determine the absorption of light.
11. A dialog box will pop up to inform you that the lamp is warming up. Do not skip this step, it only requires 90 seconds.
12. Once Calibration is complete, click OK.
13. Set up data collection so that you collect Absorbance vs. Concentration (Beer’s Law) data. Choose 450 nm as the selected wavelength. Once you start collecting data you will need to press the “Keep” button to record a data point. For each one you have to enter the concentration. This is the equilibrium concentration of the complex ion ([FeSCN²⁺]_eq), which you calculated in the table above. If you have not calculated them yet then just write down the absorbance values for each solution, which will appear on your screen when you insert the sample into the spectrophotometer.
14. When you finish collecting data press the “Stop” button. Copy and paste your data into a spreadsheet program for further analysis. Do not close the software or unplug the spectrophotometer! You still need it set up exactly as it is for Part II.
15. In the spreadsheet program create a graph of concentration vs. absorbance and set it up following the example in the introduction in this lab handout. You will need to label the axes, give your graph a title, and get it to produce a line of best fit (a trendline) and to display the equation of the line on the graph. The slope of the line is the molar absorptivity constant, epsilon (ε). You will use it to calculate the concentration of FeSCN²⁺ from absorbance measurements in Part II.
16. Once you have confirmed with your teacher that you have collected the data you need you may dispose of the contents of the cuvets. All waste liquids are to be collected in a bottle designated by your teacher. Use the provided funnel to ensure all liquid gets in the bottle. When you finish, take out the funnel and put the cover back on the bottle.

Part II

In this part of the lab you will measure the absorbance of five solutions with different initial concentrations of reactants. The absorbance can be used to calculate the equilibrium concentration of the complex ion ([FeSCN²⁺]_eq), which in turn will be used to calculate [Fe³⁺]_eq and [SCN^–]_eq

1. Obtain two small beakers. Label one “2 × 10^–3 M Fe(NO₃)₃” and label the other “2 x 10^–3 M KSCN”. These are the Experiment solutions.
2. Into the Fe(NO₃) ₃ beaker collect about 30 mL of the experiment stock solution (2 × 10^–3 M).
3. Into the KSCN beaker collect about 25 mL of the experiment stock solution (2 x 10^–3 M).
4. You will need 5 50-mL beakers into which you can measure out the amounts of each solution required. Label them Exp. 1 - 5.
5. Mix the solutions to make the experiment solutions according to the information in the table. Using a separate syringe for each solution, measure the amounts of each one needed into the labeled beakers. Do the necessary calculations to fill in the rest of the table.

6. When you are done with the syringes or pipets, take them apart and rinse very well to clean them for re-use and set them aside to dry.
7. Each experiment solution will need to be measured in the spectrophotometer. Stir each one carefully so that no cross-contamination occurs. Then fill a cuvet with each solution using a different disposable pipet for each solution. Cap them after they are full. They have a capacity of about 3 mL. Be careful to keep track of which cuvet has which experiment solution in it!
8. Do not recalibrate your spectrophotometer! It should remain in the state it was in when you finished collecting the reference data. In fact, collect the data for Part II immediately after completing your data collection for Part I.
9. Insert each experiment sample into the spectrophotometer. The readout on the screen will show the absorbance at 450 nm. You just need to write this number down; write it in the data table provided below. Every lab group member should write down the data so no one is depending on getting the data later. There is no graph to be made for this part. Each point you collect here will be mapped onto the graph based on your Part I data. This will enable you to calculate the equilibrium concentrations of the reactants and product.
10. Fill in the table below by calculating the initial concentrations, recording your absorbance measurements, and calculating the equilibrium concentrations and the value of the equilibrium constant. This can be easily done in a spreadsheet, which will prepare you for your lab report. Be sure to do these calculations before you leave the lab. Here is how to do the calculations:
    1. To use absorbance to calculate [FeSCN²⁺]_eq:
       A = absorbance measurement, ε = molar absorptivity constant, c = conc. in mol/L
       c = A/ε
       (the path length is 1 cm so that has been deliberately left out)
    2. To use [FeSCN²⁺]_eq to calculate [Fe³⁺]_eq:
       [Fe³⁺]₀ – [FeSCN²⁺]_eq = [Fe³⁺]_eq
       this is because, stoichiometrically, every unit of FeSCN²⁺ that is made uses up one unit of Fe³⁺
    3. To use [FeSCN²⁺]_eq to calculate [SCN^–]_eq:
       [SCN^–]₀ – [FeSCN²⁺]_eq = [SCN^–]_eq
       this is because, stoichiometrically, every unit of FeSCN²⁺ that is made uses up one unit of SCN^–
    4. To calculate K_eq:
       Since the reaction is: Fe³⁺ + SCN^– ⇌ FeSCN²⁺
       

       Keq =	[FeSCN2+]eq
       	[Fe3+]eq[SCN–]eq

11. Once you have confirmed with your teacher that you have collected the data you need you may dispose of the contents of the cuvets. All waste liquids are to be collected in a bottle designated by your teacher. Use the provided funnel to ensure all liquid gets in the bottle. When you finish, take out the funnel and put the cover back on the bottle.

The Formal Lab Report

Each indiviual student will write and submit an independently written formal lab report.

Introduction

1. A definition of chemical equilibrium the equilibrium constant expression.
2. The chemical equation whose equilibrium you are investigating: Fe³⁺ + SCN^– ⇌ FeSCN²⁺
3. The method, briefly, by which you determined the equilibrium concentration of FeSCN²⁺.
4. The purpose of the lab, to calculate the value of the equilibrium constant for the formation of the FeSCN²⁺ ion.

Procedure

While giving a brief overview of the steps taken to complete the experiment, be sure to include the following:

1. Why are the concentrations of Fe³⁺ and SCN^– so different in size for part 1 of the experiment where you are creating the calibration curve?
2. Why are the concentrations of Fe³⁺ and SCN^– similar in size in part 2 where you are determining unknown equilibrium concentrations of FeSCN²⁺?

Data and Graphs

1. The data used for the determination of the Beer’s Law constant for FeSCN²⁺.
2. The graph of your calibration curve.
3. A data table with the following headings:
   Sample #, [Fe³⁺] ₀, [SCN^–]₀, Absorbance, [FeSCN²⁺]_eq, [Fe³⁺] _eq, [SCN^–]_eq, K_eq
   The data table should include an average K_eq value, the standard deviation (as can be calculated using a spreadsheet), and a percent error (caculated as (std. deviation)/(average value) × 100%). Note: no other values can or should be averaged.

Sample Calculations

1. One instance of calculating equilibrium concentration of FeSCN²⁺ using Beer’s Law.
2. One instance of calculating [Fe³⁺]_eq and [SCN^–]_eq.
3. One instance of calculating the value of K_eq.

Analysis

1. The average value of K_eq, your standard deviation, and percent error.
2. Comment on factors which could have led to variation in your result. The spectrophotometer’s measurements may be assumed to be precise and accurate enough to be neglected in your answer.
3. Did the value of K_eq vary as you increased the initial concentration of KSCN? Why or why not?
4. Does the level of variation in your results raise the question of the validity
   of the name constant for K_eq? Explain.
5. Based on the size of your determined value for K_eq does this reaction favor products or reactants? Explain.

Conclusion

Comment on the educational experience of carrying out this experiment.