Equilibrium: Binding of Lewis Bases to the Fe(CN)₅^3- Anion

• To determine the value of an equilibrium constant for a simple reaction
• To use your equilibrium constant and those measured by other students to compare the relative electron-pair-donor strengths of the bases investigated
• To observe a relationship between base strength toward a particular acid and the structure of the base

Dynamic equilibrium is one of the four or five central concepts in chemistry. It is dynamic equilibrium that must be outsmarted in the synthesis of ammonia from nitrogen and hydrogen; that determines the maximum level of humidity in the air on a summer day; and that maintains balance in the complex coupled reactions of biological systems. A synthetic chemist must be cognizant of chemical equilibrium in attempting to create a target molecule, such as a potential new drug.

Dynamic equilibrium is manifested at the macroscopic scale, but its origins are at the molecular level, where motions and collisions of reacting molecules stimulate their conversion to products, and vice versa. Although possible, it is surprisingly difficult to cite everyday examples of dynamic equilibrium; for this reason, equilibrium concepts are often difficult to grasp. This is unfortunate, because an understanding of equilibrium is crucial to an appreciation for chemistry.

In this experiment, we will study the dynamic equilibrium established in reactions of type (1):

In this reaction, the Lewis base, :C, displaces the Lewis base, :B, from its adduct with the acid A. This reaction may be viewed as two successive Lewis acid-base reactions (or electron pair donation processes). In the first, the adduct AB comes apart to give the acid A and the base, :B. The base :C then donates a free electron pair to an empty orbital on the acid, A, to form a new adduct, A-C, in which acid and base are joined by a normal covalent bond. We thus see that the somewhat complex process (1) may be broken down into two fundamental Lewis processes involving donation and acceptance of an electron pair. The expression for the equilibrium constant, K_eq, for this reaction is in (2).

where [AC] signifies the molarity (concentration in moles AC per liter of solution) of species AC. The following statements can be made about the equilibrium constant expression:

1. In a solution containing arbitrary initial concentrations of AB, C, AC, and B, reaction will take place until these concentrations have adjusted to values that satisfy (2).
2. For some reactions, attainment of equilibrium is very rapid; for others it is very slow.
3. The magnitude of K_eq depends on temperature and solvent. Thus when reporting a value for K_eq for a reaction, the T and solvent must be specified.
4. Minor rearrangement of (2) gives (3):
   
   (3) K_eq[C]/[B] = [AC]/[AB]

   In this form, the equilibrium constant expression shows us that the distribution of A between the two adducts, AC and AB, is a function of the magnitude of the equilibrium constant and the concentration ratio of the two Lewis bases. The larger the concentration of C, the smaller the concentration of [B], and/or the larger the equilibrium constant, the larger the amount of adduct AC relative to adduct AB.

   For example, suppose K_eq for (1) has the value 0.01 M^-1. This tells us that in a solution containing a total of 0.1 moles per liter of A distributed between the AB and AC forms, the ratio [AC]/[AB] will be only 0.01 when [B] = [C] = 1.0 M. Thus Lewis acid A favors base B over base C by a factor of 100. Very little A is present as the adduct AC because the equilibrium constant is small. In contrast, suppose K_eq = 100 M^-1. In this case, when [B] = [C] =1 M, the ratio [AC]/[AB] = 100, so acid A prefers base C over base B by a factor of 100. Essentially all A is present in the adduct AC.

Suppose we want to experimentally determine a value for K_eq for reaction (1). In order to do this, we would begin by mixing known initial amounts of the participating species. We denote these initial concentrations [AB]_o, [C]_o, [AC]_o, and [B]_o. After mixing, the reaction will then proceed in one direction or the other at a characteristic rate until it reaches equilibrium. To assign a value to K_eq, it is necessary to measure the concentration of one of the four species, AB, C, AC, or B, at equilibrium. If we can do this, the other three can be obtained from mass balance and the equilibrium constant can readily be calculated by substituting concentrations into (2) or (3). For example, suppose that we start with [AB]_o = 0.1 M, [C]_o = 0.2 M, [B]_o = 0.05 M, and [AC]_o = 0 in the solution, and that we are able to independently measure the concentration of AB at equilibrium. We begin by setting up an "initial, change, equilibrium" table to obtain expressions for the equilibrium concentrations of all species in terms of their initial concentrations and a common variable:

The expressions for the equilibrium concentrations reflect mass balance in the solution. For example, the total amount of A distributed between the forms AB and AC should be the same after the reaction as before. Adding the equilibrium concentrations of AB and AC gives 0.1 - x + x = 0.1, the initial concentration of AB. Now suppose that we mix the reagents, allow the solution to come to equilibrium, and measure [AB] = 0.06 M at equilibrium. It follows that x = 0.04 M, and thus that [AC] = 0.04 M, [B] = 0.05+0.04 = 0.09 M, and [C] = 0.2 - 0.04 = 0.16 M. Thus

If we were able to directly measure the concentration of one of the substances at equilibrium, the experimental determination of equilibrium constants for reactions of type (1) (and in fact for any reaction) would be a simple matter, because we can always control the initial (starting) concentrations. Although this is often not possible, in this experiment we will study a reaction in which we can do this:

Click here to see chemical structures of the reactants and products. The iron reactant, Fe(CN)₅(C₅H₇N₂)^2-, is blue, with an intense light absorption at 664 nm in the visible region of the spectrum. We start with a solution containing known concentrations of Fe(CN)₅(C₅H₇N₂)^2- and C₅H₇N₂⁺ and measure the absorbance at 664 nm. We then add a known concentration of X, allow the reaction to come to equilibrium, and measure the absorbance again. We repeat the addition of known amounts of X a few times, equilibrating and measuring the absorbance at 664 each time. Each measurement of absorbance allows us to determine the concentration of Fe(CN)₅(C₅H₇N₂)^2- in the solution. Mass balance allows us to calculate the remaining three concentrations. If we write the equilibrium constant expression as in (3), we may then obtain K_eq from the slope of a plot of [Fe(CN)₅X^3-]/[Fe(CN)₅NMPz^2-] versus [X]/[NMPz⁺].

Beer's Law. In this experiment, we will determine the concentration of a dissolved substance by measuring the amount of light that it absorbs at a particular wavelength in the visible region of the electromagnetic spectrum. We will accomplish this by putting a solution containing the substance in a precision-made glass or quartz cuvette (also called a spectrometer cell). The cuvette is then placed in an instrument called an electronic absorption spectrometer, which passes light through the cuvette and determines the amount of light absorbed by the sample.

The quantitative relationship between light absorption and concentration is summarized in Beer's Law, which states that the amount of light absorbed by a substance at a particular wavelength is directly proportional to the amount of the substance per unit volume of solution and to the length of solution through which the light passes. In equation form,

where A = the absorbance (the amount of light absorbed), l = the path length of the cuvette in cm, M = molarity of absorbing substance, and e is a proportionality constant called the molar absorptivity of the substance. The value of the molar absorbtivity depends on what the absorbing substance is, and upon the wavelength of light used. In most cases, measurements are performed at the wavelength at which the substance of interests absorbs most strongly. Almost without exception, cuvettes having a path length of 1 cm are used, so the value of l in the equation above is 1. Because absorbance has no units, the units of molar absorptivity must be M^-1cm^-1.

As you proceed through the experiment, keep the following Focus Questions in mind. When you have finished the experiment, provide answers to them.

1. As you continue to add aliquots of X, you change the total volume of the solution in the cell. What effect does aliquot addition have on the concentration of iron in the solution? What effect does it have on the observed absorbance at 664 nm?
2. Is the total volume of X added large enough to affect concentration significantly? Explain.
3. If the answer to the previous question is yes, how would you "correct" the concentrations and observed absorbances for the dilution effect?
4. Enter your data into a spreadsheet and determine the equilibrium constant for reaction of your assigned base with Fe(CN)₅(NMPz)^2-. Suggested column headings are [NMPz⁺], Volume X added, [X], Absorbance at 664, [Fe(CN)₅(NMPz], [Fe(CN)₅X], [X]/[NMPz], [FeX]/[FeNMPz]. Plot [FeX]/[FeNMPz] versus [X]/[NMPz] and determine K_eq from the slope of the plot. Then calculate K_eq for each aliquot addition and average the results.
5. Is the equilibrium constant for your reaction "constant"?
6. Compare your K_eq with those determined by other groups studying different bases, X. Arrange the bases studied in order of increasing affinity for the Lewis acid, Fe(CN)₅^3-.

• Labkit
• 3 2-mL graduated pipets
• 2 10-mL volumetric flasks
• 1 10-mL syringe
• Controlled temperature water bath
• UV-Visible spectrometer
• Glass or quartz spectrometer cell
• mg balance
• Stock solution of Fe(CN)₅NMPz^2- (This is obtained by dissolving 0.0066 g Na₃Fe(CN)₅(NH₃).3H₂O in 1 mL of 0.5 M aqueous N-methylpyrazinium iodide and 1 mL of distilled water.)
• 0.5 M aqueous stock solution of N-methylpyrazinium iodide
• 5 M aqueous stock solution of dimethylsulfoxide (DMSO)
• 5 M aqueous stock solution of imidazole (Im)
• 2 M aqueous stock solution of pyrazine (Pz)

Note to instructor: Click here for recipes for preparation of solutions.

Safety glasses must be worn at all times in the laboratory. Aqueous solutions of Fe(CN)₅NMPz^2- are considered toxic. Avoid ingestion and contact with the skin. It is recommended that you wear latex gloves when handling this material or its solutions. DMSO readily penetrates the skin; avoid skin contact. Pyridine should be handled with care IN THE HOOD. Aqueous solutions of imidazole and pyrazine should be handled with care. In case of skin contact by any of these materials, flush with copious quantities of water.

Record all data in your notebook. Obtain the necessary equipment and clean the glassware thoroughly using brushes and Alconox detergent. Rinse with distilled water and dry thoroughly, inside and out.

You will find in the lab a stock solution containing 0.25 M N-methylpyrazinium iodide and 0.01 M Fe(CN)₅(NMPz)^2-. From this solution you will prepare 10 mL of a working solution that is 0.0025 M in N-methylpyrazinium iodide and 1.0 x 10^-4 M in Fe. Plan how to do this and carry out your plan. The instructor will assign you a Lewis base, X, to study.

As the experiment progresses you will record a number of electronic absorption spectra. Save each one with a different file name so that all can be recalled when you have finished.

Label your spectrometer cell with a small piece of label tape placed on one of the frosted faces. Transfer exactly 3.00 mL of working solution to a glass spectrometer cell, and record the electronic absorption spectrum between 800 and 300 nm. Then place the cell in a bath thermostatted at 60 ^oC for 15 minutes, rinse and dry the outside of the cell, and record the spectrum again. Note any changes. Add a 5- or 10-microliter aliquot of your assigned Lewis base (or solution of a Lewis base) to the cell, stopper, shake, and return to the 60-degree bath for a sufficient time to allow the reaction of the base with Fe(CN)₅NMPz^2- to come to equilibrium. Then record the spectrum again. Adjust the aliquot size depending on the size of the absorbance change produced by the first aliquot (if DA is small, use a larger aliquot). Add at least 5 more aliquots of X, each time increasing the size of the aliquot by an amount equal to the first aliquot. After the addition of each aliquot, equilibrate the system at 60 degrees, and record the spectrum. Finally, show that your equilibrium is reversible by adding an aliquot of 0.5 M N-methylpyrazinium iodide to the cell, equilibrating at 60 ^oC, and running the spectrum.

Retrieve all spectra from memory and display them overlayed on the screen. Measure the absorbance at 664 nm for each spectrum and record in your notebook. Then print the overlayed spectra.

If time allows, carry out the study for a second Lewis base.

Clean-up. When you have finished all of your work:

• Clean Labkit glassware by recommended procedures, shake off excess water, and return to the Labkit.
• Clean Pasteur pipets, graduated pipets, and vials by recommended procedures, shake off excess water, and place in the drying oven.
• Rinse the spectrometer cell with distilled water, then acetone, and aspirate dry.
• Clean and return all borrowed equipment to the instructor before leaving lab.
• Clean up your work area before leaving lab.

All iron-containing solutions should be disposed of in the heavy metal waste jar. Put broken glass in the receptacle provided for this purpose.

References

1. JM Malin, HE Toma, E Giesbrecht, J. Chem. Ed. 1977, 54, 385.
2. J. Inorg. Nucl. Chem. 1961, 20, 75.

1. This experiment.
2. The appropriate sections of your textbook.

1. The following reaction is carried out at 25 ^oC by adding successive aliquots of reagent B to a solution containing a known amount of reagent A and a known initial amount of MA.
   MA + B <===> MB + A

   After each addition of B to the solution, the amount of one of the products, MB, is measured once equilibrium has been reestablished according to Le Chatelier's Principle. Of course, the amount of MB at equilibrium increases every time an aliquot of B is added.

   The initial concentrations, the volumes of the B aliquots, and the measured concentration of MB after each aliquot addition are given below.

   Initial volume of reaction solution = 5.00 mL
   Initial [MA] in reaction solution = 0.00120 M
   Initial [A] in reaction solution = 0.050 M
   [B] in titrant solution = 2.00 M
   
   

   Total Volume B Solution Added, mL	[MB] Measured at Equilibrium, M
   0	0
   0.1	0.00024
   0.2	0.000385

   
   

   Determine the equilibrium constant for the reaction.

2. A compound is known to have an extinction coefficient of 3.8 x 10⁴ M^-1cm^-1 at 540 nm. A solution of the compound has an absorbance at this wavelength of 0.420, measured in a 1-cm spectrometer cell. What is the concentration of the compound in the solution, assuming the solution contains no other solute that also absorbs at this wavelength?