Equilibrium and Kinetics: Lewis Base Substitution in an Iron Adduct

Note to instructor: This experiment should be used as a capstone experience in kinetics and equilibrium; it is intended for students who have experience in and knowledge of these concepts.

• To learn techniques for measuring rates of relatively rapid reactions
• To explore the relationship between kinetics and equilibrium
• To carry out a pseudo-order rate study

The Relationship between Equilibrium (favorable or unfavorable?) and Kinetics (fast or slow?). A reaction is favorable if the equilibrium position favors the products (species written on the right side of the reaction); and unfavorable if the equilibrium position favors reactants (species written on the left side of the reaction). The reaction is fast if equilibrium is achieved rapidly from the starting situation; and slow if equilibrium is achieved sluggishly. The terms favorable, unfavorable, fast, and slow are qualitative terms, and different people have different opinions as to what they mean. Most chemists would agree that the reaction of carbon with oxygen to form carbon dioxide is both favorable and slow (evidence of the latter is that you can store a bag of charcoal indefinitely without having to worry about it's burning). Most would also agree that the reaction of HCl with NaOH in water solution is both favorable and fast. On the other hand, some chemists consider a reaction that is over (that is, at equilibrium) 1 millisecond (0.001 seconds) after it starts to be fast; others, used to measuring rates of reactions that are 10 million times faster, consider it to be slow. Similarly, one chemist may consider a reaction to be favorable if the concentration of product(s) at equilibrium are 60% or so of the theoretical yield; whereas another may consider a reaction to be favorable only if at equilibrium the conversion to products is 99% complete. To argue about the interpretation of these qualitative terms is common, but pointless. The point is for each individual to achieve an understanding of the terms that makes sense within her/his framework.

Consider the generic chemical reaction represented by equation (1):

K_eq measures the "favorability" of the reaction; k_f and k_r measure its "fastness" in the forward and reverse directions. These three constants are related, as we will see.

Based on what we know about equilibrium, we can write equation (2):

where [A]_e, etc., represent concentrations at equilibrium. Once a chemical reaction has reached equilibrium the concentrations of all the participants remain constant in time; there is no observable change in concentration unless the equilibrium is perturbed from outside.

Based on what we know about kinetics, we can write equations (3) and (4) for the forward and reverse rates of (1):

where the exponents a, b, d, and f are the orders of reaction with respect to each of the four participants. We should make a few important statements about equations (3) and (4):

• The forward rate depends only on the concentrations of A and B and does not depend on how much D and F are present.
• The reverse rate depends only on the concentrations of D and F and does not depend on how much A and B are present.
• k_f and k_r may (and often are) very different, so that a reaction can be rapid in the forward direction and slow in the reverse (or vice versa).
• If the forward rate exceeds the reverse rate, net reaction will proceed in the forward direction. This will have the effect of using up A and B while forming D and F, which means that the forward rate will steadily decrease while the reverse rate increases. Eventually the two rates will become equal, and we will observe no further change in any concentration.
• Except under quite special circumstances, we cannot experimentally measure the forward rate and or the reverse rate. Instead, what we measure is the net rate.
• The net rate, which is what we actually observe, is the difference between forward and reverse rates:
  
  Net rate = rate_forward - rate_reverse
  
• Equilibrium is simply the situation in which forward and reverse rates are the same, and thus the net rate is zero. Thus at equilibrium
  
  (5): Rate_forward = rate_reverse
  
  (6): net rate = 0 = k_f[A]_e^a[B]_e^b - k_r[D]_e^d[F]_e^f
  
  (7): k_f[A]_e^a[B]_e^b = k_r[D]_e^d[F]_e^f
  
  
• The net rate is proportional to the deviation of the system from the equilibrium position; the farther the reaction is from equilibrium, the faster the net rate will be.
• Although the net (observable) rate at equilibrium is zero, neither the forward rate nor the reverse rate is zero. Both processes continue to occur, but they occur equally so that it appears at the macroscopic scale that nothing is happening.

Rearranging equation (7) gives (8):

This is the relationship between equilibrium and rate constants that we anticipated above.

In writing equations (3) and (4), we have ignored a statement made at the outset of our study of chemical kinetics: that the orders of reaction with respect to the various participants need not be the same as the stoichiometric coefficients. However, if an equation represents a reaction that occurs in a single concerted step, exactly as written (rather than representing the net result of a series of steps), then the reaction orders are the same as the stoichiometric coefficients. Thus to this point, equation (9) is restricted to such one-step processes.

However, although equation (9) was developed assuming that (1) occurs in a single step, it is true for any chemical reaction, no matter how complex. The following line of reasoning suggests (but does not prove) this.

• Any reaction, no matter how complex, may be broken down into a series of steps, which may be labelled step 1, step 2, ..., step n.
• The overall reaction has an equilibrium constant, K_eq; and each elementary step m has an equilibrium constant, K_eq,m, a forward rate constant, k_m, and a reverse rate constant, k_-m.
• The equation for the reaction can be obtained by adding together the equations for the elementary steps:
  
  (10): reaction = step 1 + step 2 + ... + step n
  
  
• Therefore the overall equilibrium constant is the product of the equilibrium constants for the elementary steps:
  
  (11): K_eq = K_eq,1K_eq,2...K_eq,n
  
• Each elementary step obeys equation (8). Stringing these together thus gives
  
  (12): K_eq = k₁k₂...k_n/k_-1k_-2...k_-n

  We can conclude from this equation and equation (9) that for the overall reaction

  (13): k_f/k_r = k₁k₂...k_n/k_-1k_-2...k_-n
  

  It is tempting to conclude that

  k_f = k₁k₂...k_n
  k_r = k_-1k_-2...k_-n
  

  Although it is not necessary that this be true in order for (13) to be true, (13) does allow us to conclude that

  (14a): k_f = k₁k₂...k_n/Q
  (14b): k_r = k_-1k_-2...k_-n/Q
  

  where Q is the same in both expressions, so that it disappears when the ratio is taken.

  To illustrate these relationships consider the reaction represented by the equation in (15):

  (15) Fe(CN)₅(DMSO)^3- + NMPz⁺ <===> Fe(CN)₅(NMPz⁺) + DMSO
  

  this reaction actually occurs in two steps:

  (16a): Fe(CN)₅(DMSO)^3- <===> Fe(CN)₅^3- + DMSO with rate constants k₁, k_-1
  
  (16b): Fe(CN)₅^3- + NMPz⁺ <===> Fe(CN)₅(NMPz)^2- with rate constants k₂,k_-2.
  

  It is possible to show that for reaction (16),

  (17a) k_f = k₁k₂/(k₂[NMPz⁺] + k_-1[DMSO])
  
  (17b) k_r = k_-1k_-2/(k₂[NMPz⁺] + k_-1[DMSO])
  

  Clearly 17a and 17b are consistent with equations (13), (14a), and (14b).

Reaction System. In this experiment we will study the equilibrium and kinetics of the reaction below, in which 2 molecules of the Lewis base, acetonitrile (CH₃CN) are displaced from the Lewis acid, Fe(C₃₄H₃₂N₄)²⁺, by 2 molecules of a new Lewis base, B (B = imidazole, 2-methylimidazole, or pyridine):

Chemical structures of reactants and products are shown here. Note that this reaction is similar to reaction (15), except that 2 molecules of Lewis base are involved. As is true for (15), we will find that the simple-looking process, (18), is much more complicated than it appears!

1. Which base has the largest equilibrium constant for reaction with the iron compound? Which the smallest?
2. Which base reacts most rapidly with the iron compound? Which reacts most slowly?
3. Load each of your absorbance-time data sets into a spreadsheet. At the bottom of the absorbance column, enter the final absorbance, A_final. For each time, calculate the value of ln(A-A_final), where A is the absorbance at the selected time. Then plot ln(A-A_final) versus time. Print the plot.
4. Is the plot from (1) linear? What is the order of the reaction with respect to the iron compound?
5. What is the pseudo-order rate constant for each run?
6. What is the order of the reaction with respect to the Lewis base?

• 2 10-mL volumetric flasks
• 2 2-mL graduated pipets
• Syringe pipet pump
• Pasteur pipet
• Pasteur pipet bulb
• 1-dram vial
• 10-mL syringe
• Lewis bases
  • imidazole
  • pyridine
  • 2-methylimidazole
• stock solution containing 0.001 M iron complex, Fe(C₃₄H₃₂N₄)(CH₃CN)₂(B(C₆H₅)₄)₂, dissolved in acetonitrile.
• Glass or quartz spectrometer cell
• Electronic absorption spectrometer operable in a time-scan mode

Safety glasses must be worn at all times in the laboratory. All organic liquids should be considered toxic and should be handled in the hood. In the event of skin contact, flush the affected area copiously with running water.

Record all data in your notebook. Obtain the necessary equipment and clean the glassware (but NOT the spectrometer cell!) thoroughly using brushes and Alconox detergent. Rinse with distilled water and dry thoroughly.

Equilibrium

Plan a procedure to prepare from the stock solution provided 5 mL of a solution containing ~10^-4 M iron compound dissolved in acetonitrile. Have your procedure approved, then carry it out. This will provide all of the iron solution needed for your portion of the equilibrium study.

The instructor will assign you a Lewis base to study. Plan a procedure to prepare from pure Lewis base provided 1.0 mL of a solution containing 2.0 M Lewis base dissolved in acetonitrile. Have your procedure approved and carry it out. Then using your 2.0 M solution, prepare 1.0 mL of a solution containing 0.20 M Lewis base.

In performing your equilibrium study, you will record a number of absorbance versus wavelength scans. Each of these should be given a different name and saved, so that all scans can be recalled, overlayed, and printed when you are finished collecting data.

Transfer exactly 2.2 mL of your iron solution to a glass or quartz spectrometer cell, and scan the spectrum. (The seemingly odd volume of 2.2 mL is chosen because it corresponds to the maximum volume measurable with a 2-mL graduated pipet, and it fills the cell to the appropriate level.) This should be the spectrum of Fe(C₃₄H₃₂N₄)(CH₃CN)₂²⁺ before reaction with Lewis base.

Now add 1 microliter of your 0.20 M solution of Lewis base to the cell. Stopper and shake the cell to mix the contents, then let the solution stand for 5-10 minutes to equilibrate. Record the electronic absorption spectrum again. Based on the amount of change from the initial spectrum, you may have to increase the aliquot size from now on.

Continue adding aliquots of Lewis base solution, equilibrating, and recording the spectrum. Overlay the spectra as you go so you can see what is happening. Do you see any isosbestic points (points at which a series of spectra cross)? What is the significance of these?

Finally, add a very small amount (1 microliter if liquid, 1 mg if solid) of pure Lewis base to the cell, equilibrate, and record the spectrum.

When finished, overlay all spectra and print the overlay. You may also wish to overlay and print subsets of spectra.

See the Disposal section for instructions on discarding the solutions.

Kinetics

Prepare from the stock solution provided 10 mL of a solution containing ~10^-4 M iron compound dissolved in acetonitrile. This will provide all of the iron solution needed for your portion of the kinetics study.

Please study the same Lewis base assigned to you for the equilibrium study. IN THE HOOD, transfer 5-10 drops of your assigned Lewis base (if liquid) or a 2.0 M solution of your assigned Lewis base (if the base is a solid) to a 1-dram vial. Cap the vial and label it using your Sharpie marker.

In performing your kinetics study, you will record a number of absorbance versus time scans. Each of these should be given a different name and saved, so that all scans can be recalled, overlayed, and printed when you are finished collecting data.

You will carry out at least four kinetics runs, each using a different quantity of your assigned Lewis base. Your instructor will assign a wavelength at which you should monitor the progress of reaction (590, 650, or 708 nm). Follow the procedure below for each run:

1. Using a 2-mL graduated pipet and a syringe pipet pump, transfer exactly 2.20 mL of the iron solution to a glass or quartz spectrometer cell, and stopper the cell.
2. Run a wavelength scan of the solution in the cell to obtain the initial spectrum (this step need only be done the first time).
3. Set up the electronic absorption spectrometer to monitor absorbance at 590 nm for 360 seconds (get help from the instructor if necessary).
4. Load the syringe with the first volume of Lewis base (probably 1 microliter).
5. Remove the stopper from the spectrometer cell.
   
   The next 5 steps must be done quickly--no more than 10 seconds total.
6. Inject the aliquot of base into the cell.
7. Stopper the cell.
8. Shake the cell.
9. Place the cell in the instrument.
10. Begin collecting absorbance-time data.
    
    Now relax!
    
    
11. When the computer has finished collecting data, watch the absorbance reading on the spectrometer for 2-3 more minutes until it reaches a constant value. Then record this value.
12. Run a wavelength scan to obtain the final spectrum.
13. Empty the cell in the organic solvent waste bottle, rinse it with acetone, and aspirate dry.
14. Return to step 1.

When you have finished collecting data, recall the initial spectrum and the final spectra from all four runs, and overlay them on the screen. Print the overlay and label each scan. Then clear the screen and recall the absorbance-time plots from all four runs, overlaying them on the screen. Print the overlay and label each scan. Export each of your absorbance-time data sets to a disk.

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

• Clean all glassware with Alconox and water and shake dry.
• Rinse Pasteur pipets by inserting the nozzle of your wash bottle in the top end and squirting water through. Aspirate dry.
• Rinse the spectrometer cell with acetone and aspirate dry.
• Return all components to the labkit.
• Return all borrowed equipment to the instructor before leaving lab.

Compare your initial and final spectra, and your absorbance-time kinetic curves, with those of other groups that studied the same Lewis base. Are your results consistent? Now compare with data from groups studying other Lewis bases (a total of three bases have been studied). Then proceed to the questions.

Disposal Methods

All solutions should be poured in the organic solvent waste bottle in the hood. Dispose of broken glass in the container provided for that purpose.

References

1. Hamilton, Lewis, Kildahl, Inorg. Chem. 1979, 18, 3364.

Name

Section

Date

1. This experiment.
2. The appropriate sections of your textbook.
3. Chapter 15 of Concepts of Chemistry.

1. Consider the reaction
   
   A <===> C
   which has equilibrium constant, K_eq and forward and reverse rate constants, k_f and k_r. Assume that the reaction occurs in two steps, shown below:
   
   A <===> B with rate constants k₁, k_-1
   
   B <===> C with rate constants k₂, k_-2
   

   Starting with Net rate = k_f[A] - k_r[C], show that k_f = k₁k₂/(k_-1 + k₂) and k_r = k_-1k_-2/(k_-1 + k₂)