Kinetics: The Reaction of Fe(CN)₅((CH₃)₂SO)^3- with N-methylpyrazinium Cation

• To develop a concentration-time curve for a chemical reaction
• To use pseudo-order methods to determine a rate law
• To gain experience in planning a kinetics study

Chemical kinetics is the study of the the rates of chemical reactions, reflected in the time-dependence of the concentrations of reactants and products. The rate of a chemical reaction is generally expressed as the change in the concentration of a reactant or product per unit time. For reaction (1), then, showing nitrogen and hydrogen reacting to form ammonia, rate may be expressed in three ways, as shown.

Because by convention chemists treat reaction rate as a positive quantity, negative signs are placed in front of the concentration changes for the reactants, because reactants are used up as reaction proceeds and therefore experience negative concentration changes. Ammonia is formed as reaction proceeds, so its concentration change is positive. Other than this matter of sign, however, there is another minor problem that must be addressed. As a result of the reaction stoichiometry, the changes in concentration of the three substances in a given time period are not the same, and unless we correct for this somehow, the rate will be different depending on which of the substances we choose to express it. This problem is readily corrected by dividing the concentration change for a species by the stoichiometric coefficient for the species. Thus,

For essentially all chemical reactions, the rate depends upon the same factors. These are

• The chemical nature of reactants and products
• The concentrations of reactants and products
• The temperature
• The presence of and concentration of a catalyst

Usually the rate depends on the concentrations of reactants (and products) according to a simple mathematical form. This is shown for generic reaction 2) in 3):

Here m and n are generally NOT the same as the stoichiometric coefficients, though they are usually integers, often 1 or 2. The numbers m is called the order of the reaction for reactant A, and n is the order for reactant B. The total reaction order is m+n.

The rate constant, k, implicitly contains within its magnitude the dependence of rate on the chemical nature of the participants and the temperature dependence of the rate. The latter can be independently measured by running the reaction at a series of temperatures. The minimum goal of a kinetics study is to determine the rate law (that is, on which concentrations does rate depend, and what are the orders in these concentrations) and the value of the rate constant, k, at a particular known temperature. Frequently the study is extended to other temperatures to demonstrate the manner in which k varies as T increases. Almost invariably, rate constants (hence rates) increase as T goes up.

There are a number of experimental approaches to determining the rate law. One, the method of initial rates, involves measuring the rate at the beginning of the reaction as a function of the concentration of each reactant in turn. If, for example, it is found that the initial rate is twice as large when the starting concentration of reactant A is made twice as big, then it follows that the order of the reaction for A is 1 (that is, the exponent to which the [A] must be raised in the rate law is 1). This method suffers from a number of disadvantages, and is not widely applicable. It is utilized in the experiment, "Kinetics: The Reaction of Benzaldeyhde and Acetone."

A second method, very commonly used, is the pseudo-order method. Applied to reaction (1), it would go something like this. There are only two reactants, A and B, and we assume that A has some physical property (such as light absorbance in the visible region of the spectrum) that enables its concentration to be monitored. One then conducts a kinetics study in which the initial concentration of A is appropriate to give a reasonable value of the property being measured, and the initial concentration of B is at least 10 times larger than that of A. It is thus guaranteed that over the course of reaction, during a time period in which the amount of A substantially decreases, the concentration of B changes hardly at all; i.e., [B] remains essentially constant over the course of the reaction. In this case the rate law in (3) takes a simplified form in which the rate depends only on [A]:

Regardless of the value of n, equation (4) is integrable to give the following results, where in all cases [A]_o signifies the initial concentration of A:

The first 2 cases, n = 1 and 2, are by far the most common. When n=1, the reaction is said to be pseudo-first-order in A, and is pseudo second order when n=2. The word "Pseudo" is meant to convey that there may also be a rate dependence on [B], but that this is invisible because [B] is large.

To determine the order in [B] one then repeats the study using a different, still large, concentration of B. The values of k_obsd can then be plotted versus the concentrations of [B] to determine the dependence on [B].

In this experiment you will use the pseudo-order method to determine the rate law for reaction (6):

Click here to see the structures of the reactants and products.

This is yet another example of a reaction in which one Lewis base (DMSO) is displaced by another (C₅H₇N₂⁺, called N-methylpyrazine cation) in a Lewis adduct. As we have discussed, the donation of a pair of electrons to the acid by the base to form a normal covalent bond is the essence of this process. In this experiment, you will design a procedure to determine the dependence of rate on the concentrations of [Fe(CN)₅DMSO^3-], DMSO and N-methylpyrazine cation. By running the experiment at a number of temperatures, we will determine the dependence of reaction rate on temperature.

Here are some facts about reaction (6) that will help you in devising your procedure:

• The most easily measured concentration is that of the product, Fe(CN)₅(C₅H₇N₂)^2-. You should plan to carry out the reaction under pseudo-order conditions in this reagent.
• The iron product has a strong absorbance at 662-664 nm in the visible region of the spectrum that we will use to monitor its appearance.
• The reaction is fairly slow at room temperature, but has convenient kinetics at 40 oC. You should plan to do your study at this temperature.
• Plan to study kinetics for [N-methylpyrazinium ion] in the range 0.005-0.1 M, and for [DMSO] in the range 0.001-0.01 M.
• It will be necessary to obtain an equilibrium absorbance value at 664 nm. After you have obtained at least 8 absorbance-time points, place your reaction flask in a 90-100 oC water bath for 10 minutes, return it to 40 oC, and measure the final absorbance.
• The following solutions will be available in the lab:
  • ~10^-2 M Fe(CN)5DMSO^3- in 0.1 M aqueous DMSO.
  • 0.5 M N-methylpyrazinium iodide in 0.001 M aqueous DMSO.
  You should prepare your reaction solutions by mixing 5 mL of the iron solution with 5 mL of an appropriate dilution of the NMPz+I- solution.

1. Write the general form of the rate law for reaction (6).
2. Which substance is monitored as a function of time?
3. Which reactant(s) is (are) in excess in this kinetics study?
4. What is the pseudo-order rate law for reaction (6).
5. Use a spreadsheet to plot the data for each run according to the integrated rate laws in the table. What is the order of reaction in Fe(CN)₅DMSO^3-?
6. What is the order of the reaction in NMPz+? In DMSO?
7. Write a rate law consistent with the orders you have determined.

• 3 25-mL Erlenmeyer flasks
• 2 10-mL graduated cylinders
• 5 disposable Pasteur pipets
• 1 Pasteur pipet bulb
• Controlled temperature water bath
• UV-Visible spectrometer
• Plastic spectrometer cell
• mg balance
• spatula
• Stock solution containing 0.01 M Na₃Fe(CN)₅DMSO and 0.1 M DMSO
• N-methylpyrazinium iodide
• Dimethylsulfoxide, DMSO

Safety glasses must be worn at all times in the laboratory. Na3Fe(CN)5DMSO is 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. In case of skin contact, 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.

Develop a procedure to prepare 50 mL of an aqueous solution containing 10^-4 M Na₃Fe(CN)₅DMSO and 0.001 M DMSO. (The solution must contain DMSO in addition to the iron complex to prevent the bound DMSO from coming off prematurely). Have your procedure approved before carrying it out. After approval, carry it out.

Develop a procedure to prepare 20 mL of a 0.4 M solution of N-methylpyrazinium iodide. Have your procedure approved before carrying it out. After approval, carry it out.

Carry out the pseudo-order kinetics study that you proposed in the prelab.

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 distilled water, then acetone, and aspirate dry.
• Return all components to the labkit.
• Return all borrowed equipment to the instructor 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. Dimethylsulfoxide, DMSO, has density = 1.101 g/mL and MW = 78.13. What is the molarity of neat (i.e., pure) DMSO?
2. What volume of neat DMSO would be required to prepare 25 mL of a 0.001 M solution of DMSO in water?
3. Plan and write out in detail a pseudo-order kinetics study of reaction (6). You will be provided with a stock solution of the iron complex containing 10^-3 M DMSO, and with solid N-methylpyrazinium iodide. You will carry out the reaction at 40 ^oC by thermostatting your solutions in a water bath.