Kinetics: The Reaction of Cr^III with EDTA

(Adapted from Szafran, Pike, and Singh, Microscale Inorganic Chemistry, Wiley, 1991; C.E. Hedrick, J. Chem. Ed. 1965, 42, 479. )

• To develop a concentration-time curve (kinetics curve)for a chemical reaction
• To use the points on this curve to establish a reaction order
• To study the effect of pH on the kinetics of a reaction

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 prefix "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):

This is yet another example of a reaction in which one Lewis base (H₂O) is displaced by another (EDTA^4-) in a Lewis adduct. 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 case, one EDTA^4- ion has so many lone pairs that it can replace all 6 water molecules from the adduct of Cr³⁺ with water. The chromium EDTA adduct has a fairly strong absorbance in the visible region of the spectrum that we will use to monitor its appearance. From the manner in which the amount of product builds with time, the pseudo-order rate dependence on [Cr³⁺] will be determined. By running the experiment at a number of pH values, the rate dependence on [H⁺] can be determined. Finally, we will qualitatively study the dependence of reaction rate on temperature.

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 is 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 Cr³⁺?
6. What is the order of reaction in protons, H⁺?
7. We did not collect data to determine the reaction order in EDTA. Describe in detail an experiment that would determine this order.

• 4 25-mL Erlenmeyer flasks
• 2 2-mL graduated pipets
• 1 syringe pipet pump
• 5 disposable Pasteur pipets
• 1 Pasteur pipet bulb
• Controlled temperature water bath
• UV-Visible spectrometer
• Spectrometer cell
• mg balance
• spatula
• 0.0125 M aqueous Cr(NO₃)₃.9H₂O
• 0.10 M aqueous EDTA, pH 3.5 (see note to instructor, below)
• 0.10 M aqueous EDTA, pH 4.0
• 0.10 M aqueous EDTA, pH 4.5
• 0.10 M aqueous EDTA, pH 5.0
• 0.10 M aqueous EDTA, pH 5.5

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

Safety glasses must be worn at all times in the laboratory. Sodium hydroxide is corrosive. Avoid contact with skin and clothing. In case of skin contact, rinse copiously with water. Chromium is thought to be a carcinogen. Avoid contact with the skin. In case of skin contact, rinse with copious amounts of water.

Record all data in your notebook. ESTABLISH a clean work area. Obtain the necessary equipment and clean the glassware thoroughly using brushes and Alconox detergent. Rinse with distilled water and dry thoroughly. Organize your work area. Everything you are going to need should be there, and flasks and pipets should be labelled.

The instructor will assign you a pH value to study. Record this in your notebook.

In separate 25-mL Erlenmeyer flasks, obtain about 8 mL of EDTA solution that has been adjusted to your target pH (4.5, 5, or 5.5) and 3 mL of chromium solution. Place both Erlenmeyers in a controlled-temperature water bath regulating at 40 ^oC. Also place an empty spectrometer cell in the bath. Allow 10 minutes for the solutions and cell to adjust to temperature.

Carry out the following operations without removing the solutions or cell from the thermostatted bath. Pipet 3.75 mL of the EDTA solution to the empty cell. Then pipet 1.25 mL of chromium solution to the cell, starting to time the reaction as soon as the chromium has been added. Stopper the cell and shake the contents to insure good mixing. Immediately return the cell to the thermostatted bath. At the 45 second mark, remove the cell, quickly dry it with a Kimwipe, place it in the UV-visible spectrometer, and read the absorbance at 542 nm precisely at the 1 minute mark. IMMEDIATELY return the cell to the thermostatted bath. CAUTION: THE CELL SHOULD NOT BE OUT OF THE BATH FOR ANY LONGER THAN ABSOLUTELY NECESSARY TO OBTAIN THE ABSORBANCE READING. Take a minimum of seven additional absorbance readings at time intervals as indicated in the table below, each time minimizing the time that the cell is out of the bath.

Place the cell containing the reaction mixture in a 80-degree hot water bath for 15-20 minutes to hasten completion of reaction. Then return the cell to the 40 ^oC bath for 10 minutes. Finally, obtain the final absorbance (scan) of the reaction mixture.

Do a second run, and a third run if time allows. If desired, you may do two runs simultaneously using a convenient stagger in the start times.

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

• Discard left over chromium solution in the heavy metal waste. Left over EDTA may be flushed down the drain.
• 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.
• Clean and return all borrowed equipment to the instructor before leaving lab.
• Clean up your work area before leaving lab.

All solutions containing chromium should be placed in the heavy metal waste container. Solutions of acids and bases may be flushed down the drain with plenty of water.

Data Analysis

The reaction of aqueous Cr³⁺ with EDTA^4- is essentially irreversible, so it is not necessary to worry about the reverse reaction. Thus

This can be simplified by realizing that the concentration of EDTA is more than 10 times larger than that of Cr³⁺, so [EDTA^4-] remains essentially constant over the course of the reaction. Further, EDTA^4- serves as a buffer, so [H⁺] also stays constant as reaction proceeds. Equation (7) simplifies to

where k_obs = k[EDTA^4-]^q[H⁺]ⁿ. Thus the reaction runs under pseudo-order conditions in Cr³⁺.

However, there are a couple of complications. First, we measure the forward rate by monitoring the formation of product, Cr(EDTA)-, rather than disappearance of reactant, Cr³⁺. Before we can integrate equation (8) for various values of p, we must express the rate in terms of disappearance of Cr³⁺. In order to do this, we must assume that for every Cr³⁺ ion that reacts, a Cr(EDTA)^- ion forms; that is, that the rate of disappearance of chromium reactant is the same as the rate of appearance of chromium product. Then we can write

However, another complication arises from the fact that we follow the kinetics by measuring the absorbance at 542 nm as a function of time. This wavelength is a l_max for the product, Cr(EDTA)-, as seen in the spectra. Although Cr(EDTA)- has a much larger absorbance at 542 nm than does Cr³⁺, the latter does have a measurable absorbance there. Thus when we measure A at 542 nm, there are contributions due to an increase in the amount of product, but also due to a decrease in the amount of reactant. In such a situation, how do we treat the absorbance data in order to extract the order of the reaction in Cr³⁺ and the value of the rate constant?

It is possible to show that the order and rate constant can be obtained from a "typical" first-order plot of the absorbance data. Here's how we do it. Suppose that for simplicity in typing, we let X = Cr³⁺ and Y = Cr(EDTA)-. Then under pseudo-order conditions, reaction (6) becomes

Let e_X = the molar absorptivity of X; e_Y = the molar absorptivity of Y; A_o = the initial absorbance; and A_inf = the final absorbance, all at a particular wavelength. The following relationships hold:

First, solve (11d) for [Y] and substitute in (11a) to give

Collect terms in [X]:

Now let De = e_X - e_Y and substitute A_inf for e_Y[X]_o:

Finally, subtract A_inf from both sides:

This lets us express [X] at any time during reaction in terms of measured absorbances:

Our final step is to express the rate law, (9), in terms of absorbance. Remembering that X represents Cr³⁺ and assuming p = 1 (first order), the rate law is

We now replace [X] with the expression in (16):

Cancelling De we obtain a first order rate expression in the quantity A - A_inf:

This can be integrated in the variable A-A_inf. Thus if the reaction is first order, a plot of ln(A-A_inf) versus time should be linear, with slope -k.

In the above derivation, it has been assumed that absorbance decreases during reaction, so that A_inf is less than A at any time during reaction, and A-A_inf is therefore a positive quantity. In the event that A increases during reaction, as in this experiment, simply multiply both sides of (18) by -1 to obtain (19):

In this case a plot of ln(A_inf-A) versus t is appropriate.

Note that if the reaction is not first order, the De factor occurs as (De)ⁿ on the right of equation (17). The De term on the left will cancel only one of these, so (18) will involve a term (De)^n-1. In this case, De must be experimentally determined in order to obtain the value of the rate constant.

References

1. Szafran, Pike, and Singh, Microscale Inorganic Chemistry, Wiley, 1991; C.E. Hedrick, J. Chem. Ed. 1965, 42, 479.