KINETIC STUDY OF A LIGAND EXCHANGE REACTION
Objective: To determine the order, activation energy and rate constant of a ligand
exchange reaction involving the trans dichlorobis(ethylenediamine)cobalt (III) ion
Introduction
Absorption spectroscopy in the visible region of the spectrum is often used to study the
kinetics of chemical reactions. In absorption spectroscopy, one measures the amount of
light that is absorbed by a compound or compounds as a function of the wavelength of
the light. For example, Cu+2 reacts with ammonia to for a colored transition metal
complex according to the reaction:
Cu+2 + 4NH3  Cu(NH3)4+2
The copper-ammonia complex absorbs light, provided the energy of the light corresponds
to the energy difference between the Cu d orbitals caused by the NH3 ligands. When the
light is absorbed, an electron in a lower energy d-orbital is raised to a higher energy dorbital. This excess energy is then subsequently lost as heat. For the copper-ammonia
complex, the absorbance spectrum (absorbance vs. wavelength plot) is shown below.
1.4
Absorbance
1.2
1
0.8
0.6
0.4
0.2
0
400
500
600
700
800
Wavelength (nm)
According to the absorbance spectrum, this complex absorbs light above 560 nm, the
orange-red region of the spectrum. However, light with wavelengths less than about 560
nm, the blue region ot the spectrum, is not absorbed. Therefore, a solution of this
compound appears blue, since the blue light is transmitted.
The absorbance in the above plot is a measure of the amount of light absorbed at a
particular wavelength. To determine the absorbance, one first measures the intensity of
the light at a particular wavelength, Io, and then measures the intensity, I, after the light
has passed through the sample. The absorbance (A) is:
A = - log( I / Io ) = - log ( T ) where T = I / Io is the transmittance
According to Beer’s Law, the absorbance at a particular wavelength is directly
proportional to the distance the light has to travel through the solution (b) and the
concentration (C) of the absorbing species in solution. The proportionality constant is
called the molar absorptivity (). Therefore, A = bC. Note that  is dependent on the
wavelength of light. In the absorbance spectrum for the copper complex above, it is at a
maximum at approximately 790 nm.
In reaction kinetics, we can use Beer’s law to determine the concentration of a reacting
species as a function of time. Provided  is known at a particular wavelength and b is a
constant, C = A / b. We usually use the wavelength at which  is at its maximum value
(eg. 790 nm for the copper complex). In the reaction to be studied, both the reactant and
product absorb light to some extent at all visible wavelengths. Although it is possible to
still make use of Beer’s Law for two absorbing species, we will simply use the two
spectroscopy tools you brought with you to lab (assuming you are not color blind).
In this experiment we will take advantage of the difference in the absorbance spectra of
the cobalt complex which we synthesized last week, and that of the product when one of
the chloride ligands is replaced by a water molecule.
When this occurs, the energy difference between the cobalt d-orbitals is changed. As a
result, the absorbance spectrum changes (i.e., the color changes). The absorbance spectra
given below show the difference in absorbance of the reactant and of the product after
substitution of water for one of the chloride anions. In the reactant spectrum shown, the
complex is green as a result of the low absorbance at approximately 500 nm (green light).
The product is red in color as a result of the low absorbance above 600 nm.
0.9
0.8
product
Absorbance
0.7
0.6
0.5
reactant
0.4
0.3
0.2
0.1
0
380
480
580
680
780
Wavelength (nm)
When this reaction goes approximately half to completion, at t1/2, the absorbance
spectrum will be the average of the two curves. At this point, the mixture will absorb
light across the visible spectrum and appear gray in color. Although the time required for
the solution to turn gray is not exactly the half-life of the reaction, we can still use this
time to determine the reaction order as well as an approximate value of the rate constant
at different temperatures, from which we can determine the energy of activation of this
reaction.
Safety: Avoid contact with cobalt complex and its solutions.
Waste Disposal: Any excess cobalt complex should be saved for future use. Place
into a specially designated container in your lab. All aqueous wastes containing the
cobalt complex should be placed in a hazardous waste container designated for this
purpose. Use a large beaker to collect your solutions during the lab period, then
transfer to the waste container.
Procedure
1. Fill your 100 mL volumetric flask about ¾ full of distilled water and chill in an ice
bath. Also, chill some water to be used to fill the flask to the mark. You will also need
to chill two small test tubes and a 10 mL graduated cylinder. Weigh accurately about
1.0 g of Co[(en)2Cl2]Cl into a weighing boat and transfer it to the volumetric flask and
dissolve the complex. Dilute to the mark with cold water, mix thoroughly and return
the flask to the ice bath. (It is important to keep this solution at the low temperature
to insure that the ligand exchange reaction does not occur until we are ready. The
flask should not leave the ice bath during the lab period except when transferring
solution).
Determination of Reaction Order, Rate Constant, and Energy of Activation
We can determine the reaction order base on the time it takes for the reactant to go half
way to product and the reaction turns gray. Using the two spectroscopic tools you
brought with you today, we can determine the reaction order, the rate constant of this
reaction, and then its energy of activation. If we have two solutions of our reactant, one
with half the concentration of the other, they should both have the same half-life if the
reaction is first order since:
(1)
t1/2 = 0.693 / k
for a 1st order reaction
In a first order reaction, the half-life is not dependent on the initial concentration of the
reactant. In addition, if we measure the half-life (time for solution to turn gray), we can
determine the rate constant from k = 0.693 / t1/2. On the other hand, if the reaction is
second order, the half-life of the more concentrated solution (twice the concentration)
should be half that of the dilute solution (half the concentration) since:
(2)
t1/2 = 1 / k[complex] for a 2nd order reaction
Therefore, if the reaction is 2nd order, the half-life is inversely proportional to the
concentration. In this is the case, we can calculate the rate constant from k = 1 /
t1/2[complex].
Finally, if we determine the rate constant of the reaction in one of the above fashions at
different temperatures, we can determine the energy of activation of the reaction from the
Arrhenius equation written in the form given below:
(3)
ln k = ln A – Ea / RT
According to this equation, a plot of ln k vs 1 / T (where temperature is in kelvins) will be
a straight line with a slope of –Ea / R. Therefore, if we determine the slope of this line,
we can calculate the energy of activation from –R × slope = Ea.
1. Chill two test tubes. At the same time, heat a beaker of water to somewhere
between 40oC and 70oC.
2. Using a disposable dropper, add 2 mL of reactant to one test tube, and 1 mL of the
reactant plus 1 mL of cold water to the other. Record the temperature of your
water bath and insert the two test tubes. Watch carefully and record the time
required for the reaction to go half-way to completion, the half-life (time to turn
gray).
3. Base on the two half-lives, is the reaction first or second order? Based on your
conclusion, calculate the rate constant of this reaction at this temperature. If the
temperature of the water changes during the course of the experiment, record the
average temperature.
4. Chill down one of the small test tubes. Since you now know the order of the
reaction, you now want to determine the half-life and rate constant at a number of
different temperatures (at least four total). Heat or cool the water in your beaker
to a temperature about 10 oC different from the previous. Put about 2 mL of the
reactant solution in the small test tube, place in the water and determine the halflife and rate constant at this temperature. Again, should the temperature change,
record the average.
5. Repeat step 4 at least two more times and determine the half-life and rate constant
at the new temperature.
6. Using your data (rate constants at four or more temperatures), determine the
energy of activation for this ligand substitution reaction according to equation 3
above. Do the same with the class data.
KINETIC STUDY OF A LIGAND
EXCHANGE REACTION
DATE
NAME
PARTNER’S NAME
Mass of Co[(en)2Cl2]Cl in stock solution, grams
Concentration of Co[(en)2Cl2]Cl in stock solution, M
Half-life part 2 & 3:
Solution 1 ___________
Solution 2 ____________
Order of Reaction _____
Rate constant _________ Temperature (oC) _________
Temperature (oC)
Half-Life (s)
Rate Constant (include units)
_______________
____________
_____________
_______________
____________
_____________
_______________
____________
_____________
_______________
____________
_____________
_______________
____________
_____________
_______________
____________
_____________
Attach a copy of your Arrhenius plots
From your data
Slope of plot (include units)
y-intercept of plot
Energy of activation, kJ/mol
Frequency factor A
Class data