Introduction

     The kinetics and mechanisms of inorganic reactions can be explained by the theory of rates of reaction.^1,2  The rate of reaction is defined as the rate of change of concentration of one of the products or reagents with respect to time.  For example, for the reaction:

2A ® B + C            [1]

the rate of reaction is expressed as:

Rate = d[C]/dt = d[B]/dt = -(¹/₂)d[A]/dt

Since the rate is positive, there is a negative sign in front of the last expression.  If the rate of reaction depends on concentration, it is because the reaction mechanism involves collisions between molecules.  The more molecules present (as reflected by concentration), the faster the reaction.  The dependence of rate on concentration of a given species may be determined by obtaining the rate of reaction at different concentrations of that species, holding all other conditions constant.  Performing this experiment for all species yield a differential rate law:

d[C]/dt = k[A]^a[B]^b[C]^c        [2]

     The sum of a + b + c is called the overall order of the reaction, while each term is known as the order with respect to that compound.  For example, the reaction is 'ath' order with respect to A.  Note that the orders that are derived from experiment do not necessarily correspond to the stoichiometry of the reaction.  The actual reaction mechanism (the molecular reactions) determines the observed rate law.  Reactions usually involve the collision of two like or unlike molecules.  Another way to write reaction [1] is:

 k₁
            A + A   ®  B + C        [3]

If the reaction involves the collision of two molecules of A, then:

d[C]/dt = d[B]/dt = -(¹/₂)d[A]/dt = k₁[A]²        [4]

where k₁ is the rate constant for [3].  Reaction [3] would therefore be a bimolecular process and the reaction is second order with respect to A.  If it is discovered from experiment that d[C]/dt is instead first order with respect to A, then the reaction [4] that was proposed is incorrect and another mechanism must be found.

The Aquation of [Co(NH₃)₅Cl]²⁺

     The rate of change of a reagent of product with respect to time must be followed by some physical or chemical property of the system that changes with varying concentration.  One example is the absorption of UV-Visible light, and will be used in this kinetics experiment.  The first order rate constant for a substitution reaction of [Co(NH₃)₅Cl]²⁺ will be determined, at two different acid concentrations.  The substitution for the weaker chloro ligand by an aquo ligand will be studied.^3.4  The reaction can occur by an S_N1 mechanism, where the rate determining step is the breakage of the Co-Cl bond, or by an S_N2 mechanism involving the formation of a seven coordinate intermediate, followed by rapid loss of the chloro ligand.  In aqueous solution, both mechanisms are induistinguishable: the first predicts first order with respect to [Co(NH₃)₅Cl²⁺], while the second predicts second order overall, first order with respect to both the complex concentration and [H₂O].  Since the reaction is carried out in water, the rate law becomes:

Rate = kobs[Co(NH₃)₅Cl²⁺]        [5]

where k_obs is known as a psuedo first order rate constant, and k_obs = k₂[H₂O].  k2 is the overall second order rate constant.  A third possible mechanism is via acid catalysis, which is found to be first order in both the complex concentration and [H₃O⁺] in similar complexes to that being studied here.

     Although both the reagent complex and product complexes absorb light at 550 nm, the molar absorptivities are different for each, allowing the rate of reaction to be followed by UV-Vis spectroscopy.  The reaction is catalyzed by neither light nor oxygen, and the data will allow the formulation of a rate law and a consistent reaction mechanism to be postulated.

Experimental

Preparation of [Co(NH₃)₅Cl]Cl₂⁴

      In a 25 mL Erlenmeyer flask, dissolve 0.50 g ammonium chloride in 3.0 mL of concetrated (14.7 M) aqueous ammonia.  With continuous agitation and in small portions, add 1.00 g of finely powdered cobalt(II) chlroide hexahydrate.  Allow each portion to dissolve before adding more cobalt compound.  A yellow-pink precipitate should form, accompanied by the evolution of heat.

     In the fumehood, slowly add 0.80 mL of 30% hydrogen peroxide, with mechanical or manual stirring (note: the resulting reaction is highly exothermic).  After the solution settles, it should be dark red in colour.  Then slowly add 3.0 mL of concentrated HCl (12 M); the flask should evolve heat, and yield a purple precipitate and a blue-green supernatant liquid.  Slightly heat the mixture on a hot plate for 15 mintues, and suction filter the mixture after it has cooled to room temperature.  Wash with ice-cold water, followed by cold 6M HCl.  Finally, wash with ethanol followed by acetone, and dry at 100°C for 30 minutes.  Measure the yield.

Cobalt Complex Solutions^5,6

     Using HNO₃, prepare exactly 100 mL of two solutions that are approximately 0.10 M and 0.30 M [H₃O⁺].   The concentrations need not be exact, but the second solution should be exactly three times the concentration as the first.  Then weigh, accurately by difference, enough of the [Co(NH₃)₅Cl]Cl₂ that you synthesized to give two 100 mL solutions of concentration 1.2 × 10^-2 M.  Note that the complex does not easily dissolve; grind the solid prior to weighing.  Using several mL of the above acid solution, wash the solid into the volumetric flask.  Then fill the flask half way and swirl the solution to dissolve the solid.  Finally, fill the flask to the mark with acid solution, label, and repeat for the second flask.

Kinetic Study

     Fill two cuvettes with each of your solutions, and a third cuvette with deionized H₂O as a blank.  The spectroscopy should be conducted at 50°C.  In the HP 8452A UV-Vis spectrophotometer, measure the absorbance at 550 nm for each cell every 10 minutes for four hours.

     Assume a first order dependence of the rate of reaction on the complex formation.  The predicted rate law is then:

Rate = k_obs[complex]

     The evaluation of k_obs may be made from a first order kinetic plot of your data.  If the reaction is acid catalyzed, the rate law will be:

Rate = k[complex][H₃O⁺]ⁿ, where n = 1, 2, 3, ...

     Since a catalyst is not consumed, [H₃O⁺] is constant.  The rate constant k_obs, therefore will equal k[H₃O⁺]ⁿ.  k_obs can be derived from a plot of the two reactions, allowing the dependence on [H₃O⁺] to be determined.  In order to calculate k_obs from your measurements, you must calculate A_¥, the absorbance at infinite time.  The molar absorptivity of the aquo-complex is 21 cm^-1M^-1 at 550 nm.  The first order rate is equal to the slope of a plot of ln(A-A_¥) versus t, where A is the abosrbance of the solution at time t.

Include the following into your write-up:

1. UV-Vis spectra.
2. Tabulated data of A, A-A_¥, ln(A-A_¥) versus time.
3. Labelled first order plots.
4. Justification for using a plot of ln(A-A_¥) versus time to obtain the first order rate constants, by integrating the zero, first and second order rate laws, and showing the other possible relationships of A and t.
5. Calculation of k_obs constants and their dependence on [H₃O⁺].
6. A statement of the rate law.
7. A proposed mechanism that is consistent with the rate law.

Also address the following questions in your report:

1. What is the yellow-pink, initial precipitate formed in the synthesis of the pentaammine complex?
2.  What is responsible for the dark red colour in the second step of the synthesis?
3.  Account for the fact that trans-[Co(NH₃)₄Cl₂]⁺ undergoes substitution of one Cl^- by water at a rate that is faster by a factor of 1000 versus that of [Co(NH₃)₅Cl]²⁺, despite the fact that both react via the same mechanism.
4. Suggest a method other than spectrophotometry that will allow the determination of the rate of aquation of the cobalt(III) chloro complex.
5. Discuss briefly how square planar substitution reaction mechanisms differ from those of octahedral complexes.

References

1. Cotton, F. A.; Wilkinson, G.; Gaus, P. L., Basic Inorganic Chemistry, 3rd ed., New York: John Wiley & Sons, 1995, pp. 19-25.

2. Wulfsberg, G., Inorganic Chemistry, Sausalito, CA: 2000, pp. 839-877.

3. Belluco, U.; Ettorre, R.; Basolo, F.; Pearson, R. G.; Turco, A., Inorg. Chem. 1966, 5, 591, and references therein.

4. Schlessinger, G. G. Inorg. Synth. 1967, 9, 160.

5. This experiment was adapted from a laboratory experiment developed by Karen Henderson, University of Toronto, Scarborough College.

6. Angelici, R. J., Synthesis and Technique in Inorganic Chemistry, 2nd ed., Mill Valley, CA: University Science Books, 1986.  Call number: QD155 .A53 1986

Back to CHEM445 Main Page