Answer

1. Predict the spin-only magnetic moment (in units of Bohr-Magnetons) for the following complexes:

a. fac-[Co(NH₃)₃Cl₃]

This is Co³⁺, d⁶, with 3 weak ligands and 3 borderline ligands, so the complex is probably high spin with S = 2 and n = 4 so μ = [4(4+2)]^½ = 4.90 μ_B

b. trans-[Cr(ox)₂Br₂]^4–

This is Cr²⁺, d⁴, with all weak ligands so the complex is high spin with S = 2 and n = 4 so μ = [4(4+2)]^½ = 4.90 μ_B

c. trans-[Cr(en)₂(CN)₂]

This is Cr²⁺, d⁴, with all strong ligands so the complex is low spin with S = 1 and n = 2 so μ = [2(2+2)]^½ = 2.83 μ_B

2. The rate data shown below was found for the reaction:

[Co(NH₃)₅X]²⁺ + OH^– → [Co(NH₃)₅OH]²⁺ + X^–

What is the order of the reaction? Is this enough information to determine the mechanism of the reaction? If so, what is the mechanism? If not, does it limit the mechanistic options (give the possibilities if this is the case)? What drives the trend in the rate constants? Does this help determine the mechanism? Why or why not?

The units of the rate constant indicate that the reaction is second order, which means either an A or I mechanism. The rate constants follow the order of the size and LFSE of the ligands, i.e., the smallest ligand (F^–) and largest LFSE is the slowest rate. This suggests that the intermediate is directly bonded to the metal, implying an A mechanism. The stronger ligand binds more strongly to the metal in the intermediate, which slows down the overall rate.

3. The rate data shown below was found for the reaction:

[Co(NH₃)₅X]²⁺ + [Cr(H₂O)₆]²⁺ → Co²⁺ + 5 NH₃ + [Cr(H₂O)₅X]²⁺ + H₂O

What is the order of the reaction? Is this enough information to determine the mechanism of the reaction? If so, what is the mechanism? If not, does it limit the mechanistic options (give the possibilities if this is the case)? What drives the trend in the rate constants? Does this help determine the mechanism? Why or why not?

The units of the rate constant indicate a second order reaction, as expected for an electron transfer reaction. The order of the reaction does not indicate the mechanism but the trend in the rate constants suggests that the halide is involved in the intermediate. Further, since the halide ends being transferred from the Co-ion to the Cr-ion, it is likely that the reaction occurs via an inner sphere mechanism. The rates follow the trend of the spectrochemical series, with the weakest ligand (I^–) has the fastest rate. This is because the LFSE is smallest, allowing the metal-ligand bond to break most easily.