The following mechanism is proposed for a reaction run in aqueous solution. Hydronium ion (H3O+) is a catalyst for the reaction.
[Cr(H2O)6]2+(aq) + [Co(NH3)5Cl]2+(aq) → [(H2O)5Cr–Cl–Co(NH3)5]4+(aq) + H2O(l)
[(H2O)5Cr–Cl–Co(NH3)5]4+(aq) + H2O(l) → [Cr(H2O)5Cl]2+(aq) + [Co(NH3)5(H2O)]2+(aq)
[Co(NH3)5(H2O)]2+(aq) + H3O+(aq) → [Co(NH3)4(H2O)2]2+(aq) + NH4+(aq)
[Co(NH3)4(H2O)2]2+(aq) + H3O+(aq) → [Co(NH3)3(H2O)3]2+(aq) + NH4+(aq)
[Co(NH3)3(H2O)3]2+(aq) + H3O+(aq) → [Co(NH3)2(H2O)4]2+(aq) + NH4+(aq)
[Co(NH3)2(H2O)4]2+(aq) + H3O+(aq) → [Co(NH3)(H2O)5]2+(aq) + NH4+(aq)
[Co(NH3)(H2O)5]2+(aq) + H3O+(aq) → [Co(H2O)6]2+(aq) + NH4+(aq)
[Cr(H2O)5Cl]2+(aq) + H2O(l) → [Cr(H2O)6]3+(aq) + Cl–(aq)
a) Write the net reaction associated with the mechanism.
b) Identify the most probable slow step. Explain why you chose this step.
c) Write the rate law for the net reaction. Indicate the order of reaction for each reactant.
a) Write the net reaction associated with the mechanism.
Add all of the reactions together and eliminate species common to both sides of the reaction:
[Cr(H2O)6]2+(aq) + [Co(NH3)5Cl]2+(aq) + 5 H3O+(aq) + H2O(l) → [Cr(H2O)6]3+(aq) + [Co(H2O)6]2+(aq) + 5 NH4+(aq) + Cl–(aq)
b) Identify the most probable slow step. Explain why you chose this step.
The first step in the reaction must be the slowest step. While all of the elementary reactions are bimolecular, five of the reactions involve the hydronium ion, a catalyst that accelerates reaction rates. Two of the elementary reactions have water, the solvent, as a reactant. Although the magnitude of the rate constants for these reactions is not known, the high concentration of the water solvent means that the reactions must be relatively fast. This leaves only the first step to be rate-limiting.
c) Write the rate law for the net reaction. Indicate the order of reaction for each reactant.
Using the first step as the rate-limiting reaction gives the rate law for the net reaction:
Rate = k1[ [Cr(H2O)6]2+][ [Co(NH3)5Cl]2+]
The reaction is first order in [Cr(H2O)6]2+, first order in [Co(NH3)5Cl]2+, zero order in hydronium ion and zero order in water. The total order of reaction is 2.