Spectroscopic studies of the reaction of azide ion with the cluster [Ru3(CO)12] in acetone solvent confirmed the occurrence of process (i) under a CO atmosphere. Kinetic measurements of this rapid [Ru3(CO)12]+ N3-?[Ru3(NCO)(CO)11]-+ N2(i) reaction revealed the rate law, Rate =k[Ru][N3-], and the activation parameters ?H‡= 61.6 ± 3.4 kJ mol-1 and ?S‡= 3.5 ± 11.8 J K-1 mol-1. These results are consistent with the addition of N3- to a CO ligand of [Ru3(CO)12] to form an intermediate under either steady-state or pre-equilibrium conditions etc.
a. What is the rate constant (with units) if the rate of reaction is 1.23Ms- and the concentration of the Ru cluster is .050 M and the azide concentration is .025 M?
b. Ignoring the uncertainty values, what is the free energy valuye at 298K? Is the reaction spontaneous?