Need hewlp with a and b please. Thanks. Kinetics and mechanism of the addition o

Question

Need hewlp with a and b please. Thanks.

Kinetics and mechanism of the addition of azide ion to a carbonyl ligand of [Ru_3(CO)_12]: cluster activation Leon A. P. Kane-Maguire, Monika Manthey and Brett Robinson J. Chenu Soc., Dalton Trans., 1995, 905-908 Spectroscopic studies of the reaction of azide ion with the cluster [Ru_3(CO)_12] in acetone solvent confirmed the occurrence of process (i) under a CO atmosphere. Kinetic measurements of this rapid [Ru_3(CO)_12]+ N_3 -[Ru_3(NCO)(CO)_11]-+ N_2(i) reaction revealed the rate law, Rate =k[Ru][N_3], and the activation parameters Delta 61.6 plusminus 3.4 kJ mol'1 and AS*= 3.5 plusminus 11.8 J K'1 mol'1. These results are consistent with the addition of N_3" to a CO ligand of [Ru_3(CO)_12] to form an intermediate under either steady-state or pre-equilibrium conditions etc. What is the rate constant (with units) if the rate of reaction is 1.23 Ms' and the concentration of the Ru cluster is .050 M and the azide concentration is .025 M? Ignoring the uncertainty values, what is the free energy value at 298K? Is the reaction spontaneous?

Explanation / Answer

a. Rate = k * [Ru][N3-]

Step 1: Subtitute the values

1.23 M s-1 = k * [0.50 M] * [0.25 M]

Step 2: Simplify the right side

1.23 M s-1 = k * 0.125 M2

Step 3: find k with its units

k = 1.23 M s-1 / 0.125 M2 = 9.84 M-1 s-1

b. Step 1: know that dG = dH - TdS and

When:

dG > 0, reaction is not spontaneous.

dG < 0, reaction is spontaneous

Step 2: Put everything in the same units:

dH = 61.6 kj/mol = 61600 J

Step 3: Compute dG

dG = 61600 J/mol - (298 K * 3.5 J/mol K) = 61600 J/mol - 1043 J/mol = 60557 > 0 is not spontaneous

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