1. 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 ΔH‡= 61.6 ± 3.4 kJ mol–1 and ΔS‡= 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 1.23 Ms- 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 value at 298K? Is the reaction spontaneous?
2. What are the three main intermolecular forces? Which one describes the intermolecular forces in water? In terms of enthalpy and entropy,why does sodium azide dissolve spontaneously in water?
a. To find the rate constant, we can use the rate equation provided: Rate = k[Ru][N3-]. Given that the rate of reaction is 1.23 Ms-1, the concentration of the Ru cluster is 0.050 M, and the azide concentration is 0.025 M, we can substitute these values into the rate equation:
1.23 Ms-1 = k * (0.050 M) * (0.025 M)
Solving for k, we get:
k = 1.23 Ms-1 / ((0.050 M) * (0.025 M)) = 984 Ms-1
Therefore, the rate constant is 984 Ms-1.
b. The free energy change (ΔG) at 298K can be calculated using the equation ΔG = ΔH - TΔS, where ΔH is the enthalpy change and ΔS is the entropy change. The activation parameters provided are ΔH‡ = 61.6 ± 3.4 kJ mol-1 and ΔS‡ = 3.5 ± 11.8 J K-1 mol-1.
Since the values for ΔH and ΔS have uncertainties, we cannot directly calculate ΔG with certainty. However, we can still estimate the free energy value by assuming that the uncertainties are negligible. Using the given values without uncertainties:
ΔG = ΔH - TΔS = (61.6 kJ mol-1) - (298 K * (3.5 J K-1 mol-1) / 1000) = 61.6 kJ mol-1 - 1.043 kJ mol-1 = 60.557 kJ mol-1
To determine if the reaction is spontaneous, we check the sign of ΔG. If ΔG < 0, the reaction is spontaneous. If ΔG > 0, the reaction is non-spontaneous.
In this case, the calculated value of ΔG is positive (60.557 kJ mol-1). Therefore, the reaction is non-spontaneous. However, this conclusion may change if the uncertainties are taken into account.
2. The three main intermolecular forces are:
a) London dispersion forces: These are caused by temporary fluctuations in electron density, giving rise to instantaneous dipoles that can induce dipoles in neighboring molecules.
b) Dipole-dipole forces: These occur between polar molecules, where the positive end of one molecule is attracted to the negative end of another.
c) Hydrogen bonding: This is a special type of dipole-dipole force that occurs when a hydrogen atom is bonded to a highly electronegative atom (such as nitrogen, oxygen, or fluorine) and interacts with another electronegative atom through a lone pair of electrons.
In water (H2O), the intermolecular forces primarily responsible are hydrogen bonding. The oxygen atom in water is highly electronegative and can form hydrogen bonds with the hydrogen atoms of neighboring water molecules.
Sodium azide (NaN3) dissolves spontaneously in water due to a favorable enthalpy and entropy change. The enthalpy change is driven by the strong ion-dipole interactions between the polar water molecules and the ionic sodium and azide ions. The entropy change is driven by the increased disorder when the sodium azide solid dissociates into individual ions in solution. Overall, the increase in entropy dominates, making the dissolution spontaneous.