Question

The gas-phase reaction of \(\mathrm{NO}\) with \(\mathrm{F}_{2}\) to form NOF and \(\mathrm{F}\) has an activation energy of \(E_{a}=6.3 \mathrm{~kJ} / \mathrm{mol}\) and a frequency factor of \(A=6.0 \times 10^{8} \mathrm{M}^{-1} \mathrm{~s}^{-1}\). The reaction is believed to be bimolecular: $$ \mathrm{NO}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{NOF}(g)+\mathrm{F}(g) $$ (a) Calculate the rate constant at \(100^{\circ} \mathrm{C}\). (b) Draw the Lewis structures for the \(\mathrm{NO}\) and the NOF molecules, given that the chemical formula for NOF is misleading because the nitrogen atom is actually the central atom in the molecule. (c) Predict the structure for the NOF molecule. (d) Draw a possible transition state for the formation of NOF, using dashed lines to indicate the weak bonds that are beginning to form. (e) Suggest a reason for the low activation energy for the reaction.

Short answer

(a) The rate constant at \(100^{\circ} \mathrm{C}\) is approximately \(1.1\times 10^6 \,\text{M}^{-1}\text{s}^{-1}\). (b) In the NO molecule, nitrogen and oxygen form a double bond, with one lone pair of electrons on both atoms. In the NOF molecule, nitrogen is the central atom, forming a double bond with oxygen and a single bond with fluorine. Oxygen has two lone pairs, and fluorine has three. (c) The structure of the NOF molecule is bent due to the VSEPR electron pair geometry around the nitrogen atom, which has three electron groups. (d) In the transition state for the formation of NOF, the bond between nitrogen and oxygen, and the bond between the fluorine atoms are partially broken, while new nitrogen-fluorine and oxygen-fluorine bonds are partially formed, represented by dashed lines in the Lewis structure. (e) The low activation energy for the reaction between NO and F2 could be due to the high reactivity of the molecules involved and the strong electrostatic attraction between the positively charged nitrogen atom in NO and the negatively charged fluorine atoms in F2.

Step-by-step solution

Arrhenius Equation

\[ k = A \times e^{-\frac{E_a}{RT}} \] where: k: rate constant; A: frequency factor (\(6.0 \times 10^8 M^{-1} s^{-1}\)); Ea: activation energy (6.3 kJ/mol); R: gas constant (8.314 J/mol K); T: temperature in Kelvin (100°C + 273.15K = 373.15K). Now, we will plug in the values and solve for k.

Calculating k

\[ k = (6.0 \times 10^8 M^{-1} s^{-1}) \times e^{-\frac{6300 J / mol}{(8.314 J / mol K)(373.15 K)}} \] Calculating the result, we get:

Rate constant

\[ k \approx 1.1\times 10^6 \,\text{M}^{-1}\text{s}^{-1} \] (b) Draw the Lewis structures for the NO and NOF molecules

NO Lewis structure

For the NO molecule: - Nitrogen has 5 valence electrons. - Oxygen has 6 valence electrons. These two atoms form a double bond, with one lone pair of electrons on both nitrogen and oxygen.

NOF Lewis structure

For the NOF molecule: - Nitrogen has 5 valence electrons. - Oxygen has 6 valence electrons. - Fluorine has 7 valence electrons. In the NOF molecule, nitrogen is the central atom. Nitrogen forms a double bond with oxygen and a single bond with fluorine. Oxygen has two lone pairs, and fluorine has three lone pairs of electrons. (c) Predict the structure for the NOF molecule

NOF molecule structure

To predict the structure of the NOF molecule, we can use the VSEPR (Valence Shell Electron Pair Repulsion) theory to determine the electron pair geometry. The nitrogen atom has three electron groups surrounding it: a double bond with oxygen, a single bond with fluorine, and a lone pair. This gives it a trigonal planar electron pair geometry. However, because the lone pair occupies more space in the electron cloud, it pushes the bonded atoms closer together, resulting in a bent molecular geometry. (d) Draw a possible transition state for the formation of NOF

Transition state

In the transition state for the formation of the NOF molecule, the bond between the nitrogen and oxygen in NO and the bond between the fluorine atoms in F2 are partially broken, while new bonds (nitrogen-fluorine and oxygen-fluorine) are partially formed. These weak bonds can be represented by dashed lines in the Lewis structure. (e) Suggest a reason for the low activation energy for the reaction

Low activation energy reason

A possible reason for the low activation energy for the reaction between NO and F2 is that the molecules involved are highly reactive. As a result, the reactants can quickly form the transition state, allowing the reaction to proceed with relatively low energy input. Additionally, the presence of a strong electrostatic attraction between the positively charged nitrogen atom in NO and the negatively charged fluorine atoms in F2 may further facilitate the reaction, lowering the activation energy barrier.