The \(\mathrm{NO}_{x}\) waste stream from automobile exhaust includes species such as \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\). Catalysts that convert these species to \(\mathrm{N}_{2}\) are desirable to reduce air pollution. (a) Draw the Lewis dot and VSEPR structures of \(\mathrm{NO}, \mathrm{NO}_{2}\), and \(\mathrm{N}_{2} .(\mathbf{b})\) Using a resource such as Table 8.3 , look up the energies of the bonds in these molecules. In what region of the electromagnetic spectrum are these energies? \((\mathbf{c})\) Design a spectroscopic experiment to monitor the conversion of \(\mathrm{NO}_{x}\) into \(\mathrm{N}_{2}\), describing what wavelengths of light need to be monitored as a function of time.

To draw Lewis dot structures: 1. Count the total number of valence electrons present in the molecule. 2. Place the least electronegative atom (other than hydrogen) in the center of the molecule. 3. Distribute the remaining valence electrons as lone pairs or bonding electrons. For NO: 1. Nitrogen has 5 valence electrons, and oxygen has 6 valence electrons, so the total number of valence electrons is 11. 2. Nitrogen is the central atom since it is less electronegative than oxygen. 3. Distribute the remaining electrons by arranging as follows: - Nitrogen forms a double bond (4 electrons) with oxygen. - Place one lone pair (2 electrons) on the nitrogen. - Place two lone pairs (4 electrons) on the oxygen. - Assign the remaining electron as an unpaired electron to nitrogen. For NO2: 1. Nitrogen has 5 valence electrons, and each oxygen has 6 valence electrons, totaling 17 valence electrons. 2. Nitrogen is the central atom. 3. Distribute the remaining electrons by arranging as follows: - Nitrogen forms a double bond (4 electrons) with one oxygen and a single bond (2 electrons) with the other oxygen. - Place two lone pairs (4 electrons) on the double-bonded oxygen and three lone pairs (6 electrons) on the single-bonded oxygen. - Assign the remaining electron as an unpaired electron to nitrogen. For N2: 1. Each nitrogen has 5 valence electrons, totaling 10 valence electrons. 2. Both atoms are nitrogen, so they both form the bond. 3. Distribute the remaining electrons by arranging as follows: - Nitrogen forms a triple bond (6 electrons) with the other nitrogen. - Place one lone pair (2 electrons) on each nitrogen.

To draw VSEPR structures: 1. Identify the electron groups (both bonding and lone pairs) surrounding the central atom. 2. Determine the electron-pair geometry using the number of electron groups. 3. Determine the molecular geometry using the positions of the bonded atoms. For NO: 1. Nitrogen has 3 electron groups (1 double bond, 1 lone pair, and 1 unpaired electron). 2. Three electron groups result in a trigonal planar electron-pair geometry. 3. Since there is one lone pair/unpaired electron, the molecular geometry is bent. For NO2: 1. Nitrogen has 3 electron groups (1 double bond, 1 single bond, and 1 unpaired electron). 2. Three electron groups result in a trigonal planar electron-pair geometry. 3. Since there is one lone pair/unpaired electron, the molecular geometry is bent. For N2: 1. Nitrogen has 2 electron groups (1 triple bond). 2. Two electron groups result in a linear electron-pair geometry. 3. There are no lone pairs, so the molecular geometry is linear.

Use a reference source, such as a chemistry textbook or data tables, to find the bond energies for the bonds in the molecules: - N≡N bond in N2: 941 kJ/mol - N=O bond in NO: 605 kJ/mol - N=O bond in NO2: 607 kJ/mol - N-O bond in NO2: 201 kJ/mol

In order to determine the region of the electromagnetic spectrum associated with these bond energies, we can use the energy-wavelength relationship given by: \(E = h\times c / \lambda\) where E is the energy, h is Planck's constant (6.63×10^{-34} Js), c is the speed of light (3×10^8 m/s), and λ is the wavelength. - For the N≡N bond: - Wavelength, λ = \( \frac {h\times c}{E} \) = \( \frac {6.63 \times 10^{-34} \times 3 \times 10^8}{9.41 \times 10^5} \) ≈ 2.11×10^{-8} meters - For the N=O bond: - Wavelength, λ = \( \frac {h\times c}{E} \) = \( \frac {6.63 \times 10^{-34} \times 3 \times 10^8}{6.05 \times 10^5} \) ≈ 3.28×10^{-8} meters - For the N-O bond: - Wavelength, λ = \( \frac {h\times c}{E} \) = \( \frac {6.63 \times 10^{-34} \times 3 \times 10^8}{2.01 \times 10^5} \) ≈ 9.89×10^{-8} meters These wavelengths correspond to the ultraviolet region of the electromagnetic spectrum.

To design a spectroscopic experiment that monitors the conversion of NOx into N2, we need to observe the changes in the absorption spectra at the wavelengths corresponding to the bond energies. 1. Prepare a sample of the NOx waste stream containing NO and NO2 species. 2. Use a UV spectrometer to monitor the absorption of light at the specific wavelengths associated with the bond energies of N=O (3.28×10^{-8} m) and N-O (9.89×10^{-8} m) in the NOx compounds. 3. As the reaction progresses, the intensity of these absorptions should decrease, indicating the conversion of NO and NO2 species to N2. 4. Simultaneously, monitor the wavelength associated with the N≡N bond (2.11×10^{-8} m) to observe the formation of N2. As the conversion occurs, the intensity of this absorption should increase. 5. Continue monitoring the changes in absorption intensities as a function of time, allowing us to track the progress of the conversion from NOx species to N2.