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 NO, 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? (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 the Lewis dot and VSEPR structures of NO, NO2, and N2, we need to follow these steps: 1. Count the total number of valence electrons for each molecule. 2. Place the atoms around the central atom to form a skeleton structure. 3. Distribute the valence electrons as lone pairs or in bonds. \(NO\) - Valence electrons: 5 (N) + 6 (O) = 11 electrons - Lewis structure: O≡N \(+\) - VSEPR Shape: Linear \(NO_2\) - Valence electrons: 5 (N) + 6 (O) × 2 = 17 electrons - Lewis structure: O=N=O with a single unpaired electron on the nitrogen atom - VSEPR Shape: Bent (approximately \(120^\circ\) bond angle) \(N_2\) - Valence electrons: 5 (N) × 2 = 10 electrons - Lewis structure: N≡N - VSEPR Shape: Linear

To find the bond energies and the corresponding region in the electromagnetic spectrum, we need to consult a resource such as Table 8.3 for bond energies: \(NO\) bond energy: \(607 kJ/mol\) \(N=O\) bond energy (in \(NO_2\)): \(607 kJ/mol\) \(N-N\) triple bond energy (in \(N_2\)): \(941 kJ/mol\) Note that a real resource such as "CRC Handbook of Chemistry and Physics" should be used for most accurate values. We can now convert the bond energy values to wavelengths in the electromagnetic spectrum using the formula: \(E = h * c / \lambda\) where \(E\) is the bond energy, \(h\) is the Planck's constant (\(6.626 \times 10^{-34} Js\)), \(c\) is the speed of light (\(3 \times 10^8 m/s\)), and \(\lambda\) is the wavelength. Now we can calculate the wavelengths corresponding to the respective bond energies: \(NO\): Wavelength = \(6.626 \times 10^{-34} Js * 3 \times 10^8 m/s / (6.07 \times 10^2 J/mol) = 3.3 \times 10^{-7} m\) which is in the UV region \(NO_2\): Wavelength = \(6.626 \times 10^{-34} Js * 3 \times 10^8 m/s / (6.07 \times 10^2 J/mol) = 3.3 \times 10^{-7} m\) which is also in the UV region \(N_2\): Wavelength = \(6.626 \times 10^{-34} Js * 3 \times 10^8 m/s / (9.41 \times 10^2 J/mol) = 2.1 \times 10^{-7} m\) which is also in the UV region

To monitor the conversion of NOx into N2, we need to design a spectroscopic experiment that tracks changes in the ultraviolet region of the electromagnetic spectrum. The experiment must continuously monitor and detect the wavelengths of light that we calculated in part (b) as a function of time. 1. Prepare a gas cell that allows ultraviolet light to pass through. Fill it with a sample of NOx waste stream gases along with a catalyst that facilitates the conversion of NOx to N2. 2. Set up an ultraviolet spectrophotometer to monitor the wavelengths corresponding to the bond energies of NO, NO2, and N2 (around \(3.3 \times 10^{-7} m\) and \(2.1 \times 10^{-7} m\)). 3. Begin the experiment by shining ultraviolet light through the gas cell and continuously record the absorption spectra as a function of time. 4. Analyze the recorded data to determine the extent of conversion of NOx species into N2 by observing changes in the absorption spectrum corresponding to the specific wavelengths. By continuously monitoring the ultraviolet absorption spectra at the wavelengths of interest, we can track the progress of the conversion of NOx species into N2 in real-time.