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 8.4 , 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 approach this part of the problem, we will first calculate the total valence electrons for each molecule, then we will draw the Lewis dot structures and finally determine the VSEPR shapes. - For NO: N has 5 valence electrons and O has 6 valence electrons, thus there are a total of 5+6 = 11 valence electrons. Lewis structure: N (triple bond) O • VSEPR structure: Linear - For NO2: N has 5 valence electrons and each O has 6 valence electrons, thus there are a total of 5+6+6 = 17 valence electrons. Lewis structure: N (double bond) O - O • VSEPR structure: Bent - For N2: N has 5 valence electrons, so there are a total of 5+5 = 10 valence electrons. Lewis structure: N (triple bond) N VSEPR structure: Linear

Using Table 8.4 or a similar resource, we can find the bond energies for the molecules: - N≡N bond energy: 941 kJ/mol - N≡O bond energy: 632 kJ/mol - N=O bond energy: 542 kJ/mol Now, we can use this information to identify in what region of the electromagnetic spectrum these energies are. Bond energies are related to the energies of photons by the equation: Energy = h * frequency where h is Planck's constant (6.626 x 10^(-34) Js) and frequency can be related to the wavelength using the speed of light (c = 3 x 10^8 m/s): frequency = c / wavelength Thus, we can calculate the minimum wavelength of light corresponding to each bond energy: - For N≡N bond energy: wavelength = (6.626 x 10^(-34) * 3 x 10^8) / (941 x 10^3 * 6.022 x 10^23) ≈ 198 nm (Ultraviolet) - For N≡O bond energy: wavelength = (6.626 x 10^(-34) * 3 x 10^8) / (632 x 10^3 * 6.022 x 10^23) ≈ 299 nm (Ultraviolet) - For N=O bond energy: wavelength = (6.626 x 10^(-34) * 3 x 10^8) / (542 x 10^3 * 6.022 x 10^23) ≈ 330 nm (Ultraviolet) Therefore, the relevant bond energies are in the ultraviolet region of the electromagnetic spectrum.

To monitor the conversion of NOx molecules into N2, we can use absorption or emission spectroscopy in the ultraviolet region. This is because we need to detect the presence of nitrogen and oxygen bonds, which we found to have energies in the UV region, in order to track the reactions. In the experiment, we can monitor the absorbance or emission of light at wavelengths corresponding to the bond energies of relevant species (198 nm for N≡N, 299 nm for N≡O, and 330 nm for N=O), while providing the catalyst and controlling the reaction conditions such as temperature and pressure. By recording the changes in absorbance or emission intensity at these wavelengths over time, it will be possible to track the formation and consumption of NO, NO2, and N2 molecules. The corresponding time-dependence of the signals can be used to determine the progress of the catalytic conversion of NOx into N2.