Question

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.

Short answer

In summary, the following are the answers for each part: (a) The Lewis dot and VSEPR structures of the molecules: - NO: O≡N+, linear - NO2: O=N=O with a single unpaired electron on the nitrogen atom, bent - N2: N≡N, linear. (b) The bond energies for each molecule and their corresponding electromagnetic spectrum region: - NO: 607 kJ/mol, UV region - NO2: 607 kJ/mol, UV region - N2: 941 kJ/mol, UV region. (c) To design a spectroscopic experiment to monitor the conversion of NOx into N2, 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 \(2.1 \times 10^{-7} m\)). Fill a gas cell with a sample of NOx waste stream gases and a catalyst, shine ultraviolet light through the gas cell, and continuously record the absorption spectra as a function of time. Analyze the data to determine the extent of conversion of NOx species into N2.

Step-by-step solution

Part (a): Lewis dot and VSEPR structures

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

Part (b): Bond energies and electromagnetic spectrum region

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

Part (c): Design a spectroscopic experiment

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.

Key concepts

Lewis Structures

Lewis structures are diagrams that represent the bonds between atoms in a molecule and the lone pairs of electrons that may exist. To draw a Lewis structure:

• Count all the valence electrons for the molecule.
• Determine the central atom (often the least electronegative).
• Use pairs of electrons to form bonds between atoms.
• Distribute remaining electrons to satisfy the octet rule, if possible.

For example, in nitrogen monoxide ( NO ), we have 11 valence electrons. Nitrogen oxide has a Lewis structure with a triple bond between N and O, resulting in an O≡N extsuperscript{+} structure. It's crucial for correctly predicting the geometry and reactivity of molecules.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory helps predict the shape of molecules. According to VSEPR:

• Electron pairs around a central atom will arrange themselves to be as far apart as possible.
• This minimizes repulsion and defines the geometry of the molecule.

For NO , the shape is linear due to no lone pairs affecting its shape. For NO_2 , with a bent bond angle approximating 120°, the shape is bent due to lone electrons on nitrogen. These shapes are important for understanding how molecules interact with each other and their environments.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation. For bond energies in molecules like NO and N_2 , the relevant part of the spectrum is the ultraviolet region.

• The UV region ranges from 10 to 400 nm in wavelength.
• This region has enough energy to affect electronic transitions, which are crucial for studying bond energies and photochemical reactions.

Understanding where a molecule's bond energy falls in the electromagnetic spectrum can help predict its behavior when exposed to light, which is vital for applications in fields like spectroscopy.

Spectroscopy

Spectroscopy involves studying the interaction between matter and electromagnetic radiation to infer properties of substances. In the context of monitoring NO_x conversion to N_2 :

• An ultraviolet spectrophotometer can measure absorption, shedding light on bond energies and molecular transformations.
• By analyzing absorbed wavelengths, one can deduce structural changes and reaction kinetics.

This method, especially useful in real-time analysis, helps track chemical reactions and monitor changes efficiently. Spectroscopy is thus an invaluable tool in understanding and controlling chemical processes.

Catalysis

Catalysis accelerates a chemical reaction by lowering its activation energy, without the catalyst itself being consumed. In reducing NO_x to N_2 :

• Catalysts are crucial in converting harmful emissions into harmless nitrogen gas.
• They provide an alternative pathway for reactions, making them faster and more efficient.
• This is particularly useful in industrial processes, including pollution control.

By using catalysts, industries can efficiently reduce emissions, contributing to environmental protection and sustainability. Catalysis plays a key role in chemical transformations necessary for air quality management.

Air Pollution Control

Air pollution control encompasses methods to reduce harmful emissions into the atmosphere. Techniques like catalytic conversion are essential:

• They transform harmful compounds like NO_x in vehicle exhaust into less dangerous emissions.
• Efficient air pollution control technologies are vital for maintaining a clean environment and safeguarding public health.
• These methods help meet environmental regulations and reduce the impact of human activity.

Continued innovation in air pollution control is critical to managing and reducing the negative effects of industrial and vehicular emissions on the environment.