Question

Alcohol-based fuels for automobiles lead to the production of formaldehyde \(\left(\mathrm{CH}_{2} \mathrm{O}\right)\) in exhaust gases. Formaldehyde undergoes photodissociation, which contributes to photochemical smog: $$ \mathrm{CH}_{2} \mathrm{O}+h v \longrightarrow \mathrm{CHO}+\mathrm{H} $$ The maximum wavelength of light that can cause this reaction is \(335 \mathrm{~nm}\). (a) In what part of the electromagnetic spectrum is light with this wavelength found? (b) What is the maximum strength of a bond, in \(\mathrm{kJ} / \mathrm{mol}\), that can be broken by absorption of a photon of \(335-\mathrm{nm}\) light? (c) Compare your answer from part (b) to the appropriate value from Table \(8.4\). What do you conclude about the \(\mathrm{C}-\mathrm{H}\) bond energy in formaldehyde? (d) Write out the formaldehyde photodissociation reaction, showing Lewis-dot structures

Short answer

(a) The 335 nm wavelength light belongs to the ultraviolet region of the electromagnetic spectrum. (b) The maximum bond strength that can be broken by a photon of 335-nm light is approximately 298 kJ/mol. (c) Comparing this value to the C-H bond energy (413 kJ/mol) indicates that the bond being broken in formaldehyde is not the C-H bond, but rather the C-O bond. (d) The formaldehyde photodissociation reaction is: H≡C-O + hν → H≡C↓O + H.

Step-by-step solution

a) Identify the electromagnetic spectrum region

To identify the part of the electromagnetic spectrum with a wavelength of 335 nm, compare this value to the known boundaries of wavelength ranges for the different types of electromagnetic radiation. Ultraviolet light ranges from 10 nm to 400 nm. Therefore, since 335 nm falls within this range, the light required to cause the photodissociation reaction belongs to the ultraviolet region.

b) Calculate the maximum bond strength

To find the maximum bond strength that can be broken by absorption of a photon of 335-nm light, we first need to calculate the energy of a single photon using the Planck's relation \(E = h\nu\), where \(E\) is the energy of the photon, \(h\) is the Planck's constant \((6.626 \times 10^{-34}\, \text{Js})\), and \(\nu\) is the frequency of the light. Since the wavelength \(\lambda\) and the frequency \(\nu\) are related by the speed of light, \(c\) (\(c = \lambda\nu\)), we can rewrite this relation as: \[E = \frac{h\,c}{\lambda}\] Plug in the values of \(h\), \(c\), and \(\lambda\), and convert the energy in Joules to kJ/mol: \[E = \frac{(6.626 \times 10^{-34}\, \text{Js})\times(3 \times 10^8\, \text{m/s})}{335 \times 10^{-9}\, \text{m}} \times \frac{10^3\, \text{J}}{1\, \text{kJ}} \times \frac{1\, \text{mol}}{6.022 \times 10^{23}}\] \[E \approx 298\, \text{kJ/mol}\] The maximum bond strength that can be broken by a photon of 335-nm light is approximately 298 kJ/mol.

c) Compare the result to bond energies in Table 8.4

Comparing our calculated value of 298 kJ/mol from part (b) to the value in Table 8.4, for C-H bond energy (413 kJ/mol), we observe that our value is lower than the C-H bond energy. This suggests that the bond being broken in formaldehyde during photodissociation is not the C-H bond, but rather the C-O bond.

d) Write the formaldehyde photodissociation reaction using Lewis-dot structures

The photodissociation reaction of formaldehyde is: \[\text{H}\!\!\equiv\!\!\text{C}\!-\!\text{O} + h\nu \longrightarrow \text{H}\!\!\equiv\!\!\text{C}\!\downarrow\!\text{O} + \text{H}\] In this reaction, ultraviolet radiation causes the breaking of the C-O bond in formaldehyde (HCO), producing a free H atom and a CHO radical.

Key concepts

Photochemical Smog Explained

Photochemical smog is a type of air pollution that's created when sunlight interacts with pollutants in the atmosphere. It typically occurs in urban areas with large amounts of vehicle emissions, which contain compounds like nitrogen oxides and volatile organic compounds (VOCs). These pollutants, under the influence of sunlight, undergo various chemical reactions leading to the creation of secondary pollutants including ozone, peroxyacyl nitrates, and others.

One of the contributors to photochemical smog is formaldehyde (CH₂O), which can be released by automobiles that use alcohol-based fuels. As part of this smog, formaldehyde undergoes a process called photodissociation where it absorbs UV light and breaks down into smaller, often more reactive, particles like the CHO radical and a hydrogen atom. This specific transformation adds to the complexity of smog chemistry and aggravates the pollution problem.

Navigating the Electromagnetic Spectrum

The electromagnetic spectrum depicts the range of all possible frequencies of electromagnetic radiation, from radio waves with the longest wavelengths to gamma rays with the shortest. Visible light, which our eyes can detect, lies roughly in the middle of the spectrum.

When discussing photodissociation in chemistry, we're usually talking about the absorption of ultraviolet (UV) light, which occupies a part of the spectrum with wavelengths between 10 and 400 nanometers (nm). UV light provides enough energy to break certain chemical bonds, leading to the formation of photochemical smog.

UV Light and Chemical Reactions

Chemical reactions, like the dissociation of formaldehyde in the presence of light, require specific wavelengths within the UV range to provide the energy needed for breaking molecular bonds.

Understanding Bond Energy Calculation

Bond energy refers to the amount of energy required to break a chemical bond between two atoms. It is a critical concept in understanding chemical reactions, including photodissociation, as it determines the stability of molecules and the feasibility of chemical processes.

To calculate the bond energy that can be broken by a specific wavelength of light, like the 335 nm involved in formaldehyde photodissociation, we use the formula:
\[E = \frac{h\,c}{\lambda}\]
Here, \(E\) represents the energy of a photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of light. This calculation helps us understand the maximum bond energy that can be interrupted by photon absorption, giving insight into which bonds are susceptible to breaking under light exposure.

Lewis-dot Structures and Photodissociation

Lewis-dot structures provide a visual representation of the valence electrons in atoms and molecules, helping us to understand how atoms bond and react. In the process of photodissociation, these structures can illustrate which bonds are broken when a molecule absorbs light.

For formaldehyde, the Lewis-dot structure emphasizes the bonding between carbon, oxygen, and hydrogen atoms. Absorption of UV light can lead to the breaking of the CO bond, key for the understanding of this molecule's role in photochemical smog formation.

Visualizing Molecular Breakdown

By drawing the Lewis-dot structures before and after photodissociation, we see that the UV light causes the CO bond to break, releasing a hydrogen atom and forming a CHO radical. This visual aid reinforces comprehension of how light energy triggers changes at the molecular level.