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: $$\mathrm{CH}_{2} \mathrm{O}+h \nu \longrightarrow \mathrm{CHO}+\mathrm{H}$$ 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

The light with a wavelength of 335 nm is found in the UV-A region of the electromagnetic spectrum. The maximum strength of a bond that can be broken by absorption of a photon of 335 nm light is approximately 357.25 kJ/mol. Comparing this value to the table value for a C-H bond strength (414 kJ/mol) indicates that 335 nm light might not provide enough energy to break the C-H bond in formaldehyde, but other bonds could be broken instead. The formaldehyde photodissociation reaction with Lewis-dot structures can be written as: O=C-H + hν → O=C• + •H

Step-by-step solution

(a) Identifying the Electromagnetic Spectrum Region

To determine the part of the electromagnetic spectrum where the light with wavelength 335 nm is found, we need to know the common wavelength ranges for each region. The electromagnetic spectrum is typically categorized into the following ranges: - UV-C: 100-280 nm - UV-B: 280-315 nm - UV-A: 315-400 nm - Visible: 400-700 nm - Infrared: 700 nm - 1 mm As 335 nm falls within the range of 315-400 nm, it is in the UV-A region of the electromagnetic spectrum.

(b) Calculating Maximum Bond Strength

To find the maximum strength of a bond (in kJ/mol) that can be broken by the absorption of a photon of 335 nm light, we will first need to calculate the energy of a single photon with that wavelength. We can use the formula: \[E = \frac{hc}{\lambda}\] where: E is the photon energy, h is the Planck's constant (\(6.626 \times 10^{-34} \text{ Js}\)), c is the speed of light (\(3.0 \times 10^8 \text{ m/s}\)), λ is the wavelength of the light in meters (335 nm in this case). Next, convert the wavelength from nanometers to meters: \(335 \text{ nm} = 335 \times 10^{-9} \text{ m}\) Now, we can calculate the photon energy: \[E = \frac{(6.626 \times 10^{-34} \text{ Js})(3.0 \times 10^8 \text{ m/s})}{335 \times 10^{-9} \text{ m}}\] \[E \approx 5.932 \times 10^{-19} \text{ J}\] To convert the photon energy to kJ/mol, we need to multiply by Avogadro's number (\(6.022 \times 10^{23} \text{mol}^{-1}\)) and divide by \(10^3\) to convert from J to kJ: \[\frac{5.932 \times 10^{-19} \text{ J} \times 6.022 \times 10^{23} \text{mol}^{-1}}{10^3} = 357.25 \text{ kJ/mol}\] Thus, the maximum strength of a bond that can be broken by absorption of a photon of 335 nm light is approximately 357.25 kJ/mol.

(c) Comparing Bond Strengths

We are asked to compare the calculated bond strength (357.25 kJ/mol) to the appropriate value from Table 8.4. Since formaldehyde has a C-H bond, we need to find the value for a C-H bond in the table. The table value for a C-H bond strength is approximately 414 kJ/mol. Our calculated bond strength (357.25 kJ/mol) is slightly less than the C-H bond strength from the table (414 kJ/mol), which may indicate that the light with a wavelength of 335 nm might not provide enough energy to break the C-H bond in formaldehyde. However, it is important to note that other bonds present in formaldehyde could be broken instead.

(d) Writing Lewis-Dot Structures for Photodissociation

To represent the formaldehyde photodissociation reaction, showing the Lewis-dot structures for each molecule, we can draw the structures as follows: CH2O (formaldehyde): O=C-H, H attached to C CHO (formyloxyl radical): O=C•, H attached to C H (hydrogen atom): • Now, we can write the formaldehyde photodissociation reaction: O=C-H + hν → O=C• + •H In this reaction, the absorption of light energy (hν) dissociates formaldehyde (O=C-H) into a formyloxyl radical (O=C•) and a hydrogen atom (•H).

Key concepts

Formaldehyde

Formaldehyde, with the chemical formula \( \mathrm{CH}_2\mathrm{O} \), is a simple organic compound composed of carbon, hydrogen, and oxygen. It is an aldehyde, a group of chemical substances commonly used in industrial applications. Formaldehyde is known for being highly reactive and a significant constituent in various chemical reactions.

• It is a colorless gas at room temperature with a distinct pungent smell.
• It naturally occurs in the environment, mostly during the decay of organic materials.
• In automotive exhaust, formaldehyde can form through incomplete combustion, contributing to air pollution.

Formaldehyde is also well-studied for its role in photodissociation. This process occurs when it absorbs light energy and breaks down into smaller molecular fragments, an important reaction behind the formation of smog.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses the entire range of electromagnetic radiation, varying in wavelength and frequency. It includes an array of electromagnetic waves, from longer wavelengths like radio waves to shorter ones like gamma rays.

• Each region of the spectrum has its own typical wavelength range and energy level.
• Light in the ultraviolet (UV) region, specifically, holds enough energy to cause various photochemical reactions.

When discussing formaldehyde photodissociation, we focus on UV-A light, which spans wavelengths from 315 nm to 400 nm. Light at 335 nm falls within this range, meaning it belongs to the UV-A part of the electromagnetic spectrum. UV-A light has lower energy compared to UV-B and UV-C, making it less potent in initiating high-energy reactions but still plays a role in inducing reactions like the breakdown of formaldehyde.

Bond Energy

Bond energy refers to the measure of bond strength within a chemical compound. It is defined as the amount of energy required to break one mole of bonds in a chemical substance.

• The higher the bond energy, the stronger the bond.
• The energy required is usually expressed in kilojoules per mole (kJ/mol).

In formaldehyde, bonds between carbon and hydrogen (C-H) are an important consideration when studying reactions. For instance, when calculating the maximum bond strength that UV-A light at 335 nm could break, we found it to be approximately 357.25 kJ/mol. This value is slightly lower than the standard bond energy for a C-H bond, which is about 414 kJ/mol. This implies that while the energy from UV-A light at this wavelength may not suffice to break a C-H bond, it might still affect other bonds within the formaldehyde molecule.

Lewis-dot Structures

Lewis-dot structures are diagrams that represent the bonding between atoms in a molecule and the lone pairs of electrons that may exist. They are useful for visualizing the structure and stability of molecules.

• Each dot in the Lewis-dot structure represents a valence electron.
• These structures help predict the arrangement of atoms within a molecule.

For photodissociation of formaldehyde, we write the Lewis-dot structure as follows:

- The formaldehyde molecule (\( \mathrm{CH}_2\mathrm{O} \)) can be represented as \( \text{O=C-H}_2 \), with oxygen double-bonded to carbon and two hydrogens single-bonded to carbon.- Upon absorption of light energy (\( hu \)), formaldehyde dissociates into a formyloxyl radical \( \text{O=C}\cdot \) and a hydrogen atom \( \cdot \text{H} \).
This representation allows us to understand the changes occurring in the bonding structure during photodissociation. The Lewis-dot structures help emphasize the electron rearrangement in molecules during chemical reactions, aiding in visualizing how the absorption of light leads to breaking and forming new bonds.