Question

Alcohol-based fuels for automobiles lead to the production of formaldehyde (CH \(_{2} \mathrm{O} )\) in exhaust gases. Formaldehyde undergoes photodissociation, which contributes to photo-chemical 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 -nm light? (c) Compare your answer from part (b) to the appropriate value from Table \(8.3 .\) What do you conclude about \(\mathrm{C}-\mathrm{H}\) bond energy in formaldehyde? (d) Write out the formaldehyde photodissociation reaction, showing Lewis-dot structures.

Short answer

The given wavelength of 335 nm falls within the ultraviolet (UV) part of the electromagnetic spectrum. The maximum bond energy that can be broken by absorption of a photon of 335 nm light is 358 kJ/mol. Comparing this value to Table 8.3, the C-H bond energy in formaldehyde is weaker than the C-H bond energy in methane. The formaldehyde photodissociation reaction with Lewis-dot structures is: H O | | C=O \(+ hv \longrightarrow\) C-H + H

Step-by-step solution

Determine the part of the electromagnetic spectrum

For this step, we need to figure out which part of the electromagnetic spectrum the given wavelength of light (335 nm) falls in. The electromagnetic spectrum is generally divided into the following categories (from longest to shortest wavelength): - Radio waves - Microwaves - Infrared - Visible light - Ultraviolet (UV) - X-rays - Gamma rays 335 nm falls within the ultraviolet (UV) part of the spectrum, which has wavelengths from 10 to 400 nm.

Calculate the maximum bond energy

To calculate the maximum bond energy that can be broken by absorption of a photon of light with a wavelength of 335 nm, we can use the following equation: $$E = \frac{hc}{\lambda}$$ where: - \(E\) is the energy of the photon (in Joules) - \(h\) is the Planck's constant (\(6.626 \times 10^{-34} Js\)) - \(c\) is the speed of light (\(3.00 \times 10^8 ms^{-1}\)) - \(\lambda\) is the wavelength of the light (in meters, so we'll need to convert 335 nm to meters) First, we convert the wavelength to meters: \(335 nm * (1m / 10^9 nm) = 3.35 \times 10^{-7} m\) Now, we can calculate the energy of the photon: $$E = \frac{(6.626 \times 10^{-34} Js) (3.00 \times 10^8 ms^{-1})}{3.35 \times 10^{-7} m} = 5.95 \times 10^{-19} J$$ To find the bond energy in kJ/mol, we need to convert Joules to kJ/mol: $$E_{kJ/mol} = \frac{5.95 \times 10^{-19} J * (1 kJ / 10^3 J) * (6.022 \times 10^{23} mol^{-1})}{1} = 358 kJ/mol$$ So, the maximum bond energy that can be broken by absorption of a photon of 335 nm light is 358 kJ/mol.

Compare bond energy to Table 8.3 and draw conclusions

Comparing our calculated bond energy (358 kJ/mol) to the values in Table 8.3, we notice that the C-H bond energy in formaldehyde is weaker than the C-H bond energy in methane (which is around 414 kJ/mol).

Write out the photodissociation reaction with Lewis-dot structures

Formaldehyde (CH2O) has the following Lewis-dot structure: H | C=O | H After photodissociation, the reaction produces CHO and H: O | C-H + H So, the formaldehyde photodissociation reaction with Lewis-dot structures can be written as: H O | | C=O \(+ hv \longrightarrow\) C-H + H

Key concepts

Understanding the Electromagnetic Spectrum

When we study light and its interactions with matter, a core concept we encounter is the electromagnetic spectrum. This spectrum represents the entire range of electromagnetic radiation, from the longest wavelengths (like radio waves) to the very shortest (like gamma rays). Electromagnetic radiation is a form of energy that travels through space at the speed of light, roughly 299,792 kilometers per second.
In the middle of the spectrum lies the visible light, which is what we can see with our own eyes. Stretching beyond the blue end of visible light, we encounter ultraviolet (UV) radiation. UV has shorter wavelengths and, therefore, more energy compared to visible light. In our textbook problem, it's mentioned that formaldehyde can absorb a photon with a wavelength of 335 nanometers (nm). This places the light in the UV region, which ranges from about 10 to 400 nm. UV light's high energy makes it capable of breaking chemical bonds, leading to phenomena such as photodissociation.

Bond Dissociation Energy Explained

The strength of a chemical bond can be understood through the concept of bond dissociation energy (BDE), which is the amount of energy required to break a bond between two atoms and separate them into individual, gaseous atoms. Measured in kilojoules per mole (kJ/mol), BDE is a crucial factor in chemical reactions.
Let's relate this to our formaldehyde problem. Sunlight or UV light has enough energy to break certain chemical bonds. We calculated that a photon with a wavelength of 335 nm has an energy of about 358 kJ/mol. This value represents the maximum BDE that can be overcome by the photon; in other words, any chemical bond with energy less than or equal to this amount is susceptible to being broken upon absorbing such a photon. The concept of BDE is significant in fields such as environmental chemistry, where the breakdown of pollutants or other chemicals can lead to the formation or reduction of harmful substances.

Photochemical Smog and Its Formation

Photochemical smog is a type of air pollution that's formed when sunlight acts on airborne pollutants, such as nitrogen oxides and volatile organic compounds (VOCs). This reaction results in a mixture of several secondary pollutants, including ozone, peroxyacetyl nitrates, and aldehydes. A classic example of these series of reactions is the photodissociation of formaldehyde, as noted in the textbook exercise.
When the bond within a formaldehyde molecule is broken by UV light, it creates radicals, which are highly reactive species. These radicals can further react with other molecules in the air, perpetuating a cycle of complex chemical reactions that lead to the hazardous cocktail we call photochemical smog. Smog is a public health concern because of its potential to cause or aggravate respiratory problems and other health issues, as well as its role in environmental degradation.

Lewis-Dot Structures and Their Significance

The Lewis-dot structure is a simple but powerful tool used in chemistry to represent the valence electrons of atoms within molecules. In formaldehyde (CH₂O), we depict carbon with four valence electrons, oxygen with six, and each hydrogen with one. These dots are arranged to show how the electrons are shared (in bonds) or unpaired.
In our problem, the photodissociation of formaldehyde leads to the splitting of a C-H bond. The Lewis-dot structure helps us visualize how the electrons are redistributed when formaldehyde absorbs sufficient energy (from a UV photon) to break that bond. By understanding how electrons are shared and moved around, chemists can predict the products of chemical reactions and explain the molecular basis of observed phenomena, such as the formation of photochemical smog.