Problem 27 - Chemistry The Central Science

Question

The average bond enthalpies of the \(\mathrm{C}-\mathrm{F}\) and \(\mathrm{C}-\) Cl bonds are 485 \(\mathrm{kJ} / \mathrm{mol}\) and 328 \(\mathrm{kJ} / \mathrm{mol}\) , respectively. (a) What is the maximum wavelength that a photon can possess and still have sufficient energy to break the \(\mathrm{C}-\mathrm{F}\) and \(\mathrm{C}-\mathrm{Cl}\) bonds, respectively? (b) Given the fact that \(\mathrm{O}_{2}, \mathrm{N}_{2},\) and \(\mathrm{O}\) in the upper atmosphere absorb most of the light with wavelengths shorter than \(240 \mathrm{nm},\) would you expect the photodissociation of \(\mathrm{C}-\mathrm{F}\) bonds to be significant in the lower atmosphere?

Step-by-Step Solution

Answer

The maximum wavelengths for breaking the C-F and C-Cl bonds are calculated using Planck's equation, \(E = \dfrac{hc}{\lambda}\), with the given bond enthalpies of 485 kJ/mol and 328 kJ/mol, respectively. After calculations, we compare the maximum wavelength of the C-F bond with 240 nm to determine if the photodissociation of C-F bonds is significant in the lower atmosphere. If the maximum wavelength of the C-F bond is larger than 240 nm, the photodissociation would not be significant in the lower atmosphere.

Step 1: Calculate maximum wavelength for C-F bond

First, we will calculate the maximum wavelength for the C-F bond. We will use the Planck's equation and set the energy equal to the average bond enthalpy: \(E_{CF} = \dfrac{hc}{\lambda_{CF}}\) Given: \(E_{CF} = 485 kJ/mol\) Convert the energy to joules: \(E_{CF} = 485 \times 10^{3} J/mol\) Now, solve for the maximum wavelength (\(\lambda_{CF}\)): \(\lambda_{CF} = \dfrac{hc}{E_{CF}}\)

Step 2: Calculate maximum wavelength for C-Cl bond

Next, we will calculate the maximum wavelength for the C-Cl bond. We will use the same approach, setting the energy equal to the average bond enthalpy: \(E_{C-Cl} = \dfrac{hc}{\lambda_{C-Cl}}\) Given: \(E_{C-Cl} = 328 kJ/mol\) Convert the energy to joules: \(E_{C-Cl} = 328 \times 10^{3} J/mol\) Now, solve for the maximum wavelength (\(\lambda_{C-Cl}\)): \(\lambda_{C-Cl} = \dfrac{hc}{E_{C-Cl}}\)

Step 3: Determine if photodissociation is significant in the lower atmosphere

We'll compare the maximum wavelength of the C-F bond with 240 nm to determine if the photodissociation of C-F bonds is significant in the lower atmosphere. If the maximum wavelength of the C-F bond is larger than 240 nm, then C-F bonds would not absorb enough energy from light to break, and the photodissociation would not be significant in the lower atmosphere.

Step 4: Putting it all together

We have learned that: 1. To find the maximum wavelength that can break a bond, we use the Planck's equation \(E = \dfrac{hc}{\lambda}\), where E represents the bond energy, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. 2. We calculated the maximum wavelengths for both the C-F and C-Cl bonds using the provided bond enthalpies. 3. We compared the maximum wavelength for the C-F bond with the cutoff value of 240 nm to determine if the photodissociation would be significant in the lower atmosphere.

Key Concepts

Photon Energy

Photon energy is a fundamental concept in chemistry and physics. It refers to the energy carried by a single photon, which is the smallest measurable unit of light and other forms of electromagnetic radiation. To calculate photon energy, you can use Planck's equation, given by: \[ E = \frac{hc}{\lambda} \] Where:

• \(E\) represents photon energy
• \(h\) is Planck's constant \(6.626 \times 10^{-34} \mathrm{J \cdot s}\)
• \(c\) is the speed of light \(3.00 \times 10^{8} \mathrm{m/s}\)
• \(\lambda\) stands for wavelength

The energy of a photon is inversely proportional to its wavelength. This means that shorter wavelengths correspond to higher energies. Photons with sufficient energy can break chemical bonds, leading to reactions such as photodissociation.

Photodissociation

Photodissociation refers to the breaking of a chemical bond in a molecule due to the absorption of a photon. This process plays a significant role in atmospheric chemistry, as it can affect the stability and concentration of various gases in the atmosphere.
For example, when a molecule absorbs a photon with enough energy, the energy is transferred to the bond, causing it to break. This can lead to the formation of reactive fragments or radicals. In the context of the C-F bond, we evaluate whether the absorbed photon wavelength is enough to break the bond. Given the bond energy, if the photon energy (calculated using the wavelength) does not surpass this value in the lower atmosphere, the photodissociation will not be significant.
Lower energy (longer wavelength) photons fail to provide the necessary energy to break the bond. This assessment helps determine the behavior and lifetime of chemicals in atmospheric layers.

Wavelength Calculation

Calculating the maximum wavelength that can still effectively break a chemical bond is crucial in various fields, such as chemistry and environmental science. The process involves using the bond enthalpy in conjunction with Planck's equation to find the longest wavelength that will induce photodissociation.
Steps to calculate the maximum wavelength are:

• Start with the bond enthalpy (e.g., \(485\ \mathrm{kJ/mol}\) for a C-F bond)
• Convert bond enthalpy to Joules per molecule to use in photon energy terms
• Use Planck's equation \(\lambda = \frac{hc}{E}\) to find the wavelength \(\lambda\)

If the calculated maximum wavelength is longer than the cutoff wavelength (e.g., 240 nm), photons in the natural environment will not provide enough energy to break the bond.
This calculation is vital for predicting how different compounds behave under solar radiation, especially in understanding atmospheric chemistry and the potential for pollutants to break down in the lower atmosphere.