Question

One reaction of a chlorofluorocarbon implicated in the destruction of stratospheric ozone is \(\mathrm{CFCl}_{3}+h v \longrightarrow \mathrm{CFCl}_{2}+\mathrm{Cl}\) (a) What is the energy of the photons ( \(h v\) ) required to bring about this reaction, expressed in kilojoules per mole? (b) What is the frequency and wavelength of the light necessary to produce the reaction? In what portion of the electromagnetic spectrum is this light found?

Short answer

a) The energy of the photons required for the reaction is 159 kJ/mol. b) The frequency and wavelength of the light necessary to produce the reaction are approximately 3.983 x 10^14 Hz and 7.53 x 10^-7 m respectively. This light is found in the visible light portion of the electromagnetic spectrum.

Step-by-step solution

Calculate the Energy for the Reaction

Firstly, the energy change for the reaction (ΔE) needs to be calculated. From the given bond energies, this can be done using the formula: ΔE = (Bond energies of products) - (Bond energies of reactants). For the given reaction, the bond energies are: CFCl3 = 339 kJ/mol, CFCl2 = 339 kJ/mol, and Cl = 159 kJ/mol. So, ΔE = (339 + 159) - 339 = 159 kJ/mol. The energy of the photons needed for the reaction is therefore 159 kJ/mol.

Calculate the Frequency

For calculating the frequency, we can use the equation E = hv. Here, h refers to Planck's constant which is 6.626 x 10^-34 Js. The energy obtained in step 1 should be converted to Joules for calculation which is (159 x 10^3)/6.022 x 10^23 = 2.64 x 10^-19 J. Then, using E = hv, frequency (v) = E/h = 2.64 x 10^-19 J / 6.626 x 10^-34 Js = 3.983 x 10^14 Hz.

Calculate the Wavelength

The wavelength can be calculated using the speed of light equation c = λv, where c is the speed of light (3 x 10^8 m/s). Rearranging this equation we get λ = c/v. Substituting the values, we get λ = (3 x 10^8 m/s)/(3.983 x 10^14 Hz) = 7.53 x 10^-7 m.

Identify the Part of the Electromagnetic Spectrum

The wavelength calculated in the previous step (λ = 7.53 x 10^-7 m) fits into the visible light of the electromagnetic spectrum. Therefore, the light required to produce this reaction can be found in the visible light range of the electromagnetic spectrum.

Key concepts

Chlorofluorocarbon Reactions

Chlorofluorocarbons (CFCs) are chemicals composed of chlorine, fluorine, and carbon. They are known for their role in ozone depletion, an environmental concern that has led to global regulatory measures like the Montreal Protocol.

As detailed in our example, CFCs can undergo photodissociation – a type of chemical reaction where a compound breaks down due to the absorption of light (photons). When a CFC molecule absorbs a photon with sufficient energy, it can break apart into constituent radicals.

For instance, in the reaction \( \mathrm{CFCl}_{3} + hν \longrightarrow \mathrm{CFCl}_{2} + \mathrm{Cl} \), a chlorofluorocarbon molecule breaks down, releasing a chlorine atom. This chlorine atom can then go on to react with ozone, causing its depletion. This is just one step in a cycle of reactions involving chlorine that contribute to stratospheric ozone depletion.

The energy required for this specific reaction is calculated based on the bond energies of reactants and products, emphasizing the need for a precise match between photon energy and the energy required to break molecular bonds.

Photodissociation in Chemistry

Photodissociation is a chemical process by which a molecule is broken down into smaller parts as a result of absorbing light. The term 'photo' refers to light, and 'dissociation' to the breaking of chemical bonds. It's a crucial concept in understanding reactions like the one involving CFCs and ozone depletion.

In the given exercise, photons with a precise energy level are required for the CFC molecule to break down. This energy directly relates to the strength of the chemical bonds within \( \mathrm{CFCl}_{3} \). When the molecule absorbs a photon with energy equal to or greater than the bond energy, it results in the breaking of a bond and the formation of a radical, in this case, a chlorine atom.

Understanding the balance of energy is vital to grasp photodissociation reactions. It connects directly with the energy of the photons, which depends on their frequency and wavelength, concepts rooted in the electromagnetic spectrum of physics.

Electromagnetic Spectrum in Physics

The electromagnetic spectrum encompasses all possible wavelengths and frequencies of electromagnetic radiation, from gamma rays to radio waves. This spectrum is fundamental for understanding the energy and behavior of photons involved in chemical reactions like photodissociation.

Each portion of the spectrum corresponds to a different range of energies. For example, visible light, which occurs in the spectrum where the reaction for CFC breakdown is found, has a specific range of wavelengths and frequencies. In our exercise, the identified wavelength places the required light within the visible spectrum.

By understanding the connection between the energy of photons and their place on the electromagnetic spectrum, students can piece together why certain reactions occur under specific lighting conditions and predict the type of radiation that would initiate similar reactions. This holistic approach ties together photon energy (from chemistry) with its electromagnetic characteristics (from physics), illustrating the interdisciplinary nature of scientific inquiry.