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Ch.18 - Chemistry of the Environment
All textbooksBrown 15th EditionCh.18 - Chemistry of the EnvironmentProblem 74b
Chapter 18, Problem 74b

he concentration of H2O in the stratosphere is about 5 ppm. It undergoes photodissociation according to:


H2O(𝑔)⟶H(𝑔)+OH(𝑔)


b.Given that the average bond enthalpy for an O−H bond is 463 kJ/mol, calculate the maximum wavelength for a photon that could cause this dissociation.

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1
Identify the energy required to break one mole of O-H bonds, which is given as 463 kJ/mol.
Convert the energy from kJ/mol to J/mol by multiplying by 1,000 (since 1 kJ = 1,000 J).
Use the formula for energy of a photon: E = h * c / λ, where E is the energy in joules, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters.
Rearrange the formula to solve for wavelength (λ): λ = h * c / E.
Substitute the values for h, c, and the energy (in J/mol) into the equation to calculate the maximum wavelength in meters.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Photodissociation

Photodissociation is a process in which a chemical compound breaks down into its constituent atoms or simpler molecules upon absorbing light (photons). In the context of the given question, water vapor (H2O) in the stratosphere can absorb ultraviolet light, leading to the dissociation into hydrogen (H) and hydroxyl (OH) radicals. Understanding this concept is crucial for analyzing how light interacts with molecules and the energy required for such reactions.

Bond Enthalpy

Bond enthalpy, or bond dissociation energy, is the amount of energy required to break a specific bond in a molecule in the gas phase. For the O−H bond in water, the average bond enthalpy is given as 463 kJ/mol. This value is essential for calculating the energy of the photon needed to cause the dissociation of water, as it directly relates to the energy required to break the bonds holding the molecule together.
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Photon Energy and Wavelength Relationship

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. To find the maximum wavelength that can cause the dissociation of H2O, one must rearrange this equation to solve for λ using the bond enthalpy as the energy input. This relationship is fundamental in understanding how light can induce chemical reactions.
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