The concentration of H 2 O in the stratosphere is about 5 ppm. It undergoes photodissociation according to: H 2 O(g) → H(g) + OH(g) (b) Using Table 8.3, calculate the wavelength required to cause this dissociation.

Hi everyone for this problem. We're told the photo dissociation of Freon 11 is as follows. What is the wavelength of photons required to initiate this reaction. And were given a hint to use bond energies. So our goal here is to calculate wavelength. Okay, and the relationship between the energy of a photon and the wavelength of light is described by this equation. That equation is energy equals H. C. Over lambda. Okay. And Hs Plank's constant C. Is our speed of light. And lambda is wavelength. And so because this question is asking us to solve for wavelength, we need to rearrange this equation so that we're solving for wavelength. When we rearrange it, we get wavelength is equal to H. C. Over energy. Okay, so let's just define some of these variables. H represents plank's constant and that value is 6.626 times 10 to the negative 34 jewel seconds. And see is our speed of light which is 3.00 times 10 to the eighth meters per second. Okay. So what we don't have is energy. So we need to solve for our energy in order to solve for wavelength and we can solve for energy by finding out our delta H for our reaction. So the entropy, the standard entropy change for our reaction and the standard entropy change for our reaction is going to equal the sum of our reactant since minus the sum of our products. And I'll explain what that means. Okay, so we're going to be using our equation here and the bond anthro peas for everything in our equation to solve for our standard entropy for the reaction. Okay, so we're going to need the bond length opis. Okay, and we'll write that to the side. So our standard heat of formation for our carbon chlorine bond is 328 kg joules per mole. Our standard heat of formation for our carbon flooring bond is 485 killer jewels per mole. Standard heat of formation for our so this is all that we need. This is all that's given. Okay, so let's go ahead and use this. So our standard entropy change for our reaction is going to equal our reactant, the sum of our reactant minus the sum of our products. So we need to look at our equation to solve for this. So for our reactant, since we have to moles of carbon chlorine bond, okay so we're going to multiply our number of moles by the standard heat of formation. So our chlorine bond, carbon chlorine bond is going to be killer jewels per mole plus Our carbon flooring bond, we only have one mole of that. So it's 485 kg joules per mole. So the sum of our reactant minus the sum of our products for our products, we have a carbon chlorine bond and we have three moles of that. So we'll multiply it by its Standard heat of formation. 328 killer joules per mole Plus our carbon flooring bond. We only have one mole of that. So this is 485 killer jules Permal. Okay, so we're going to get a standard Anthony change for our reaction of 328 kg joules per mole. So now what we can do with this is go from killer joules per mole to energy of photons required. Okay, this is how we're going to get our energy. Okay so let's go ahead and continue this off. So we just said we have 328 kg joules per mole. That is our standard entropy change for our reaction. So we're going to first go from kilo jewels, two jewels. So in one kill a jewel We have jewels our killer jewels cancel. And we're left with jewels. Now we want to go from moles to photon and we can do this using avocados number. So in one mole There is 6.022 times 10 to the photons. Okay so our are moles cancel and we're left with jewels photon. Okay so this is going to give us a final answer of 5.4467 times 10 to the negative 19 jewel photons. And this is going to be our energy that we're going to plug into our equation above to solve for wavelength. Okay, so using this using the standard entropy change for our reaction. We're able to go from killer joules per mole, two jewels per photon. So now we have everything that we need to solve for our wavelength. Okay, so let's go ahead and plug in all of our values. So we said Plank's constant is 6. Times 10 to the negative 34 jewel seconds. And this is going to be multiplied by our speed of light. And this is over our energy that we just calculated, which we said is five 4467 times to the -19 jules over photon. Okay, so let's go ahead and calculate. And when we do we're going to get 3.65 times 10 to the negative seven m. So we can go ahead and convert this two nanometers. Since that's the unit that's normally used for wavelength. And so in one nanometer there is to the negative nine m. So our meters will cancel and will be left with nanometers. And so our final wave length is going to be 365 nanometers. And this is going to be our final answer. This is the wavelength of photons required to initiate this reaction. That's the end of this problem. I hope this was helpful

Ch.18 - Chemistry of the Environment

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Brown 14th Edition

Ch.18 - Chemistry of the Environment

Problem 82b

Chapter 18, Problem 82b

The concentration of H₂O in the stratosphere is about 5 ppm. It undergoes photodissociation according to: H₂O(g) → H(g) + OH(g) (b) Using Table 8.3, calculate the wavelength required to cause this dissociation.

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Identify the reaction: \( \text{H}_2\text{O} \rightarrow \text{H} + \text{OH} \). This is a photodissociation reaction where water is broken down into hydrogen and hydroxyl radicals.

Determine the bond energy required to break the \( \text{O-H} \) bond in water. Use Table 8.3 to find the bond dissociation energy for \( \text{O-H} \).

Convert the bond energy from kilojoules per mole (kJ/mol) to joules per molecule. Use Avogadro's number \( 6.022 \times 10^{23} \text{ mol}^{-1} \) for this conversion.

Use the energy-wavelength relationship given by the equation \( E = \frac{hc}{\lambda} \), where \( E \) is the energy per photon, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J s} \), and \( c \) is the speed of light \( 3.00 \times 10^8 \text{ m/s} \).

Rearrange the equation to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \). Substitute the values for \( h \), \( c \), and \( E \) to find the wavelength required for the dissociation.

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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 components upon absorbing light. In the case of water vapor (H2O), it can dissociate into hydrogen (H) and hydroxyl radicals (OH) when exposed to ultraviolet (UV) radiation. Understanding this concept is crucial for analyzing how light interacts with molecules in the atmosphere and the resulting chemical reactions.

Wavelength and Energy 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. This relationship is essential for calculating the wavelength required to provide enough energy to break chemical bonds during photodissociation. Knowing how to manipulate this equation allows for the determination of the specific wavelength needed for a given reaction.

Parts Per Million (ppm)

Parts per million (ppm) is a unit of measurement used to describe the concentration of a substance in a solution or mixture. In the context of atmospheric chemistry, a concentration of 5 ppm indicates that there are 5 molecules of H2O for every million molecules of air. This concept is important for understanding the relative abundance of water vapor in the stratosphere and its potential impact on photodissociation processes.