Ch.18 - Chemistry of the Environment

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.18 - Chemistry of the Environment

Problem 17a

Chapter 18, Problem 17a

The dissociation energy of a carbon-bromine bond is typically about 276 kJ/mol. (a) What is the maximum wavelength of photons that can cause C-Br bond dissociation?

Verified step by step guidance

Step 1: Understand that the dissociation energy of a bond is the energy required to break that bond. In this case, we are given the dissociation energy of a carbon-bromine bond in kJ/mol. We need to convert this energy into Joules (J) because the formula we will use requires the energy in Joules. To do this, we use the conversion factor 1 kJ = 1000 J and 1 mol = 6.022 x 10^23 molecules (Avogadro's number).

Step 2: Use the formula for the energy of a photon, E = h * c / λ, where E is the energy, 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. We are solving for λ, so we rearrange the formula to get λ = h * c / E.

Step 3: Substitute the values of h, c, and E (converted to Joules per molecule in step 1) into the formula. Remember to keep the units consistent, i.e., use Joules for energy, meters per second for the speed of light, and Joules*seconds for Planck's constant.

Step 4: Calculate the value of λ. This will give you the maximum wavelength of photons that can cause C-Br bond dissociation.

Step 5: Check your answer. The wavelength should be in the range of ultraviolet or visible light, as these are the types of light that typically have enough energy to break chemical bonds.

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Key Concepts

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

Dissociation Energy

Dissociation energy is the amount of energy required to break a bond between two atoms in a molecule. It is typically expressed in kilojoules per mole (kJ/mol) and indicates the strength of the bond; higher values correspond to stronger bonds. In this context, the dissociation energy of the carbon-bromine bond is 276 kJ/mol, which is crucial for determining the energy of photons needed for bond dissociation.

Photon Energy

Photon energy is the energy carried by a single photon, which can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the photon. This relationship shows that the energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength, allowing us to relate energy to wavelength using the equation λ = c/ν, where c is the speed of light.

Wavelength and Energy Relationship

The relationship between wavelength and energy is fundamental in quantum chemistry. As the wavelength of light increases, its energy decreases, and vice versa. This inverse relationship is expressed in the equation E = hc/λ, where λ is the wavelength. To find the maximum wavelength that can cause C-Br bond dissociation, one must convert the dissociation energy from kJ/mol to joules per photon and then apply this equation to solve for λ.

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Textbook Question

(b) Use the energy requirements of these two pro- cesses to explain why photodissociation of oxygen is more important than photoionization of oxygen at altitudes below about 90 km.

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Textbook Question

From the data in Table 18.1, calculate the partial pressures of carbon dioxide and argon when the total atmospheric pressure is 1.05 bar.

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Textbook Question

Air pollution in the Mexico City metropolitan area is among the worst in the world. The concentration of ozone in Mexico City has been measured at 441 ppb (0.441 ppm). Mexico City sits at an altitude of 7400 feet, which means its atmospheric pressure is only 0.67 atm. (a) Calculate the partial pressure of ozone at 441 ppb if the atmospheric pressure is 0.67 atm.

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Textbook Question

(a) Distinguish between photodissociation and photoionization.

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Textbook Question

The dissociation energy of a carbon-bromine bond is typically about 276 kJ/mol. (b) Which kind of electromagnetic radiation—ultraviolet, visible, or infrared—does the wavelength you calculated in part (a) correspond to?