Problem 17 - Chemistry The Central Science In Si Units

Question

The dissociation energy of a carbon-iodine bond is typically about \(240 \mathrm{~kJ} / \mathrm{mol}\). (a) What is the maximum wavelength of photons that can cause \(\mathrm{C}-\mathrm{I}\) bond dissociation? (b) Which kind of electromagnetic radiation-ultraviolet, visible, or infrared \(-\) does the wavelength you calculated in (a) correspond to? part

Step-by-Step Solution

Answer

(a) The maximum wavelength is about 500 nm. (b) This corresponds to visible light.

Step 1: Introduction to the Problem

We are given the dissociation energy of a carbon-iodine bond, which is typically about \(240 \mathrm{~kJ} / \mathrm{mol}\), and need to find the maximum wavelength of the photons that can cause this bond dissociation. We'll also determine the type of electromagnetic radiation this wavelength corresponds to.

Step 1: Convert Energy to Joules per Photon

First, convert the bond dissociation energy from \(\mathrm{kJ/mol}\) to \(\mathrm{J/photon}\). Know that 1 mole contains Avogadro's number \(6.022 \times 10^{23}\) molecules. So, the energy per photon is \(240 \times 10^3 \mathrm{~J/mol} \div 6.022 \times 10^{23} \mathrm{/mol} \approx 3.986 \times 10^{-19} \mathrm{~J/photon}\).

Step 2: Use the Energy-Wavelength Relationship

The energy of a photon \(E\) is related to its wavelength \(\lambda\) by the equation \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant \(6.626 \times 10^{-34} \mathrm{~J}\cdot\mathrm{s}\) and \(c\) is the speed of light \(3.00 \times 10^8 \mathrm{~m/s}\). Solve for \(\lambda\): \(\lambda = \frac{hc}{E}\).

Step 3: Calculate the Wavelength

Substitute the values of \(h\), \(c\), and \(E\) into the wavelength formula: \(\lambda = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{3.986 \times 10^{-19}}\). Calculate to find \(\lambda \approx 5.00 \times 10^{-7} \mathrm{~m}\) or \(500 \mathrm{~nm}\).

Step 4: Determine the Type of Electromagnetic Radiation

The calculated wavelength of \(500 \mathrm{~nm}\) falls within the visible light range of the electromagnetic spectrum, which is approximately \(380 - 750 \mathrm{~nm}\).

Step 6: Conclusion and Summary

The maximum wavelength of photons that can dissociate a \(\mathrm{C}-\mathrm{I}\) bond is approximately \(500 \mathrm{~nm}\), which corresponds to visible light.

Key Concepts

Carbon-Iodine Bond

A carbon-iodine bond is a type of chemical bond formed between a carbon atom and an iodine atom. This bond is typically a type of covalent bond. In a covalent bond, the atoms share electrons to create a more stable arrangement. The dissociation energy of this bond indicates how much energy it takes to break the bond.
Each bond type has a specific dissociation energy, which is a measure of bond strength. For the carbon-iodine bond, the dissociation energy is about 240 kJ/mol.

• This high energy indicates that the bond is relatively strong.
• A larger dissociation energy means that more energy is required to break the bond.

Understanding the dissociation energy is crucial in fields like chemistry and biochemistry, as it helps predict how a chemical will react under certain conditions.

Energy-Wavelength Relationship

The energy-wavelength relationship is a fundamental concept in physics, describing how the energy of a photon relates to its wavelength. This relationship is expressed by the equation:
\[ E = \frac{hc}{\lambda} \]
Where:

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

This equation highlights that

• An increase in energy results in a decrease in wavelength, making them inversely proportional.
• It allows calculation of a photon's wavelength if its energy is known and vice versa.

Understanding this relationship helps us to explore phenomena such as absorption in spectroscopy and predict the behavior of photons in various materials.

Electromagnetic Radiation

Electromagnetic radiation is a form of energy that travels through space at the speed of light. It includes a wide range of wavelengths and frequencies, forming what is known as the electromagnetic spectrum.
This spectrum ranges from short wavelengths like gamma rays, to long wavelengths like radio waves:

• Microwaves, used for cooking and communication
• Infrared, which is felt as heat
• Visible light, which can be seen by the human eye
• Ultraviolet, which can be harmful in large doses
• X-rays, used for medical imaging

Each type of electromagnetic radiation carries energy, and its applications are based on its energy and wavelength characteristics. In the case of the carbon-iodine bond, knowing the type of electromagnetic radiation needed for bond dissociation is crucial in practical applications like material safety and chemical analysis.

Visible Light Range

The visible light range is the portion of the electromagnetic spectrum that can be detected by the human eye. Wavelengths in this range usually span from 380 nm to about 750 nm.
Each color in visible light correlates to a specific wavelength:

• Violet has the shortest wavelength, just under 400 nm.
• Red has the longest, around 700 nm.

In this problem, the wavelength calculated from the dissociation energy of the carbon-iodine bond is 500 nm. This places it within the visible light spectrum. Consequently, the photon energy at this wavelength is capable of being perceived as light by humans. Recognizing where a particular wavelength falls within the spectrum is essential when working with light-sensitive processes or visual applications.