Problem 32 - Chemistry: The Central Science

Question

An important reaction in the formation of photochemical smog is the photodissociation of \(\mathrm{NO}_{2}\) = $$ \mathrm{NO}_{2}+h w \longrightarrow \mathrm{NO}(g)+\mathrm{O}(g) $$ The maximum wavelength of light that can cause this reaction is \(420 \mathrm{~nm}\). (a) In what part of the electromagnetic spectrum is light with this wavelength found? (b) What is the maximum strength of a bond, in kJ/mol, that can be broken by absorption of a photon of 420 -nm light? (c) Write out the photodissociation reaction showing Lewis-dot structures.

Step-by-Step Solution

Answer

(a) The 420 nm wavelength light is found in the visible light range of the electromagnetic spectrum, specifically in the violet region. (b) The maximum strength of a bond that can be broken by absorption of a photon of 420 nm light is 180.60 kJ/mol. (c) The photodissociation reaction showing Lewis dot structures is: :NO=O (g) + hν → :N=O (g) + O (g)

Step 1: Identifying the part of the electromagnetic spectrum for 420 nm wavelength light

Referring to the electromagnetic spectrum chart, 420 nm wavelength light falls in the visible light range (specifically, violet). Part (b):

Step 2: Calculating the energy of a photon with a 420 nm wavelength

First, we need to convert the wavelength from nm to meters: \(420 nm = 420 \times 10^{-9} m\). Now, we'll use the formula E = hc/λ to calculate the energy of a photon of 420 nm light. E = \( \frac{(6.626 \times 10^{-34} Js)(2.998 \times 10^{8} m/s)}{420 \times 10^{-9} m} \) E = \(3.0023 \times 10^{-19} J\) Next, we will convert the energy from Joules to kJ/mol. There are \(6.022 \times 10^{23}\) particles (atoms/molecules) in a mole. Energy in kJ/mol = \( \frac{3.0023 \times 10^{-19} J}{1 photon} \times \frac{6.022 \times 10^{23} photons}{1 mol} \times \frac{1 kJ}{10^3 J} \) Energy in kJ/mol = \(180.60 kJ/mol\) So, the maximum strength of a bond that can be broken by absorption of a photon of 420 nm light is 180.60 kJ/mol. Part (c):

Step 3: Drawing Lewis dot structures for the photodissociation reaction of NO₂

The reaction can be written using Lewis dot structures as: :NO=O (g) + hν → :N=O (g) + O (g)

Key Concepts

Electromagnetic spectrum

The electromagnetic spectrum is a comprehensive range of all types of electromagnetic radiation. These radiations vary based on frequency and wavelength. The spectrum ranges from gamma rays, which have the shortest wavelength, to radio waves, which have the longest wavelength.

When discussing the photodissociation of NO₂ in the formation of photochemical smog, we're focusing on a specific point in the spectrum: visible light. Light with a wavelength of 420 nm falls within the visible region of the electromagnetic spectrum. Specifically, it is associated with violet light. This part of the spectrum is visible to the human eye, which means it induces the perception of color.

• Radio Waves: Longest wavelength, low energy.
• Microwaves: Used for cooking and certain communications.
• Infrared (IR): Heat radiation.
• Visible Light: 380 nm to 750 nm, where 420 nm is violet.
• Ultraviolet (UV): Shorter wavelength than visible light.
• X-rays: Used for medical imaging.
• Gamma Rays: Shortest wavelength, highest energy.

Understanding where a specific wavelength falls on the electromagnetic spectrum helps clarify what kinds of reactions or interactions that light can induce.

Bond energy

Bond energy is a critical concept when analyzing chemical reactions, especially those involving light like photodissociation. It refers to the amount of energy required to break one mole of the specified bonds in a chemical substance in its gaseous state.

In the given exercise, we are concerned with the energy needed to break the bond in NO₂ using a 420 nm light photon. To determine the bond energy, we calculate the energy of a single photon and then scale it up to a mole of molecules. Using the equation: \[ E = \frac{hc}{\lambda} \]where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)), \( c \) is the speed of light (\( 2.998 \times 10^8 \, \text{m/s} \)), and \( \lambda \) is the wavelength in meters.

• Calculate the energy of one photon.
• Convert photon energy (J) to molar energy (kJ/mol) using Avogadro's number (\( 6.022 \times 10^{23} \)).
• The resulting energy tells us about the strength of the bond that can be broken.

This calculation shows that a photon with a wavelength of 420 nm can break a bond with a strength of up to 180.60 kJ/mol, indicating that not all bonds in molecules can be dissociated with visible light, only those with suitable energy thresholds.

Lewis dot structures

Lewis dot structures are a simple way to represent the electrons involved in the chemical bonds between atoms. This method is an essential tool for visualizing the valence electrons and understanding molecular structures.

In photochemical reactions like the one illustrated with NO₂, Lewis dot structures help us see how the photodissociation occurs. Each element is represented by its chemical symbol, with dots around it indicating the valence electrons. In NO₂:

• Nitrogen (N): Typically makes three bonds, with one lone pair (shown as dots).
• Oxygen (O): Forms double bonds or has two lone pairs.
• The photodissociation of \(:NO=O\) results in \(:N=O\) and \(O\), with photons facilitating the breaking of the bond.

The structure before and after photodissociation shows the transformation from a bonded to an unbonded state for one of the oxygen atoms. This demonstrates the importance of Lewis dots in predicting and understanding chemical reactions and their reactivity with light.