Alcohol-based fuels for automobiles lead to the production of formaldehyde \(\left(\mathrm{CH}_{2} \mathrm{O}\right)\) in exhaust gases. Formaldehyde undergoes photodissociation, which contributes to photochemical smog: $$ \mathrm{CH}_{2} \mathrm{O}+h \nu \longrightarrow \mathrm{CHO}+\mathrm{H} $$ The maximum wavelength of light that can cause this reaction is $335 \mathrm{nm} .(\mathbf{a})$ In what part of the electromagnetic spectrum is light with this wavelength found? (b) What is the maximum strength of a bond, in \(\mathrm{kJ} / \mathrm{mol}\), that can be broken by absorption of a photon of 335 -nm light? (c) Compare your answer from part (b) to the appropriate value from Table 8.3 . What do you conclude about \(\mathrm{C}-\mathrm{H}\) bond energy in formaldehyde? (d) Write out the formaldehyde photodissociation reaction, showing Lewis-dot structures.

Step by step solution

01

(a) Identifying the region of the electromagnetic spectrum

To find the electromagnetic spectrum region, we need to know the wavelength. We are given the wavelength as 335 nm. We can find the region by using the general classification guide, such as: - Ultraviolet (UV): 100 nm to 400 nm - Visible: 400 nm to 700 nm - Infrared (IR): 700 nm to 1 mm Our given wavelength of 335 nm falls under the ultraviolet (UV) category.

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(b) Calculating the maximum bond strength

To find the maximum bond strength that can be broken by the absorption of 335 nm light, we need to use the formula: \(E = \cfrac{hc}{\lambda}\) where E is the energy per photon, h is the Planck's constant (6.626 x 10^{-34} Js), c is the speed of light (3 x 10^8 m/s), and \(\lambda\) is the wavelength. First, we need to convert \(\lambda\) to meters: \(335\ nm = 335 \times 10^{-9}\ m\) Now we can find the energy per photon: \(E = \cfrac{6.626 \times 10^{-34}\ Js \times 3.00 \times 10^8\ m/s}{335 \times 10^{-9}\ m} = 5.929 \times 10^{-19}\ J/photon\) To find the energy per mole of photons, we multiply by Avogadro's number \(N_A (6.022 \times 10^{23} mol^{-1})\): \(E_{mol} = 5.929 \times 10^{-19}\ J/photon \times 6.022 \times 10^{23}\ mol^{-1} = 356.911 \times 10^3\ J/mol = 356.9\ kJ/mol\) So, the maximum bond strength that can be broken is 356.9 kJ/mol.

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(c) Comparing the C-H bond energy

Referring to Table 8.3, the C-H bond energy in formaldehyde is 339 kJ/mol. Comparing this with the bond energy found in part (b), we can see that the bond energy of formaldehyde is less than the energy per mole of photons (339 kJ/mol < 356.9 kJ/mol). Therefore, the C-H bond in formaldehyde can be broken by 335 nm light.

04

(d) Formaldehyde photodissociation reaction with Lewis-dot structures

Formaldehyde (\(\mathrm{CH_2O}\)) has a central carbon (C) atom with a double bond to an oxygen (O) atom and two single bonds to two hydrogen (H) atoms: O = C - H | H The photodissociation reaction, showing Lewis-dot structures, occurs as follows: O H ═ C - H + hν ⟶ O + H | H

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