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Chapter 18: Problem 21

The dissociation energy of \(\mathrm{N}_{2}\) is very high, $941 \mathrm{~kJ} / \mathrm{mol}$. (a) Calculate the wavelength of the photons that possess sufficient energy to dissociate \(\mathrm{N}_{2} .(\mathbf{b})\) In which region of the electromagnetic spectrum does this light fall? Does this light have enough energy to photoionize \(\mathrm{N}_{2}\) ?

Short Answer

Expert verified
The wavelength of photons with sufficient energy to dissociate N₂ molecules is 1.271 x 10^(-7) m or 127.1 nm, which falls under the Ultraviolet (UV) region of the electromagnetic spectrum. However, these photons do not have enough energy to photoionize N₂, as the ionization energy of N₂ is approximately 1500 kJ/mol, which is higher than its dissociation energy of 941 kJ/mol.

Step by step solution

01

Convert the dissociation energy to Joules

The dissociation energy is given in kJ/mol, which needs to be converted to Joules (J) to be used in the energy equation. Since 1 kJ = 1000 J, Dissociation energy = 941 kJ/mol × (1000 J / 1 kJ) = 941,000 J/mol
02

Calculate the energy per photon

To find the energy per photon, we need to divide the dissociation energy by Avogadro's number (6.022 x 10^23 mol^(-1)): Energy per photon = 941,000 J/mol ÷ (6.022 x 10^23 mol^(-1)) = 1.562 x 10^(-19) J
03

Calculate the wavelength of the photons

Using the energy equation, we can now find the wavelength of the photons: \( \lambda = \dfrac{h \times c}{E} \) \( \lambda = \dfrac{ (6.626 \times 10^{-34} \text{ J s}) \times (3.0 \times 10^{8} \text{ m/s})}{1.562 \times 10^{-19} \text{ J}} \) \( \lambda = 1.271 \times 10^{-7} \text{ m} \)
04

Determine the region of the electromagnetic spectrum

The wavelength of the photons is 1.271 x 10^(-7) m or 127.1 nm, which falls under the Ultraviolet (UV) region of the electromagnetic spectrum.
05

Determine if the light has enough energy to photoionize N₂

The ionization energy of N₂ is approximately 1500 kJ/mol, which is higher than the dissociation energy of 941 kJ/mol. Therefore, the photons with a wavelength of 127.1 nm have enough energy to dissociate N₂ but do not have enough energy to photoionize N₂.

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