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Chapter 18: Problem 17

The dissociation energy of a carbon-iodine bond is typically about $240 \mathrm{~kJ} / \mathrm{mol} .(\mathbf{a})$ 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 part (a) correspond to?

Short Answer

Expert verified
The maximum wavelength of photons that can cause C-I bond dissociation is \(5.0 \times 10^{-7} \mathrm{m}\) or 500 nm, which corresponds to visible electromagnetic radiation.

Step by step solution

01

Recall the Planck's equation for energy and wavelength

First, let's recall the Planck's equation that relates the energy (E) of a photon with its wavelength (\(\lambda\)): \(E = \frac{hc}{\lambda}\) where h is the Planck's constant (h = \(6.626 \times 10^{-34}\) J∙s) and c is the speed of light (c = \(3.0 \times 10^8\) m/s).
02

Calculate the energy in joules per molecule

The dissociation energy is given in kJ/mol. We need to convert this value to J/molecule. The Avogadro's number helps us to do this conversion: \(\textrm{Energy per molecule (J/molecule)} = \frac{\textrm{Energy per mole (J/mol)}}{\textrm{Avogadro's number (molecule/mol)}}\) The dissociation energy of C-I bond is 240 kJ/mol, first convert it to joules: \(240 \mathrm{\: kJ/mol} \times \frac{1000\: \mathrm{J}}{1 \:\mathrm{kJ}} = 2.4 \times 10^5 \mathrm{\:J/mol}\) Now, use the Avogadro's number (6.022 × 10²³ molecules/mol) to find the energy per molecule: \(E = \frac{2.4 \times 10^5 \:\mathrm{J/mol}}{6.022 \times 10^{23} \:\mathrm{molecules/mol}} = 3.99 \times 10^{-19} \:\mathrm{J/molecule}\)
03

Calculate the maximum wavelength of photons

Using the Planck's equation and the energy calculated in step 2, we can find the maximum wavelength that can break the carbon-iodine bond: \(\lambda = \frac{hc}{E}\) \(\lambda = \frac{(6.626 \times 10^{-34} \:\mathrm{J\: s})(3.0 \times 10^8 \:\mathrm{m/s})}{3.99 \times 10^{-19} \:\mathrm{J/molecule}} = 5.0 \times 10^{-7} \:\mathrm{m}\)
04

Determine the electromagnetic radiation type

Let's find which category of electromagnetic radiation the calculated wavelength falls under: - Ultraviolet radiation: wavelength < 400 nm - Visible radiation: 400 nm < wavelength < 700 nm - Infrared radiation: wavelength > 700 nm With the calculated wavelength of 5.0 x 10⁻⁷ m (500 nm), it corresponds to visible electromagnetic radiation. #Conclusion#: The maximum wavelength of photons that can cause C-I bond dissociation is 5.0 × 10⁻⁷ m or 500 nm, which corresponds to the visible electromagnetic radiation.

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Most popular questions from this chapter

Common lab spectrometers can detect absorbance down to 0.0002 with good reliability. Consider a dissolved harmful organic substance with a molar mass of \(120.5 \mathrm{~g} / \mathrm{mol}\), which can be detected in this spectrometer. It shows an extinction coefficient of $\varepsilon=1.43 \times 10^{3} \mathrm{M}^{-1} \mathrm{~cm}^{-1}$ at 320 \(\mathrm{nm}\), its absorption maximum (A Closer Look, p. 620). (a) Calculate the minimum concentration of the organic substance detectable by this spectrometer (path length \(1 \mathrm{~cm}\) ). (b) Convert the minimum observable molarity to ppb.

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