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Chapter 17

Q. 17.1

Photon Energies

By how many kilojoules per mole is the energy of O_{2} increased when it absorbs ultraviolet radiation with a wavelength of 147 nm? How much is the energy of CO_{2} increased when it absorbs infrared radiation with a wavenumber of 2 300 cm^{−1} ?

Step-by-Step

Verified Solution

For the ultraviolet radiation, the energy increase is

\Delta E = hv = h\frac{c}{λ}

          = (6.626 × 10^{−34}  J  ·  s)[\frac{(2.998 × 10^{8}  m/s)}{(147  nm)(10^{−9}  m/nm)}] = 1.35 × 10^{−18} J/molecule

                     (1.35 × 10^{−18}  J/molecule)(6.022 × 10^{23}  molecules/mol) = 814 kJ/mol

This is enough energy to break the O \xlongequal[]{} O  bond in oxygen. For CO_{2}, the energy increase is

\Delta E = hv = h\frac{c}{λ} = hc\widetilde{v}           (recall that \widetilde{v} = \frac{1}{λ})

                                   = (6.626 × 10^{−34}  J  ·  s)(2.998 × 10^{8} m/s)(2  300 cm^{−1})(100 cm/m)

= 4.6 × 10^{−20} J/molecule = 28 kJ/mol

Infrared absorption increases the amplitude of the vibrations of the CO_{2} bonds.

Test Yourself     What is the wavelength, wavenumber, and name of radiation with an energy of 100 kJ/mol? (Answer: 1.20 μm, 8.36 × 10^{3}  cm^{−1} , infrared)