The bond enthalpy of O2 is 498.7 kJ/mol. Calculate the maximum wavelength (nm) of a photon that can cause the dissociation of an O2 molecule. Strategy We want to calculate the wavelength of a photon that will break an O=O bond. Therefore, we need the amount of energy in one bond. The bond enthalpy

Question

The bond enthalpy of [latex]O_{2}[/latex] is 498.7 kJ/mol. Calculate the maximum wavelength (nm) of a photon that can cause the dissociation of an [latex]O_{2}[/latex] molecule.

Strategy We want to calculate the wavelength of a photon that will break an O=O bond. Therefore, we need the amount of energy in one bond. The bond enthalpy of [latex]O_{2}[/latex] is given in units of kJ/mol. The units needed for the energy of one bond are J/molecule. Once we know the energy in one bond, we can calculate the minimum frequency and maximum wavelength needed to dissociate one [latex]O_{2}[/latex] molecule. The conversion steps are

kJ/mol ⟶ J/molecule ⟶ frequency of photon ⟶ wavelength of photon

Accepted Answer

First we calculate the energy required to break one O=O bond:

[latex]\frac{498.7 imes 10^{3} J}{1 \cancel{mol}} imes \frac{1 \cancel{mol}}{6.022 imes 10^{23} molecules}=8.281 imes 10^{-19}\frac{J}{molecule} [/latex]

The energy of the photon is given by E = hv [Equation (7.2)]. Therefore,

[latex]E=hν[/latex] (7.2)

[latex]ν=\frac{E}{h}=\frac{8.281 imes 10^{-19 } J}{6.63 imes 10^{-34} J ⋅ s}[/latex]

[latex]=1.25 imes 10^{-15} s^{-1}[/latex]

Finally, we calculate the wavelength of the photon, given by [latex]λ = c/ν[/latex] [see Equation (7.1)], as follows:

[latex]u=λν[/latex] (7.1)

[latex]λ =\frac{3.00 imes 10^{8 } m/s}{1.25 imes 10^{15} s ^{-1} }[/latex]

[latex]2.40 imes 10^{-7} m=240 nm[/latex]

Comment In principle, any photon with a wavelength of 240 nm or shorter can dissociate an [latex]O_{2}[/latex] molecule.

Question 20.1: The bond enthalpy of O2 is 498.7 kJ/mol. Calculate the maxim...

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