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Chapter 9: Problem 145

The isolated \(\mathrm{O}^{2-}\) ion is unstable so it is not possible to measure the electron affinity of the \(\mathrm{O}^{-}\) ion directly. Show how you can calculate its value by using the lattice energy of \(\mathrm{MgO}\) and the Born-Haber cycle. [Useful information: \(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}(g) \Delta H^{\circ}=\) \(148 \mathrm{~kJ} / \mathrm{mol} .]\)

Short Answer

Expert verified
The electron affinity of the \(\mathrm{O}^{-}\) ion can be calculated by building a Born-Haber cycle for the formation of \(\mathrm{MgO}\), then subtracting the known values for the lattice energy of \(\mathrm{MgO}\), sublimation energy of \(\mathrm{Mg}(s)\), and all other energy changes, from the total energy for the cycle.

Step by step solution

01

The lattice energy of MgO

Firstly, we need to know the lattice energy of \(\mathrm{MgO}\). The lattice energy could be obtained from a handbook or calculated previously in a chemical equation. The lattice energy of \(\mathrm{MgO}\) is given by: \(\mathrm{MgO}(s) \rightarrow \mathrm{Mg}^{2+}(g) + \mathrm{O}^{2-}(g)\), where \(\Delta H\) is the lattice energy.
02

Apply Born-Haber Cycle

To obtain the electron affinity of the \(\mathrm{O}^{-}\) ion, we need to set up a Born-Haber cycle for the formation of \(\mathrm{MgO}\). The cycle will need to include the following steps: \(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}(g)\), \(\mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g)\), \(\mathrm{Mg}^{+}(g) \rightarrow \mathrm{Mg}^{2+}(g)\), \(\mathrm{O}_2(g) \rightarrow 2\mathrm{O}(g)\), and finally, the reaction that we are really interested in, \(\mathrm{O}^{-}(g) \rightarrow \mathrm{O}^{2-}(g)\)
03

Calculate the electron affinity of \(\mathrm{O}^{-}\) ion

The electron affinity of \(\mathrm{O}^{-}\) ion is calculated by summing all other energies in the Born-Haber cycle and subtracting the lattice energy of \(\mathrm{MgO}\) and the sublimation energy of \(\mathrm{Mg}(s)\), which is the energy required to convert \(\mathrm{Mg}(s)\) to \(\mathrm{Mg}(g)\). The obtained value will be the electron affinity of \(\mathrm{O}^{-}\)

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