The electron affinity of oxygen is -141 kJ/mol, corresponding to the reaction O(g) + e^- → O^-(g). The lattice energy of K₂O(s) is 2238 kJ/mol. Use these data along with data in Appendix C and Figure 7.10 to calculate the 'second electron affinity' of oxygen, corresponding to the reaction O^-(g) + e^- → O^2-(g)

Verified step by step guidance

1. Identify the Born-Haber cycle for the formation of K2O(s) from its elements in their standard states.
2. Write the equation for the formation of K2O(s) from K(s) and O2(g), and break it down into individual steps, including sublimation, ionization, bond dissociation, and electron affinity.
3. Use Hess's Law to relate the lattice energy, the first electron affinity, and the unknown second electron affinity to the enthalpy change of the overall reaction.
4. Set up the equation using the given lattice energy, the first electron affinity, and other necessary thermodynamic data from Appendix C and Figure 7.10.
5. Solve for the second electron affinity of oxygen by rearranging the equation and substituting the known values.

Key Concepts

Electron Affinity

Electron affinity is the energy change that occurs when an electron is added to a neutral atom in the gas phase, forming a negatively charged ion. A negative value indicates that energy is released during this process, making it favorable. For oxygen, the first electron affinity is -141 kJ/mol, meaning energy is released when an electron is added to form O^-.

Lattice Energy

Lattice energy is the amount of energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. In the case of K₂O, the lattice energy of 2238 kJ/mol indicates a strong attraction between K⁺ and O^2- ions, which is crucial for understanding the stability of the ionic compound.

Second Electron Affinity

The second electron affinity refers to the energy change associated with adding a second electron to a negatively charged ion, forming a doubly charged anion. This process is generally endothermic, meaning it requires energy input, as the negatively charged ion repels the incoming electron. For oxygen, calculating the second electron affinity involves considering the energy required to overcome this repulsion, which can be derived from the first electron affinity and lattice energy.