Use the Born–Haber cycle and data from Appendix IIB and Table 10.3 to calculate the lattice energy of CaO. (ΔHsub for calcium is 178 kJ>mol; IE1 and IE2 for calcium are 590 kJ>mol and 1145 kJ>mol, respectively; EA1 and EA2 for O are -141 kJ>mol and 744 kJ>mol, respectively.)

Verified step by step guidance

1. Identify the steps involved in the Born-Haber cycle for the formation of CaO from its elements in their standard states.
2. Write the chemical equations for each step: sublimation of Ca, ionization of Ca, dissociation of O2, electron affinity of O, and formation of CaO.
3. Use the given data: \( \Delta H_{\text{sub}} \) for Ca, \( \text{IE}_1 \) and \( \text{IE}_2 \) for Ca, \( \text{EA}_1 \) and \( \text{EA}_2 \) for O, and the enthalpy of formation of CaO.
4. Apply Hess's Law to relate the enthalpy changes of each step to the lattice energy of CaO.
5. Solve for the lattice energy of CaO by rearranging the equation obtained from Hess's Law.

Key Concepts

Born-Haber Cycle

The Born-Haber cycle is a thermodynamic cycle that relates the lattice energy of an ionic compound to other energy changes involved in its formation. It combines various enthalpy changes, such as sublimation, ionization, and electron affinity, to calculate the lattice energy, which is the energy released when gaseous ions form a solid ionic lattice.

Lattice Energy

Lattice energy is the amount of energy released when one mole of an ionic solid is formed from its gaseous ions. It is a measure of the strength of the forces between the ions in an ionic compound. Higher lattice energy indicates stronger ionic bonds, which typically results in higher melting points and greater stability of the compound.

Ionization Energy and Electron Affinity

Ionization energy is the energy required to remove an electron from an atom or ion, while electron affinity is the energy change that occurs when an electron is added to a neutral atom. These concepts are crucial in the Born-Haber cycle as they help quantify the energy changes associated with the formation of cations and anions, which are essential for calculating lattice energy.