Given the following values for steps in the formation of CaO(s) from its elements, draw a Born–Haber cycle similar to that shown in Figure 6.7. Eea1 for O1g2 = -141 kJ/mol Eea2 for O1g2 = 745.1 kJ/mol Heat of sublimation for Ca1s2 = 178 kJ/mol Ei1 for Ca1g2 = 590 kJ/mol Ei1 for Ca1g2 = 1145 kJ/mol Bond dissociation energy for O21g2 = 498 kJ/mol Lattice energy for CaO1s2 = 3401 kJ/mol

Verified step by step guidance

1. Identify the steps involved in the formation of CaO(s) from its elements: sublimation of Ca(s), ionization of Ca(g), dissociation of O2(g), electron affinity of O(g), and lattice energy of CaO(s).
2. Write the sublimation reaction for calcium: Ca(s) → Ca(g) and note the energy change as 178 kJ/mol.
3. Write the first ionization reaction for calcium: Ca(g) → Ca⁺(g) + e⁻ and note the energy change as 590 kJ/mol. Then, write the second ionization reaction: Ca⁺(g) → Ca²⁺(g) + e⁻ and note the energy change as 1145 kJ/mol.
4. Write the bond dissociation reaction for oxygen: 1/2 O₂(g) → O(g) and note the energy change as 1/2 * 498 kJ/mol.
5. Write the electron affinity reactions for oxygen: O(g) + e⁻ → O⁻(g) with energy change -141 kJ/mol, and O⁻(g) + e⁻ → O²⁻(g) with energy change 745.1 kJ/mol. Finally, consider the lattice energy for the formation of CaO(s) from Ca²⁺(g) and O²⁻(g) as -3401 kJ/mol.

Key Concepts

Born-Haber Cycle

The Born-Haber cycle is a thermodynamic cycle that relates the lattice energy of an ionic compound to the enthalpy changes involved in its formation from its constituent elements. It provides a systematic way to analyze the energy changes during the formation of ionic compounds, including sublimation, ionization, electron affinity, and lattice energy. This cycle helps in understanding the stability and solubility of ionic compounds.

Lattice Energy

Lattice energy is the energy released when gaseous ions combine to form an ionic solid, or conversely, the energy required to separate one mole of a solid ionic compound into its gaseous ions. It is a crucial factor in determining the stability of ionic compounds, as higher lattice energies typically indicate stronger ionic bonds and greater stability. Lattice energy can be calculated using the Born-Haber cycle, making it essential for understanding ionic compound formation.

Ionization Energy and Electron Affinity

Ionization energy is the energy required to remove an electron from a neutral atom in the gas phase, while electron affinity is the energy change that occurs when an electron is added to a neutral atom. These two concepts are vital in the formation of ionic compounds, as they determine how easily an atom can lose or gain electrons, influencing the overall energy changes in the Born-Haber cycle. Understanding these energies helps predict the reactivity and stability of elements when forming ionic bonds.