(b) Using data from Appendix C, Figure 7.11, Figure 7.13, and the value of the second ionization energy for Ca, 1145 kJ/mol, calculate the lattice energy of CaCl2.

Verified step by step guidance

1. Identify the Born-Haber cycle for the formation of CaCl2, which involves the following steps: sublimation of Ca, ionization of Ca, dissociation of Cl2, and electron affinity of Cl.
2. Write the equation for the formation of CaCl2 from its elements in their standard states: Ca(s) + Cl2(g) -> CaCl2(s).
3. Use Hess's Law to relate the enthalpy changes of each step in the Born-Haber cycle to the lattice energy of CaCl2.
4. Calculate the enthalpy change for each step: sublimation of Ca, first and second ionization energies of Ca, bond dissociation energy of Cl2, and electron affinity of Cl.
5. Combine all the enthalpy changes using Hess's Law to solve for the lattice energy of CaCl2.

Key Concepts

Lattice Energy

Lattice energy is the 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. A higher lattice energy indicates a more stable ionic compound, as it reflects stronger ionic interactions. Lattice energy can be calculated using the Born-Haber cycle, which relates ionization energies, electron affinities, and the formation of the solid.

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion. The second ionization energy specifically refers to the energy needed to remove a second electron after the first has been removed. This value is crucial in determining the stability of the resulting ion and plays a significant role in calculating lattice energy, as it reflects the energy changes associated with ion formation.

Born-Haber Cycle

The Born-Haber cycle is a thermodynamic cycle that relates the lattice energy of an ionic compound to other measurable quantities, such as ionization energies, electron affinities, and enthalpy changes. It provides a systematic way to calculate lattice energy by considering the steps involved in forming an ionic solid from its constituent elements. This cycle is essential for understanding the energy changes that occur during the formation of ionic compounds like CaCl2.