The lattice energy for LiCl can be calculated by using the Born-Haber cycle. This cycle relates the lattice energy to various thermodynamic quantities such as sublimation energy, ionization energy, and electron affinity.
Here are the steps involved in calculating the lattice energy for LiCl based on the data provided:
- Sublimation Energy of Li (s) = +166 kJ/mol: This is the energy required to convert solid lithium into gaseous lithium.
- Formation Enthalpy of Cl (g) = +119 kJ/mol: This is the energy required to convert Cl2 gas into two moles of chlorine gas atoms (Cl). Note that this is half of the bond dissociation energy of Cl2, which would be about +242 kJ/mol for one mole).
- First Ionization Energy of Li (g) = +520 kJ/mol: This value indicates the energy needed to remove one electron from a gaseous lithium atom to form Li+.
- Electron Affinity of Cl (g) = -349 kJ/mol: This value represents the energy change when a gaseous chlorine atom gains an electron to form Cl–.
Now, we can set up the equation according to the Born-Haber cycle:
Lattice Energy (U) = Sublimation Energy of Li + Formation Enthalpy of Cl + Ionization Energy of Li + Electron Affinity of Cl
Substituting the values into the equation:
Lattice Energy (U) = (166) + (119) + (520) - (349)
Calculating this gives us:
Lattice Energy (U) = 166 + 119 + 520 - 349 = 456 kJ/mol
Thus, the lattice energy for LiCl is approximately +456 kJ/mol. A positive value indicates the energy required to break the ionic bonds in the solid lattice structure of LiCl.