Question

Calculate the lattice energy of potassium oxide (K2O) given that the ionic radii of K+ and O2- are 152 pm and 140 pm respectively, and the lattice enthalpy of formation of K2O is -3803 kJ/mol.

Answer 1

To calculate the lattice energy of potassium oxide  K2O , we can use the Born-Lande equation:Lattice energy  U  =  N * A * Z^+ * Z^- * e^2  /  4 *  * 0 * r0 Where:N = Avogadro's number  6.022 x 10^23 mol^-1 A = Madelung constant  for K2O, A = 1.74756 Z^+ = charge of the cation  K+ = +1 Z^- = charge of the anion  O2- = -2 e = elementary charge  1.602 x 10^-19 C 0 = vacuum permittivity  8.854 x 10^-12 C^2 J^-1 m^-1 r0 = sum of ionic radii  K+ and O2- First, let's calculate r0:r0 = ionic radius of K+ + ionic radius of O2-r0 = 152 pm + 140 pmr0 = 292 pmr0 = 292 x 10^-12 mNow, we can plug these values into the Born-Lande equation:U =  6.022 x 10^23 mol^-1 * 1.74756 * 1 * 2 *  1.602 x 10^-19 C ^2  /  4 *  * 8.854 x 10^-12 C^2 J^-1 m^-1 * 292 x 10^-12 m U =  1.052 x 10^5 C^2 J^-1 m^-1  /  3.665 x 10^-11 C^2 J^-1 m^-1 U  2.87 x 10^6 J/molHowever, this value is in J/mol, and we need to convert it to kJ/mol:Lattice energy  U   2.87 x 10^6 J/mol *  1 kJ / 1000 J   2870 kJ/molSo, the lattice energy of potassium oxide  K2O  is approximately 2870 kJ/mol.