Question

Calculate the lattice energy of CaO given the following information: the distance between the Ca2+ and O2- ions is 2.32 Å, the charge on the ions is +2 and -2 respectively, and the Madelung constant for CaO is 1.74.

Answer 1

To calculate the lattice energy of CaO, we can use the Born-Lande equation:Lattice Energy = -  Madelung constant * e^2  /  4 *  * 0 * r0  *  1 -  1 / n  where:- Madelung constant = 1.74  given - e is the elementary charge = 1.602 x 10^-19 C- 0 is the vacuum permittivity = 8.854 x 10^-12 C/Nm- r0 is the distance between the ions = 2.32  = 2.32 x 10^-10 m  converted from  to m - n is the Born exponent, which is typically between 5 and 12 for ionic compounds. For simplicity, we will use an average value of n = 9.Now, we can plug in the values into the equation:Lattice Energy = -  1.74 *  1.602 x 10^-19 C ^2  /  4 *  *  8.854 x 10^-12 C/Nm  *  2.32 x 10^-10 m   *  1 -  1 / 9  Lattice Energy = -  1.74 *  2.566 x 10^-38 C   /  4 *  *  8.854 x 10^-12 C/Nm  *  2.32 x 10^-10 m   *  1 -  1 / 9  Lattice Energy = -  4.464 x 10^-38 C  /  1.110 x 10^-21 Nm  *  8 / 9 Lattice Energy = -  4.018 x 10^17 Nm  *  8 / 9 Lattice Energy = -  3.572 x 10^17 Nm The lattice energy of CaO is approximately -3.572 x 10^17 Nm.