Chapter 15, Problem 15B.3E

Interpretation Introduction

Interpretation:

The lattice enthalpy of the calcium sulphide has to be estimated using Born-Mayer equation.

Concept Introduction:

Born-Mayer equation is an equation which is used to calculate the lattice energy of a crystalline ionic compound.

$\begin{array}{l}\text{E = }\frac{{\text{-N}}_{\text{A}}{\text{Mz}}^{\text{+}}{\text{z}}^{\text{-}}{\text{e}}^{\text{2}}}{{\text{4πÎ}}_{\text{o}}{\text{r}}_{\text{o}}}\text{(1-}\frac{\text{ρ}}{{\text{r}}_{\text{o}}}\text{)}\\ {\text{N}}_{\text{A}}\text{= avagadro constant}\\ \text{M=Madelung constant,relating to the geometry of the crystal}\\ {\text{z}}^{\text{+}}\text{=charge number of cation}\\ {\text{z}}^{\text{-}}\text{=charge number of anion}\\ \text{e= elementary charge,1}{\text{.6×10}}^{\text{-19}}\text{C}\\ {\text{Î}}_{\text{o}}\text{= permittivity of freespace}\\ {\text{r}}_{\text{o}}\text{= diatance to closest ion}\\ \text{ρ = a constant dependant on the compressibility of the crystal ; 30pm works well for all alkali metal halides}\text{.}\end{array}$