Which compound in each of the following pairs has the larger lattice energy? Note: \({\rm{B}}{{\rm{a}}^{{\rm{2 + }}}}\) and \({{\rm{K}}^{\rm{ + }}}\) have similar radii; \({{\rm{S}}^{{\rm{2 - }}}}\) and \({\rm{C}}{{\rm{l}}^{\rm{ - }}}\) have similar radii. Explain your choices.

(a) \({{\rm{K}}_{\rm{2}}}{\rm{O}}\) or \({\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{O}}\)

(b) \({{\rm{K}}_{\rm{2}}}{\rm{S}}\) or \({\rm{BaS}}\)

(c) \({\rm{KCl}}\) or \({\rm{BaS}}\)

(d) \({\rm{BaS}}\) or \({\rm{BaC}}{{\rm{l}}_{\rm{2}}}\)

The energy required to dissociate the ions in a crystal lattice into individual gaseous ions is known as lattice energy.

Since\({\rm{N}}{{\rm{a}}^{\rm{ + }}}\)has a smaller radius than\({{\rm{K}}^{\rm{ + }}}\).This leads to\({\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{O}}\)having larger lattice energy than\({{\rm{K}}_{\rm{2}}}{\rm{O}}\).

Therefore,\({\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{O}}\)has lattice energy than\({{\rm{K}}_{\rm{2}}}{\rm{O}}\).

Since there are higher charges on\({\rm{Ba}}\)than\({\rm{K}}\), whereas radii of the ions are almost similar.

Therefore, \({\rm{BaS}}\) has larger lattice energy than \({{\rm{K}}_{\rm{2}}}{\rm{S}}\).

(c)

Since there are higher charges on \({\rm{Ba}}\) and \(S\), whereas radii of the ions are almost similar.

Therefore, \({\rm{BaS}}\) has larger lattice energy than \({\rm{KCl}}\).

(d)

Since there are higher charges on \({\rm{S}}\) than \({\rm{Cl}}\), whereas radii of the ions are almost similar.

Therefore, \({\rm{BaS}}\) has larger lattice energy than \({\rm{BaC}}{{\rm{l}}_2}\).