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Question

Rationalize the following lattice energy values:$\begin{matrix} \text{Compound} & & \text{Lattice Energy (kJ/mol)}\\ \hline \\ \begin{array} { l } { \text { CaSe } } \\ { \mathrm { Na } _ { 2 } \mathrm { Se } } \\ { \text { CaTe } } \\ { \mathrm { Na } _ { 2 } \mathrm { Te } } \end{array} & & \begin{array} { l } { - 2862 } \\ { - 2130 } \\ { - 2721 } \\ { - 2095 } \end{array} \end{matrix}$

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The lattice energy represents the amount of energy required to dissociate 1 mole of an ionic solid into the gaseous ions.

$\textbf{Lattice energy, U = \dfrac{k'Q_{1}Q_{2}}{r_{o}}}$

Lattice energy is directly proportional to the charges of the ions and is inversely related to the internuclear distance. It is also inversely proportional to the size of the ions.

Hence, lattice energies are highest for substances with small, highly charged ions.

Here, we have

$\textbf{CaSe, Na_2Se, CaTe and Na_2Te}$

Ca$^{2+}$ has a greater charge than Na$^{+}$ because of which CaSe and CaTe will have higher lattice energies compared to Na$_2$Se and Na$_2$Te.

Also, Se$^{2-}$ is smaller than Te$^{2-}$ because of which lattice energy of anions containing Se$^{2-}$ will be higher as compared to Te$^{2-}$ anion.

The effect of charge on the lattice energy is greater than the effect of size. Hence, these factors combine to give the following trend in lattice energies:

$\textbf{CaSe > CaTe > Na_2Se > Na_2Te}$

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