Electrovalent bonding Questions in English

(D) The lattice energy $(U)$ of an ionic crystal is defined as the energy released when gaseous ions combine to form one mole of the solid ionic crystal.
According to the Born-Landé equation,the lattice energy is inversely proportional to the inter-ionic distance $(r_0)$.
Since the inter-ionic distance $r_0$ is the sum of the ionic radii of the cation $(r_c)$ and the anion $(r_a)$,we have $r_0 = r_c + r_a$.
Therefore,the lattice energy $U$ is proportional to $\frac{1}{(r_c + r_a)}$.

(B) According to the Born-Haber cycle for the formation of $LiF(s)$:
$\Delta H_f^{\circ} = \Delta H_{sub}(Li) + \frac{1}{2} \Delta H_{diss}(F_2) + IE(Li) + EGE(F) + U$
Where $U$ is the lattice enthalpy.
Substituting the given values:
$-594 = 155 + \frac{150}{2} + 520 + (-313) + U$
$-594 = 155 + 75 + 520 - 313 + U$
$-594 = 437 + U$
$U = -594 - 437 = -1031 \ kJ \ mol^{-1}$
The magnitude of the lattice enthalpy is $|-1031| = 1031 \ kJ \ mol^{-1}$.