Lattice energy quantifies the stability of ionic compounds. It represents the energy released when separate, gaseous ions combine to form a solid crystal lattice structure. A higher lattice energy signifies a stronger attraction between the oppositely charged ions, resulting in a more stable ionic compound. The magnitude of this energy is often indirectly determined using the Born–Haber cycle.
The Driving Force of Lattice Energy
The stability of an ionic lattice is governed by electrostatic attraction, described by Coulomb’s Law. This law states that the force of attraction is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them. In lattice energy, the strength of the bond is influenced primarily by the magnitude of the ion charges and the distance between the nuclei.
Higher ion charges, such as \(Mg^{2+}\) and \(O^{2-}\), result in a stronger attractive force than lower charges, like \(Na^{+}\) and \(Cl^{-}\). The magnitude of lattice energy is directly proportional to the product of these ion charges. Ion charge is typically the primary determinant when comparing different compounds. The distance between the ions becomes the main variable for comparison only when the charges are identical.
The Direct Relationship Between Ion Size and Lattice Energy
The distance between the ions, known as the internuclear distance (\(r\)), is the sum of the ionic radii of the cation and the anion. Since lattice energy is inversely proportional to this internuclear distance, any increase in ion size leads to a decrease in the overall lattice energy.
As ions become larger, the distance separating their nuclei increases, which significantly weakens the electrostatic attraction between them. This inverse relationship means that larger ions are held together less tightly in the crystal lattice. Consequently, less energy is released when the lattice forms, resulting in a lower magnitude of lattice energy. Generally, smaller ions can pack more closely together, enabling a stronger attractive force and a higher lattice energy.
Real-World Examples of Size Effects
The inverse relationship between ion size and lattice energy is clearly demonstrated when comparing compounds that share a common ion. For example, when examining the alkali metal fluorides, the lattice energy decreases as the cation gets larger. Lithium fluoride (\(\text{LiF}\)) has a significantly higher lattice energy than potassium fluoride (\(\text{KF}\)) because the lithium ion (\(\text{Li}^{+}\)) is much smaller than the potassium ion (\(\text{K}^{+}\)).
A similar effect occurs when the cation is held constant and the anion size changes, such as in the lithium halides. The lattice energy sequence follows the order \(\text{LiF} > \text{LiCl} > \text{LiBr} > \text{LiI}\). This decreasing trend is caused by the increasing size of the halide ions, from the small fluoride ion (\(\text{F}^{-}\)) to the much larger iodide ion (\(\text{I}^{-}\)). The greater internuclear distance in lithium iodide (\(\text{LiI}\)) results in the weakest attraction and the lowest lattice energy within this series.