The stability of an ionic compound, like table salt, is tied to the forces holding its positive and negative ions together in a crystal lattice structure. This attraction is quantified by lattice energy (LE). Lattice energy is the energy required to break one mole of a solid ionic compound into its separate, gaseous ions, or the energy released when those gaseous ions combine to form the solid. The magnitude of this energy measures the strength of the ionic bond and the overall stability of the compound.
Defining Lattice Energy and Ionic Size
Lattice energy measures the strength of the electrostatic pull between the ions within the crystal. A higher lattice energy indicates a stronger attraction, resulting in a more stable compound with a higher melting point. Since this energy cannot be measured directly, chemists calculate it using the Born-Haber cycle, an application of Hess’s law.
Ionic size is the second variable determining the magnitude of lattice energy. Ionic radius is the effective distance from the nucleus of an ion to its outer electron shell when it is part of an ionic crystal. In any ionic solid, the distance separating the two oppositely charged nuclei is the sum of the cation’s and the anion’s radii. This internuclear distance, along with the charges on the ions, forms the basis for calculating the strength of the attraction.
The Inverse Relationship: How Size Affects Lattice Energy
The relationship between lattice energy and size is governed by the principles of electrostatic attraction. The force of attraction between two charged particles follows Coulomb’s Law, which states that the attractive force is inversely proportional to the square of the distance separating the charges. As ionic size increases, the distance between the nuclei of the positive and negative ions also increases.
This greater distance results in a weaker electrostatic force and a lower lattice energy. The relationship is inverse: as the size of the ions increases, the lattice energy decreases. For example, comparing Lithium Fluoride (LiF) and Cesium Fluoride (CsF), both share the fluoride anion but have different cations. Because the lithium ion (\(\text{Li}^+\)) is smaller than the cesium ion (\(\text{Cs}^+\)), the distance between the ions in LiF is smaller. This closer proximity leads to a stronger attraction and a higher lattice energy for LiF than for CsF.
The Overriding Influence of Ionic Charge
While ionic size is an important factor, the magnitude of the ionic charge exerts a greater influence on lattice energy. According to Coulomb’s Law, the attractive force is not only inversely related to the distance, but it is also directly proportional to the product of the charges on the ions. If you double the charge on both the cation and the anion, the attractive force increases by a factor of four.
The effect of charge is more dramatic than the effect of distance. Consider Sodium Chloride (NaCl) and Magnesium Oxide (MgO). In NaCl, the ions (\(\text{Na}^+\) and \(\text{Cl}^-\)) yield a charge product of \(1 \times 1 = 1\). In MgO, the ions (\(\text{Mg}^{2+}\) and \(\text{O}^{2-}\)) result in a charge product of \(2 \times 2 = 4\). Even though the ions in MgO are slightly larger than those in NaCl, the fourfold increase in the charge product causes the lattice energy of MgO to be nearly four times greater than that of NaCl.
In practice, the charge on the ions is the dominant factor used to predict the relative magnitude of lattice energy. Only when comparing compounds with the same charge product, such as \(\text{LiF}\) and \(\text{CsF}\) (both \(1 \times 1\)), does the inverse relationship with ionic size become the determining factor. The size component fine-tunes the energy, while the charge component sets the overall energy scale.