Ionic compounds are held together by powerful electrostatic attractions between positively and negatively charged ions, which arrange themselves into a highly ordered, three-dimensional structure known as a crystal lattice. The energy associated with the formation and stability of this structure is described by the term “lattice energy.” The question of whether lattice energy is endothermic or exothermic often causes confusion. This ambiguity arises because the answer depends entirely on the specific definition being used: the formation of the solid or its breaking apart.
The Definition of Lattice Energy
Lattice energy is fundamentally a measure of the strength of the ionic bonding within a solid crystal structure. It quantifies the energy change involved when one mole of an ionic compound is either formed from or separated into its constituent ions in the gaseous state. The crystal structure is a repeating pattern where every positive ion (cation) is surrounded by negative ions (anions), and vice versa. These strong forces of attraction are governed by Coulomb’s law.
Energy Released During Ionic Solid Formation
When gaseous ions are brought together from an infinite separation to form a stable, crystalline ionic solid, the process results in a release of energy. This formation process is defined as exothermic, meaning energy flows out of the system and into the surroundings. For example, when gaseous sodium ions (\(\text{Na}^+\)) and chloride ions (\(\text{Cl}^-\)) combine to form solid table salt (\(\text{NaCl}\)), a significant amount of energy is liberated.
The system moves from a high-energy state (separated, free-moving gaseous ions) to a lower-energy, more stable state (the orderly solid lattice). The energy released is assigned a negative sign (\(\Delta H\)), which is the convention for an exothermic reaction. The more energy released during the formation, the stronger the ionic attractions and the more stable the solid.
Energy Required for Ionic Solid Dissociation
The alternative perspective defines lattice energy as the energy input needed to completely separate one mole of the solid ionic compound into its isolated gaseous ions. Breaking the strong electrostatic attractions that hold the crystal lattice together requires a large amount of energy to be supplied to the system. This process of dissociation is therefore endothermic, meaning energy is absorbed.
Because energy must be absorbed to overcome the attractive forces, this definition of lattice energy is assigned a positive sign (\(\Delta H\)). This definition is frequently used in the context of the Born-Haber cycle, which is a method for indirectly calculating this value.
Factors Determining Energy Magnitude
The magnitude of the lattice energy is determined by two primary physical properties of the ions. The strength of the electrostatic attraction between the ions is directly proportional to the product of their charges. Therefore, ions with greater charges, such as \(\text{Mg}^{2+}\) and \(\text{O}^{2-}\), will have a much higher lattice energy than ions with single charges like \(\text{Na}^{+}\) and \(\text{Cl}^{-}\).
The second factor influencing the energy magnitude is the distance between the centers of the ions, which is related to their ionic radii. The attractive force is inversely proportional to the distance between the ions. Smaller ions can approach each other more closely, leading to a shorter internuclear distance and a stronger attractive force. Combining a high charge with a small ionic radius, such as in magnesium oxide (\(\text{MgO}\)), results in an exceptionally high lattice energy.
Calculating Lattice Energy
Lattice energy cannot be measured directly because the process of forming a solid from gaseous ions is too complex to isolate. Instead, it is determined indirectly using a method based on Hess’s Law, known as the Born-Haber cycle. This cycle is a series of steps that connect the formation of the ionic compound from its constituent elements to the formation of the compound from its gaseous ions.
The calculation requires combining several experimentally measurable thermodynamic values to find the single unknown, the lattice energy. These required values include the enthalpy of formation of the solid, the ionization energy of the metal, the electron affinity of the nonmetal, and the energies required to convert the elements into gaseous atoms (atomization and dissociation energies). By summing the enthalpy changes for every step in the cycle, the unknown lattice energy can be calculated, providing an accurate value for the strength of the ionic bonding.