9.2
The Born-Haber Cycle
Lattice Energy
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a co…
Formation of ionic bonds requires an electron transfer from a metal to a nonmetal atom - a process that is often endothermic. However, when elemental sodium and chlorine react to form a solid sodium chloride crystal, it's a highly exothermic process. But where is the energy coming from?
According to Coulomb’s law, cations and anions are attracted to each other by strong electrostatic forces into a solid array or lattice. The resulting lattice structure is stabilized by decreasing the potential energy, which is released as heat, an exothermic reaction.
The total energy associated with the formation or breakdown of a crystalline lattice into its gaseous constituents is called lattice energy.
In a solid ionic compound, a large number of charged particles interact with each other making it difficult to determine the exact value of the lattice energy experimentally. However, it can be calculated using Hess’s law in a hypothetical series of steps called the Born–Haber cycle, which represents the formation of an ionic compound from its constituent elements.
For example, the Born-Haber cycle for sodium chloride formation considers two alternate routes, one direct and another indirect. The direct route represents the standard enthalpy of formation of NaCl from elemental sodium and chlorine.
The indirect route has five steps. In the first step, solid-state sodium is converted into its gaseous form. Next, diatomic chlorine molecules dissociate into gaseous chlorine atoms.
The third and fourth steps account for the electron transfer to form ions. An electron is removed from the gaseous sodium to form a sodium cation. The electron is then taken up by the gaseous chlorine to form a chloride anion.
In the final step, the electrostatic attraction between the gaseous ions leads to the formation of the lattice structure.
Hess’s law states that the change in the overall enthalpy of a stepwise process is the sum of the enthalpy changes of each step. Meaning the enthalpy value of the direct route equals the sum of enthalpies of the five steps.
By solving the equation for lattice energy, a large negative value is determined, which signifies an exothermic reaction.
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Q1: Why is sodium chloride formation exothermic when ionic bonding requires energy?
Ionic bond formation involves electron transfer, which is endothermic. However, the resulting cations and anions attract each other through strong electrostatic forces, forming a stable lattice structure. This lattice formation releases significant energy as heat, making the overall process highly exothermic. The energy released from lattice stabilization exceeds the energy required for electron transfer.
Q2: What is lattice energy and how does it relate to ionic compound stability?
Lattice energy is the total energy required to separate one mole of solid ionic compound into gaseous ions, or equivalently, the energy released when gaseous ions combine to form a solid lattice. A larger magnitude of lattice energy indicates stronger electrostatic attractions between ions and greater stability of the ionic compound. For sodium chloride, the lattice energy is 769 kJ/mol.
Q3: How does the Born-Haber cycle calculate lattice energy indirectly?
The Born-Haber cycle applies Hess's law by breaking ionic compound formation into five hypothetical steps: sublimation of the metal, dissociation of nonmetal molecules, ionization of metal atoms, electron affinity of nonmetal atoms, and lattice formation. Since enthalpy is a state function, the sum of enthalpy changes for these steps equals the standard enthalpy of formation. Solving for lattice energy yields a large negative value, confirming the exothermic lattice formation.
Q4: How do ion size and charge affect lattice energy?
Lattice energy increases rapidly as ion charges increase and ion sizes decrease. Doubling the charges of both cation and anion quadruples the lattice energy. For example, MgO has a much higher lattice energy (3900 kJ/mol) than LiF (1023 kJ/mol) due to higher ion charges. Smaller ions like F– produce higher lattice energies than larger ions like I– when bonded to the same cation, demonstrating the effect of trends in lattice energy ion size and charge.
Q5: Why are lattice energies much higher than covalent bond dissociation energies?
Lattice energies typically range from 600–4000 kJ/mol, while covalent bond dissociation energies are typically 150–400 kJ/mol for single bonds. This difference exists because lattice energy involves many simultaneous electrostatic interactions between numerous cations and anions in an extended crystal structure, whereas bond dissociation energy measures the interaction between just two atoms in a covalent bond.
Q6: Can the Born-Haber cycle determine electron affinity if other values are known?
Yes, the Born-Haber cycle can calculate any one quantity in the lattice energy equation if all other values are known. If the enthalpy of sublimation, ionization energy, bond dissociation enthalpy, lattice energy, and standard enthalpy of formation are available, the cycle can be rearranged to determine the electron affinity of an atom. This demonstrates the versatility of Hess's law in thermochemical calculations.
Q7: What are the five steps in the Born-Haber cycle for sodium chloride?
The five steps are: (1) sublimation of solid sodium to gaseous sodium, (2) dissociation of diatomic chlorine into gaseous chlorine atoms, (3) ionization of gaseous sodium to form Na+ cations, (4) electron affinity of gaseous chlorine to form Cl– anions, and (5) electrostatic attraction between gaseous ions forming the solid lattice. These steps represent an indirect route equivalent to the direct formation of NaCl from its elements.