9701 #A2 Chemical Energetics: lattice energy and born haber cycle #chemistry #9701 #p4chemistry #p4

The "whole process" described in the sources refers to the use of Born-Haber cycles to determine the lattice energy of ionic compounds. Because lattice energy cannot be measured directly through a single experiment, this cycle applies Hess’s Law to calculate it using various experimental enthalpy changes. 1. Defining Lattice Energy Lattice energy ($\Delta H_{latt}^\ominus$) is the enthalpy change that occurs when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions. This process is always exothermic (negative), as energy is released when ions of opposite charges come together to form a stable crystalline lattice. 2. The Step-by-Step Construction of the Cycle To calculate lattice energy, the elements must be converted from their standard states into gaseous ions through a series of steps: Atomisation of the Metal: The solid metal is converted into gaseous atoms ($\Delta H_{at}^\ominus$). This is an endothermic process. Ionisation of the Metal: Gaseous metal atoms lose electrons to become gaseous cations. This requires Ionisation Energy ($IE$). Atomisation of the Non-metal: The non-metal element (often a diatomic gas like $Cl_2$) is converted into gaseous atoms ($\Delta H_{at}^\ominus$). Ionisation of the Non-metal: Gaseous non-metal atoms gain electrons to become gaseous anions. This involves Electron Affinity ($EA$). While the first electron affinity is usually exothermic, subsequent electron affinities (forming ions like $O^{2-}$) are endothermic due to repulsion between the incoming electron and the negative ion. Formation of the Lattice: The gaseous cations and anions combine to form the solid ionic compound, releasing the lattice energy. 3. Energy Level Diagrams and Calculation The process is best represented as an energy level diagram. In these diagrams: Upward arrows represent endothermic steps where energy is absorbed (e.g., atomisation and ionisation). Downward arrows represent exothermic steps where energy is released (e.g., enthalpy of formation, first electron affinity, and lattice energy). The Standard Enthalpy Change of Formation ($\Delta H_f^\ominus$)—the energy change when a compound is formed from its elements in their standard states—serves as the "direct route". By Hess's Law, this direct route is equal to the sum of all the individual steps in the "indirect route" (the Born-Haber cycle). 4. Summary Calculation The lattice energy can be found by rearranging the following relationship: $\Delta H_f^\ominus = \text{Sum of all intermediate enthalpy changes} + \Delta H_{latt}^\ominus$ When performing these calculations, it is vital to account for the stoichiometry of the compound (e.g., doubling the atomisation energy and electron affinity if there are two chloride ions in $MgCl_2$) and the correct signs (positive or negative) of each enthalpy change. #chemistry #9701 #0620