Born-Haber Cycles

Enthalpy of Atomization ($ΔH_{at}$): The energy required to form one mole of gaseous atoms from an element in its standard state. This is always endothermic as it involves breaking metallic or covalent bonds.

Ionization Enthalpy ($IE$): The energy required to remove one mole of electrons from one mole of gaseous atoms to form gaseous 1+ ions. Subsequent ionization energies (e.g., $IE_2$) are always higher due to increased attraction from the nucleus.

Electron Affinity ($EA$): The enthalpy change when one mole of gaseous atoms gains one mole of electrons. The first electron affinity is usually exothermic, but the second is endothermic because energy is needed to overcome the repulsion between the negative ion and the incoming electron.

Step 1: The Baseline: Start by placing the elements in their standard states on a horizontal line. This is the reference point for the cycle.

Step 2: Upward (Endothermic) Steps: Draw arrows upwards for processes that require energy. This includes atomizing the metal and non-metal, and the ionization of the metal atoms.

Step 3: Downward (Exothermic) Steps: Draw arrows downwards for processes that release energy. This typically includes the first electron affinity of the non-metal and the final lattice formation step.

Step 4: Closing the Loop: The enthalpy of formation ($ΔH_f$) connects the elements directly to the ionic solid. According to Hess's Law, the direct route ($ΔH_f$) equals the sum of all indirect steps.

Check Stoichiometry: Always verify the number of moles in the chemical equation. For a compound like $MgCl_2$, you must double the enthalpy of atomization and the electron affinity for chlorine because two moles of chlorine atoms are involved.

State Symbols are Mandatory: Marks are frequently lost for omitting $(s)$, $(g)$, or $(l)$. The definitions of these enthalpy changes are strictly tied to specific physical states.

Sign Consistency: Ensure that endothermic steps (atomization, ionization) have positive values and exothermic steps (formation, lattice enthalpy) have negative values in your final calculation.

The 'Direct vs Indirect' Rule: Use the formula: $\Delta H_f = \sum \Delta H_{atomization} + \sum IE + \sum EA + \Delta H_{latt}$. Rearrange this to solve for the unknown, usually $\Delta H_{latt}$.

Confusing Bond Enthalpy and Atomization: For diatomic gases like $Cl_2$, the enthalpy of atomization is half the bond dissociation enthalpy because atomization produces one mole of atoms, while bond breaking produces two.

Second Electron Affinity Sign: Students often assume all electron affinities are exothermic. Remember that $EA_2$ is always endothermic ($+$) because you are adding a negative electron to an already negative ion.

Direction of Lattice Enthalpy: Be careful whether the question asks for lattice formation (exothermic, arrow down) or lattice dissociation (endothermic, arrow up). They are equal in magnitude but opposite in sign.