Born-Haber Cycle, Enthalpy of Hydration, Solution, & Bond Enthalpy

Definition: Enthalpy change when one mole of an ionic crystal is formed from its gaseous ions under standard conditions. \Delta H_{LE} is negative (exothermic).
Used to measure the strength of bonding in ionic compounds.
Lattice Dissociation Enthalpy: Energy needed to convert 1 mole of solid crystal into its scattered gaseous ions; always positive (endothermic).
Born-Haber cycles are used to determine lattice enthalpy, based on Hess’s Law.
\Delta H{LE}° \text{ (salt)} = \Delta Hf° \text{ (salt)} - \Sigma \text{(all other enthalpy changes)}

Enthalpy of formation (\Delta H_f): 1 mole of a compound is formed from its elements in their standard states under standard conditions.
Enthalpy of atomization (\Delta H_{at}): 1 mole of gaseous atoms is formed from its element under standard conditions.
Ionization energy (\Delta H_{IE}): 1 mole of electrons is removed from 1 mole of gaseous atoms under standard conditions (endothermic).
Electron affinity enthalpy (\Delta H_{ea}): 1 mole of electrons is added to one mole of gaseous atoms under standard conditions. First electron affinities are usually negative; subsequent ones are positive.

Effective nuclear charge: How much of the nuclear charge is experienced by each electron.
Shielding: Inner electrons shield outer electrons from the full attractive force of the nucleus.
Ionization energies increase across a period and decrease down a group.

Vertical line represents the enthalpy scale.
Horizontal line represents the x-axis, with the ionic solid on this line.
Elements in their standard states are placed on a line above the ionic solid, corresponding to zero energy.

Charges of the ions: Greater charges lead to greater attraction and higher lattice enthalpy.
Distance between ions: Smaller distance leads to greater attraction and higher lattice enthalpy.

Enthalpy change when 1 mole of gaseous ions become hydrated (surrounded by water molecules).
Exothermic process due to bond formation between the ion and water molecules.
Smaller and more highly charged ions have more exothermic enthalpy of hydration.

Enthalpy change when 1 mole of a solute dissolves in a solvent to form an infinitely dilute solution.
ΔHsolution=−ΔHlattice+ΔHhydration

Energy required to break one mole of a chemical bond in a gaseous substance under standard conditions; always positive.
\Delta H = \text{Bonds Broken} - \text{Bonds Formed}
Average values that do not account for variations in bond strength in different compounds or energy changes due to state changes.