Lattice Energy

Full Notes

Lattice enthalpies and Born–Haber cycles have been outlined in more detail here.
This page is just what you need to know for OCR A-level :)

Lattice Enthalpy (ΔH_latt) is the enthalpy change when 1 mol of an ionic lattice forms from gaseous ions.

It is always exothermic and can be considered a measurement of the bonding strength in ionic compounds.

Lattice energies can’t be measured directly in an experiment however can be determined using experimental data with Hess’s Law.

Born–Haber cycles are a type of Hess cycle used to calculate lattice energy.

Key Definitions

Enthalpy change of atomisation (ΔH_at):
The enthalpy change when 1 mole of gaseous atoms is formed from an element in its standard state.
Example Na(s) → Na(g)

Lattice enthalpy (ΔH_LE):
The enthalpy change when 1 mole of an ionic solid is formed from its gaseous ions.
Example Na⁺(g) + Cl⁻(g) → NaCl(s)
Lattice energy is always exothermic (negative value).

First Ionisation Energy First ionisation energy (1st IE) is the energy required to remove 1 mole of electrons from 1 mole of gaseous atoms of an element (to form 1 moles worth of ions with a 1+ charge).
Example Na(g) → Na⁺(g) + e⁻
First ionisation energy is always exothermic (negative value).

Electron Affinity

• First electron affinity is the energy change when 1 mole of gaseous atoms gains electrons to form 1 mole of 1⁻ ions.
  Example Cl(g) + e⁻ → Cl⁻(g)
  This is usually exothermic.
• Second electron affinity is for adding an electron to a negatively charged ion (e.g. O⁻ to O²⁻), and is endothermic due to repulsion.

Constructing a Born–Haber Cycle

1. Write the enthalpy of formation equation (solid compound from elements).
2. Convert elements to gaseous atoms (atomisation enthalpy).
3. Remove electrons from metal atoms (ionisation energy).
4. Add electrons to non-metal atoms (electron affinity).
5. Combine gaseous ions to form lattice (lattice enthalpy).

Example Born–Haber Cycle for NaCl

• Step 1: Formation of NaCl (ΔH_f)
  Na(s) + ½Cl₂(g) → NaCl(s)
• Step 2: Atomisation of Na (ΔH_atom)
  Na(s) → Na(g)
• Step 3: Atomisation of Cl₂ (ΔH_atom)
  ½Cl₂(g) → Cl(g)
• Step 4: Ionisation Energy of Na (IE₁)
  Na(g) → Na⁺(g) + e⁻
• Step 5: Electron Affinity of Cl (EA₁)
  Cl(g) + e⁻ → Cl⁻(g)
• Step 6: Lattice Enthalpy (ΔH_le)
  Na⁺(g) + Cl⁻(g) → NaCl(s)

By rearranging these enthalpy changes and substituting experimental values into the cycle we can use Hess’s Law to calculate ΔH_le.

Bond Strength from Lattice Energy

A more negative (larger magnitude) lattice energy means stronger electrostatic attraction between ions. This allows us to use lattice energies as a measure of bonding strength in ionic compounds.

Factors Affecting Lattice Enthalpy

Charge and ionic radius affect the magnitude of lattice enthalpy:

• Charge: Higher ion charge = stronger electrostatic attraction between ions = more exothermic lattice enthalpy.
  Example Mg²⁺ gives more exothermic lattice enthalpies than Na⁺.
• Ionic radius: Smaller radius = stronger attraction = more exothermic lattice enthalpy.

Down a group, ionic radius increases and lattice enthalpy becomes less exothermic.

Solution and Hydration Enthalpies

Born–Haber cycles can also be used when dealing with enthalpies of solution and hydration.

Enthalpy of solution (ΔH_sol):
The enthalpy change when 1 mole of an ionic compound dissolves in enough water to form an infinitely dilute solution.

Example NaCl(s) → Na⁺(aq) + Cl⁻(aq)

Enthalpy of hydration (ΔH_hyd):
The enthalpy change when 1 mole of gaseous ions dissolves in water to form aqueous ions.

Example

Na⁺(g) → Na⁺(aq)
Cl⁻(g) → Cl⁻(aq)

Energy Cycle for Solution Enthalpy

An energy cycle can be constructed that links enthalpy of solution (ΔH_sol), hydration enthalpies (ΔH_hyd) and lattice energy (ΔH_latt):

Matt’s exam tip

For these energy cycles, the lattice enthalpy is given as a positive value as the arrow direction is going from the ionic solid to the gaseous ions, this is breaking apart the lattice. This is the exact same value as lattice energy however it has a positive sign (+ΔH) rather than negative as it is an endothermic process.

Energy cycle equation:

• ΔH_LE is positive (energy needed to break lattice).
• ΔH_hyd is negative (energy released when ions are hydrated).

Factors Affecting Enthalpy of Hydration

The magnitude of ΔH_hyd depends on:

• Ionic charge:
  Higher charge = stronger attraction to water = more exothermic ΔH_hyd.
  Example Mg²⁺ has more negative ΔH_hyd than Na⁺.
• Ionic radius:
  Smaller ions = stronger electrostatic attraction to water = more exothermic ΔH_hyd.
  Example Li⁺ is more exothermic than Cs⁺.

So, small, highly charged ions have more exothermic hydration enthalpies.

Summary

• Lattice enthalpy is the energy released when 1 mole of an ionic solid forms from gaseous ions.
• Born–Haber cycles are used to calculate lattice enthalpies from experimental data.
• Factors affecting lattice enthalpy: ionic charge and ionic radius.
• Enthalpy of solution = lattice enthalpy + hydration enthalpies.
• Hydration enthalpies are more exothermic for small, highly charged ions.