Lattice Enthalpy (OCR A Level Chemistry)

• Thermodynamics literally means heat and movement and is the branch of physical chemistry that deals with heat, energy, temperature and the physical properties of matter
• Energy cycles are special representations of enthalpy changes for ionic compounds using the principles of Hess's Law
• In order to understand how energy cycles work you need a good knowledge of some key enthalpy change definitions
• Enthalpy change (ΔH) refers to the amount of heat energy transferred during a chemical reaction, at a constant pressure
• The definitions you need to know are:
  • enthalpy of formation
  • ionisation enthalpy
  • enthalpy of atomisation
  • bond enthalpy
  • electron affinity

Enthalpy of formation

• The enthalpy of formation (ΔH_f^ꝋ) is the enthalpy change when 1 mole of a compound is formed from its elements under standard conditions
  • Standard conditions in this syllabus are a temperature of 298 K and a pressure of 100 kPa

• The ΔH_f^ꝋ can be endothermic or exothermic as the energy change is the sum of the bonds broken and formed, so the enthalpy change can have positive or negative values
• Equations can be written to show the standard enthalpy change of formation (ΔH_f^ꝋ) for compounds
• For example, the enthalpy of formation sodium chloride is shown as:

Na (s) + ½Cl₂ (g) → NaCl (s)            ΔH_f^ꝋ = -411 kJ mol ^-1

• Notice that enthalpy of formation only refers to compounds
  • By definition the enthalpy of formation of elements is zero

Ionisation enthalpy

• The ionisation enthalpy (ΔH_ie^ꝋ) of an element is the amount of energy required to remove an electron from a gaseous atom of an element to form a gaseous ion under standard conditions
• Ionisation enthalpy is always endothermic as energy is need to overcome the attraction between an electron and the nucleus
• The first ionisation energy is the energy required to remove one mole of electrons from one mole of gaseous atoms of an element to form one mole of gaseous 1+ ions
  • E.g. the first ionisation energy of gaseous sodium:

Na (g) → Na⁺ (g) + e^–          ΔH_ie^ꝋ = +500 kJ mol^-1

Enthalpy change of atomisation

• The standard enthalpy change of atomisation (ΔH_at^ꝋ) is the enthalpy change when 1 mole of gaseous atoms is formed from its element under standard conditions
• The ΔH_at^ꝋ is always endothermic as energy is always required to break any bonds between the atoms in the element, to break the element into its gaseous atoms
  • Since this is always an endothermic process, the enthalpy change will always have a positivevalue

• Equations can be written to show the standard enthalpy change of atomisation (ΔH_at^ꝋ) for elements
• For example, sodium in its elemental form is a solid
• The standard enthalpy change of atomisation for sodium is the energy required to form 1 mole of gaseous sodium atoms:

Na (s) → Na (g)           ΔH_at^ꝋ = +108 kJ mol ^-1

Bond enthalpy

• The amount of energy required to break one mole of a specific covalent bond in the gas phase is called the bond dissociation energy
  • Bond dissociation energy (E) is usually just simplified to bond energy or bond enthalpy

• In symbols, the type of bond broken is written in brackets after E
  • Eg. E (H-H) is the bond energy of a mole of single bonds between two hydrogen atoms

• Bond enthalpy is usually treated as a bond breaking process, so it is quoted in data tables as an endothermic energy change with positive values
  • For bond forming processes simply put a negative sign in front of the value

• Equations can be written to show the bond enthalpy
• For example, chlorine in its elemental form is a gas
• The bond enthalpy of chlorine is shown as

Cl₂ (g) → 2Cl (g)    E(Cl-Cl) = +242 kJ mol ^-1

• Notice this looks very similar to atomisation enthalpy for chlorine
• However, atomisation enthalpy, by definition, produces 1 mole of atoms, whereas bond enthalpy is expressed per mole of bonds
• So the atomisation enthalpy of chlorine would be half the bond enthalpy

½Cl₂ (g) → Cl (g)    ΔH_at^ꝋ = +121 kJ mol ^-1

• If the element was a liquid, instead of a gas, then atomisation enthalpy would also include vaporisation enthalpy - a change of state, before the bonds are broken

Lattice energy

• As with bond enthalpy, lattice enthalpy (ΔH_latt^ꝋ) can be expressed as a formation or dissociation process
• As a formation process, it is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions (under standard conditions)
• The ΔH_latt^ꝋ is therefore exothermic, as when ions are combined to form an ionic solid lattice there is an extremely large release of energy
  • Since this is an exothermic process, the enthalpy change will have a negative value
  • Because of the huge release in energy when the gaseous ions combine, the value will be a very large negative value

• The large negative value of ΔH_latt^ꝋ suggests that the ionic compound is much more stable than its gaseous ions
  • This is due to the strong electrostatic forces of attraction between the oppositely charged ions in the solid lattice
  • Since there are no electrostatic forces of attraction between the ions in the gas phase, the gaseous ions are less stable than the ions in the ionic lattice
  • The more exothermic the value is, the stronger the ionic bonds within the lattice are

• The ΔH_latt^ꝋ of an ionic compound cannot be determined directly by one single experiment
• Multiple experimental values and an energy cycle are used to find the ΔH_latt^ꝋ of ionic compounds
• The lattice energy (ΔH_latt^ꝋ) of an ionic compound can be written as an equation
  • For example, sodium chloride is an ionic compound formed from sodium (Na⁺) and chloride (Cl^-) ions
  • Since the lattice energy is the enthalpy change when 1 mole of sodium chloride is formed from gaseous sodium and chloride ions, the equation for this process is:

Na⁺(g) + Cl^-(g) → NaCl (s)  ΔH_latt^ꝋ = -776 kJ mol ^-1