Lattice Energy and Associated Enthalpy Changes

Enthalpy Change of Atomisation

The enthalpy change when 1 mole of gaseous atoms is formed from its element under standard conditions.
Symbol: ΔH_{at}^\ominus
Standard conditions are a temperature of 298 K and a pressure of 101 kPa.
ΔH_{at}^\ominus is always endothermic because energy is required to break bonds between atoms in the element to form gaseous atoms.
The enthalpy change will always have a positive value.

Examples

Potassium:
- Elemental form: solid
- K(s) → K(g)
Mercury:
- Elemental form: liquid
- Hg(l) → Hg(g)

Electron Affinity

The first electron affinity (EA1) is generally exothermic. Second and third electron affinities are always endothermic.
EA1: Enthalpy change when 1 mole of electrons is added to 1 mole of gaseous atoms to form 1 mole of gaseous ions with a single negative charge under standard conditions.
EA1 is usually exothermic, so the value is usually negative.
Successive electron affinities (EA2, EA3) represent the formation of 1 mole of gaseous ions with 2- and 3- charges, respectively.
Second and third electron affinities are endothermic because the incoming electron is added to an already negative ion.
Energy is required to overcome repulsive forces between the incoming electron and the negative ion, so values are positive.

Electron Affinity Equations

Equation	Endothermic/Exothermic
X(g) + e^- → X^-(g)	Exothermic
X^-(g) + e^- → X^{2-}(g)	Endothermic
X^{2-}(g) + e^- → X^{3-}(g)	Endothermic

Factors Affecting Electron Affinity

Depends on how strongly the incoming electron is attracted to the nucleus.
Greater attractive forces → more energy released → more exothermic (more negative EA1 value).
Factors are the same as those affecting ionization energy:
- Nuclear Charge: Greater nuclear charge → stronger attractive forces.
- Distance: Greater distance → weaker attraction.
- Shielding: Greater number of shells → greater shielding effect → weaker attraction.

Trends in Electron Affinity

Electron affinities of non-metals become more exothermic across a period, with a maximum at Group 17.
Generally, a downwards trend in the size of the electron affinities of the elements in Group 16 and 17.
Electron affinities generally become less exothermic down the group, except for oxygen and fluorine.

Group 16 and 17

Chlorine has a greater nuclear charge than sulfur.
Chlorine has a greater attractive force, so EA1 of Cl is more exothermic than for S.
Down the group:
- Outermost electrons are held less tightly because they are further away.
- Increased electron shells cause increased shielding.
- It gets more difficult to add an electron to the outer shell.
- Less energy is released, so EA1 becomes less exothermic.
Exception: Fluorine
- Smaller atomic radius → high electron density.
- More repulsion between the incoming electron and existing electrons.
- Repulsive forces reduce attractive forces, so EA1 of fluorine is less exothermic than expected.

Lattice Energy

'Lattice energy is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions.'
Values highly EXOTHERMIC strong electrostatic attraction between oppositely charged ions a lot of energy is released as the bond is formed relative values are governed by the charge density of the ions.
Example Lattice Energy Definition NaCl(s) → Na+(g) + Cl–(g)
The lattice energy (ΔH_{latt}^\ominus) is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions.
ΔH_{latt}^\ominus is always exothermic, indicating a large release of energy when ions combine to form a solid lattice. This means it has a negative value.
Large negative value suggests the ionic compound is much more stable than its gaseous ions due to strong electrostatic forces of attraction.
More exothermic value indicates stronger ionic bonds within the lattice.
Cannot be determined directly by a single experiment; multiple experimental values and an energy cycle are used.
The lattice energy (ΔH_{latt}^\ominus) of an ionic compound can be written as an equation.

Examples of Lattice energy equations:

Magnesium chloride:
- Mg^{2+}(g) + 2Cl^-(g) → MgCl_2(s)
Magnesium oxide:
- Mg^{2+}(g) + O^{2-}(g) → MgO(s)
Lithium chloride:
- Li^+(g) + Cl^-(g) → LiCl(s)

Lattice Energy and Periodicity

Lattice energy can also be determined from Coulomb’s law:
- Directly proportional to charge on each ion.
- Inversely proportional to size of compound (sum of ionic radii).
Lattice energies decrease for compounds of a particular cation with increasing atomic number of the anion, and vice versa.

Factors Affecting Lattice Energy

As the size of the ion increases, the lattice energy becomes less exothermic.
Larger ions mean the center of positive charge is farther from the negative charge.
Larger ion = weaker attraction = smaller lattice energy
Charge is more spread out over larger ions, which are also further apart.
The attraction between ions occurs between the centers of the ions, so the bigger the ions, the bigger the distance between the center of the ions
Therefore, the electrostatic forces of attraction between the oppositely charged ions in the lattice are weaker

Examples

The lattice energy of caesium fluoride (CsF) is less exothermic than the lattice energy of potassium fluoride (KF)
Since both compounds contain a fluoride (F-) ion, the difference in lattice energy must be due to the caesium (Cs+) ion in CsF and potassium (K+) ion in KF
Potassium is a Group 1 and Period 4 element
Caesium is a Group 1 and Period 6 element.
The Cs+ ion is larger than the K+ ion.
There are weaker electrostatic forces of attraction between the Cs+ and F- ions compared to K+ and F- ions
As a result, the lattice energy of CsF is less exothermic than that of KF
Lattice energy gets more exothermic with increased ionic charge, resulting in stronger electrostatic attraction.
Larger charge = stronger attraction = larger lattice energy
Ion charge is generally more important than ion size.
- The force of attraction between oppositely charged particles is directly proportional to the product of the charges.
For example, Larger charge means the ions are more strongly attracted.
The lattice energy of calcium oxide (CaO) is more exothermic than the lattice energy of potassium chloride (KCl)
- Calcium oxide is an ionic compound which consists of calcium (Ca2+) and oxide (O2-) ions
- Potassium chloride is formed from potassium (K+) and chloride (Cl-) ions
- The ions in calcium oxide have a greater ionic charge than the ions in potassium chloride
- This means that the electrostatic forces of attraction are stronger between the Ca2+ and O2- compared to the forces between K+ and Cl-

Born-Haber Cycles

Used to calculate lattice energy (ΔH_{latt}^\ominus) of an ionic compound.
Requires knowing:
- Enthalpy change of formation (ΔH_f^\ominus).
- The sum of various enthalpy changes involved when going from elements in their standard states to their gaseous ions (ΔH_1^\ominus). This includes:
  - Enthalpy change of atomization of each element.
  - First ionization energy of the metal.
  - Successive ionization energies of the metal (if applicable).
  - First electron affinity of the non-metal.
  - Successive electron affinities of the non-metal (if applicable).
Order is important: atomization → ionization → electron affinity.
Hess’s law: the enthalpy change in a chemical reaction is the same regardless of the route taken, as long as the final and initial conditions and states of reactants and products are the same for each route

Calculating Lattice Energy

Lattice energy cannot be measured directly; it is calculated using a Born-Haber cycle.
Formula: ΔH{latt} = ΔHf - ΔH_1
Example cycle using Lithium Fluoride: ΔH_{latt} = AH - {AH [Li] + AH° [Li] + AH° [F] + AH [F]}
Important Enthalpy Changes:
- Enthalpy change of formation of NaCl: Na(s) + ½Cl_2(g) → NaCl(s)
- Enthalpy of atomisation of sodium: Na(s) → Na(g)
- Enthalpy of atomisation of chlorine: ½Cl_2(g) → Cl(g)
- 1st Ionisation Energy of sodium: Na(g) → Na^+(g) + e^-
- Electron Affinity of chlorine: Cl(g) + e^- → Cl^-(g)
- Lattice Enthalpy of NaCl: Na^+(g) + Cl^-(g) → NaCl(s)