Chemistry Chapter 19: Lattice Energy

CHEMISTRY KEYWORDS:

Lattice Energy, ΔH_latt: Energy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions.

Ion Polarisation: Distortion of the electron cloud of an anion by a neighbouring cation. The distortion is greatest when the cation is small and highly charged.

Polarising Power (of a Cation): Ability of a cation to attract the electron cloud of an anion and distort it.

Standard Enthalpy Change of Solution, ΔH_sol: Energy absorbed or released when 1 mole of an ionic solid dissolves in sufficient water to form a very dilute solution under standard conditions.

Ion-Dipole Bond: A bond formed between an ion and a polar compound.

 

CHEMISTRY DEFINITIONS:

Standard Enthalpy Change of Atomisation, ΔH_at: Enthalpy change when 1 mole of gaseous atoms is formed from its element under standard conditions.

First Electron Affinity, 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.

Second Electron Affinity, EA₂: Enthalpy change when 1 mole of electrons is added to 1 mole of gaseous 1- ions to form 1 mole of gaseous 2- ions under standard conditions.

Standard Enthalpy Change of Hydration, ΔH_hyd: Enthalpy change when 1 mole of a specified gaseous ion dissolves in sufficient water to form a very dilute solution under standard conditions.

 

CHEMISTRY IMPORTANT NOTES:

When ions combine to form an ionic solid, a significant amount of energy is released; the reaction is highly exothermic. This energy is given out when ions of opposite charges come together to form a crystalline lattice.

It is the gaseous ions that combine to form the ionic solid.

Lattice energy is always exothermic; the value of ΔH_latt is always negative, as it specifies the bonding together of ions and not the separation of ions.

The large exothermic value of lattice energy shows that the ionic lattice is very stable with respect to its gaseous ions. The more exothermic the lattice energy, the stronger the ionic bonding in the lattice.

Lattice energy is more accurately called the lattice enthalpy.

Lattice energy is the internal energy change when 1 mole of an ionic compound is formed from its gaseous ions at 298 K.

Values of ΔH_at are always positive (endothermic), as energy must be supplied to break the bond holding the atoms in the element together.

The energy change occurring when a gaseous non-metal atom accepts one electron is called the electron affinity.

Electron affinities for non-metal atoms get more negative (more exothermic) across a period with a maximum at Group 17, but the pattern is not always clear. The trend is less negative (less exothermic) electron affinities as you go down the group, apart from the first member in the group.

The stronger the attraction, the greater the amount of energy released.

·       The greater the nuclear charge, the greater the attractive force between the nucleus and outer electrons. More energy is released when an atom gains an electron.

·       The further away the outer shell electrons are from the positive nuclear charge, the less the attractive force between the nucleus and the outer shell electrons is. Since the number of electron shells (and atomic radius) increases down Groups 16 and 17, electron affinity decreases going from Chlorine to Bromine to Iodine.

·       The greater the number of electron shells, the greater the power of inner shell electrons to shield the outer shell electrons from the nuclear charge. This helps to decrease the electron affinity as you go from Chlorine to Iodine.

Lattice energy and ion size: (As ion size increases, the lattice energy becomes less exothermic.)

·       Lattice energy gets less exothermic as the size of the cation increases from Li⁺ to Cs⁺.

·       Lattice energy gets less exothermic as the size of the anion increases from F^- to I^-.

Ions with the same ionic charge have a lower charge density if their radius is larger, resulting in weaker electrostatic forces of attraction in the ionic lattice.

Lattice energy and ion charge: (Lattice energy becomes more exothermic as ionic charge increases)

For ions of similar size, the greater the ionic charge, the higher the charge density, resulting in stronger ionic bonds being formed.

Ion polarisation results in a distortion of the electron cloud of the anion, and the anion is no longer spherical.

Factors affecting ion polarisation:

1.       The degree of polarisation of an anion depends on:

·       Charge density of cation.

·       Ease with which an anion can be polarised: its polarizability.

2.       An anion is more likely to be polarised if:

·       Cation is small

·       Cation has a charge of 2+ or 3+

·       Anion is large

·       Anion has a charge of 2- or 3-

The more positive the enthalpy change, the more stable the carbonate relative to its oxide and carbon dioxide.

BaCO₃ > SrCO₃ > CaCO₃ > MgCO₃

Trend of ion polarisation:

·       Carbonate ion has a relatively large ionic radius, so a small highly charged cation easily polarises it.

·       Increase in ionic radius down the group: Mg⁺² < Ca⁺² < Sr⁺² < Ba⁺²

·       The smaller the ionic radius of the cation, the better it is at polarising the carbonate ion.

·       Degree of polarisation of the carbonate ion: Mg⁺² > Ca⁺² > Sr⁺² > Ba⁺²

·       The greater the polarisation of the carbonate ion, the easier it is to weaken a carbon-oxygen bond in the carbonate and form carbon dioxide and the oxide on heating.

Unequal changes in the lattice energies of the Group 2 carbonates and the Group 2 oxides as the cation size increases can be related to the increasing thermal stability down the group. 

A compound is likely to be soluble in water only if ΔH_sol is negative or has a small positive value; substances with large positive values of ΔH_sol are relatively insoluble.

The value of ΔH_hyd is more exothermic for ions with the same charge but smaller ionic radii. Charge density is greater when the ionic radius is smaller, lower shielding. This effect is greater than the effect of increased nuclear charge.

The value of ΔH_hyd is more exothermic for ions with the same radii but a larger charge. Charge density is greater, as the charge is greater for the same size of atom. A greater number of positive charges in the nucleus, so ion-dipole attractions are stronger.

Solubility of Group 2 sulfates decreases as the radius of the metal ion increases.

Change in hydration enthalpy down the group:

·       Smaller ions (with the same charge) have greater enthalpy changes of hydration.

·       Enthalpy change of hydration decreases (less exothermic). Mg⁺² > Ca⁺² > Sr⁺² > Ba⁺²

·       Decrease is relatively large down the group and depends entirely on the increase in size of the cation, as the anion is unchanged.

Change in lattice energy down the group:

·       Lattice energy is greater if ions with the same charge forming the lattice are small.

·       Lattice energy decreases. Mg⁺² > Ca⁺² > Sr⁺² > Ba⁺²

·       Lattice energy is also inversely proportional to the sum of the radii of the anion and cation.

·       Sulfate ion contributes a relatively greater part to the change in lattice energy down the group.

·       Decrease in lattice energy is relatively smaller down the group and more by the size of the large sulfate ion than the size of the cations.

Lattice energy of sulfates decreases (less exothermic) by relatively smaller values down the group. Enthalpy change of hydration decreases (less exothermic) by relatively larger values down the group. By using Hess’s Law, the value of ΔH_sol becomes more endothermic down the group. Solubility of Group 2 sulfates decreases down the group. 

 

SUMMARY:

ΔH_latt = ΔH_f – ΔH₁ (Hess’s Law)

ΔH_latt + ΔH_sol = ΔH_hyd

The lattice energy is the energy change when gaseous ions come together to form 1 mole of a solid lattice under standard conditions.

The standard enthalpy change of atomisation is the enthalpy change when 1 mole of gaseous atoms is formed from the element in its standard state under standard conditions.

The first electron affinity is the 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.

A Born-Haber cycle is a type of enthalpy cycle (Hess cycle) that includes lattice energy, enthalpy change of formation and relevant electron affinities, enthalpy changes of atomisation and enthalpy changes of ionisation.

The thermal stability of carbonates and nitrates of Group 2 elements depends on the degree to which the Group 2 cation is able to polarise the larger anion:

·       Smaller cations have a high charge density and are better polarisers of a given anion.

·       Larger anions are more polarised by a given cation.

The standard enthalpy change of solution is the enthalpy change when 1 mole of an ionic solid dissolves in sufficient water to form a very dilute solution. It may be exothermic or endothermic.

The enthalpy change of hydration is the enthalpy change when 1 mole of gaseous ions dissolves in sufficient water to form a very dilute solution. It is always exothermic.

Hess’s law can be applied to construct energy cycles to determine enthalpy changes of solution and enthalpy changes of hydration.

The decrease in solubility of Group 2 sulfates down the group can be explained in terms of the relative values of the enthalpy change of hydration and the corresponding lattice energy.