Born - Haber Cycles

Enthalpy of Formation

The enthalpy of formation \left(\Delta_{\text{f}}\text{H}^{\varnothing}\right), is the enthalpy change when one mole of a compound is formed from its constituent elements under standard conditions with all reactants and products being in their standard states.

\text{Na}_{\text{(s)}}+\frac{1}{2}\text{Cl}_{2\text{(g)}}\rarr\text{NaCl}_{\text{(s)}}

Ionisation Enthalpy

First Ionisation Enthalpy \left(\Delta_{\text{ie 1}}\text{H}^{\varnothing}\right):
The first ionisation enthalpy is the enthalpy change needed to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous ions with a +1 charge.

\text{X}_{\text{(g)}}\rarr\text{X}^+_{\text{(g)}}+\text{e}^-

Second Ionisation Enthalpy \left(\Delta_{\text{ie 2}}\text{H}^{\varnothing}\right):
The second ionisation enthalpy is the enthalpy change needed to remove one mole of electrons from one mole of gaseous +1 ions to form one mole of gaseous ions with a +2 charge.

\text{X}^+_{\text{(g)}}\rarr\text{X}^{2+}_{\text{(g)}}+\text{e}^-

Enthalpy of Atomisation

The enthalpy of atomisation of an element \left(\Delta_{\text{at}}\text{H}^{\varnothing}\right), is the enthalpy change when one mole of gaseous atoms is formed from the element in its standard state.

\text{X}_{\text{(s)}}\rarr\text{X}_{\text{(g)}}

Bond Dissociation Enthalpy

The bond dissociation enthalpy \left(\Delta\text{diss}\text{H}^{\varnothing}\right), is the standard enthalpy change when one mole of a covalent bond is broken to create two gaseous atoms or free radicals.

\text{X}_{2\text{(s)}}\rarr 2\text{X}_{\text{(g)}}

Electron Affinity

First Electron Affinity \left(\Delta_{\text{ea 1}}\text{H}^{\varnothing}\right):
The first electron affinity is the enthalpy change when one mole of gaseous atoms gains one mole of electrons to form one mole of gaseous ions with a -1 charge.

This is an exothermic process for atoms that usually form negative ions. The ions formed are more stable than the atoms.

\text{X}_{\text{(g)}}+\text{e}^-\rarr\text{X}^-_{\text{(g)}}

Second Electron Affinity \left(\Delta_{\text{ea 2}}\text{H}^{\varnothing}\right):
The second electron affinity is the enthalpy change when one mole of gaseous -1 ions gains one mole of electrons to form one mole of gaseous ions with a -2 charge.

This is an endothermic process. This is because energy is required to overcome repulsion between negative ions and the electrons.

\text{X}^-_{\text{(g)}}\rarr\text{X}^{2-}_{\text{(g)}}+\text{e}^-

Enthalpy of Hydration

The enthalpy of hydration \left(\Delta_{\text{hyd}}\text{H}^{\varnothing}\right), is the enthalpy change when one mole of gaseous ions forms one mole of aqueous ions. \Delta_{\text{hyd}}\text{H}^{\varnothing} is always exothermic since bonds are made between the ions and the water molecules.

\Delta_{\text{hyd}}\text{H}^{\varnothing} is larger when the charge density of the ion is higher since the ion will more strongly attract the water molecules. For example, fluoride ions will have more negative hydration enthalpies than chloride ions.

\text{X}_{\text{(g)}}\rarr\text{X}_{{(aq)}}

Enthalpy of Solution

The enthalpy of solution \left(\Delta_{\text{solution}}\text{H}^{\varnothing}\right), is the standard enthalpy change when one mole of an ionic solid completely dissolves in a solvent so that the ions are well separated and they do not interact with each other.

\Delta_{\text{solution}}\text{H}^{\varnothing} tends to be either mildly exothermic or endothermic.

If the \Delta_{\text{solution}}\text{H}^{\varnothing} solution is exothermic, the substance is most likely soluble. If the\Delta_{\text{solution}}\text{H}^{\varnothing} is endothermic, the substance is most likely insoluble.

\text{XY}_{\text{(s)}}\rarr\text{X}^+_{{(aq)}}+\text{Y}^-_{\text{(aq)}}

Lattice Enthalpy

Enthalpy of Lattice Formation \left(\Delta_{\text{latt}}\text{H}^{\varnothing}\right):
The enthalpy of lattice formation is the standard enthalpy change when one mole of an ionic crystal lattice is formed from its constituent ions in gaseous form. (\Delta_{\text{latt}}\text{H}^{\varnothing}) is usually negative (exothermic).

\text{X}^+_{\text{(g)}}+\text{Y}^-_{\text{(g)}}\rarr\text{XY}_{\text{(s)}}

It is possible to define the enthalpy of lattice dissociation. This is simply the negative equivalent of \left(\Delta_{\text{latt}}\text{H}^{\varnothing}\right).