What is lattice enthalpy? How do you calculate the lattice enthalpy of sodium chloride by using Born-Haber’s cycle?

Lattice enthalpy, also known as lattice energy, is the energy released or absorbed when gaseous ions come together to form an ionic solid. It is a measure of the strength of the ionic bond in a compound. Lattice enthalpy is a crucial factor in determining the stability and properties of ionic compounds.

Born-Haber's cycle is a series of hypothetical steps used to calculate the lattice enthalpy of an ionic compound. It combines different thermodynamic quantities, such as ionization energy, electron affinity, and enthalpy of sublimation, to calculate the overall lattice enthalpy of the compound.

To calculate the lattice enthalpy of sodium chloride (NaCl) using Born-Haber's cycle, we need to follow these steps:

Step 1: Write the balanced equation for the formation of NaCl from its elements.

The equation for the formation of NaCl is:

1/2 Na2(g) + 1/2 Cl2(g) → NaCl(s)

Step 2: Break down the steps in the Born-Haber's cycle:

a. Sublimation of sodium (Na) metal:

Na(s) → Na(g) ΔHsub

b. Ionization of sodium (Na) gas to form Na+ ion:

Na(g) → Na+(g) + e^- ΔHion

c. Dissociation of chlorine (Cl2) gas to form Cl atoms:

Cl2(g) → 2 Cl(g) 1/2 ΔHdiss

d. Electron affinity of chlorine (Cl) gas to form Cl^- ion:

Cl(g) + e^- → Cl^-(g) ΔHea

e. Formation of NaCl solid from Na+ and Cl^- ions:

Na+(g) + Cl^-(g) → NaCl(s) ΔHf

Step 3: Apply Hess's law to construct the Born-Haber's cycle:

The sum of the enthalpy changes in all the steps is equal to the lattice enthalpy (ΔHlattice) of NaCl:

ΔHlattice = ΔHsub + ΔHion + 1/2 ΔHdiss + ΔHea + ΔHf

Step 4: Substitute the known values for each enthalpy change:

You will need to look up the values for the sublimation enthalpy (ΔHsub), ionization enthalpy (ΔHion), dissociation enthalpy (ΔHdiss), electron affinity (ΔHea), and enthalpy of formation (ΔHf) of NaCl and its constituent elements. These values are usually provided in reference tables.

Step 5: Calculate the lattice enthalpy:

Simply add up all the enthalpy changes from the steps above to get the lattice enthalpy (ΔHlattice) of NaCl.

It's important to note that Born-Haber's cycle is based on various assumptions and simplifications, and the calculated value might not perfectly match the experimental value due to factors like lattice defects and thermal effects. Nonetheless, Born-Haber's cycle is a valuable theoretical tool for estimating lattice enthalpies of ionic compounds.