5.5.d. Lattice Enthalpy

The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociates into its ions in gaseous state. NaCl(s) → Na⁺(g) + Cl⁻(g); ∆latticeH⁰ = +788 kJ mol⁻¹.

Lattice enthalpy describes the energy required to separate one mole of an ionic solid into its ions in the gas phase. For example, when sodium chloride (NaCl) is broken apart into sodium ions (Na⁺) and chloride ions (Cl⁻), it requires energy, resulting in a positive lattice enthalpy value, such as +788 kJ/mol for NaCl.

Think of lattice enthalpy like pulling apart a magnet that’s been stuck to a metal surface. Just as it takes energy to pull the magnet away (which might be difficult if the magnet is strong), it similarly takes energy to separate the ions in a crystalline salt like NaCl.

Since it is impossible to determine lattice enthalpies directly by experiment, we use an indirect method where we construct an enthalpy diagram called a Born-Haber cycle.

The Born-Haber cycle is a thermodynamic cycle that shows how to calculate the lattice enthalpy using measured quantities. This involves various steps including sublimation of the metal, ionization of atoms, and the formation of gaseous ions. The lattice enthalpy can then be inferred as the sum of these steps.

Consider it like planning a road trip where you can’t directly measure the distance between two points but know the distances of various legs of the journey. You can add those distances to get the total distance. Here, the individual steps of the Born-Haber cycle are the ‘legs’ of the journey to calculate the lattice enthalpy.

Let us now calculate the lattice enthalpy of Na+Cl−(s) by following steps given below :

1. Na(s) → Na(g) (sublimation of sodium metal, ∆subH⁰ = 108.4 kJ mol⁻¹)
2. Na(g) → Na⁺(g) (ionization of sodium atoms, ionization enthalpy ∆iH⁰ = 496 kJ mol⁻¹)
3. ½Cl2(g) → Cl(g) (dissociation of chlorine, this reaction enthalpy is half the bond dissociation enthalpy, ½∆bondH⁰ = 121 kJ mol⁻¹)
4. Cl(g) → Cl⁻(g) (electron gained by chlorine atoms, ∆egH⁰ = −348.6 kJ mol⁻¹).

To find the lattice enthalpy of sodium chloride, we take the following steps, where each step represents a change in energy:

1. Sublimation is turning solid sodium into gas, which requires energy.
2. Next, ionization involves removing an electron from the gaseous sodium atom, which also requires energy.
3. Then we break the bond in gaseous chlorine to form individual chlorine atoms, using half the energy of the bond dissociation.
4. Finally, when a chlorine atom gains an electron to form a chloride ion, energy is released. The total lattice enthalpy can then be calculated using these values in a Born-Haber cycle by adding and subtracting them accordingly.

Imagine baking a cake. First, you gather the ingredients (sublimation), then you mix them (ionization), next you prepare some of the components (dissociation of chlorine), and finally, you put everything together to bake it (electron gain). Just like you combine the ingredients in various steps, you compute the lattice enthalpy step-by-step using energy changes.

The enthalpy of solution of AB(s), ∆solH⁰, in water is, therefore, determined by the selective values of the lattice enthalpy, ∆latticeH⁰, and enthalpy of hydration of ions, ∆hydH⁰ as ∆sol H⁰ = ∆latticeH⁰ + ∆hydH⁰.

The lattice enthalpy is an essential factor because it tells us how strong the ionic bonds are in a solid. When that solid dissolves in water, the energy involved in overcoming these bonds (lattice enthalpy) and the energy released when ions are surrounded by water (hydration enthalpy) must be considered. The overall enthalpy of solution indicates whether the solid will dissolve or not.

Think of lattice and hydration enthalpy like climbing a hill and then coming down. The effort you put into climbing (lattice enthalpy) needs to be weighed against the enjoyment when you slide down and enjoy the view (hydration enthalpy). The final decision of whether the journey is worth it (overall solubility) depends on the net energy gained or lost through this process.

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