IB Chemistry home > Syllabus 2016 > Energetics > Lattice enthalpy

Syllabus ref: 15.1

Ionic substances exist in giant structures of repeating ions all held together by electrostatic forces.

Electrostatic force between ions

Although not a bond in the classical covalent sense of the word, electrostatic forces hold oppositely charges ions together in an ionic crystal lattice. This force is dependent on the magnitude of the charges on the ions and inversely proportional to the distance between them.

Where: z1 is the magnitude of the positive ion, z2 is the magnitude of the charge on the negative ion and 'r' is the distance between them.

Consequently, ions with greater charges are held together more tightly and smaller ions form more effective bonds than larger ions. The following examples should make the effect of changing both ionic charge and ionic radius clear.

Example: The force of attraction between sodium and chloride ions:

This is dependent on the magnitude of the ionic charges. Sodium ions have a 1+ charge and chloride ions have a 1- charge. The distance between them is considered to be the sum of the ionic radii of the two ions.

  • Sodium ions have an ionic radius of 0.098nm
  • Chloride ions have a radius of 0.181nm

Therefore the distance between is 0.098 + 0.181 = 0.279nm

The force of attraction is proportional to 1 x 1 /(0.279)2 = 12.8

This number is meaningless in isolation, but could be used to compare the force of attraction between other ions in an ionic lattice. You will not be asked to do this in an exam

The previous example considered the force between two singly charged ions. For comparison we can look at the force of electrostatic attraction between two singly charged ions of different radii, such as caesium iodide.

Example: The force of attraction between caesium and iodide ions:

This is dependent on the magnitude of the ionic charges. Caesium ions have a 1+ charge and iodide ions have a 1- charge. The distance between them is the sum of the ionic radii of the two ions.

  • Caesium ions have an ionic radius of 0.169nm
  • Iodide ions have a radius of 0.219nm

Therefore the distance between is 0.169 + 0.219 = 0.388nm

The force of attraction is proportional to 1 x 1 /(0.388)2 = 6.6

We can see that this value, proportional to the electrostatic force of attraction, is about one half that of sodium chloride. The 'bond' is weaker.

A similar comparison could examine the effect of changing the magnitude of charge on the ions, for example in the force of attraction between magnesium and oxide ions in magnesium oxide.

Example: The force of attraction between magnesium and oxide ions:

Magnesium ions have a 2+ charge and oxide ions have a 2- charge. The distance between them is the sum of the ionic radii of the two ions.

  • Magnesium ions have an ionic radius of 0.065nm
  • Oxide ions have a radius of 0.140nm

Therefore the distance between is 0.065 + 0.140 = 0.205nm

Thus, the force of attraction is proportional to 2 x 2 /(0.205)2 = 95.2

This value is far bigger than that of sodium chloride, a factor of seven times. The force of attraction between magnesium and oxide ions is considerably larger than that of sodium chloride.


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Forces within the lattice

An ionic lattice is the giant framework of repeating positive and negative ions in three dimensions. In the section above we looked at the forces that exist between two oppositely charged ions.

In an ionic lattice each positive ion is surrounded by negative ions and so feels a force of attraction towards all of them. The same case applied to each negative ion, it is surrounded by positive ions and feels the forces of attraction towards all of these neighbours.

Sodium ion surrounded by chloride ions
Chloride ion surrounded by sodium ions

The whole crystal lattice consists of billions upon billions of these ions, each positive surrounded by negative ions and each negative surrounded by positive ions. The forces of attraction pull all of the ions into the best arrangement possible in which all of the forces are at a maximum. This gives us the final crystal lattice structure:


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The lattice enthalpy

The electrostatic forces hold the crystal lattice together. To break the lattice apart and overcome these forces, energy must be applied. The amount of energy required to break apart one mole of an ionic lattice is called the lattice enthalpy.

Definition

Lattice enthalpy is the energy required to break 1 mole of an ionic lattice into its individual constituent ions at infinite separation. It is an endothermic process, ΔH is +ve.

NaCl(s) Na+(g) + Cl-(g)

Note that some examination boards define lattice enthalpy as the energy released on forming one mole of a crystal lattice from its constituent gaseous ions at infinite separation. Numerically, of course, this has the same magnitude but different sign.

By considering the number of nearest neighbours, the structural arrangement of the ions and the types of ions involved in a lattice, it is possible to calculate the total sum of the forces involved in a specific lattice and from this, the energy required to break up the lattice into individual ions in a gaseous state.

This is called the theoretical lattice enthalpy.

Lattice enthalpies are usually found experimentally , the experimental lattice enthalpy. If there is good agreement between the theoretical and the experimental values, the crystal structure is considered to be totally ionic.

Poor agreement suggests that the structure is not entirely ionic.


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