1 THERMODYNAMICS
1.1 ENTHALPY CHANGES AND IONIC LATTICES Metals and nonmetals react to form ionic compounds. When just two elements are involved these are ionic compounds, for example sodium chloride, NaCl, sodium oxide, Na2O, and magnesium oxide, MgO. Ionic compounds form giant regular structures. These are called lattices. The regular arrangement of ions is reflected in the shape of the compounds’ crystals. The strength of the bonding in a lattice is given by its lattice enthalpy.
Lattice enthalpies There are two ways to define lattice enthalpy: the enthalpy of lattice formation and the enthalpy of lattice dissociation. The enthalpy of lattice formation is the enthalpy change when one mole of a crystalline compound is formed from gaseous ions scattered an infinite distance apart (Figure 1). The enthalpy change for an ionic compound MX consisting of ions with single charges is represented as M+(g) + X−(g) → MX(s)
Na+(g) + Cl–(g)
Enthalpy
Enthalpy of lattice dissociation
Enthalpy of lattice formation
= +786 kJ mol–1
= –786 kJ mol–1
NaCI(s) Figure 2 A simple enthalpy diagram showing the lattice enthalpy of sodium chloride
A larger exothermic enthalpy of lattice formation is favoured by a greater charge on the ions, smaller ions and a closer packing in the lattice.
QUESTIONS 1. Why does the enthalpy of lattice dissociation always have a positive value?
This is always an exothermic process. The enthalpy of lattice dissociation is the enthalpy change when one mole of lattice is broken up to produce gaseous ions an infinite distance apart. For an ionic compound MX consisting of ions with single charges, this is represented as MX(s) → M+(g) + X−(g) In other words, the process is the reverse of lattice formation. It is an endothermic process. –
+
+ –
–
+
+ Lattice formation
– –
Lattice dissociation
– + Gaseous ions
+
– + – +
+ – + –
– + – +
Ionic lattice
Figure 1 Lattice formation and dissociation
The value of a lattice enthalpy depends on:
›› the charges on the ions ›› the size of the ions ›› the type of lattice formed (the pattern in which they pack together).
Using lattice enthalpies Why are lattice enthalpies of interest? The main reason is to test our ideas of ionic bonding. Our simple model is one in which spherical ions of opposite charge pack together in a giant ionic lattice. By doing some mathematics, theoretical values for lattice enthalpies can be worked out. A second reason is to increase our understanding of why some compounds do not exist. For example, why MgCl2 and not MgCl or MgCl3? Lattice enthalpies cannot be measured directly (it is impossible to carry out experiments in which gaseous ions are spread out at infinite distances). However, they can be calculated from other experimental data using a special form of Hess’s law called the Born–Haber cycle.
1.2 BORN–HABER CYCLES As we have said, it is impossible to measure lattice enthalpies directly. But they can be calculated using Born–Haber cycles. To do this for an ionic compound you need these data:
›› enthalpy of formation ›› ionisation energy
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