格子エネルギーとボーン＝ハーバーサイクル

The energy locked in a lattice

• Forming an ionic solid involves several enthalpy steps.
• The lattice energy 晶格能 is the big energy release.
• A Born–Haber cycle 玻恩哈伯循环 ties them all together.

The key enthalpy changes

• atomisation 原子化 $\Delta H_{\text{at}}$: energy to make one mole of gaseous atoms (always positive).
• lattice energy $\Delta H_{\text{latt}}$: change when one mole of solid lattice forms from gaseous ions (always negative).
• first electron affinity 电子亲和能: change when gaseous atoms each gain an electron (usually negative); going down a group it gets less exothermic (larger atom).

A Born-Haber cycle for sodium chloride

Born–Haber cycle and lattice strength

• A Born–Haber cycle links the formation of an ionic solid with atomisation, ionisation energy, electron affinity and lattice energy. Use Hess's law to find any unknown step.
• The lattice energy is more negative (stronger) when:
  • the ionic charge is higher ($\text{Mg}^{2+}$ beats $\text{Na}^{+}$), and
  • the ionic radius 离子半径 is smaller.

An ionic solid such as sodium chloride is a giant regular lattice of ions.

What makes lattice energy large

• Lattice energy is more exothermic for smaller, more highly charged ions.
• This is why MgO has a far larger lattice energy than NaCl.

Smaller ions and higher charges give a stronger lattice energy

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