Lattice energy and Born-Haber cycles
Introduced| English | Meaning |
|---|---|
| lattice energy/ˈlætɪs ˈenədʒi/ | The enthalpy change associated with forming an ionic solid from gaseous ions, or the reverse process under a stated sign convention. |
| Born–Haber cycle/bɔːn ˈheɪbə ˈsaɪkl/ | Born–Haber cycle |
| atomisation/əˌtɒmaɪˈzeɪʃn/ | atomisation |
| electron affinity/ɪˈlektrɒn əˈfɪnɪti/ | The enthalpy change when one mole of gaseous atoms or ions each gain an electron. |
| ionic radius/aɪˈɒnɪk ˈreɪdɪəs/ | A measure of an ion's size, commonly inferred from distances between ions in crystals. |
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 enthalpy change when one mole of an ionic solid forms from gaseous ions is the ______ energy.
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Born–Haber cycles use Hess's law to find it.
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
The Born–Haber cycle
Lattice energy can't be measured directly, so it is found from a cycle of measurable steps.
The lattice energy is:
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Strong ionic bonds form, so lattice energy is exothermic (negative).
Going down Group 17, the first electron affinity becomes:
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A bigger atom pulls the incoming electron in less strongly, so EA is less exothermic.
Match each Born-Haber term to its meaning.
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Each item links the term to its correct meaning.
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.
A Born–Haber cycle lets you find an unknown enthalpy step by using:
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Because enthalpy is conserved, going round the cycle relates all the steps, so any one can be found.
Lattice energy is most negative (strongest) for ions with:
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Higher charge and smaller radius both increase the attraction between the 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
You've got it
- atomisation (+, makes gaseous atoms); lattice energy (−, lattice forms from gaseous ions); electron affinity (usually −)
- a Born–Haber cycle uses Hess's law to find any unknown enthalpy step
- lattice energy is stronger (more negative) for higher charge and smaller radius