Lattice Energy: MDCAT Chemistry notes
Lattice Energy MDCAT notes: definition and sign, effect of ionic charge and size, LiF and NaF trends, and the Born-Haber cycle worked for NaCl.
Definition
Lattice energy is the energy released when one mole of an ionic crystal is formed from its gaseous ions:
$$\mathrm{Na^+(g) + Cl^-(g) \rightarrow NaCl(s)}\qquad \Delta H_L = -787\ \mathrm{kJ\,mol^{-1}}$$
Similarly $\mathrm{Mg^{2+}(g) + O^{2-}(g) \rightarrow MgO(s)}$ represents the lattice energy of MgO. Because energy is released, lattice energy (in this definition) has a negative value. It is also called crystal energy. The more negative it is, the more stable the crystal and the higher its melting point.
Factors affecting lattice energy
Lattice energy depends on the charge-to-size ratio of the ions:
- Charge: higher ionic charges give a much larger lattice energy. MgO ($\mathrm{Mg^{2+}}$, $\mathrm{O^{2-}}$) has a far larger lattice energy than NaCl.
- Size: smaller ions come closer together, so the attraction is stronger and the lattice energy larger.
It does not depend on room temperature or other external conditions.
| Series | Order of lattice energy (magnitude) | Reason |
|---|---|---|
| Sodium halides | NaF > NaCl > NaBr > NaI | Halide ion size increases |
| Alkali metal chlorides | LiCl > NaCl > KCl > CsCl | Cation size increases |
| Mixed | LiF > NaCl > KCl > CsI | LiF has the smallest ions; CsI the largest |
| Charge effect | $\mathrm{CaCl_2}$ > KCl | $\mathrm{Ca^{2+}}$ carries double charge |
Born-Haber cycle
Lattice energy cannot be measured directly, so it is calculated with the Born-Haber cycle, an application of Hess's law. It is used for ionic solids. The formation of an ionic compound from its elements is split into steps:
- Atomization of the metal (sublimation), endothermic.
- Atomization of the non-metal (half the bond dissociation energy for a diatomic element), endothermic.
- Ionization of the metal (ionization energy), endothermic.
- Ionization of the non-metal by gaining an electron (electron affinity), usually exothermic.
- Gaseous ions combine to form the lattice (lattice energy), exothermic.
There is no "de-ionization" step.
Key formulas
$$\Delta H_f = \Delta H_{at}(\text{metal}) + \Delta H_{at}(\text{non-metal}) + IE + EA + \Delta H_L$$
$$\Delta H_L = \Delta H_f - \left[\Delta H_{at}(\text{metal}) + \Delta H_{at}(\text{non-metal}) + IE + EA\right]$$
Worked example: NaCl
Data (kJ/mol): $\Delta H_f = -411$, atomization of Na $= +108$, atomization of Cl ($\tfrac12$ of $\mathrm{Cl_2}$) $= +121$, IE of Na $= +496$, EA of Cl $= -349$.
$$\Delta H_L = -411 - (108 + 121 + 496 - 349) = -411 - 376 = -787\ \mathrm{kJ\,mol^{-1}}$$
Remember to take half the dissociation energy of a diatomic halogen, since only one mole of atoms is needed per mole of NaX.
Common MDCAT traps
- Lattice energy for formation of the crystal from gaseous ions is negative.
- Highest lattice energy goes to the smallest, most highly charged ions: LiF among alkali halides, NaF among sodium halides.
- In calculations, use $\tfrac12$ of the bond dissociation energy and keep the sign of electron affinity negative.
- Born-Haber cycle applies to ionic solids, not molecular, metallic or covalent solids.
Quick revision
- Lattice energy increases with ionic charge and decreases with ionic size.
- Lattice energy of NaCl is about $-787\ \mathrm{kJ\,mol^{-1}}$.
- Born-Haber cycle is an application of Hess's law.
- Among KCl, LiCl and $\mathrm{CaCl_2}$, KCl has the lowest lattice energy.
- Lattice energy is also called crystal energy.