Lattice Enthalpy — Revision Notes

⚡ 30-Second Revision

Definition — Energy change when 1 mole of ionic solid forms from gaseous ions (exothermic, $Delta H_{lattice} < 0$).
Born-Haber Cycle — Indirect method using Hess's Law.

$Delta H_f^circ = Delta H_{sub} + IE + \frac{1}{2}Delta H_{diss} + EA + Delta H_{lattice}$

Factors

1. Ionic Charge: $Delta H_{lattice} propto q_1 q_2$ (most dominant). 2. Ionic Radii: $Delta H_{lattice} propto 1/r$ (smaller ions = higher magnitude).

Properties — Higher magnitude $Delta H_{lattice}$ = higher melting point, greater stability, often lower solubility (if hydration enthalpy is not sufficiently high).

2-Minute Revision

Lattice enthalpy is the energy released when one mole of an ionic solid forms from its constituent gaseous ions, or the energy required to break it apart. It's a crucial measure of ionic bond strength and stability.

Since direct measurement is impossible, it's determined indirectly via the Born-Haber cycle, an application of Hess's Law. This cycle sums up various enthalpy changes: sublimation of metal, ionization of metal, dissociation of non-metal, electron gain by non-metal, and finally, lattice formation.

The magnitude of lattice enthalpy is primarily governed by ionic charges (directly proportional to product of charges, $q_1 q_2$) and ionic radii (inversely proportional to interionic distance, $1/r$).

Higher charges and smaller ions lead to a significantly larger (more negative) lattice enthalpy. This strong attraction translates to high melting points, hardness, and often low solubility in water, unless the hydration enthalpy is even greater.

5-Minute Revision

Lattice enthalpy ($Delta H_{lattice}$) is the enthalpy change associated with the formation of one mole of an ionic compound from its gaseous ions. By convention, this process is exothermic, meaning energy is released, and $Delta H_{lattice}$ is negative.

For example, $Na^+(g) + Cl^-(g) \rightarrow NaCl(s)$, $Delta H_{lattice} = -787,\text{kJ/mol}$. It's a direct measure of the strength of the electrostatic forces holding the ions in the crystal lattice, thus indicating the stability of the ionic compound.

Direct measurement of lattice enthalpy is not feasible. Instead, it's calculated using the Born-Haber cycle, which is a thermochemical cycle based on Hess's Law. This cycle breaks down the overall enthalpy of formation ($Delta H_f^circ$) of an ionic compound into a series of steps whose enthalpy changes are measurable:

1
Sublimation of metal ($Delta H_{sub}$): $M(s) \rightarrow M(g)$ (Endothermic)
2
Ionization of metal (IE): $M(g) \rightarrow M^+(g) + e^-$ (Endothermic)
3
Dissociation of non-metal ($Delta H_{diss}$): $rac{1}{2}X_2(g) \rightarrow X(g)$ (Endothermic)
4
Electron Gain Enthalpy (EA): $X(g) + e^- \rightarrow X^-(g)$ (Exothermic, usually)
5
Lattice formation ($Delta H_{lattice}$): $M^+(g) + X^-(g) \rightarrow MX(s)$ (Exothermic)

The sum of these steps equals the enthalpy of formation: $Delta H_f^circ = Delta H_{sub} + IE + \frac{1}{2}Delta H_{diss} + EA + Delta H_{lattice}$. By knowing all other terms, $Delta H_{lattice}$ can be calculated.

Two crucial factors influence the magnitude of lattice enthalpy:

1
Ionic Charge — The most significant factor. Lattice enthalpy is directly proportional to the product of the charges of the ions ($q_1 q_2$). For instance, MgO ($Mg^{2+}O^{2-}$) has a much higher lattice enthalpy than NaCl ($Na^+Cl^-$) because the product of charges is $2 \times 2 = 4$ for MgO, versus $1 \times 1 = 1$ for NaCl.
2
Ionic Radii — Lattice enthalpy is inversely proportional to the sum of the ionic radii ($r_{cation} + r_{anion}$). Smaller ions can approach each other more closely, leading to stronger electrostatic attractions and a higher magnitude of lattice enthalpy. For example, LiF has a higher lattice enthalpy than CsF due to the smaller size of $Li^+$ compared to $Cs^+$.

High lattice enthalpy implies a very stable ionic compound, which typically correlates with high melting points, hardness, and often low solubility in polar solvents like water (unless the hydration enthalpy is exceptionally high). For NEET, practice Born-Haber cycle calculations and be adept at comparing lattice enthalpies based on charge and size.

Prelims Revision Notes

Lattice enthalpy ($Delta H_{lattice}$) is the energy change when one mole of an ionic solid is formed from its constituent gaseous ions. It is an exothermic process (negative value) because energy is released as stable bonds form. Conversely, breaking the lattice into gaseous ions is endothermic (positive value). It's a direct measure of the strength of ionic bonds and the stability of the ionic crystal.

Born-Haber Cycle: This is the indirect method to determine lattice enthalpy, based on Hess's Law. The cycle sums up various enthalpy changes that lead to the formation of an ionic compound from its elements. For an MX type compound: $Delta H_f^circ = Delta H_{sub} (M) + IE (M) + \frac{1}{2}Delta H_{diss} (X_2) + EA (X) + Delta H_{lattice} (MX)$

Key Enthalpy Terms in Born-Haber Cycle:

$Delta H_f^circ$ — Standard enthalpy of formation (elements $ightarrow$ compound).
$Delta H_{sub}$ — Enthalpy of sublimation (solid metal $ightarrow$ gaseous metal atoms). Always positive.
IE — Ionization Enthalpy (gaseous atom $ightarrow$ gaseous cation + $e^-$). Always positive.
$Delta H_{diss}$ — Enthalpy of dissociation (diatomic molecule $ightarrow$ gaseous atoms). Positive. Remember to use $rac{1}{2}Delta H_{diss}$ for one mole of atoms.
EA — Electron Gain Enthalpy (gaseous atom + $e^- \rightarrow$ gaseous anion). First EA is usually negative (exothermic), but subsequent EAs (e.g., $O^- \rightarrow O^{2-}$) are positive (endothermic) due to electron-electron repulsion.
$Delta H_{lattice}$ — Lattice Enthalpy (gaseous ions $ightarrow$ solid ionic compound). Negative.

Factors Affecting Lattice Enthalpy: The magnitude of lattice enthalpy is directly proportional to the product of ionic charges and inversely proportional to the interionic distance.

1
Ionic Charge ($q_1 q_2$) — Higher charges lead to much stronger electrostatic attraction and significantly larger (more negative) lattice enthalpy. This is the most dominant factor. Example: MgO ($+2,-2$) has much higher lattice enthalpy than NaCl ($+1,-1$).
2
Ionic Radii ($r_{cation} + r_{anion}$) — Smaller ions allow for closer packing and shorter interionic distances, resulting in stronger electrostatic forces and higher magnitude of lattice enthalpy. Example: LiF has higher lattice enthalpy than CsF due to smaller $Li^+$ and $F^-$ ions.

Relationship with Properties: High magnitude of lattice enthalpy implies:

High stability of the ionic compound.
High melting point.
High hardness.
Often low solubility in water (unless hydration enthalpy is even higher).

Vyyuha Quick Recall

To remember the factors affecting Lattice Enthalpy: Charge Rules Size.

Charge: Higher Charge = Higher Lattice Enthalpy. Rules: Radius (size) is the secondary factor. Size: Smaller Size = Higher Lattice Enthalpy.