# Lattice Enthalpy ## Thermodynamic Terms - **Thermodynamics** deals with heat, energy, temperature and the physical properties of matter - Energy cycles are special representations of enthalpy changes for ionic compounds using **Hess's Law** - Understanding energy cycles requires knowledge of key enthalpy change definitions

**Enthalpy change ($\Delta H$)** is the amount of heat energy transferred during a chemical reaction at constant pressure

### Key Definitions Required The following enthalpy change definitions are essential: - Enthalpy of formation - Ionisation enthalpy - Enthalpy of atomisation - Bond enthalpy - Electron affinity --- ## Enthalpy of Formation

**Enthalpy of formation ($\Delta H_f$)** is the enthalpy change when 1 mole of a compound is formed from its elements under standard conditions

### Standard Conditions - Temperature: **298 K** - Pressure: **100 kPa** ### Key Points - $\Delta H_f$ can be **endothermic** or **exothermic** (sum of bonds broken and formed) - Enthalpy change can have **positive** or **negative** values - Applies only to **compounds**

By definition, the enthalpy of formation of elements is **zero**

### Example Equation For sodium chloride: $$\text{Na (s)} + \frac{1}{2}\text{Cl}_2\text{ (g)} \rightarrow \text{NaCl (s)} \quad \Delta H_f^\circ = -411 \text{ kJ mol}^{-1}$$ --- ## Ionisation Enthalpy

**Ionisation enthalpy ($\Delta H_{ie}$)** is the energy required to remove an electron from a gaseous atom to form a gaseous ion under standard conditions

### Key Characteristics - Always **endothermic** (energy needed to overcome electron-nucleus attraction) - First ionisation energy: removes **one mole of electrons** from **one mole of gaseous atoms** to form **one mole of 1+ ions** ### Example: Sodium $$\text{Na (g)} \rightarrow \text{Na}^+\text{ (g)} + e^- \quad \Delta H_{ie}^\circ = +500 \text{ kJ mol}^{-1}$$ --- ## Enthalpy Change of Atomisation

**Enthalpy of atomisation ($\Delta H_{at}$)** is the enthalpy change when 1 mole of gaseous atoms is formed from its element under standard conditions

### Key Characteristics - Always **endothermic** (breaking bonds requires energy) - Energy always required to break bonds in the element - Always has a **positive** value ### Example: Sodium For sodium in its elemental solid form: $$\text{Na (s)} \rightarrow \text{Na (g)} \quad \Delta H_{at}^\circ = +108 \text{ kJ mol}^{-1}$$ --- ## Bond Enthalpy

**Bond enthalpy ($E$)** is the energy required to break one mole of a specific covalent bond in the gas phase

### Alternative Names - Bond dissociation energy - Bond energy ### Notation - Written with bond type in brackets: $E$(H–H), $E$(Cl–Cl) - Usually quoted as **endothermic** (bond breaking) with **positive** values - For bond **forming**: simply use **negative** sign ### Example: Chlorine $$\text{Cl}_2\text{ (g)} \rightarrow 2\text{Cl (g)} \quad E\text{(Cl–Cl)} = +242 \text{ kJ mol}^{-1}$$ ### Relationship to Atomisation

Bond enthalpy is per mole of **bonds**; atomisation enthalpy produces 1 mole of **atoms**

For chlorine: - **Atomisation enthalpy** = $\frac{1}{2}$ × bond enthalpy - $$\frac{1}{2}\text{Cl}_2\text{ (g)} \rightarrow \text{Cl (g)} \quad \Delta H_{at}^\circ = +121 \text{ kJ mol}^{-1}$$ ### Liquid Elements If the element is a **liquid**, atomisation enthalpy includes: - Vaporisation enthalpy (change of state) - Bond breaking energy --- ## Lattice Enthalpy ### Definition and Sign Convention

**Lattice enthalpy ($\Delta H_{latt}$)** is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions

- Expressed as a **formation** process - **Exothermic** (ions combine to form ionic solid → large energy release) - Has a **negative** value - Very **large negative** value due to huge energy release ### Example: Sodium Chloride $$\text{Na}^+\text{(g)} + \text{Cl}^-\text{(g)} \rightarrow \text{NaCl (s)} \quad \Delta H_{latt}^\circ = -776 \text{ kJ mol}^{-1}$$ --- ## Significance of Lattice Enthalpy ### Stability Indicator - Large negative $\Delta H_{latt}$ indicates the **ionic compound** is much more **stable** than its **gaseous ions** - Due to **strong electrostatic forces** between oppositely charged ions in the solid lattice - No electrostatic forces between gaseous ions → gaseous ions are **less stable**

The more exothermic the value, the stronger the ionic bonds within the lattice

### Cannot Be Measured Directly - $\Delta H_{latt}$ **cannot** be determined by a single experiment - Requires **multiple experimental values** and an **energy cycle** - Born-Haber cycles are used to calculate lattice enthalpy values --- ## Summary Table: Key Thermodynamic Terms | Term | Symbol | Sign | Definition | |------|--------|------|------------| | **Enthalpy of formation** | $\Delta H_f$ | +/− | Formation of 1 mol compound from elements (standard conditions) | | **Ionisation enthalpy** | $\Delta H_{ie}$ | + | Removal of electron from gaseous atom (standard conditions) | | **Atomisation enthalpy** | $\Delta H_{at}$ | + | Formation of 1 mol gaseous atoms from element (standard conditions) | | **Bond enthalpy** | $E$ | + | Breaking 1 mol of specific covalent bonds (gas phase) | | **Lattice enthalpy** | $\Delta H_{latt}$ | − | Formation of 1 mol ionic lattice from gaseous ions (standard conditions) |