Other Enthalpies of Physical and Chemical Changes
In addition to formation, neutralization, and combustion, there are several other enthalpy changes that are important in thermochemistry. Each describes a specific type of physical or chemical process.
Enthalpy of Solution (ΔH_sol°)
Definition:
The standard enthalpy of solution (ΔH_sol°) is the enthalpy change when one mole of a solute dissolves completely in a solvent (usually water) to form an infinitely dilute solution under standard conditions.
Process:
The dissolution process involves two main energy changes:
- Breaking of solute-solute bonds (lattice energy): Endothermic (energy absorbed)
- Formation of solute-solvent bonds (hydration energy): Exothermic (energy released)
\[ \Delta H_{\text{sol}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hydration}} \]
Worked Example:
Problem: When 5.00 g of sodium hydroxide (NaOH) is dissolved in 100 cm³ of water, the temperature rises from 22.0°C to 35.5°C. Calculate the enthalpy of solution of NaOH. (Specific heat capacity of solution = 4.18 J g⁻¹ °C⁻¹, density = 1.0 g/cm³, molar mass of NaOH = 40.0 g/mol)
Solution:
\[ \Delta T = 35.5 – 22.0 = 13.5^\circ C \]
\[ m_{\text{solution}} = 100 \, \text{g} \quad (\text{water mass, assuming solute mass negligible for heat capacity}) \]
\[ q = mc\Delta T = 100 \times 4.18 \times 13.5 = 5643 \, \text{J} = 5.643 \, \text{kJ} \]
\[ n_{\text{NaOH}} = \frac{5.00}{40.0} = 0.125 \, \text{mol} \]
\[ \Delta H_{\text{sol}} = -\frac{5.643}{0.125} = -45.14 \, \text{kJ/mol} \]
The negative sign indicates that the dissolution of NaOH is exothermic.
Enthalpy of Hydration (ΔH_hyd°)
Definition:
The standard enthalpy of hydration (ΔH_hyd°) is the enthalpy change when one mole of gaseous ions is dissolved in water to form an infinitely dilute solution under standard conditions.
Key Points:
- Always exothermic (negative) because ion-dipole attractions release energy.
- The magnitude depends on the charge density of the ion:
- Higher charge density (smaller size, higher charge) → more negative ΔH_hyd°
- Lower charge density (larger size, lower charge) → less negative ΔH_hyd°
Example Values:
Relationship with Enthalpy of Solution:
\[ \Delta H_{\text{sol}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hyd}}(M^+) + \Delta H_{\text{hyd}}(X^-) \]
Where:
- ΔH_lattice is always positive (endothermic)
- ΔH_hyd is always negative (exothermic)
- The overall sign of ΔH_sol depends on which term dominates
4.6.3: Enthalpy of Atomization (ΔH_at°)
Definition:
The standard enthalpy of atomization (ΔH_at°) is the enthalpy change when one mole of gaseous atoms is formed from an element in its standard state under standard conditions.
Key Points:
- Always endothermic (positive) because bonds are broken.
- For metals: Atomization involves overcoming metallic bonding.
- For diatomic gases (H₂, O₂, Cl₂): Atomization involves breaking the covalent bond.
Examples:
Note: For diatomic elements, the bond dissociation enthalpy (ΔH_bond) is exactly twice the enthalpy of atomization per mole of atoms.
Bond Dissociation Enthalpy (ΔH_bond)
Definition:
The bond dissociation enthalpy (ΔH_bond) is the enthalpy change when one mole of a specific covalent bond is broken in the gaseous phase.
Key Points:
- Always endothermic (positive) because breaking bonds requires energy.
- Bond dissociation enthalpy is a measure of bond strength.
- Different bonds have different strengths:
- Single bonds < Double bonds < Triple bonds
- Stronger bonds have higher ΔH_bond values
Examples:
Relationship with Atomization:
For diatomic molecules: ΔH_at° (per mole of atoms) = ½ × ΔH_bond
Enthalpy of Vaporization (ΔH_vap°)
Definition:
The standard enthalpy of vaporization (ΔH_vap°) is the enthalpy change when one mole of a liquid is converted to gas at its boiling point under standard conditions.
Key Points:
- Always endothermic (positive) because intermolecular forces are overcome.
- The magnitude reflects the strength of intermolecular forces:
- Hydrogen bonding → high ΔH_vap (e.g., water: +40.7 kJ/mol)
- London dispersion forces → low ΔH_vap (e.g., methane: +8.2 kJ/mol)
Examples:
Enthalpy of Fusion (ΔH_fus°)
Definition:
The standard enthalpy of fusion (ΔH_fus°) is the enthalpy change when one mole of a solid is converted to liquid at its melting point under standard conditions.
Key Points:
- Always endothermic (positive) because intermolecular forces are partially overcome.
- Generally smaller than ΔH_vap° because melting does not completely separate molecules.
Examples:
Summary of Other Enthalpy Changes
Summary Table: Core Enthalpy Definitions
Key Points to Remember
- State symbols are essential. Always include them when writing thermochemical equations.
- “One mole” appears in most definitions. Pay attention to what quantity the enthalpy change is referenced to.
- Elements in standard states have ΔH_f° = 0. This is a defined reference point.
- Strong acid + strong base neutralization is constant at -57 kJ/mol. Weak acids/bases give different values.
- Calorimetry experiments involve assumptions: No heat loss, known specific heat capacity, complete reaction.
- Bomb calorimeters measure ΔU at constant volume; ΔH is calculated using ΔH = ΔU + Δn_g RT.
- Enthalpy of solution = lattice energy + hydration energy. The overall sign depends on which term dominates.
- Bond dissociation enthalpies are always positive. Bond breaking requires energy input.
