Enthalpies of solution and hydration

Need to know

What you need to know

• **Standard Enthalpy Change of Solution ($\Delta H_{\text{sol}}^{\ominus}$):** This is the enthalpy change when one mole of a substance dissolves in a large excess of solvent to form a solution that is 'infinitely dilute'. For sodium chloride, the equation is: $\text{NaCl(s)} + \text{aq} \rightarrow \text{Na}^{+}(\text{aq}) + \text{Cl}^{-}(\text{aq})$. This value can be exothermic (negative) or endothermic (positive).
• **Standard Enthalpy Change of Hydration ($\Delta H_{\text{hyd}}^{\ominus}$):** This is the enthalpy change when one mole of isolated gaseous ions is dissolved in water to form hydrated aqueous ions. For a sodium ion, the equation is: $\text{Na}^{+}(\text{g}) + \text{aq} \rightarrow \text{Na}^{+}(\text{aq})$. This process is always exothermic because new, stable ion-dipole forces are formed between the ion and polar water molecules.

Explanation

Dissolving: An Energetic Tug-of-War

1. The overall energy change of dissolving (ΔH_sol) is found using a Hess cycle, linking the energy to break the lattice (+ΔH_latt) and the energy released when ions hydrate (ΣΔH_hyd).
2. Dissolving is favoured if the energy released by hydration is greater than the energy needed to break the lattice, making the overall process exothermic.
3. Hydration enthalpy (ΔH_hyd) is more exothermic for ions with a higher charge and smaller radius, as this creates a stronger attraction to water molecules.
4. By combining Born-Haber cycles (for lattice energy) and hydration cycles, we can construct a full thermodynamic picture to predict and explain solubility.