Heat of phase changes and dissolution Knowledge-Based Study

Study notes

1. Phase Changes and Latent Heat

   A phase change is a physical transition of a substance from one state of matter (solid, liquid, or gas) to another. During a phase change, heat is transferred between the system and its surroundings without altering the temperature of the substance, provided the system is at its transition temperature.

   This heat exchanged at constant temperature is known as latent heat, or transition enthalpy. Because breaking or forming intermolecular attractions requires or releases energy:

   • Endothermic Phase Transitions: Energy is absorbed from the surroundings to overcome intermolecular forces. Examples include melting (fusion), vaporization (boiling/evaporation), and sublimation.
   • Exothermic Phase Transitions: Energy is released to the surroundings as intermolecular attractions form. Examples include freezing (solidification), condensation, and deposition.

   The standard molar enthalpy of fusion, $\Delta H_{\text{fus}}$, is the heat required to melt one mole of a solid at its melting point. Conversely, the standard molar enthalpy of vaporization, $\Delta H_{\text{vap}}$, is the heat required to vaporize one mole of a liquid at its boiling point.

   Calculating Energy of Phase Changes

   Unlike single-phase heating where temperature varies according to the formula $q = m c \Delta T$, phase transitions occur at constant temperature. Therefore, the heat transferred depends exclusively on the quantity of substance and its characteristic enthalpy of transition.

   The heat involved in a phase change is calculated using:

   $q = n \Delta H$  or  $q = m \Delta H$

   • q is the heat absorbed or released (usually in kJ or J).
   • n is the amount of substance in moles.
   • m is the mass of the substance in grams.
   • $\Delta H$ is the molar enthalpy (kJ/mol) or specific latent heat (J/g or kJ/g) of the phase change.

   Because energy is conserved, the enthalpy change for a reverse process is equal in magnitude but opposite in sign:

   • $\Delta H_{\text{solidification}} = -\Delta H_{\text{fus}}$
   • $\Delta H_{\text{condensation}} = -\Delta H_{\text{vap}}$
   • $\Delta H_{\text{deposition}} = -\Delta H_{\text{sub}}$

   The Energetics of Dissolution

   When a solute dissolves in a solvent to form a solution, energy is either absorbed or released. The overall heat exchange occurring during this process at constant pressure is called the enthalpy of solution ($\Delta H_{\text{soln}}$).

   For an ionic compound dissolving in water, the dissolution process can be conceptualized as occurring in distinct thermodynamic steps:

   1. Separation of Solute Particles (Lattice Energy): Breaking the ionic lattice into gaseous ions requires energy input to overcome ionic bonds. This step is strongly endothermic ($\Delta H_{\text{lattice}} > 0$).
   2. Separation of Solvent Molecules: Overcoming intermolecular attractions between solvent molecules (such as hydrogen bonding in water) is also endothermic.
   3. Solvation / Hydration: Attractive interactions form between the separated ions and polar solvent molecules. This step releases energy and is strongly exothermic ($\Delta H_{\text{hyd}} < 0$).

   Applying Hess's Law, the overall enthalpy of solution is approximated by the competition between lattice energy and hydration energy:

   $\Delta H_{\text{soln}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hyd}}$

   Classification of Solution Processes

   The sign and magnitude of $\Delta H_{\text{soln}}$ determine whether the temperature of the solution rises or falls as the solute dissolves:

   • Endothermic Dissolution ($\Delta H_{\text{soln}} > 0$): Occurs when the energy absorbed to separate ions (lattice energy) is greater than the energy released upon hydration ($|\Delta H_{\text{lattice}}| > |\Delta H_{\text{hyd}}|$). The process absorbs heat from the surroundings, resulting in a temperature drop of the solution. A practical example is dissolving ammonium nitrate ($\text{NH}_4\text{NO}_3$) in water, which is utilized in instant cold packs.
   • Exothermic Dissolution ($\Delta H_{\text{soln}} < 0$): Occurs when the energy released during hydration exceeds the lattice energy ($|\Delta H_{\text{hyd}}| > |\Delta H_{\text{lattice}}|$). Heat is released to the solution, causing its temperature to rise. A common example is dissolving sodium hydroxide ($\text{NaOH}$) or calcium chloride ($\text{CaCl}_2$) in water, which is utilized in instant hot packs.