Energy of phase changes Knowledge-Based Study

Study notes

1. Phase Transitions and Energetics

   A phase change is a physical transition of a substance from one state of matter (solid, liquid, or gas) to another. During any phase change, the chemical composition of the substance remains identical, but the distance and electrostatic interactions between particles change significantly.

   Phase changes are governed by the exchange of thermal energy between a system and its surroundings:

   • Endothermic Phase Changes: Energy must be absorbed from the surroundings to overcome or disrupt intermolecular attractive forces. These processes include melting (fusion), vaporization, and sublimation.
   • Exothermic Phase Changes: Energy is released to the surroundings as attractive intermolecular forces pull particles closer together into more ordered arrangements. These processes include freezing (solidification), condensation, and deposition.

   An essential principle of phase changes is that temperature remains constant during a pure substance's phase transition at constant pressure. The thermal energy supplied does not increase particle kinetic energy; instead, it increases potential energy as intermolecular bonds are overcome.

   Quantifying Energy of Phase Changes

   The quantity of heat absorbed or released during a phase change at constant pressure is directly proportional to the amount of substance undergoing the transition.

   The two primary molar enthalpies are:

   • Molar Enthalpy of Fusion ($\Delta H_{fus}$): The heat required to completely melt one mole of a solid substance at its melting point. For water, $\Delta H_{fus} = 6.01\text{ kJ/mol}$.
   • Molar Enthalpy of Vaporization ($\Delta H_{vap}$): The heat required to vaporize one mole of a liquid at its boiling point. For water, $\Delta H_{vap} = 40.67\text{ kJ/mol}$.

   Notice that for any given substance, $\Delta H_{vap}$ is significantly larger than $\Delta H_{fus}$. Melting requires only partial disruption of intermolecular forces allowing particles to slide past one another, whereas vaporization requires completely overcoming all intermolecular attractions to separate particles into an ideal gas-like state.

   By Hess's law, the enthalpy of sublimation ($\Delta H_{sub}$) equals the sum of the enthalpy of fusion and enthalpy of vaporization:

   $$\Delta H_{sub} = \Delta H_{fus} + \Delta H_{vap}$$

   For the reverse exothermic processes, the magnitudes are identical but the signs are opposite:

   • $\Delta H_{cryst} = -\Delta H_{fus}$
   • $\Delta H_{cond} = -\Delta H_{vap}$
   • $\Delta H_{dep} = -\Delta H_{sub}$

   Analyzing Heating and Cooling Curves

   A heating curve plots temperature versus heat added over time. The curve alternates between two distinct regimes:

   1. Sloped Segments (Single Phase Present): Heat added increases the average kinetic energy of the molecules, resulting in a temperature rise. Heat is calculated using specific heat capacity: $$q = m \cdot c \cdot \Delta T$$
   2. Horizontal Plateaus (Two Phases in Equilibrium): Added heat serves exclusively as latent heat to overcome intermolecular forces (changing potential energy), so temperature stays constant. Heat is calculated using enthalpy of phase change: $$q = n \cdot \Delta H \quad \text{or} \quad q = m \cdot \Delta H_{specific}$$

   Total Heat Calculation Example

   To calculate the total energy needed to heat a mass $m$ from below its melting point to above its boiling point, sum the individual terms:

   $$q_{total} = q_{solid} + q_{fusion} + q_{liquid} + q_{vaporization} + q_{gas}$$

   Where:

   • $q_{solid} = m \cdot c_{solid} \cdot (T_{mp} - T_{initial})$
   • $q_{fusion} = n \cdot \Delta H_{fus}$
   • $q_{liquid} = m \cdot c_{liquid} \cdot (T_{bp} - T_{mp})$
   • $q_{vaporization} = n \cdot \Delta H_{vap}$
   • $q_{gas} = m \cdot c_{gas} \cdot (T_{final} - T_{bp})$