Topic 6.5 Notes – Energy of Phase Changes

1. What Happens During a Phase Change

A phase change is a physical change between solid, liquid, and gas. The substance stays chemically the same. Only the spacing and attractions between particles change.

The most important idea:

• Temperature remains constant during a phase change.

Temperature measures average kinetic energy.
During melting or boiling, the kinetic energy doesn’t increase. Instead, the added energy changes potential energy by breaking or forming intermolecular forces (IMFs).

Energy Flow and Direction

Endothermic (q > 0)
Energy is absorbed by the system:

• Melting (s → l)
• Vaporization (l → g)
• Sublimation (s → g)

Particles move farther apart. IMFs are broken. System energy increases.

Exothermic (q < 0)
Energy is released by the system:

• Freezing (l → s)
• Condensation (g → l)
• Deposition (g → s)

Particles move closer. IMFs form. System energy decreases.

A common AP trap is saying temperature increases during boiling. It does not. The energy goes into overcoming IMFs, not speeding particles up.

2. Molar Enthalpy of Phase Changes

The energy required per mole for a phase change is the molar enthalpy of phase transition.

$$q = n\Delta H_{\text{phase}}$$

• $q$ = heat absorbed or released
• $n$ = moles
• $\Delta H_{\text{phase}}$ = molar enthalpy (kJ/mol)

Heat depends directly on the amount in moles. Double the moles → double the heat.

Key Enthalpy Terms

• $\Delta H_{\text{fus}}$
  Solid → liquid
  Endothermic
  Only some IMFs break.

• $\Delta H_{\text{vap}}$
  Liquid → gas
  Endothermic
  Nearly all IMFs break.
  Usually much larger than $\Delta H_{\text{fus}}$.

• $\Delta H_{\text{sub}}$
  Solid → gas
  $\Delta H_{\text{sub}} = \Delta H_{\text{fus}} + \Delta H_{\text{vap}}$

Reverse Processes

Energy relationships are symmetric:

• $\Delta H_{\text{cond}} = -\Delta H_{\text{vap}}$
• $\Delta H_{\text{freeze}} = -\Delta H_{\text{fus}}$

The magnitude is the same. The sign flips.

That equality shows up often in conceptual multiple-choice questions. If vaporization is +40 kJ/mol, condensation must be −40 kJ/mol.

Quick Example

If 0.50 mol of a liquid has $\Delta H_{\text{vap}} = 32\text{ kJ/mol}$:

$$q = (0.50)(32) = 16\text{ kJ}$$

16 kJ absorbed to vaporize.
Condensing the same amount would release 16 kJ.

3. Heating and Cooling Curves

A heating curve shows temperature vs. heat added. The graph below is for water.

Heating curve for water

Sloped Regions

• Temperature changes.
• Use $q = mc\Delta T$.
• Kinetic energy changes.

Flat Plateaus

• Phase change.
• Temperature constant.
• Use $q = n\Delta H$.
• Potential energy changes (IMFs).

Notice the flat regions at 0°C and 100°C. Those are melting and boiling, where two phases coexist.

The boiling plateau is longer because $\Delta H_{\text{vap}}$ is larger than $\Delta H_{\text{fus}}$.

Cooling curves are the same picture reversed. Signs flip, magnitudes stay the same.

4. Multi-Step Energy Calculations

AP questions often combine warming and phase changes.

Here’s how the thinking flows:

1. Identify starting phase and temperature.
2. Identify final phase and temperature.
3. Break into pieces:
   • Temperature change → $q = mc\Delta T$
   • Phase change → $q = n\Delta H$
4. Convert grams to moles if $\Delta H$ is in kJ/mol.
5. Add all heat values with correct signs.

If a problem gives 25.0 g of a substance that melts at 10°C and boils at 80°C, and you start at 5°C and end at 95°C, you will likely have five segments. Students lose points by skipping one.

Units matter a lot here. If $\Delta H$ is kJ/mol and you use grams directly, your answer will be wrong even if your setup looks correct.

5. Phase Diagrams and Energy Relationships

A phase diagram shows which phase exists at different temperature and pressure combinations. The example below is for water, with temperature on the x-axis and pressure on the y-axis.

Phase diagram for water

Important features:

• Phase boundaries
  The lines separating Ice, Water, and Steam. Crossing a line means a phase change.

• Triple point
  The single point where all three phases coexist.

• Critical point
  The high-temperature, high-pressure point where the liquid-gas boundary ends. Above this, a supercritical fluid forms.

Energy connection:

Moving solid → liquid → gas requires increasing energy.
Stronger IMFs lead to:

• Higher melting and boiling points
• Larger $\Delta H_{\text{fus}}$ and $\Delta H_{\text{vap}}$

On the diagram, increasing pressure raises the boiling point because particles need more energy to escape into the gas phase.