Phase changes involve large energy transfers without changing temperature.

Simplified phase diagram of water showing the regions where solid, liquid, and vapor are stable, separated by equilibrium boundaries (fusion, vaporization, and sublimation curves). The labeled triple point and critical point provide anchor concepts for when phase boundaries (where $\Delta H_{fus}$ and $\Delta H_{vap}$ apply) are encountered. Source

In AP Chemistry, you quantify these transfers using molar enthalpy of fusion and molar enthalpy of vaporization, scaled by the amount of substance undergoing the phase change.

Molar enthalpies used for phase-change calculations

Molar enthalpy of fusion, ΔHfus

Key points for using $\Delta H_{fus}$:

• Applies only to the solid–liquid phase change.

• Reported in kJ/mol (or J/mol).

• The tabulated magnitude corresponds to melting; the reverse direction uses the opposite sign.

Molar enthalpy of vaporization, ΔHvap

Key points for using $\Delta H_{vap}$:

• Applies only to the liquid–gas phase change.

• Reported in kJ/mol (or J/mol).

• The tabulated magnitude corresponds to boiling/vaporising; the reverse direction uses the opposite sign.

Core relationship: scaling by moles

In these problems, the phase-change energy is proportional to the number of moles that change phase.

Use this relationship only for the phase-change step itself; temperature change steps are handled differently and should not be mixed into this equation.

Choosing the correct molar enthalpy and sign

To match the syllabus language (“absorbed during melting/boiling” vs “released during freezing/condensing”), decide the process direction first.

• Melting (solid $\rightarrow$ liquid): energy is absorbed by the system

  • Use $+\Delta H_{fus}$ in $q=n\Delta H_{phase}$

• Freezing (liquid $\rightarrow$ solid): energy is released by the system

  • Use $-\Delta H_{fus}$

• Boiling/vaporising (liquid $\rightarrow$ gas): energy is absorbed by the system

  • Use $+\Delta H_{vap}$

• Condensing (gas $\rightarrow$ liquid): energy is released by the system

  • Use $-\Delta H_{vap}$

Sign discipline is essential:

• $q>0$ means the system absorbs heat (endothermic phase change).

• $q<0$ means the system releases heat (exothermic phase change).

Converting the given sample information into moles

The equation requires $n$ in moles. Most AP questions provide a mass and a molar mass (or enough information to find it).

• If given mass $m$ (in g), find moles using:

  • $n = \dfrac{m}{M}$

• Use the moles of the substance actually undergoing the phase change (typically the same chemical formula given for $\Delta H_{fus}$ or $\Delta H_{vap}$).

Common unit checks:

• If $\Delta H$ is in kJ/mol, keep $q$ in kJ.

• If $\Delta H$ is in J/mol, keep $q$ in J.

• Convert only once at the end if needed (1 kJ = 1000 J).

What the calculation represents physically

When you compute $q=n\Delta H_{fus}$ or $q=n\Delta H_{vap}$, you are accounting for energy associated with overcoming or forming interparticle attractions during a phase change:

• Melting/boiling: energy goes into separating particles enough to change phase.

• Freezing/condensing: energy is released as particles come closer and form more stabilising interactions.

These molar enthalpies are used specifically because the temperature does not change during the phase change step; the energy transfer changes the phase, not the kinetic energy distribution.

High-frequency pitfalls to avoid

• Do not use $q=mc\Delta T$ for the phase-change segment; use $q=n\Delta H_{phase}$.

• Match the correct $\Delta H$ to the phase boundary:

  • solid–liquid uses $\Delta H_{fus}$, liquid–gas uses $\Delta H_{vap}$.

• Include the correct sign for freezing/condensing (released energy implies negative $q$ for the system).

• Use the correct amount: the energy depends on how many moles actually change phase, not the total moles present if the process is partial.

• Keep significant figures consistent with the given data and avoid mixing kJ and J within the same step.