Boiling and molecular energies: A pure liquid is in equilibrium with its vapor exactly at its boiling point. On average, molecules in the liquid phase and in the vapor phase have equal __________.

Introduction / Context:
Thermal equilibrium between phases at the boiling point is a cornerstone of phase-change thermodynamics. Understanding which molecular-average properties are equal clarifies what is controlled by temperature and what is controlled by phase structure.

Given Data / Assumptions:

• Pure substance at its boiling point.
• Liquid and vapor phases coexisting at equilibrium (no net evaporation or condensation).
• Uniform temperature across both phases.

Concept / Approach:
Average translational kinetic energy of molecules in any idealized phase depends solely on absolute temperature. Since both phases are at the same temperature at equilibrium, molecules in liquid and vapor have the same average kinetic energy. However, potential energy and total energy differ due to distinct intermolecular configurations and binding energies in the phases. Intermolecular forces are stronger in liquids; in vapors, molecules are much farther apart on average.

Step-by-Step Solution:
Equal temperature at equilibrium implies equal average molecular kinetic energy.Potential energy differs because of different average separations and bonding environments.Total energy (kinetic + potential) therefore differs between phases.

Verification / Alternative check:
From kinetic theory: average translational kinetic energy per molecule is (3/2) k_B T (idealized); same T in both phases → same kinetic energy.

Why Other Options Are Wrong:
Intermolecular forces of attraction: stronger in liquids; not equal.Potential energy: lower (more negative) in liquids due to stronger interactions; not equal.Total energy: sum differs because potential energy differs.

Common Pitfalls:
Equating equal temperature with equal total energy; forgetting that phase changes involve latent heat which reflects potential-energy changes at constant temperature.

Final Answer:
kinetic energy