(a) Using the heat of vaporization in Appendix B, calculate...

(a) Using the heat of vaporization in Appendix B, calculate the entropy change for the vaporization of water at $25^{\circ} \mathrm{C}$ and at $100^{\circ} \mathrm{C}$. (b) From your knowledge of microstates and the structure of liquid water, explain the difference in these two values.

Key Concepts

Entropy

Entropy is a thermodynamic quantity that measures the amount of disorder or randomness in a system. It is directly related to the number of microstates available, reflecting how energy is distributed among the molecules. During vaporization, a substantial increase in entropy occurs as the system transitions from an ordered liquid phase to a much more disordered vapor phase.

Heat of Vaporization

The heat of vaporization is the energy required to convert a liquid into a vapor at a constant temperature and pressure. It is used to determine the entropy change during the phase transition by dividing by the temperature at which vaporization occurs, linking the energy input to a probabilistic increase in molecular arrangements.

Phase Transition

A phase transition involves the conversion of a substance from one state (such as liquid) to another (such as vapor). In thermodynamics, the entropy change accompanying a phase transition is significant because it accounts for the dramatic increase in the number of microstates available in the vapor phase compared to the liquid phase.

Temperature Dependence

The process of vaporization is temperature dependent, as the entropy change (?S = Q/T) is inversely proportional to the temperature. A lower temperature during vaporization results in a higher value of entropy change for a given heat of vaporization, emphasizing the interplay between thermal energy and the organization of molecules.

Microstates and Liquid Water Structure

In statistical mechanics, microstates represent the various configurations that a system's molecules can adopt. Liquid water has a highly structured arrangement due to hydrogen bonding, which limits the number of accessible microstates. When water transitions to vapor, the molecular interactions are drastically reduced, leading to a significant increase in the number of microstates and, consequently, a larger entropy change.

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