<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

Changes of State and Free Energy

Demonstrates calculations used to demonstrate entropy change at phase transition temperatures.

Atoms Practice
Estimated10 minsto complete
%
Progress
Practice Changes of State and Free Energy
Practice
Progress
Estimated10 minsto complete
%
Practice Now
Changes of State and Free Energy

An increase in the level of energy can cause a change in state

Credit: Jon Sullivan
Source: http://commons.wikimedia.org/wiki/File:Geysers_steam_boiling_Yellowstone.jpg
License: CC BY-NC 3.0

How are energy and changes of state related?

Energy in a body of water can be gained or lost depending on conditions.  When water is heated above a certain temperature steam is generated.  The increase in heat energy creates a higher level of disorder in the water molecules as they boil off and leave the liquid.

Changes of State and Free Energy

At the temperature at which a change of state occurs, the two states are in equilibrium with one another. For an ice-water system, equilibrium takes place at 0°C, so \begin{align*}\Delta G°^\circ\end{align*}ΔG° is equal to 0 at that temperature. The heat of fusion of water is known to be equal to 6.01 kJ/mol, and so the Gibbs free energy equation can be solved for the entropy change that occurs during the melting of ice. The symbol \begin{align*}\Delta S_{\text{fus}}\end{align*}ΔSfus represents the entropy change during the melting process, while \begin{align*}T_{\text{f}}\end{align*}Tf is the freezing point of water.

\begin{align*}\Delta G & = 0 = \Delta H - T \Delta S\\ \Delta S_{\text{fus}} & = \frac{\Delta H_{\text{fus}}}{T_{\text{f}}} = \frac{6.01 \text{ kJ/mol}}{273 \text{ K}} = 0.0220 \text{ kJ/K} \cdot \text{mol} = 22.0 \text{ J/K} \cdot \text{mol}\end{align*}ΔGΔSfus=0=ΔHTΔS=ΔHfusTf=6.01 kJ/mol273 K=0.0220 kJ/Kmol=22.0 J/Kmol

The entropy change is positive as the solid state changes into the liquid state. If the transition went from the liquid to the solid state, the numerical value for \begin{align*}\Delta S\end{align*}ΔS would be the same, but the sign would be reversed since we are going from a less ordered to a more ordered situation.

A similar calculation can be performed for the vaporization of liquid to gas. In this case we would use the molar heat of vaporization. This value would be 40.79 kJ/mol. The \begin{align*}\Delta S_{\text{vap}}\end{align*}ΔSvap would then be as follows:

\begin{align*}\Delta S = \frac{40.79 \text{ kJ/mol}}{373 \text{ K}} = 0.1094 \text{ kJ/K} \cdot \text{mol} = 109.4 \text{ J/K} \cdot \text{mol}\end{align*}ΔS=40.79 kJ/mol373 K=0.1094 kJ/Kmol=109.4 J/Kmol

The value is positive, again reflecting the increase in disorder going from liquid to vapor. Condensation from vapor to liquid would give a negative value for \begin{align*}\Delta S\end{align*}ΔS.

Summary

  • Calculations are shown for determining entropy changes at transition temperatures (ice → water or water → vapor and reverse).

Practice

Questions

Read the material on the link below and answer the following questions:

http://www.everyscience.com/Chemistry/Physical/Entropy/f.1311.php

  1. Is the transfer of heat reversible or irreversible at the transition temperature?
  2. If the phase transition is exothermic, is the entropy change positive or negative?
  3. What is Trouton’s Rule?

Review

Questions

  1. What precautions need to be taken in selecting a value for \begin{align*}\Delta H\end{align*}ΔH?
  2. Why is temperature selection important?
  3. Why would the entropy of vaporization be so much larger than the entropy of fusion?

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / notes
Show More

Image Attributions

  1. [1]^ Credit: Jon Sullivan; Source: http://commons.wikimedia.org/wiki/File:Geysers_steam_boiling_Yellowstone.jpg; License: CC BY-NC 3.0

Explore More

Sign in to explore more, including practice questions and solutions for Changes of State and Free Energy.
Please wait...
Please wait...