Use this simulation to practice identifying the relative slope of chemical potential versus temperature or pressure for various liquids, solids and vapors. The simulation randomizes what exactly you have to identify. After guessing, you can see the correct answer with the “solution” checkbox. You must select the solution box before moving to the next step. You can click “new problem” at any time. Test your knowledge of how chemical potential relates to temperature, pressure and phase. In combination with other learning methods, self-testing is an effective way of internalizing complex thermodynamic concepts.
The chemical potential \(\mu\) (J/(K-mol)) is equal to the Gibbs free energy \(G\) for a single component. The differential of the chemical potential and Gibbs free energy is:
$$d\mu = dG = V\,dP - S\,dT,$$
where \(V\) is volume, \(P\) is pressure, \(S\) is entropy and \(T\) is temperature.
The slope of \(\mu\) versus pressure is proportional to the specific volume \(V\) at constant temperature. The slope of \(\mu\) versus temperature is proportional to the negative of the entropy at constant pressure. Thus, the slope of the vapor chemical potential line versus pressure at constant temperature will be orders of magnitude steeper than the slope of the solid or liquid chemical potential lines versus pressure. Likewise, a chemical in its vapor state has a higher entropy than its liquid state, so the slope of the vapor line versus temperature at constant pressure will be steeper than the solid or liquid lines.
All compounds exist in the phase with the lowest chemical potential for that temperature and pressure. As such, the intersection of two chemical potential lines for different phases represents the boiling point, melting point, sublimation point or triple point [1].
Reference
[1] P. W. Atkins and J. de Paula, Atkins' Physical Chemistry, 8th ed., New York: Oxford University Press, 2006.
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Neil Hendren. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.