07.09 -The Molecular Basis of Equations of State: Concepts and Notation

Nature of Molecular Interactions - Macro To Nano(8min). (uakron.edu) Instead of matching the critical point, we can use experimental data for density vs. temperature from NIST as a means of characterizing the attractive energy and repulsive volume. A plot of compressibility factor vs. reciprocal temperature exhibits fairly linear behavior in the liquid region. Matching the slope and intercept of this line characterizes two parameters. This characterization may be even more useful than using the critical point if you are more interested in liquid densities than the critical point. In a similar manner, you could derive an EOS based on square-well (SW) simulations and use the SW EOS to match the NIST data(11min), as shown in this sample calculation of the ε and σ values for the SW potential. In this lesson, we learn how to characterize the forces between individual atoms, which may seem quite unreal or impractical when you first encounter it. On the other hand, "nanotechnology" is a scientific discipline that explores how the manipulation of nanostructure is now quite real with very significant practical implications. "The world's smallest movie" shows dancing molecules, (IBM, 2min) demonstrating the reality of molecular manipulation, and the accompanying text explains some of the practical implications. Along similar lines, researchers at LLNL and CalTech have developed 3D printers that can display "voxels" (the 3D analog of pixels) of ~1nm3. That's around 10-100 atoms per voxel. Since 2013-14, chemical/materials engineers have been building nanostructures (TEDX, 13min) in the same way that civil engineers build infrastructure.
Comprehension Questions:
1. What does the y-intercept represent in a plot of compressibility factor vs. reciprocal temperature?
2. What parameter does the y-intercept help to characterize, b or ε?
3. What does the x-intercept represent in a plot of compressibility factor vs. reciprocal temperature?
4. What parameter does the x-intercept help to characterize, b or ε?
5. Apply the SW EOS given in the second video to the isochore at 16.1 mol/L. Do you get the same values for ε/k and σ? Explain.