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Intermolecular Potentials and the Second Virial Coefficient

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Abstract

Through exercises embedded in this worksheet, students explore the relationship between intermolecular potentials and the second virial coefficient. Students examine and adjust parameters associated with the hard-sphere, square-well, and Lennard-Jones potentials, noting differences while investigating the correlation between the form of these potentials and molecular interactions (Figure 1). They subsequently use these potentials to compute the second virial coefficient and explore the coefficient's temperature dependence for several substances. As a final exercise, students use computed values of B to investigate the temperature dependence of the compression factor, Z. Based on these computations and the resulting graphs, students assess the dependence of the virial coefficient on molecular interactions and ambient conditions. As a result, students gain a deeper understanding of the significance of the second virial coefficient and its intrinsic relationship to molecular properties. Student and instructor's versions of this worksheet are available in Mathcad 2001i and Mathcad 8 formats. The instructor's version contains additional notes and solutions to selected problems.

Figure 1. The hard sphere and Lennard-Jones potentials, US(r) and ULJ(r), as a function of r, the distance between the centers of the particles.

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Version	Student	Instructor
Mathcad 2001i	IMPotential2001i.mcd	IMPotentialInstructor2001i.mcd
Mathcad 8	IMPotential8.mcd	IMPotentialInstructor8.mcd

Version	Student	Instructor
Mathcad 2001i	IMPotential.pdf	IMPotentialInstructor.pdf

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Keywords

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Gases; Mathematics / Symbolic Mathematics; Physical Properties; Thermodynamics;

JCE Citation