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JCE SymMath: Symbolic Mathematics in Chemistry
Theresa Julia Zielinski Monmouth University West Long Branch, NJ 07764-1898
Intermolecular Potentials and the Second Virial Coefficient by Patrick L. Holt, Department of Chemistry & Physics, Bellarmine University, Louisville, Kentucky 40205;
[email protected] File Names: IMPotential2001i.mcd, IMPotentialInstructor2001i.mcd, IMPotential8.mcd, IMPotentialInstructor8.mcd, IMPotential.pdf, IMPotentialInstructor.pdf Keywords: Physical Chemistry, Upper Division Undergraduate, Gases, Thermodynamics, Physical Properties, Computer-based Learning, Symbolic Mathematics
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.
Requires: MathCad 8, MathCad 2001i or higher
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
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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.
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Figure 3. The distribution of particles, N, over the first four vibrational energy states of CO as a function of the temperature T. The number of particles in each energy state approaches a constant as the temperature increases.
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Figure 5. The real part of the wave function for a particle in a box with a finite barrier as a function of the location of the particle in the box, (inside the box, the barrier, and outside the box regions are shown from left to right in the image).
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