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Chem 300 - Ch 16/#3 Today’s To Do List l More on IM Forces l A bit on Potential Energy l Lennard-Jones & Other Potentials l What is a London Dispersion force?? l The return of Van der Waals

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2 Interacting Linear Molecules

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B 2V & Potential Energy [u(r)]

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Compare with “Real” Equations of State l Attractive and repulsive (excluded volume) forces: l Attractive forces are influential at far distances and are (-) l Excluded volume effects are short-range and are (+)

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Reasonable forms for u(r)

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Lennard-Jones Potential

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To Evaluate B 2V l Find & for selected gas l Substitute & into Lennard-Jones equation l Substitute L-J into expression for B l Integrate l With B 2V gas pressure can be calculated from virial eq.

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Lennard-Jones Potential

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Significance of & l Compare gases at molecular level l Examples: /k He 10.2 256 Ar 120 341 Xe 229 406 CO 100 376 CO 2 189 449

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What are these Attractive forces? l Dipole-Dipole l Dipole-Induced dipole l London Dispersion

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All are C/r 6 dependent l They differ in the size of the coefficient, C

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Permanent & Induced Dipoles

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(1) Dipole-Dipole u dd (r)

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(2) Induced Dipole Moment l Proportional to the electric field strength of the neighboring dipole: l induced = E = polarizability (dimensions of volume) E = electric field strength

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(3) London Dispersion Force l Exists even without perm dipole l QM effect l Electronic Wave function of one molecule is momentarily distorted by passing molecule l Creates an instant induced dipole l Feeds back to other molecule

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Compare 2 HCl molecules

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Other Potential Functions (1) l Hard-sphere Potential Mimic molecules as hard spheres of diameter For r u(r) = 0 H-SP assumes no attractive force Pretty good at high T l Substitution gives: B 2V = (2 2 N)/3 (T-indep)

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Hard Sphere(a) & Square- Well(b) Potentials

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Other Potential Functions (2) l Square-Well Potential For r< u(r) = for < r< u(r) = - for r > u(r) = 0 S-WP assumes crude attractive potential Gives T-dependent B 2V Reduces to HSP when = 1 or =0

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Van der Waals Again l P = [RT/(V m -b)] - a/V 2 m l Compare with Z = 1 + B 2V /V m +...

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Next Time l Start Chapter 19: 1st Law P-V work State Functions 1st Law Adiabatic Processes

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