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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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Real gases 1.4 Molecular interactions 1.5 The van de Waals equation 1.6 The principle of corresponding states Real gases do not obey the perfect gas law.

Real gases 1.4 Molecular interactions 1.5 The van de Waals equation 1.6 The principle of corresponding states Real gases do not obey the perfect gas law.

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