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Chem 300 - Ch 16/#3 Today’s To Do List

Chem 300 - Ch 16/#3 Today’s To Do List. More on IM Forces A bit on Potential Energy Lennard-Jones & Other Potentials What is a London Dispersion force?? The return of Van der Waals. 2 Interacting Linear Molecules. B 2V & Potential Energy [u(r)]. Compare with “Real” Equations of State.

matthew-mendoza
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Chem 300 - Ch 16/#3 Today’s To Do List

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

  2. 2 Interacting Linear Molecules

  3. B2V & Potential Energy [u(r)]

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

  5. Reasonable forms for u(r)

  6. Lennard-Jones Potential

  7. To Evaluate B2V • Find  &  for selected gas • Substitute  & into Lennard-Jones equation • Substitute L-J into expression for B • Integrate • With B2V gas pressure can be calculated from virial eq.

  8. Lennard-Jones Potential

  9. Significance of  &  • Compare gases at molecular level • Examples: /k • He 10.2 256 • Ar 120 341 • Xe 229 406 • CO 100 376 • CO2 189 449

  10. What are these Attractive forces? • Dipole-Dipole • Dipole-Induced dipole • London Dispersion

  11. All are C/r6 dependent • They differ in the size of the coefficient, C

  12. Permanent & Induced Dipoles

  13. (1) Dipole-Dipole udd(r)

  14. (2) Induced Dipole Moment • Proportional to the electric field strength of the neighboring dipole: • induced = E •  = polarizability (dimensions of volume) • E = electric field strength

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

  16. Compare 2 HCl molecules

  17. Other Potential Functions (1) • Hard-sphere Potential • Mimic molecules as hard spheres of diameter  • For r< u(r) = for r> u(r) = 0 • H-SP assumes no attractive force • Pretty good at high T • Substitution gives: B2V = (22N)/3 (T-indep)

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

  19. Other Potential Functions (2) • 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 B2V • Reduces to HSP when  = 1 or  =0

  20. Van der Waals Again • P = [RT/(Vm-b)] - a/V2m • Compare with • Z = 1 + B2V/Vm + ...

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

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