Chem 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

2 Interacting Linear Molecules

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

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 (+)

Reasonable forms for u(r)

Lennard-Jones Potential

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.

Lennard-Jones Potential

Significance of  &  l Compare gases at molecular level l Examples:  /k  He Ar Xe CO CO

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

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

Permanent & Induced Dipoles

(1) Dipole-Dipole u dd (r)

(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

(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

Compare 2 HCl molecules

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)

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

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

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

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