chem 300 - ch 16/#3 today’s to do list l more on im forces l a bit on potential energy l...
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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
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2 Interacting Linear Molecules
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B2V & Potential Energy [u(r)]
2 0
22 1
V AB N rT u r kT dr( ) ex p ( ) /
A sim p le ex p ress io n fo r u (r) is n eed ed .
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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 (+)
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Reasonable forms for u(r)
u r cr
u r crnn
( )
( )
66 (when r large)
(r small, n = 9 -12)
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Lennard-Jones Potential
u r r r( )
41 2 6
= m easu re o f in te rm o lec a ttrac tio n
= m easu re o f m o lecu la r s iz e
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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.
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Lennard-Jones Potential
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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
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What are these Attractive forces?
Dipole-Dipole Dipole-Induced dipole London Dispersion
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All are C/r6 dependent
They differ in the size of the coefficient, C
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Permanent & Induced Dipoles
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(1) Dipole-Dipole udd(r)
ddu rr
kT( )
( )( )
2
0 3
11
2
2
2
2 6
4
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(2) Induced Dipole Moment
Proportional to the electric field strength of the neighboring dipole:
induced = E = polarizability (dimensions of
volume)• E = electric field strength
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inducedu ( )( / )
( )r
r
2 4
4
2
0
0
6
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(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
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dispuI II I r
r( ) ( )
3
20
1 2
1 2
1 22 64
I = Ionization Energy
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Compare 2 HCl molecules
Dipole-dipole -1.82 x 10-78 J -m6
Dipole-induceddipole
-0.56 x 10-78 J -m6
Londondispersion
-10.6 x 10-78 J -m6
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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)
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Hard Sphere(a) & Square-Well(b) Potentials
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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
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Van der Waals Again
P = [RT/(Vm-b)] - a/V2m
Compare with• Z = 1 + B2V/Vm + ...
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Next Time
Start Chapter 19: 1st Law• P-V work• State Functions• 1st Law• Adiabatic Processes