20 B Week II Chapters 9 -10)

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• 20 B Week II Chapters 9 -10)

Macroscopic Pressure Microscopic pressure( the
kinetic theory of gases no potential
energy) Real Gases van der Waals Equation of
State London Dispersion Forces Lennard-Jones
V(R ) and physical bonds Chapter 10 3 Phases
of Matter Solid, Liquid and Gas of a single
component system( just one type of molecule, no
solutions) Phase Transitions A(s) ??A(g)
Sublimation/Deposition A(s) ??A(l)
Melting/Freezing A(l) ??A(g)
Evaporation/Condensation
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Example Volume occupied by a CO2 molecule in
the solid compared to volume associated with
CO2 in the gas phase. The solid. The mass
density(r) of solid CO2 (dry ice) r1.56 g cm-3
1 mole of CO2 molecular weight M44.01 g mol-1
occupies a molar volume V M/r V 44.01 g mol-1
/1.56 g cm-3 28.3 cm-3 mol-1 1 cm-3 10-3 L
mL Which is approximately the excluded volume per
mol-1 0.028.3 L mol-1 The Ideal Gas Volume at
T300 K and P1 atm PVNkTnRT V/nRT/P
(0.0821 L atm mol-1 K-1)(273 K)/(1 atm) 22.4 L
mol-1 The Real Volume of CO2(g) under these
conditions is 22.2 L mol-1 Why is the Real
molar volume smaller than the Ideal gas Volume?
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Gas
Liquid
Solid
?ltlt kT EKE
?gtgtkT EPE
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Real Gas behavior is more consistent with the
van der Waals Equation of State than PVnRT
PnRT/(V nb) a(n/V)2 nN/NA and
RNak n number of moles b NA???excluded
volume per mole (V-nb) repulsive effect a
represents the attraction between
atoms/molecules. The Equations of State can be
determined from theory or by experimentally
fitting P, V, T data! They are generally more
accurate than PVnRTNkT but they are not
universal
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2e
2e
2
1 Å 0.1 nm Å is an Angstrom
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The London Dispersion or Induced Dipole Induced
Dipole forces Weakest of the Physical Bonds but
it is always present!
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Which of these atoms have the strongest physical
bond? Which of the diatomic molecules have the
strongest physical bond? Why is CH4 on this list?
Bond dipoles
(kT/ ?? ratio predicts deviations from Idea gas
behavior. Since ltPEgt 0 for real gases If kTgtgt?
which forces are dominant? Repulsive forces
dominate and PgtNkT/V for real gases If kTltlt?
which forces are dominant Attractive forces
dominate and PltNkT/V for real gases
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Bond dipoles
(kT/ ?? ratio predicts deviations from Idea gas
behavior. Since ltPEgt 0 for real gases If kTgtgt?
which forces are dominant? Repulsive forces
dominate and PgtNkT/V for real gases If kTltlt?
which forces are dominant Attractive forces
dominate and PltNkT/V for real gases
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PE
PEKE
KE
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Gas
Liquid
Solid
Temperature
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2e
2e
2
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Real Gases and Intermolecular Forces
Lennard-Jones Potential V(R ) 4?(R/?)12
-(R/?)6
kT gtgt ?
Total Energy EKE V(R) KE
Ar Ar /He He
? well depth is proportional Ze (or Mass) but
its the of electrons that control the well
depth
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(kT/ ?? ratio controls deviations away from Idea
gas behavior. kTgtgt? repulsive forces dominate
and PgtNkT/V kTltlt? attrative forces dominate and
PltNkT/V
The effects of the intermolecular force, derived
the potential energy, is seen experimentally
through the Compressibility Factor
ZPV/NkT ZPV/NkTgt1 when repulsive forces
dominate ZPV/NkTlt1 when attractive forces
dominate ZPV/NkT1 when ltV(R )gt0 as for the
case of an Ideal Gas.
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Real Gas behavior is more consistent with the
van der Waals Equation of State than PVnRT
PnRT/(V nb) a(n/V)2 nN/NA and RNAk
b NA???excluded volume per mole (V-nb) repulsive
effect a represents the attraction between
atoms/molecules. The Equations of State can be
determined from theory or by experimentally
fitting P, V, T data! They are generally more
accurate than PVnRTNkT but they are not
universal
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(kT/ ?? ratio controls deviations away from Idea
gas behavior. kTgtgt? repulsive forces dominate
and PgtNkT/V kTltlt? attrative forces dominate and
PltNkT/V
The effects of the intermolecular force, via the
potential energy, is seen experimentally through
the Compressibility Factor ZPV/NkT ZPV/NkTgt1
when repulsive forces dominate ZPV/NkTlt1 when
attractive forces dominate ZPV/NkT1 when ltV(R
)gt0 as for the case of an Ideal Gas.
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Excluded Volume (V-nb)(V - nNA??? ?(V N
??? and Two Body Attraction a(n/V)2
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The Compressibility factor Z can be written in
terms of the van der Waals Equation of State
ZPV/nRT V/(V-nb) (a/RT)(n/V)2
Z V/(V-nb) (a/RT)(n/V)21/1-b(n/V)
(a/RT)(n/V)2
Repulsion Zgt1
Attraction Zlt1
When a and b are zero, Z 1 Since PVRT n1
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Electro-negativity of atoms
In a molecule the more Electronegative atom in a
bond will transfer electron density from the
less Electronegative atom This forms dipole
along a bond
Re
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Dipole-Dipole interaction ? partial on an atom Re
HCl bond length
Not the Real Dimer Structure
Real Dimer Structure
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Notice the difference between polar molecules
(dipole moment ??0) and non-polar molecules (no
net dipole moment ?0) CO2 and CH4
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Dipole-Dipole
Hydrogen Bonding due lone pairs on the O and N
atoms
??e
???e
Dipole moment ??eRe
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The Potential Energy of Chemical Bonds Versus
Physical Bonds
Physical Bonds
Chemical Bonds
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