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• 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

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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

20 B Week II Chapters 9 -10)


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) r=1.56 g cm-3

1 mole of CO2 molecular weight M=44.01 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 T=300 K and P=1 atm PV=NkT=nRT

V/n=RT/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?


Hard Sphere diameter

Gas

Liquid

Solid

<< kT E~KE

>>kT E~PE


Real Gas behavior is more consistent with

the van der Waals Equation of State than PV=nRT

P=[nRT/(V– nb)] – [a(n/V)2] n=N/NA and R=Nak

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 PV=nRT=NkT

but they are not universal


<V(R )> = 0

For R

Very Large

Density N/V is low

Therefore

P=(N/V)kT is low

2e

2e

+2

2+

R

1 Å = 0.1 nm

Å is an Angstrom

Fig. 9-18, p. 392


Real Gases and Intermolecular Forces

Real Molecular potentials can be fitted to the form

V(R ) = 4{(R/)12 -(R/)6}

Lennard-Jones Potential

~ hard sphere diameter

  • well depth or

    Dimer Bond Dissociation

    D0= 


The London Dispersion

or Induced Dipole Induced Dipole forces

Weakest of the Physical Bonds but it is always present!


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 <PE> ~ 0 for real gases

If kT>> which forces are dominant?

Repulsive forces dominate and P>NkT/V for real gases

If kT<< which forces are dominant

Attractive forces dominate and P<NkT/V for real gases


Bond dipoles

(kT/  ratio predicts deviations from Idea gas behavior.

Since <PE> ~ 0 for real gases

If kT>> which forces are dominant?

Repulsive forces dominate and P>NkT/V for real gases

If kT<< which forces are dominant

Attractive forces dominate and P<NkT/V for real gases


H2O P-T Phase Diagram

PE

PE+KE

KE


Hard Sphere diameter

Gas

Liquid

Solid

Temperature


<V(R )> = 0

For R

Very Large

Density N/V is low

Therefore

P=(N/V)kT is low

2e

2e

+2

2+

R

Fig. 9-18, p. 392


Real Gases and Intermolecular Forces

Lennard-Jones Potential

V(R ) = 4{(R/)12 -(R/)6}

kT >> 

Total Energy

E=KE + V(R)~ KE

Ar+ Ar /He + He

 well depth is proportional Ze (or Mass) but it’s the # of electrons that control the well depth


Real Gases and Intermolecular Forces

Lennard-Jones Potential

V(R ) = 4{(R/)12 -(R/)6}

kT << 

 well depth


(kT/  ratio controls deviations away from Idea gas behavior.

kT>> repulsive forces dominate and P>NkT/V

kT<< attrative forces dominate and P<NkT/V

The effects of the intermolecular force, derived

the potential energy, is seen experimentally through the

Compressibility Factor Z=PV/NkT

Z=PV/NkT>1 when repulsive forces dominate

Z=PV/NkT<1 when attractive forces dominate

Z=PV/NkT=1 when <V(R )>=0 as for the case of an Ideal Gas.


Real Gas behavior is more consistent with

the van der Waals Equation of State than PV=nRT

P=[nRT/(V– nb)] – [a(n/V)2] n=N/NA and R=NAk

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 PV=nRT=NkT

but they are not universal


(kT/  ratio controls deviations away from Idea gas behavior.

kT>> repulsive forces dominate and P>NkT/V

kT<< attrative forces dominate and P<NkT/V

The effects of the intermolecular force,

via the potential energy, is seen experimentally through the

Compressibility Factor Z=PV/NkT

Z=PV/NkT>1 when repulsive forces dominate

Z=PV/NkT<1 when attractive forces dominate

Z=PV/NkT=1 when <V(R )>=0 as for the case of an Ideal Gas.


Excluded Volume: (V-nb)~(V - nNA ~(V – N

and

Two Body Attraction: a(n/V)2


The Compressibility factor Z can be written in terms of the van der Waals Equation of State

Z=PV/nRT= V/{(V-nb) – (a/RT)(n/V)2}

Z= V/{(V-nb) – (a/RT)(n/V)2}=1/{[1-b(n/V)] – (a/RT)(n/V)2}

Repulsion

Z>1

Attraction

Z<1

When a and b are zero, Z = 1 Since PV=RT n=1


 van der Waals Equation of Statee

e

Electro-negativity of atoms

Dipole moment =eRe

A measure of the charge separation along the bond

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


 van der Waals Equation of Statee

e

Dipole-Dipole interaction

∂ partial on an atom

Re HCl bond length

Dipole moment =eRe

Measure of the charge separation

Not the Real Dimer Structure

Real Dimer Structure


Notice the difference between polar molecules van der Waals Equation of State

(dipole moment ≠0)

and non-polar molecules (no net dipole moment =0)

CO2 and CH4


Dipole-Dipole van der Waals Equation of State

Hydrogen Bonding due lone pairs on the O and N atoms

e

e

Dipole moment =eRe


The Potential Energy of Chemical Bonds van der Waals Equation of State

Versus Physical Bonds

Physical Bonds

Chemical Bonds


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