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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)


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?


20 b week ii chapters 9 10

Hard Sphere diameter

Gas

Liquid

Solid

<< kT E~KE

>>kT E~PE


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

<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


20 b week ii chapters 9 10

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= 


20 b week ii chapters 9 10

The London Dispersion

or Induced Dipole Induced Dipole forces

Weakest of the Physical Bonds but it is always present!


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

H2O P-T Phase Diagram

PE

PE+KE

KE


20 b week ii chapters 9 10

Hard Sphere diameter

Gas

Liquid

Solid

Temperature


20 b week ii chapters 9 10

<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


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

Real Gases and Intermolecular Forces

Lennard-Jones Potential

V(R ) = 4{(R/)12 -(R/)6}

kT << 

 well depth


20 b week ii chapters 9 10

(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.


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

(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.


20 b week ii chapters 9 10

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

and

Two Body Attraction: a(n/V)2


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

 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


20 b week ii chapters 9 10

 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


20 b week ii chapters 9 10

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


20 b week ii chapters 9 10

Dipole-Dipole van der Waals Equation of State

Hydrogen Bonding due lone pairs on the O and N atoms

e

e

Dipole moment =eRe


20 b week ii chapters 9 10

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

Versus Physical Bonds

Physical Bonds

Chemical Bonds