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

e 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

e 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 (dipole moment ≠0) and non-polar molecules (no net dipole moment =0) CO2 and CH4

Dipole-Dipole Hydrogen Bonding due lone pairs on the O and N atoms e e Dipole moment =eRe

The Potential Energy of Chemical Bonds Versus Physical Bonds Physical Bonds Chemical Bonds

20 B Week II Chapters 9 -10)