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

Example: Volume occupied by a CO 2 molecule in the solid compared to volume associated with CO 2 in the gas phase. The solid. The mass density(  of solid CO 2 (dry ice)  =1.56 g cm -3 1 mole of CO 2 molecular weight M =44.01 g mol -1 occupies a molar volume V= M /  V= g mol -1 /1.56 g cm -3 = 28.3 cm -3 mol -1 1 cm -3 = L= mL Which is approximately the excluded volume per mol -1 = L mol -1 The Ideal Gas Volume at T=300 K and P=1 atm PV=NkT=nRT V/n=RT/P= ( L atm mol -1 K -1 )(273 K)/(1 atm) = 22.4 L mol -1 The Real Volume of CO 2 (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 Solid Liquid Gas  kT E~PE  << kT E~KE

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/N A and R=N a k n= number of moles b~ N A    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

Fig. 9-18, p R R = 0 For R Very Large Density N/V is low Therefore P=(N/V)kT is low = 0 For R Very Large Density N/V is low Therefore P=(N/V)kT is low +2 2e 1 Å = 0.1 nm Å is an Angstrom

Real Gases and Intermolecular Forces  well depth or Dimer Bond Dissociation D 0 =   ~ hard sphere diameter Real Molecular potentials can be fitted to the form V(R ) = 4  {(R/  ) 12 -(R/  ) 6 } Lennard-Jones Potential

The London Dispersion or Induced Dipole Induced Dipole forces Weakest of the Physical Bonds but it is always present!

(kT/  ratio predicts deviations from Idea gas behavior. Since ~ 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 Which of these atoms have the strongest physical bond? Which of the diatomic molecules h ave the strongest physical bond? Why is CH 4 on this list?

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

H 2 O P-T Phase Diagram PE KE PE+KE

 Hard Sphere diameter Solid Liquid Gas Temperature

Fig. 9-18, p R R = 0 For R Very Large Density N/V is low Therefore P=(N/V)kT is low = 0 For R Very Large Density N/V is low Therefore P=(N/V)kT is low +2 2e

Real Gases and Intermolecular Forces  well depth is proportional Ze (or Mass) but it’s the # of electrons that control the well depth Lennard-Jones Potential V(R ) = 4  {(R/  ) 12 -(R/  ) 6 } Ar+ Ar /He + He kT >>  Total Energy E=KE + V(R)~ KE

Real Gases and Intermolecular Forces  well depth Lennard-Jones Potential V(R ) = 4  {(R/  ) 12 -(R/  ) 6 } kT << 

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 =0 as for the case of an Ideal Gas. (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

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/N A and R=N A k b~ N A    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

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 =0 as for the case of an Ideal Gas. (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

Excluded Volume: (V-nb)~(V - nN A    (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

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 Dipole moment  =  eR e A measure of the charge separation along the bond  e  e ReRe

Dipole-Dipole interaction ∂ partial on an atom R e HCl bond length Dipole moment  =  eR e Measure of the charge separation  e  e Real Dimer Structure Not the Real Dimer Structure

Notice the difference between polar molecules (dipole moment  ≠0) and non-polar molecules (no net dipole moment  =0) CO 2 and CH 4

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

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