week 11/th: lecture units ‘28 & 29’...week 11/th: lecture units ‘28 & 29’ ©...

Week 11/Th: Lecture Units ‘28 & 29’

© DJMorrissey, 2o12

Unit 27: Real Gases Unit 28: Intermolecular forces -- types of forces between molecules -- examples Unit 29: Crystal Structure -- lattice types -- unit cells -- simple cubic cells, filling efficiency Unit 30: Chemical Spontaneity -- entropy, 2nd Law of Thermo Issues: Homework Set 8 due on Saturday @ 08:00AM

The Atomium, Brussels, Belgium a bcc unit cell

Week 11/Th: Lowering the Energy Content


We have descriptions of the simplest “state” of a pure material (the gas phase) and gas mixtures – let’s lower the energy content (T) … all gases will condense and then at lower energy content (T) they will freeze.

Vapor (gas) Liquid Solid

Vaporization or boiling Melting

Condensation Fusion or Solidification

Internal Energy

sublimation

Liquids: incompressible – particles are in contact with one-another “fluid” shape – particles can/do move around Solids: incompressible – particles are in contact with one-another “fixed” shape – particles retain positions, but can vibrate

Week 11/Th: Gas à Liquid Phase Change


The condensed phases (liquid & solid) are formed when the energy content of the gas phase is dropped (temperature is lowered) below the strength of the “Van der Waals Forces” acting between the particles. Consider the variation of the boiling points of hydrides of the nonmetal Main Group elements plus the Rare Gases (Group 18 or VIIIA).

Note: besides the Group 18 atoms, these all have tetrahedral arrangement Observations: Higher mass – Higher BP Less polar – Lower BP Top row Hydrides – unusual High BP

Week 11/Th: The Weakest Intermolecular Force


“Van der Waals Forces” act between the particles: The weakest force, the one that are always present, are called the “disperson” force. When atoms or molecules come close together, the electron clouds interact and induce a small polarization (the electrons repel one another) that is attractive on-average.

Week 11/Th: The Common Intermolecular Force


“Van der Waals Forces” act between the particles: The most common intermolecular force is the attraction between polarized (or dipolar) molecules. Recall that all asymmetric molecules will be polarized to a greater or less extent.

Week 11/Th: The Strongest Intermolecular Force


“Van der Waals Forces” act between the particles: The strongest force between molecules is called hydrogen bonding and only occurs between top-row elements that have lone pairs and other molecules that have hydrogen atoms. Examples:

DNA base pairs

Water

Ammonia & Aqueous ammonia

Week 11/Th: Force Decision Tree


Dispersion Forces

Dispersion forces of BULKY molecules are stronger than those of similar molar masses that are compact.

Dispersion forces of heavy molecules are stronger than those of similar molecules with lower molar masses and even some polar molecules with lower molar masses.

Metallic Bonds in solid

Ionic Bonds / Coulomb Force

Hydrogen Bonds

Dipole-dipole / Coulomb Force

Covalent Network of Bonds

Ionic?

Network?

Metal?

Nonmetal

Covalent

F-H N-H, or O-H?

Polar?

Nonpolar

Week 11/Th: Types of Solids (Forces)


Molecular Solids – almost every pure material (except those listed below) >Atoms or molecules at the lattice points that are held by van der Waals forces. For example, Ar -- (London) dispersion force CO -- permanent dipole-dipole interaction (Coulomb force) H2O -- above plus H-bonds > Packing depends on geometry & stoichiometry Metallic Solids – (small number) 75% of elements and their alloys >Atoms at the lattice points that are held together by delocalized electrons .. >Packing depends on the density. (Covalent) Network Solids – (very few) related to carbon >Atoms are held in position by covalent (chemical) bonds >Packing depends on covalent electronic structure Ionic Solids – (small number) Salts >Ions at the lattice points that are held together by the Coulomb force. >Pack (usually) spherical ions into lattice depending on the relative sizes of ions & the stoichiometry of the compound.

Week 11/Th: Types of Solids


Lattice -- 3D macroscopic object made up from individual repeating blocks called unit cells Unit cell – smallest 3D microscopic object that satisfies the geometrical and stoichiometric requirements of the lattice and of the compound

Week 11/Th: Unit Cells – Not for Memorization


Lattice -- 3D object Unit Cell – 3D object 3 edges & 3 angles

NAME ANGLES SIDES Cubic α = β = γ = 90o a=b=c Tetragonal α = β = γ = 90o a=b≠c Orthorhombic α = β = γ = 90o a≠b≠c Monoclinic α = γ = 90o ≠ β a≠b≠c Triclinic α ≠ β ≠ γ ≠ 90o a≠b≠c Hexagonal 120o, 90o a≠b Trigonal α = β = γ ≠ 90o a=b=c

Week 11/Th: Lattices – Not for Memorization


(only) 14 Bravais Lattice Unit Cells

Week 11/Th: Simple Cubic Lattice, Empty Space


eff =Volumeoccupied /VolumeUnitCell

= # Atoms∗VAtom a*b*c

= # Atoms∗VAtom / a3

= 1( ) 43πr3

"

#$

%

&' / a3

= 1( ) 43πr3

"

#$

%

&' / 2r( )3

=4πr3

3∗8r3=π6

SC lattice has empty space, what fraction is occupied?

Simple Cubic Lattice

Packing Efficiency = π/6 52.4%

How many atoms in the SC unit cell? Eight corners of cell Eight cells meet at a corner

Week 11/Th: Packing Efficiency


#Atoms Edge Packing Efficiency per U.C. Length ____________________________________________________ SC 1 a= 2 r π/6 ( 52.4% ) BCC 2 a=√(8/3) r (3)3/2 π/24 ( 68.0% ) FCC 4 a= √8 r (2)3/2 π/3 ( 74.1% ) _____________________________________________________

Face Centered Cubic

Body Centered Cubic

Week 11/Th: Metal Alloys


Atoms Radii (pm) Zn / Cu 138 / 128 Ni / Cu 124 / 128 Be / Cu 112 / 128 Sb / Cu / Sn 141 / 128 / 158 Sn / Pb 158 / 175 C / Cr / Fe 77 / 128 / 126

Substitutional Alloy Interstitial Alloy

week 11/th: lecture units ‘28 & 29’...week 11/th: lecture units ‘28 & 29’ ©...

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