Bonds Between Atoms

1
Section 1

• Bonds Between Atoms

2
The Six States of Matter

• Bose - Einstein Condensate
• Solid
• Liquid
• Gas
• Plasma
• Quark - gluon soup

3
Change of State

• Boiling temperature (pressure) for different
  substances
• Helium boils at 4K - Quartz melts at 2000K!
• Interplay of bonding thermal agitation

4
Bonding V Thermal Agitation

• Kinetic (molecular) theory of gases
• Brownian motion in liquids
• Lattice vibrations in solid
• Type of bond strongly influences the structure
  properties of solids

5
Bohrs Model - Postulates

• Newtonian mechanics
• Circular orbits
• Quantisation of angular momentum (Correspondence
  Principle)
• Quantisation of energy

6
De Broglies Hypothesis 1

• Light can behave as particles, so particles can
  behave as waves
• E mc2 pc
• E hn hc/l
• Assume both OK for particles waves)
• Combine to show -
• l h/p

7
De Broglies Hypothesis 2

• Standing particle waves are an explanation of
  ang. mom. quantisation
• Combine-
• pr nh/2p, n1,2,3,

8
Bohrs Model - Findings

• Accurately predicts-
• hydrogen spectrum
• ionisation energy for hydrogen - 13.6 eV
• Bohr radius for hydrogen - 0.0529 nm
• Fails miserably for larger atoms (but good for
  hydrogenic ions)
• Proof of Bohr energy level Bohr radius formulae
  - C J 5th Ed. P916/7/8

9
Bohr Model - Outline 1

• Total Energy P.E(electric) K.E
• Angular Momentum Quantisation Eqn.
• Circular Motion Coulomb Force
• Energy Quantisation Equation

10
Bohr Model - Outline 2

• E (1/2)mv2 - keZe2/r
• mvr nh/2p
• mv2/r keZe2/r2
• Ei - Ef hn

11
Bohr Model - Outline 3

• (1) (3) E -keZe2/2r
• (2) (3) rn (0.0529nm) x n2/Z
• Combining above equations -
• En -(13.6eV) x Z2/n2

12
Bohr Model - Outline 4

• Bohr radius 0.0529nm
• Rydberg equation -

13
Hydrogen Spectrum

• Spectrometer with diffraction grating c. 600
  lines per mm
• Rydberg formula accurately predicts Lyman,
  Balmer, Paschen Blackett series of spectral
  lines

14
1st Ionisation Energy V Z

• Bohr-
• Screening by inner electrons - IP same for all

15
Quantum Theory 1
16
Quantum Theory 2
17
Schrodingers Quantum Numbers

• n - principal quantum number - same as in Bohrs
  model
• l - orbital (angular momentum) number
• ml - magnetic quantum number
• ms - spin quantum number
• Electron energy determined by n l
• Not possible to have zero angular mom.

18
Permitted Values (Shell Model)

• l goes 0 to (n - 1)
• ml goes -l to l
• ms is -1/2 or 1/2
• (Erwin Schrodinger)

19
Pauli Exclusion Principle

• No two fermions can exist in identical energy
  quantum states
• Fermions - half integer spin anti-symmetric
  wave functions
• Electrons, protons neutrons are fermions
• (Wolfgang Pauli)

20
Electron Configuration (Shell Model)

• Electron energy depends on n l
• Levels fill according to this table
• Digit in table is principal number - 2n2
  electrons
• Letter is orbital number - 2(2l1) electrons
• s,p,d,f orbitals - l 0,1,2,3
• K,L,M sub-shells - n 1,2,3

21
Sample Configurations

• H - 1s1
• He - 1s2
• Li - 1s22s1
• B - 1s22s22p1
• Na - 1s22s22p63s1
• Al - 1s22s22p63s23p1
• K - 1s22s22p63s23p64s1
• Ga - 1s22s22p63s23p64s23d104p1

22
Principal Q. Number Energy
23
Electron Probability Clouds 1

• Bohr Model -
• nth orbit is a circle of radius rn
• Electron is always found exactly at a distance
  rn from the nucleus

24
Electron Probability Clouds 2
25
Electron Probability Clouds 3
26
Explaining IP V Z Graph
27
Atomic Radius

• Metallic radius (tight)
• Covalent radius
• Van der Waals (loose - noble gases)

28
First Ionisation Potential
29
Potassium - Elec. Config.

• 4s state is lower in energy than 3d - due to
  Schrodinger eqn.
• Elec config atomic radius similar to Li, Na
  Ga
• Hence similar 1st IP

30
Solids

• In theory, all substances can exist as solids
• Some exist as solids under very exotic conditions
• Solid helium - 2He4 -solid at 4.22K

31
Atoms in Solids

• In solids atoms are close together
• How does this effect the electrons?
• Core electrons - close to nucleus - little
  effected by other atoms
• Valence electrons - screened far from nucleus -
  looking for a lower energy state
• QM allows new energy state to be calculated

32
Types of Solids

• The primary difference between the (five) types
  of solids is the mechanism (three) that holds
  them together
• These mechanisms are responsible for many
  physical characteristics, such as melting
  boiling points, hardness and water solubility

33
Five Types of Solids

• Ionic solids
• Covalent solids
• Polar molecular solids
• Nonpolar molecular solids
• Metallic solids

34
Molecular Metal

• Japanese physicists have developed (Feb 2001) a
  molecular metal - C18H12NiS12
• Neutral Molecule
• Earlier molecular metals had molecules of
  different chemical species
• Ni(tmdt)2 metallic from 0.6 K to room temperature
• Close-packed structure arranged in perfectly
  straight planes

35
Three (electrostatic) Mechanisms

• Primary bonding (strongest)
• ionic
• covalent
• Secondary Bonding
• Intermolecular forces (weakest)
• hydrogen bonds
• dipole-dipole
• dipole-induced dipole
• London Dispersion Forces
• Metallic bonding

36
Mechanisms v Solid State
37
Quartz Table Salt
38
Magnesium - Metallic Bond
39
HCl - Permanent Dipoles
40
Solid State Structures
41
Three (electrostatic) Mechanisms

• Primary or Chemical bonding (strongest)
• ionic
• covalent
• Secondary or Physical bonding
• Intermolecular forces (weakest)
• hydrogen bonds
• dipole-dipole
• dipole-induced dipole
• London Dispersion Forces
• Metallic bonding

42
Ionic Bonding

• Exchange electron(s)
• Occurs between atoms from Groups I VII (NaCl)
• Also between II VI (MgF2)
• Energetically favourable - exothermic (Lattice
  energy)

43
Strength of Ionic Bond

• Bigger charge on ion means stronger bond
• Smaller atomic radius means stronger bonds

44
Electron Affinity V Z kJ/mol
45
Sodium Chloride Bond

• Loss of 5.1 eV to strip e- from Na - I.Pot.
• Gain of 3.6 eV adding e- to Cl - E.affin.
• Nett loss of 1.5 eV/bond - exothermic?
• Attraction of ions releases energy - r0.236 nm-

46
Equilibrium Position
47
Molecular Pot. Energy

• Pauli principle (or Heisenberg) introduces a
  repulsive force which stops the molecule from
  collapsing
• Repulsive force falls off exponentially

48
Sodium Chloride Lattice

• 6 face-centred Na ions (blue) nearest
• 12 Cl (green) at mid-point of outer edges are
  next
• 8 Na at corners next

49
Madelung Constant

• If the calculation is carried out for 1 mole or
  6x1023 molecules, the figure 2.13 becomes 1.74756
  (Md)
• This is the same for all face centred cubic
  lattices

50
NaCl Lattice Energy

• Using the Madelung constant-
• This compares well with experiment (see slide 43)
• QM correction amounts to 10

51
Metallic Bonding

• Formed by elements with 1,2 or 3 valence
  electrons
• All ions in lattice are positively charged so
  should repel one another
• Electron sea in vicinity of metal ions act to
  bond the material
• Metallic bonds are omnidirectional - malleable
  ductile
• Ions in metal should be further apart than ionic
  solid-
• 0.382nm for sodium metal
• 0.281nm for common salt
• Higher valence often means a stronger bond (the
  ions must have similar radii in both metals)

52
Types of Metals

• 75 of elements are metals
• Group I II Al form simple metals
• Have s p valence electrons
• Mg, Na, K
• Transition metals have d valence electrons
• Bonds 5 times stronger
• Like ionic bonds
• Fe, Co, Ni
• Post-transition not as strong
• Cu, Zn, Ag

53
Covalent Bonding 1

• Electron(s) sharing
• C - 1s22s22p2
• QM mixing - hybrid sp3 bond
• Occurs between non-metallic elements

54
Covalent Bonding 2

• Main form of molecular bonding
• Molecule is in a lower energy state than for
  individual atoms

55
Potential Energy H-H Bond
56
Multi-bond Atoms
57
The Story of Polyethlene

• Accidental discovery 1932 - LDPE - ethylene
  reactions at high pressure - soft low melting
• Ziegler Catalyst 1953 - HDPE more rigidboiling
  water - stress cracks -MDPE - hula-hoop!

58
Molecular Structure 1

• Methane
• All CH bonds found to have same strength
• Symmetrical molecule
• Similar structure in diamond crystal
• Polymers usually have convoluted shape

59
Buckyball, Diamond Graphite
60
Intermolecular Bonding

• NaCl crystal is made up of individual ions as
  opposed to sodium chloride molecules
• Most solids are composed of molecules
• Molecules involve secondary bonding

61
Secondary Bonding - Intermolecular

• van der Waals Forces
• Polar molecules - permanent dipole
• hydrogen
• dipole-dipole
• Nonpolar Molecule - induced dipole
• Nonpolar Mol. - fluctuating induced dipole
• London dispersion forces - LDF

62
Bonding Energy
63
Bond Energy Melting Point
64
Electric Dipole Moment

• Pair of opposite charges
• Magnitude of DM charge X distance
• Direction - towards the positive charge
• Units - Cm

65
Water Molecule (Polar)

• Why is the angle 104.5O?
• Total dipole moment?
• Vector problem
• DP 2ed 2e(0.097)cos 52.20 1.91 x 10-29 Cm
• Actual is 0.64 x 10-30 Cm

66
Hydrogen Bond

• Oxygen atoms have excess negative charge
• Hydrogen atoms have excess positive charge
• Dipoles bond by electrostatic attraction
• Tetrahedral shape - 109.50

67
Water Molecule

• Partial positive charges associated with hydrogen
  corners
• Partial negative charges with lone pairs
• Lone pairs repel one another squeeze the
  hydrogens together

68
Dipole-dipole

• H - bond a special case (HCl water)
• Electron affinity is key to understanding
• Larger molecules mean stronger D/D bonds - more
  electrons larger radii

69
Bond Energy

• O--H Covalent 464 kJ/mol
• H2O/ H2O Polar 19 kJ/mol B.P 373K
• H--Cl Covalent 429 kJ/mol
• HCl/HCl Polar 3.3 kJ/mol B.P 188K

70
Dipole - Induced Dipole

• When Ar atom comes close to HCl dipole, electrons
  in Ar shift to one side
• Bond energy - 1 kJ/mol

71
Induced Dipole - Ind. Dipole

• Electron distribution produces induced dipole
  moment in both He atoms
• May be very weak - 0.076 kJ/mol - B.P 4.2 K
• LDF

72
Boiling Points - Noble Gases

• Helium 4 K
• Neon 27 K
• Argon 87 K
• Krypton 121 K
• Xenon 165 K
• Radon 211 K

73
Dip./Dip. LDF

• These forces can occur together
• Ethane fluoroethane same size same number of
  electrons
• Only 10 K extra B.P due to permanent dipole - LDF
  dominates!

74
Trichloromethane Tetrachloromethane
75
Trichloromethane Tetrachloromethane

• CHCl3 is highly polar - B.P 334.2 K
• CCl4 is non-polar - B.P 349.8 K
• CCl4 is a bigger molecule - extra LDF more than
  compensates for loss of Dip./Dip. interaction!

76
Bonds Physical Properties

• Mechanical
• Electrical
• Thermal
• Magnetic
• Optical

• Pure carbon - two allotropes are-
• Graphite - soft, sg 2.22, reflects light, good
  conductor, mp c.3652 0C
• Diamond - hard, sg 3.51, transparent, poor
  conductor, mp 3550 0C

77
Melting Points Bonds