Title: Chemical Bonding
1Chemical Bonding
2What is a Chemical Bond?
- a bond is a force of attraction between two atoms
- the source of the force are attractions and
repulsions between electrons and the atomic
nucleii - before we get into detail, do the Ball Stick
activity, to get an idea of what molecules look
like.
3Review of Grade 11
- Quantum theory
- electron configuration
- orbital diagrams
- Lewis diagrams
4Quantum Mechanics and Atomic Orbitals
- Quantum mechanics is a mathematical treatment
into which both the wave and particle nature of
matter could be incorporated.
5Quantum Mechanics
- since the electron is both a wave and a particle
it is impossible to give its location or speed
with certainty. - gives a probability density map of where an
electron has a certain statistical likelihood of
being at any given instant in time.
6Quantum Numbers
- The probability map reveals the atomic orbitals,
and their corresponding energies. - An orbital is described by a set of three quantum
numbers.
7Principal Quantum Number, n
- This relates to the energy of the electron
- As n becomes larger, the atom becomes larger and
the electron is further from the nucleus. - This is directly related to the period of the
atom on the Periodic Table
8Angular momentum quantum number, l
- This quantum number defines the shape of the
orbital. - There are 4 shapes
- s - begins at n 1
- p - begins at n 2
- d - begins at n 3
- f - begins at n 4
- Theoretical g, h, i, etc. orbitals exist, but no
atoms have been created to use them.
9Magnetic Quantum Number, ml
- Magnetic quantum numbers give the
three-dimensional orientation of each orbital. - s - has 1 orientation
- p - has 3 orientations
- d - has 5 orientations
- f - has 7 orientations
10s Orbitals
11p Orbitals
- propeller shaped
- Have two lobes with a node between them.
12d Orbitals
- Four of the five orbitals have 4 lobes the other
resembles a p orbital with a doughnut around the
center.
13f orbitals (flowers)
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15Spin Quantum Number, ms
- electrons have spin, which creates a magnetic
field - there are two spin states possible, 1/2 and -1/2
- a single orbital can hold a maximum of two
electrons, which must have opposite spin (Pauli
Exclusion Principle).
16Electron Address
- thus every electron location is defined in terms
of 4 things - Principal Quantum Number - 1 to 7
- Angular Quantum Number s, p, d or f
- Magnetic Quantum Number implied by number of
electrons in each shape s has 2, p has 6, d has
10 and f has 14 - Spin Quantum Number why each orbital can
contain 2 electrons
17Electron Configurations
- Electrons tend to occupy the lowest energy
orbitals. - Thus the electron configuration of an atom is the
arrangement of the electrons from the lowest
energy level to the highest.
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19Electron Configurations
- Consist of
- Number denoting the energy level.
- Letter denoting the type of orbital.
- Superscript denoting the number of electrons in
those orbitals. - For instance
- Iron (Fe) contains 26 electrons
- 1s22s22p63s23p64s23d6
- watch the order of filling
20Electron Configuration
- Potassium - 19 electrons
- 1s22s22p63s23p64s1
- Silver - 47 electrons
- 1s22s22p63s23p64s23d104p65s24d9
- Tungsten - 74 electrons
- 1s22s22p63s23p64s23d104p65s24d105p66s24f145d4
- Plutonium - 94 electrons
- 1s22s22p63s23p64s23d104p65s24d105p66s24f145d10
6p67s25f6
21- Write the correct electron configuration for the
following - Si, S, P, Ca, As, Fe, Br, Kr, At, U, Na1, F1-,
Ne
22Electron Configuration
- Si - 14 e1- 1s22s22p63s13p3
- S - 16 e1- 1s22s22p63s23p4
- P - 15 e1- 1s22s22p63s23p3
- Ca - 20 e1- 1s22s22p63s23p64s14p1
- As - 33 e1- 1s22s22p63s23p64s23d104p3
- Fe - 26 e1- 1s22s22p63s23p64s23d6
- Br - 35 e1- 1s22s22p63s23p64s23d104p5
- Kr - 36 e1- 1s22s22p63s23p64s23d104p6
- At - 85 e1- 1s22s22p63s23p64s23d104p65s24d105p
66s24f145d106p5 - U - 92 e1- 1s22s22p63s23p64s23d104p65s24d105p66s
24f145d106p67s25f4 - Na1 - 10 e1- 1s22s22p6
- F1- - 10 e1- 1s22s22p6
- Ne - 10 e1- 1s22s22p6
23Electron Promotion
- promotion of an outer s electron to the
adjacent p orbital. - turns non-bonding electrons into bonding
electrons - allows atoms to make more chemical bonds and
achieve a lower energy - applies to elements from groups 2, 13 and 14 only
- for these elements promotion is the rule
24Electron Promotion
- Element Unhybridized Hybridized
- beryllium 1s22s2 1s22s12p1
- boron 1s22s22p1 1s22s12p2
- carbon 1s22s22p2 1s22s12p3
25Orbital Diagrams
- are another way to illustrate the position of
electrons. - They are best learned by comparison with electron
configuration - Na (11 protons, 11 electrons)
- electron configuration 1s22s22p63s1
- orbital diagram
- 1s 2s 2p 3s
-
- ?? ?? ?? ?? ?? ?
26Orbital Diagrams
- Representative
- Group Element Electron configuration
Orbital Diagram - 1s 2s 2p
- 1 lithium 1s22s1 ?? ?
- 2 beryllium 1s22s12p1 ?? ? ?
- 13 boron 1s22s12p2 ?? ? ? ?
- 14 carbon 1s22s12p3 ?? ? ? ? ?
- 15 nitrogen 1s22s22p3 ?? ?? ? ? ?
- 16 oxygen 1s22s22p4 ?? ?? ?? ? ?
- 17 fluorine 1s22s22p5 ?? ?? ?? ?? ?
- 18 neon 1s22s22p6 ?? ?? ?? ?? ??
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30- Na1, F1-, Ne are all the same
31Electron dot (Lewis) diagrams
- gives information only concerning the valence
electrons. - the electrons on the outside of an atom
- the electrons responsible for bonding
- the electrons gained or lost when an atom
ionizes. - the electrons in the s and p orbitals of the
highest energy level reached by the electrons of
an atom. - In this class when valence electrons are
mentioned, the only elements concerned are those
in groups 1, 2, and 13 through 18. - all atoms in the same group have the same Lewis
diagram !!
32Lewis diagrams
- group 1
- group 2
- group 13
- group 14
- group 15
- group 16
- group 17
- group 18
-
33Lewis diagrams
- Repeat last assignment, making lewis diagrams.
34Lewis Diagram Answers
- Fe and U have no lewis diagrams
35What do Orbital and Lewis diagrams tell us?
- both give information about valence electrons.
- if valence electrons are paired, they cannot be
used for bonding with other atoms. They are
lone-pair electrons. - unpaired valence electrons are bonding electrons.
36- 5 valence electrons
- 1 lone pair
- 3 bonding electrons this atom makes 3 chemical
bonds.
37- 4 valence electrons
- 0 lone pair
- 4 bonding electrons this atom makes 4 chemical
bonds
38- 7 valence electrons
- 3 lone pair
- 1 bonding electrons this atom makes 1 chemical
bond
39- 8 valence electrons
- 4 lone pair
- 0 bonding electrons this atom makes 0 chemical
bonds
40Valence level expansion
- Some compounds occur which cannot be easily
explained - PF5, SF6, ClF7, ArF8
- in each case the number of chemical bonds is
equal to the number of valence electrons. - this can only happen if electrons are promoted to
a higher energy level. In this case it is the
adjacent d orbital.
41PF5
- the normal orbital diagram looks like this
- with valence level expansion it looks like this
42Valence level expansion
- includes
- elements of groups 15 to 18, from period 3 down
- periods 1 and 2 do not have a d orbital to
promote to. - Please note that valence level expansion is the
exception, not the rule.
43Chemical Bonding
- is all about the electrons.
- in most of our discussions we will concentrate
the valence electrons. - since there are 4 of these orbitals in any
quantum it requires 8 electrons (an octet) to
fill them. - the tendency of atoms to try to fill out the
outer s and p shells is the octet rule. - exception atoms from groups 2 and 13
44Chemical Bonding
- Bonding can happen in one of two ways
- To share electrons -
- The outer orbitals of 2 atoms overlap so that
each atom is in the vicinity of a full set of
valence electrons. - This type of bonding is called covalent bonding.
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46Chemical bonding
- Atoms gain or lose electrons to arrive at a full
set of valence electrons. - When atoms gain or lose electrons they become
ions. - Ions are attracted to ions of opposite charge and
repelled by ions of the same charge. - This type of bonding is called ionic bonding
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48How Many Bonds ???
- the number of bonds made by atoms in the s and
p blocks of the Periodic Table is determined by
how many electrons they are away from an octet
49How Many Bonds ???
Group Valence Electrons Covalent Bonds Ionic Bonds
1 1 1 1 (1)
2 2 21 2 (2)
13 3 31 3 (3)
14 4 41 -
15 5 3 (52) 3 (3-)
16 6 2 (62) 2 (2-)
17 7 1 (72) 1 (1-)
18 8 0 (82) 0
1electron promotion 2valence level expansion 1electron promotion 2valence level expansion 1electron promotion 2valence level expansion 1electron promotion 2valence level expansion
50- most of our discussion will be centred on
covalent bonding.
51Electronegativity
- is a measure of how strongly an atom is holding
on to its valence electrons. - If an atom loses an electron fairly easily it has
a low electronegativity (and tends to be a
cation). - If an atom tends not to lose electrons, but tends
to steal them from other atoms (and become an
anion) it has a high electronegativity.
52- To determine what type of bond exists between two
atoms you subtract their respective
electronegativities - if the electronegativity difference is 0.2 or
less, the bond is covalent - if the electronegativity difference is 1.7 or
greater the bond is ionic.
53Electronegativity
- If the electronegativity difference between two
atoms is between 0.3 and 1.6 the bond is
polar-covalent. - The greater the electronegativity difference the
greater the ionic character of the bond
54Polar-Covalent Bonding
- Covalent bonding implies equal sharing of
electrons. - If sharing is not equal, the electrons in a bond
will spend more time with one atom than the
other.
55Polar-Covalent Bonding
- The atom where the electrons spend more time will
have a net negative charge, while the atom at the
other end of the bond will be positive. - This type of bond is polar-covalent.
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57Assignment
- Determine the electronegativity difference for
each chemical bond. If the bond is polar
covalent draw an arrow in the direction of the
dipole, from positive to negative - C - H
- END 2.5 - 2.1 0.4
- polar covalent bond
- N - H B - F S - O
- P - H Si - Cl Cu - Br N - I
- Br - Cl O - H C - Cl C - O
58- N - H
- END 3.0 2.1 0.9
- polar covalent bond N - H
- B - F
- END 2.0 4.0 2.0
- ionic bond B3F1-
- S O
- END 2.5 3.5 1.0
- polar covalent bond S - O
59- P - H
- END 2.1 2.1 0.0
- covalent bond P H
- Si - Cl
- END 1.8 3.0 1.2
- polar covalent bond Si - Cl
- Cu - Br
- END 1.9 2.8 0.9
- polar covalent bond Cu - Br
60- N I
- END 3.0 2.5 0.5
- polar covalent bond N - I
- Br Cl
- END 2.8 3.0 0.2
- covalent bond Br Cl
- O H
- END 3.5 2.1 1.4
- polar covalent bond O H
-
61- C Cl
- END 2.5 3.0 0.5
- polar covalent bond C Cl
- C O
- END 2.5 3.5 1.0
- polar covalent bond C O
62Back to the Ball Stick
- determine the electronegativity difference and
bond type for each bond in each of the molecules
in the activity.
63Covalently-Bonded Structures
- we now have to consider molecules made of several
atoms. - most of the following discussion will concern
itself with molecules made with covalent or
polar-covalent bonds. - ionic bonds (and others) will return later in the
unit.
64Lewis Structures
- Lewis structures allow us to predict how atoms
will come together to make molecules. - Lewis structures are representations of molecules
showing all electrons, bonding and nonbonding.
65Writing Lewis Structures
- Find the sum of valence electrons of all atoms in
the polyatomic ion or molecule. - If it is an anion, add one electron for each
negative charge. - If it is a cation, subtract one electron for each
positive charge.
5 3(7) 26
66Writing Lewis Structures
- The central atom is the least electronegative
element that isnt hydrogen. Connect the outer
atoms to it by single bonds.
Keep track of the electrons 26 ? 6 20
67Writing Lewis Structures
- Fill the octets of the outer atoms.
Keep track of the electrons 26 ? 6 20 ? 18 2
68Writing Lewis Structures
- Fill the octet of the central atom.
Keep track of the electrons 26 ? 6 20 ? 18
2 ? 2 0
69Writing Lewis Structures
- If you run out of electrons before the central
atom has an octet - form multiple bonds until it does.
70Exceptions to Octet Rule
- Electron Promotion
- group 2 central atom will have 4 electrons
- group 13 central atom will have 6 electrons
- Valence Level Expansion
- group 15 central atom will have 10 electrons
- group 16 central atom will have 12 electrons
- group 17 central atom will have 14 electrons
- group 18 central atom will have 16 electrons
71Writing Lewis Structures
- Write Lewis Structures for the following
molecules
F2 SiF4
BCl3 C3H8
SeH2 C3H6
MgH2 C3H4
72Molecular Shapes
- The shape of a molecule plays an important role
in its reactivity. - By noting the number of bonding and nonbonding
electron pairs we can easily predict the shape of
the molecule.
73What Determines the Shape of a Molecule?
- Simply put, electron pairs, whether they be
bonding or nonbonding, repel each other. - By assuming the electron pairs are placed as far
as possible from each other, we can predict the
shape of the molecule.
74Valence Shell Electron Pair Repulsion Theory
(VSEPR)
- The best arrangement of a given number of
electron domains is the one that minimizes the
repulsions among them.
75Molecular Geometries
- the shape of any molecule can be predicted based
on two things - Group number of the central atom
- number of atoms bonded to the central atom
76Group 2 Geometries
Central Atom Bonding Electrons Lone Pair Electrons Bond Type Shape Example
Magnesium 2 0 all single linear MgI2
one double linear MgO
- In this domain, there is only one molecular
geometry linear. - NOTE If there are only two atoms in the
molecule, the molecule will be linear no matter
what the electron domain is.
77Group 13 Geometries
Central Atom Bonding Electrons Lone Pair Electrons Bond Type Shape Example
Boron 3 0 all single trigonal planar BI3
one double linear BIO
one triple linear BN
- because there are no lone pair electrons the
molecular is planar (flat).
78Group 14 Geometries
Central Atom Bonding Electrons Lone Pair Electrons Bond Type Shape Example
Carbon 4 0 all single tetrahedral CH4
one double trigonal planar COH2
one triple, or two double linear HCN CO2
79Summary for Groups 2, 13 14
- because there are no lone pair electrons
- central atom bonded to 1 atom linear
- central atom bonded to 2 atoms linear
- central atom bonded to 3 atoms trigonal
planar - central atom bonded to 4 atoms
tetrahedral
80Group 15 Geometries
Central Atom Bonding Electrons Lone Pair Electrons Bond Type Shape Example
Nitrogen 3 1 all single trigonal pyramidal NH3
one double angular NOH
one triple linear N2
5 0 all single trigonal bipyramidal NCl5
81Group 16 Geometries
Central Atom Bonding Electrons Lone Pair Electrons Bond Type Shape Example
Oxygen 2 2 all single angular H2O
one double linear O2
6 0 all single octahedral OF6
82Group 17 18 Geometries
- group 17
- normally makes 1 chemical bond (linear)
- with valence level expansion can make 7 bonds
(ClF7). - group 18
- normally makes no bonds
- with valence level expansion can make 8 bonds
(ArF8).
83Larger Molecules
- In larger molecules, it makes more sense to talk
about the geometry about a particular atom rather
than the geometry of the molecule as a whole. - This molecule is tetrahedral about the first
carbon, planar trigonal about the second and
angular about the single-bonded oxygen.
84Larger Molecules
- This approach makes sense, especially because
larger molecules tend to react at a particular
site in the molecule.
85Using VSEPR Theory
- Determine the shape of each molecule, or atom
within the molecule
F2 SiF4
PCl3 C3H8
SeH2 C3H6
MgH2 C3H4
86Polarity
- previously we discussed bond dipoles.
- But just because a molecule possesses polar bonds
does not mean the molecule as a whole will be
polar.
87Polarity
- By adding the individual bond dipoles, one can
determine the overall dipole moment for the
molecule. - In other words we can see if the dipoles
reinforce each other, or cancel out.
88Polarity
89Assignment
- Perform the following activities for the
molecules in the Balls Sticks Activity - Draw a lewis structure
- Draw a structural diagram and indicate shape.
- Determine the electronegativity difference for
each bond type and determine whether the bond is
covalent, polar covalent or ionic - Determine if they will be polar, or non-polar.
90Properties of Molecules
91Properties of Molecules
- are determined by how the molecules interact with
each other. - How they interact is determined by the forces of
attraction between molecules. - These are called intermolecular forces the
forces which act between molecules, to draw them
together, forming the various phases of matter.
92How do we measure force ?
- the best way is by temperature.
- temperature is a measure of kinetic energy the
lowest temperature represents zero kinetic
energy. - for a substance to melt or boil the kinetic
energy must overcome the intermolecular force. - the higher the melting temperature or boiling
temperature, the greater the intermolecular force.
93Van der Waals Forces
- occur between covalently bonded molecules.
- three kinds
- London disersion
- dipole-dipole attraction
- hydrogen bonding
94London Dispersion Forces
- are the dominant forces between covalently
bonded, non-polar molecules - based on the formation of instantaneous dipoles.
- the more electrons in a molecule, the stronger
the force.
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96Relationship of Boiling Point to Number of
Electrons and Molar Mass
- Melting Point Boiling Point
- e- C C
- CH4 10 - 182 -161
- C2H6 18 - 183 - 88
- C3H8 26 - 190 - 44
- C4H10 34 - 138 - 0.5
- C8H18 66 - 57 125
97London dispersion forces
- are influenced by shape
- Normal Pentane (C5H12)
- m.p. -130C,
- b.p. 36C
- Neopentane (C5H12)
- m.p. -20C,
- b.p. 9C
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101Dipole-Dipole attraction
- is a force which acts between polar molecules
(ex. H2S). - results from the attraction of the opposite poles
of the permanent molecular dipoles. - These substances generally have higher melting
and boiling points than non-polar molecules with
similar molecular weights (or numbers of
electrons).
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103Ion-Dipole Interactions
- A fourth type of force, ion-dipole interactions
are an important force in solutions of ions. - The strength of these forces are what make it
possible for ionic substances to dissolve in
polar solvents.
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105Dipole-Dipole Interactions
- The more polar the molecule, the higher is its
boiling point.
106How Do We Explain This?
- The nonpolar series (SnH4 to CH4) follow the
expected trend. - The polar series follows the trend from H2Te
through H2S, but water is quite an anomaly.
107Hydrogen Bonding
- a specialized form of dipole-dipole attraction.
- It occurs as when O, N, and F are bonded to H,
owing to the large electronegativity difference
- O - H 3.5 - 2.1 1.4
- N - H 3.1 - 2.1 1.0
- F - H 4.1 - 2.1 2.0
108Hydrogen Bonding
- This is a stronger force than standard
dipole-dipole attraction. - Molecules with hydrogen bonding will have boiling
points and melting points quite a bit higher than
molecules that have only dipole-dipole or London
dispersion forces. - Hydrogen bonding is responsible for many of the
unusual properties of water.
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111Hydrogen bonding
- is responsible for folding, final structure and
function of proteins - holds the DNA strands together, but allows them
to be unzipped for copying and gene expression.
112Relationship Between Polarity, Force and Boiling
Point
- e- B.P. (C) Polarity Force
- C2H6 18 - 161 Non-polar London
- Dispersion
- H2S 18 - 60 Polar Dipole - Dipole
- H2O 10 100 Very polar Hydrogen Bonds
113In Summary
- Non-Polar Molecule
- London Dispersion Force
- More electrons, higher B.P., M.P.
- If isoelectronic, more compact higher M.P., lower
B.P. - Polar Molecule
- Dipole-Dipole Attraction
- Higher B.P. M.P. than London
- If both polar, higher electronegativity
difference has higher B.P. M.P - If have O-H, N-H, or F-H bond, hydrogen bonding,
much higher M.P. B.P
114Ionic Bonding
- generally occurs in compounds of metals and
non-metals (salts). - It is the result of the attraction of oppositely
charged ions. - The structures formed are very orderly and are
given the name crystal lattice. - Ionic solids are called crystals.
115Ionic Bonding
- No sharing of electrons occurs between the ions
in the crystal lattice. - As a result, ionic solids are brittle.
- Ionic solids conduct electricity only in the
molten state, and not very well. - Ionic solids are characterized by very high
melting and boiling points.
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117Metallic Bonding
- is the bonding which occurs between metals in the
Periodic Table. - It is characterized by close packing of the
atoms, with the electrons delocalized that is,
they are free to jump from atom to atom, filling
unoccupied orbitals.
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119Metallic Bonding
- This free sharing of electrons allows metals to
conduct electricity freely (copper conducts
electricity 100 000 times better than molten
NaCl). - The free electrons also act as a lubricant,
allowing metal atoms to slide over one another
without affecting the integrity of the material.
Thus metals are malleable and ductile. - This bond is strong, giving most metals high
melting and boiling points. - This bond is also variable.
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121Network Covalent Bonding
- regular covalent bond, expanded to 2 or 3
dimensions in a network which is theoretically
infinite - Network solids include diamonds, graphite,
quartz, and most rocks. - very hard (diamonds are the hardest substance
known). - brittle,
- do not conduct electricity.
- crystals.
- very high melting and boiling points
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124Intermolecular Forces Affect Many Physical
Properties
- The strength of the attractions between
particles can greatly affect the properties of a
substance or solution.
125Viscosity
- Resistance of a liquid to flow is called
viscosity. - It is related to the ease with which molecules
can move past each other. - Viscosity increases with stronger intermolecular
forces and decreases with higher temperature.
126Surface Tension
- Surface tension results from the net inward
force experienced by the molecules on the surface
of a liquid.
127Vapor Pressure
- At any temperature, some molecules in a liquid
have enough energy to escape. - As the temperature rises, the fraction of
molecules that have enough energy to escape
increases.
128Intermolecular Forces in Summary
129Strength of Attraction
Molecular (London dispersion) 1 to 50
Molecular (dipole-dipole) 5
Molecular (hydrogen bonding) 15
Ionic 50
Metallic 20 to 80
Network Covalent 100
130Melting and Boiling Point
Molecular (London dispersion) very low (nitrogen boils at - 196 ?C) VARIABLE
Molecular (dipole-dipole) low (H2S boils at -61 ?C)
Molecular (hydrogen bonding) medium (H2O boils at 100 ?C)
Ionic high (NaCl boils at 1413 ?C)
Metallic variable (Hg _at_ 357 ?C, W _at_ 5660 ?C)
Network Covalent very high (SiO2 boils at 2600 ?C)
131Properties of Solids
Molecular (London dispersion) soft, waxy
Molecular (dipole-dipole) more rigid
Molecular (hydrogen bonding) crystalline, brittle
Ionic long-range crystalline, hard, brittle
Metallic short-range crystalline, ductile, malleable
Network Covalent long-range crystalline, hard, brittle
132Conductance of Heat and Electricity
Molecular (London dispersion) non-conductor
Molecular (dipole-dipole) non-conductor
Molecular (hydrogen bonding) non-conductor
Ionic conductor in liquid or dissolved phase
Metallic conductor in solid or liquid phase
Network Covalent non-conductor in 3d form, some conductance in 2d
133Solubility in H2O
Molecular (London dispersion) Not soluble
Molecular (dipole-dipole) Soluble
Molecular (hydrogen bonding) Soluble
Ionic Soluble
Metallic Not soluble
Network Covalent Not soluble
134Other Stuff
135Coordinate Covalent bonds
- is defined as a covalent bond where one atom
provides both of the electrons
136Polyatomic Ions
- we can use coordinate covalent bond theory to
explain most ions
137Resonance
- This is the Lewis structure we would draw for
ozone, O3.
-
138Resonance
- But this is at odds with the true, observed
structure of ozone, in which - both OO bonds are the same length.
- both outer oxygens have a charge of ?1/2.
139Resonance
- One Lewis structure cannot accurately depict a
molecule such as ozone. - We use multiple structures, resonance structures,
to describe the molecule.
140Resonance
- Just as green is a synthesis of blue and yellow
- ozone is a synthesis of these two resonance
structures.
141Resonance
- In truth, the electrons that form the second CO
bond in the double bonds below do not always sit
between that C and that O, but rather can move
among the two oxygens and the carbon. - They are not localized, but rather are
delocalized.
142Resonance
- The organic compound benzene, C6H6, has two
resonance structures. - It is commonly depicted as a hexagon with a
circle inside to signify the delocalized
electrons in the ring.