Chapter 1Carbon Compounds and Chemical

Bonds

Organic Chemistry

Organic chemistry is the chemistry of compounds containing carbon. The name mistakenly implies that all organic compounds are associated with living systems. While many carbon- containing compounds are the basis of life, there are many organic compounds that have nothing to do with living systems.

The practice of organic chemistry goes back thousands of years. A discovery of a wine residue in a Sumerian jug shows that the technology of winemaking is almost 7500 years old.

sugar (C12H22O11)

sweet principle of sugar cane

fermentation ethyl alcohol (C2H5OH)

Whence Wine?A recent article in the Chronicle of Higher Eduction (August 15, 2003) details the research of Patrick E. McGovern, a chemistry professor at the University of Pennsylvania. Blending chemistry and archeology, Prof. McGovern is an expert on the origins of winemaking. His research suggests that the art of fermenting grapes began some 9,000 years ago when human society was transforming from hunter-gatherer to communities based on agriculture and animal husbandry.

.

The research of Prof. McGovern and others points to the widespread production of wine throughout the middle east in the region of the countries of Iran, Iraq and Turkey during the Sumerian and later civilizations. It is believed that the domestication of grapes for winemaking began somewhere in this region, and that all modern grapes for winemaking are descended from that original domesticated wild subspecies

Demise of the Life Force Idea

Early in the 19th century, numerous "organic compounds" were prepared from nonliving sources. The first such example was the synthesis of urea (a constituent of urine) by evaporation of a solution of ammonium cyanate, an "inorganic compound."

1828: Friedrich Wohler

ammonium cyanate urea

evaporationNH4OCN H2NCONH2

Structural Isomerism

In addition to disproving vitalism, the Wohler experiment shows the properties of molecules depend on the way atoms are linked. The structure is important. This idea was further developed in the late 19th century.

Empirical and Molecular Formulas

During the 19th century, quantitative methods for determining chemical composition were developed by Justis Liebig, J.J. Berzelius, and J.B. Dumas. The chemical analyses could only provide empirical formulas, the simplest possible ratio of the elements.

Cannizzaro showed that while the same empirical formula of CH2 is found in ethylene, cyclopentane, and cyclohexane, their molecular formulas are C2H4, C5H10, and C6H12, respectively.

In 1860, at the famous Karlsruhe Conference called by August Kekulé, the Italian chemist Stanislao Cannizzaro used the earlier arguments of Amedeo Avogadro (1811) to assign proper molecular formulas to many simple organic compounds.

7

• Structural Theory• Central Premises• Valency: atoms in organic compounds form a

fixed number of bonds

• Carbon can form one or more bonds to other carbons

In all cases, the tetravalency of carbon is maintained.

8

• Isomers• Isomers are different molecules with the same molecular

formula• Many types of isomers exist• Example

• Consider two compounds with molecular formula C2H6O• These compounds cannot be distinguished based on

molecular formula; however they have different structures• The two compounds differ in the connectivity of their

atoms

9

• Constitutional Isomers• Constitutional isomers are one type of isomer• They are different compounds that have the

same molecular formula but different connectivity of atoms• They often differ in physical properties (e.g.

boiling point, melting point, density) and chemical properties

CHH

HCH

CH

OHH

H

CHH

HCH

CH

HHO

CHH

HCH

O CH

H

HH

H

CHH

HCH

C HH

C C

C

H

HH H

H

H

Assemble the following atoms into plausible structures consistent with the valencies of the atoms.

(A) C3H8O (B) C3H6

QUIZ Chapter 1 Sections 2 and 3

three constitutional isomers

two constitutional isomers

Comment on their physical properties

11

• Three Dimensional Shape of Molecules• Virtually all molecules possess a 3-dimensional shape

which is often not accurately represented by drawings• It was proposed in 1874 by van’t Hoff and le Bel that the

four bonds around carbon where not all in a plane but rather in a tetrahedral arrangement i.e. the four C-H bonds point towards the corners of a regular tetrahedron

Li. -e- Li+

F:

::. +e-

F:

:::

- Li+F-

lithium fluoride

F:

::.F:

:: . + F:

:: :F:

::

fluorine

Chemical Bonds

The first descriptions of the nature of chemical bonds were put forward in 1916 by Gilbert Newton Lewis (1875-1946) and Walther Kossel (1888-1956). (Remember, the structure of the atom had been deduced only a few years earlier by Ernest Rutherford and Niels Bohr ).

(A) Ionic bonds are formed by the transfer of one or more valence-level electrons from one atom to another.

Two types of chemical bonds were recognized:

(B) Covalent bonds are formed when atoms share valence-level electrons.

Both types of bonds lead to electronic configurations around atoms that mimic a noble gas--filled outermost electronic levels.

13

• Chemical Bonds: The Octet Rule• Octet Rule• Atoms form bonds to produce the electron

configuration of a noble gas (because the electronic configuration of noble gases is particularly stable) • For most atoms of interest this means achieving

a valence shell configuration of 8 electrons corresponding to that of the nearest noble gas • Atoms close to helium achieve a valence shell

configuration of 2 electrons • Atoms can form either ionic or covalent bonds

to satisfy the octet rule

Row 2 Li Be B C N O F

increasing electronegativity

Group 7F Cl Br I

decreasing electronegativity

Ionic bonds are formed when atoms of very different electronegativities interact.

Ionic Bonds

When atoms lose or gain electrons, they develop charges and are called ions. Positively charged ions are cations, and negatively charged ions are called anions.

.lithium cation fluoride anionLi+ F-

Electronegativity

Electronegativity measures the tendency of an atom to attract electrons. Electronegativity increases in going left to right across a row in the Periodic Table. In some groups, it decreases in going down a column.

most electronegative

least electronegative

Linus Pauling (1901-1994)Nobel Prize in Chemistry 1954Nobel Peace Prize 1962

Electronegativity is the ability of an atom to attract electrons

16

• Ionic Bonds• When ionic bonds are formed atoms gain or lose electrons to

achieve the electronic configuration of the nearest noble gas • In the process the atoms become ionic

• The resulting oppositely charged ions attract and form ionic bonds

• This generally happens between atoms of widely different electronegativities

• Example• Lithium loses an electron (to have the configuration of

helium) and becomes positively charged • Fluoride gains an electron (to have the configuration of

neon) and becomes negatively charged• The positively charged lithium and the negatively charged

fluoride form a strong ionic bond (actually in a crystalline lattice)

17

• Covalent Bonds• Covalent bonds occur between atoms of similar

electronegativity (close to each other in the periodic table)• Atoms achieve octets by sharing of valence electrons• Molecules result from this covalent bonding• Valence electrons can be indicated by dots (electron-dot

formula or Lewis structures) but this is time-consuming• The usual way to indicate the two electrons in a bond is to

use a line (one line = two electrons)

N N

Multiple Covalent Bonds and the Octet RuleCovalent bonds between atoms may involve 4 or 6 electrons. These are called multiple covalent bonds.

Example N2

Each nitrogen atom has 5 outermost or valence-level electrons...

.:N

The covalent bonding in N2 involves 6 electrons:

or :N N:

The Octet RuleBy sharing 6 electrons, each nitrogen achieves the electron configuration of neon with an octet of electrons in the valence level. This tendency to reach 8 electrons in the valence level is called the octet rule.

Examples of the Octet Rule

The above structures are called Lewis structures in honor of G.N. Lewis. In a Lewis structure, all the valence-level (outermost) electrons are shown as dots. The Lewis structure of an atom is the chemical symbol with the valence-level electrons shown as dots.

::

::C HH

H

Hmethane

N N

nitrogen

::O HH

water

:H F

hydrogen fluoride

:

::

Gilbert Newton Lewis (1875-1946)A leading physical chemist at UC Berkeleyduring the early decades of the 20th century.

Several simple rules allow us to draw proper Lewis Structures:

For main group elements, the number of valence electrons a neutral atom brings to a Lewis structure is the same as its group number in the periodic table. Carbon, for example, is in Group IVA and it has four valence electrons; the halogens (e.g., fluorine) are in Group VIIA and each has seven valence electrons; hydrogen is in Group IA and has one valence electron.

2.

If the structure we are drawing is a negative ion (an anion), we add one electron for each negative charge to the original count of valence electrons. If the structure is a positive ion (a cation), we subtract one electron for each positive charge.

3.

Lewis structures show the connections between atoms in a molecule or ion using only the valence electrons or the atoms involved. Valence electrons are those of an atom’s outermost shell.

1.

Several simple rules allow us to draw proper Lewis Structures:

4. In drawing Lewis structures we try to give each atom the electronconfiguration of a noble gas. To do so, we draw structures where atoms share electrons to form covalent bonds or transfer electrons to form ions.

a. Hydrogen forms one covalent bond by sharing its electron with an electron of another atom so that it can have two valence electrons, the same number as in the noble gas helium.

b. Carbon forms four covalent bonds by sharing its four valence electrons with four valence electrons from other atoms, so that it can have eight electrons (the same as the electron configuration of neon, satisfying the octet rule).

c. To achieve an octet of valence electrons, elements such as nitrogen, oxygen, and the halogens typically share only some of their valence electrons through covalent bonding, leaving others as unshared electron pairs.

23

• Writing Lewis Structures (short form)• Atoms bond by using their valence electrons• The number of valence electrons is equal to the group

number of the atom• Carbon is in group 4A and has 4 valence electrons• Hydrogen is in group 1A and has 1 valence electron• Oxygen is in group 6A and has 6 valence electrons• Nitrogen is in group 5A and has 5 valence electrons

• To construct molecules the atoms are assembled with the correct number of valence electrons

• If the molecule is an ion, electrons are added or subtracted to give it the proper charge

• The structure is written to satisfy the octet rule for each atom and to give the correct charge

• If necessary, multiple bonds can be used to satisfy the octet rule for each atom

24

• Example• Write the Lewis structure for the chlorate ion (ClO3

-)• The total number of valence electrons including

the electron for the negative charge is calculated

• Three pairs of electrons are used to bond the chlorine to the oxygens

• The remaining 20 electrons are added to give each atom an octet

25

• The carbonate ion with 24 valence electrons and two negative charges must incorporate a double bond to satisfy the octet rule for every atom

• The organic molecules ethene (C2H4) and ethyne (C2H2) must also use multiple bonds to satisfy the octet rule for each atom

26

• Exceptions to the Octet Rule• The octet rule applies only to atoms in the

second row of the periodic table (C, O, N, F) which are limited to valence electrons in the 2s and 2p orbitals• In higher rows other orbitals are accessible and

more than 8 electrons around an atom are possible• Example: PCl5 and SF6

Electron-Deficient MoleculesThere are many exceptions to the octet rule among compounds derived from early main group elements in Period 2 (Be and B). The chemical reactivity of these compounds reflects their electron-deficiency.

Examples

berylium chloride

BeCl2

borontrifluoride

BF3

.. + 2

:: . ::

:: or

::

::

only 4 valence electrons around Be

Be :Cl :Be:Cl::Cl -Be-Cl::Cl

. .. + 3

:: .

::

::

:: : or

::

::

::

only 6 valence electrons around B

B :F :B:F:F:

:F -B-F:F:

:F

Electron-Deficient MoleculesBerylium chloride exists as a monomer only in the gas phase. In the solid state, a polymeric structure forms:

Boron trifluoride reacts rapidly with chemical species that donate an electron pair:

there is an octet of electronsin the valence-level around Be

Be Be BeCl

Cl

Cl

Cl

Cl

ClBe

BF3 +

:::

- fast ::

::

:: :

::

: -or

- there is an octetof electrons in the valence-levelaround B

F: :B:F:F:

:FF:

B FF

FF

QUIZ Chapter 1 Sections 4, 5 and 6Which electronic structure below is the correct Lewis structure of H2CO, where the hydrogen atoms are bonded to the carbon atom?

solution: There are 12 valence electrons.

::

:

A B C D

choices.. ........

..............

..........CHH

OCHH

CHH

O CHH

O:O.. .. ..

Only C is consistent with the Octet Rule.

30

• Formal charge• A formal charge is a positive or negative charge

on an individual atom• The sum of formal charges on individual atoms

is the total charge of the molecule or ion• The formal charge is calculated by subtracting

the assigned electrons on the atom in the molecule from the electrons in the neutral atom• Electrons in bonds are evenly split between the

two atoms; one to each atom• Lone pair electrons belong to the atom itself

31

• Examples • Ammonium ion (NH4)+

• Nitrate ion (NO3)-

Examples of Formal Charges

::CH4 CHH

HH:: atom

valence electrons in:free atom bonded state

H

C

formalcharge

1 - 1 0

4 - 4 0

::NH3 NH

HH:: atom

valence electrons in:free atom bonded state

H

N

formalcharge

1 - 1 0

5 - (3 + 2) 0

Examples of Formal Charges

atomvalence electrons in:

free atom bonded state

H

N

formalcharge

1 - 1 0

5 - 4 +1

::NH4 NH

H

HH::

: : ::

::CO3

2- C:O:

:O::O:

atomvalence electrons in:

free atom bonded state

C

O

O

formalcharge

4 - 4 0

6 - 6 0

6 - (6 + 1) -1

34

• A Summary of Formal Charges

35

• Resonance• Often a single Lewis structure does not accurately

represent the true structure of a molecule• The real carbonate ion is not represented by any of the

structures 1,2 or 3

• Experimentally carbonate is known not to have two carbon-oxygen single bonds and one double bond; all bonds are equal in length and the charge is spread equally over all three oxygens

36

• The real carbonate ion can be represented by a drawing in which partial double bonds to the oxygens are shown and partial negative charge exists on each oxygen• The real structure is a resonance hybrid or mixture of

all three Lewis structures• Double headed arrows are used to show that the

three Lewis structures are resonance contributors to the true structure• The use of equilibrium arrows is incorrect since

the three structures do not equilibrate; the true structure is a hybrid (average) of all three Lewis structures

37

• One resonance contributor is converted to another by the use of curved arrows which show the movement of electrons• The use of these arrows serves as a bookkeeping device to assure all

structures differ only in position of electrons

• A calculated electrostatic potential map of carbonate clearly shows the electron density is spread equally among the three oxygens• Areas which are red are more negatively charged; areas of blue have

relatively less electron density

38

• Rules for Resonance:• Individual resonance structures exist only on paper

• The real molecule is a hybrid (average) of all contributing forms

• Resonance forms are indicated by the use of double-headed arrows

• Only electrons are allowed to move between resonance structures• The position of nuclei must remain the same• Only electrons in multiple bonds and nonbonding electrons

can be moved• Example: 3 is not a resonance form because a hydrogen atom has

moved

39

• Rules for Resonance:• All structures must be proper Lewis

structures

40

• The energy of the actual molecule is lower than the energy of any single contributing form• The lowering of energy is called resonance stabilization

• Equivalent resonance forms make equal contributions to the structure of the real molecule• Structures with equivalent resonance forms tend to be greatly

stabilized• Example: The two resonance forms of benzene contribute equally and

greatly stabilize it

• Unequal resonance structures contribute based on their relative stabilities • More stable resonance forms contribute more to the structure of the

real molecule

41

• Rules to Assign Relative Importance of Resonance Forms• A resonance form with more covalent bonds is

more important than one with less• Example: 6 is more stable and more

important because it has more total covalent bonds

42

• Resonance forms in which all atoms have a complete valence shell of electrons are more important• Example: 10 is more important because all

atoms (except hydrogen) have complete octets

43

• Resonance forms with separation of charge are less important• Separation of charge cost energy and results in a less

stable resonance contributor• Example: 12 is less important because it has charge

separation

• Forms with negative charge on highly electronegative atoms are more important• Those with positive charge on less electronegative atoms

are also more important

44

• Example• The nitrate ion is known to have all three

nitrogen-oxygen bond lengths the same and the negative charge spread over all three atoms equally

45

• Example• Resonance theory can be used to produce three

equivalent resonance forms • Curved arrows show the movement of

electrons between forms • When these forms are hybridized (averaged)

the true structure of the nitrate ion is obtained

Quantum Mechanics

The development of quantum mechanics in the late 1920s led to a better understanding of the relationship between electronic and molecular structures.

Louis de Broglie, as a graduate student working on his Ph D in physics at the Sorbonne in 1924, reasoned: If radiant energy under some conditions behaved as a stream of particles, could not particles under some conditions show the properties of radiant energy...a wave?

He proposed that an electron in an orbit around a nucleus (a Bohr orbit) would have wave properties. There would be a characteristic wavelength (l) associated with an electron in a particular Bohr orbit (an electron of particular energy):

l = h/mvwhere h is Planck's constant,m is the mass of the electron,and v is its velocity.

Wave MechanicsA wave may be a traveling wave moving in a direction (x), or a standing or stationary wave between two points.

A wave is described mathematically as a repeating function (, psi) with positive and negative numerical values that repeat as a function of distance (X) and time.

wavefunction

(+)

(-)

(+)

(-)

x

A wave is a series of crests and troughs that repeat.

Standing WavesA standing wave is a wave oscillating perpendicular to an axis between two fixed points. An example is the string of a musical instrument such as a violin. When plucked or bowed, the string vibrates in standing or stationary waves. The waves do not travel along the string. Only an integral number of half waves may exist between the fixed points.

Standing Waves

The points where the wave function Y remains zero is a node. In addition to each end where the string is attached, there may be 0, 1,2, etc. nodes along the string.

0 nodes

1 node

2 nodes

49

• Quantum Mechanics• A mathematical description of bonding that

takes into account the wave nature of electrons• A wave equation is solved to yield a series of

wave functions for the atom• The wave functions psi () describe a series of

states with different energies for each electron• Wave Equations are used to calculate:• The energy associated with the state of the

electron• The probability of finding the electron in a

particular state

50

• Phase sign: Wave equations, when solved, may be positive, negative or zero• In analogy to a wave in a lake, when the wave is

above the average lake level, the sign is positive ( = +) ; when it is below the lake level it is negative ( = - )

• When the wave is exactly at average lake level it has a sign of 0 and this is called a node ( = 0)

• Wave equations can reinforce each other if they have the same sign or interfere with each other if they have different signs

Erwin Schrodinger (1887-1961)Schrodinger obtained his Ph D in Physics at the University of Zurich in 1910 and then served in the Austrian Army during WWI. After the war he resumed his career in science. In 1925, while at the University of Zurich, he published his famous wave equation that helped launch the field of quantum mechanics. In later years, he was forced to flee Austria with the rise of Nazism, and lived and worked in England and Ireland.

:

:.

Atomic Orbitals

a complete standing electron wave

alloweda mismatch

not allowed

This required "fit" for the electron wave seemed consistent with the already accepted quantization of electron energies in the Bohr model.

Erwin Schrodinger (University of Zurich) in 1926 worked out the mathematical equations describing the motions of an electron as a standing wave around the nucleus in terms of its energy. Only certain circular orbits around the nucleus have a correct circumference to accommodate an integral number of waves, a complete standing wave. Other circular orbits would not provide a good fit for an electron wave and are not allowed.

:

Atomic Orbitals

When the wave function is evaluated for different values of the total energy of the electron, a series of solutions result. Each solution consists of a specific wave function (Y) associated with a different value of energy (E) for the electron.

.

The wave functions give numerical values (positive and negative phasing) for regions in space around the nucleus for electrons of specified energies. These mathematical solutions by themselves do not have physical meaning. However, Y 2 for a particular location (x, y, z) expresses the PROBABILITY of finding an electron for a particular location in space

Plots of Y 2 in three dimensions generate the shapes of the familiars, p, and d atomic orbitals (AOs), which we use as our models for atomic structures.

The Schrodinger Equation

:

:

For the system of one electron and one proton (the hydrogen atom), Schrodinger worked out the complicated mathematical expression for the wave function (Y) that describes the position of the electron in three-dimensional space (x,y,z coordinates) around the nucleus.

54

• Atomic Orbitals (AOs)• The physical reality of is that when squared

( 2) it gives the probability of finding an electron in a particular location in space• Plots of 2 in three dimensions generate the

shape of s, p, d and f orbitals• Only s and p orbitals are very important in

organic chemistry• Orbital: a region in space where the

probability of finding an electron is large• The typical representation of orbitals are

those volumes which contain the electron 90-95% of the time

55

• 1s and 2s orbitals are spheres centered around the nucleus• Each orbital can accommodate 2 electrons• The 2s orbital is higher in energy and

contains a nodal surface ( = 0) in its center

56

• Each 2p orbital has two nearly touching spheres (or lobes)• One sphere has a positive phase sign and the other a

negative phase sign; a nodal plane separates the spheres• There are three 2p orbitals which are perpendicular

(orthoganol) to each other• Each p orbital can accommodate 2 electrons for a total

of 6 electrons• All three p orbitals are degenerate (equal in energy)

• The 2p orbitals are higher in energy than the 1s or 2s

57

• The sign of the wave function does not indicate a greater or lesser probability of finding an electron in that location• The greater the number of nodes in an

orbital the higher its energy• 2s and 2p orbitals each have one node

and are higher in energy than the 1s orbital which has no nodes

58

• Atoms can be assigned electronic configuration using the following rules:• Aufbau Principle: The lowest energy orbitals

are filled first• Pauli Exclusion Principle: A maximum of two

spin paired electrons may be placed in each orbital• Hund’s Rule: One electron is added to each

degenerate (equal energy orbital) before a second electron is added

1s

2s2p

B C N O F Ne

Examples: Some Second Row Elements

Hund's rule

Pauli exclusionprinciple

What is an example of the Aufbau Principle?

1s2 2s2 2p6 3s2 (no charge)

1s2 2s2 2p6 (charge of +2)

1s2 2s2 2p6 (charge of -2)

Mg

Mg2+

O2-

Quiz Chapter 1 Section 10

Provide the chemical symbol (including charge) of the chemical species with the following electron configurations:

Add the missing electrons in the diagram below as arrows (up or down to indicate spin) for the ground electronic state of atomic carbon.

1s

2s

2p

elec

tron

ic e

nerg

y

Molecular OrbitalsWhen atoms combine to form molecules, the electrons reside in molecular orbitals. Only two electrons may be placed in each molecular orbital with paired spins.

Two important assumptions are:

(1) Each pair of electrons resides in a localized region near the nuclei of the atoms that are forming the molecular orbital.

(2) The shapes of the localized molecular orbital are related in a simple way to the shapes of the combining atomic orbitals.

62

• Molecular Orbitals (MOs)• A simple model of bonding is illustrated by forming molecular H2

from H atoms and varying distance:• Region I: The total energy of two isolated atoms• Region II: The nucleus of one atom starts attracting the

electrons of the other; the energy of the system is lowered• Region III: at 0.74 Å the attraction of electrons and nuclei

exactly balances repulsion of the two nuclei; this is the bond length of H2

• Region IV: energy of system rises as the repulsion of the two nuclei predominates

63

• This simple model of bonding does not take into account the fact that electrons are not stationary but constantly moving around• Heisenberg uncertainty principle: the position and

momentum of an electron cannot simultaneously be known

• Quantum mechanics solves this problem by talking about the probability ( 2) of finding an electron at a certain location in space • As two atoms approach each other their atomic

orbitals (AOs) overlap to become molecular orbitals (MOs) • The wave functions of the AOs are combined to yield

the new wave functions of the MOs• The number of MOs that result must always equal the

number of AOs used

64

• Example: H2 molecule• As the hydrogen atoms approach each other their 1s

orbitals (1s) begin to overlap • The MOs that form encompass both nuclei• The electrons are not restricted to the vicinity of one

nucleus or another• Each MO has a maximum of 2 spin-paired electrons• Addition of wave functions of the two atoms leads to

a bonding molecular orbital• Subtraction of wave functions of the two atoms leads

to an anti-bonding molecular orbital • The mathematic operation by which wave functions

are added or subtracted is called the linear combination of atomic orbitals (LCAO)

65

• Bonding Molecular Orbitals (molec)• AOs combine by addition (the AOs of the same phase sign

overlap)• The wave functions reinforce• The value of increases between the two nuclei (b)• The value of 2 (electron probability density) in the region

between the two nuclei increases (a)• The two electrons between the nuclei serve to attract the

nuclei towards each other• This is the ground state (lowest energy state) of the MO

66

• Antibonding molecular orbital ( *molec)• Formed by interaction of AOs with opposite phase signs• Wave functions interfere and a node is produced ( = 0)• In the region between the two nuclei• A node is produced• On either side of the node is small• 2 (electron probability density) is small

67

• Electrons in the antibonding orbital avoid the region between the two nuclei• Repulsive forces between the nuclei predominate

and electrons in antibonding orbitals make nuclei fly apart

68

• The energy of electrons in the bonding orbitals is substantially less than the energy of electrons in the individual atoms• The energy of electrons in the antibonding orbitals is

substantially more• In the ground state of the hydrogen molecule electrons

occupy the lower energy bonding orbital only

Examples of Covalent Bonds

.2 H H2

.2 F F2

1s 1s bond

H H H H

2p 2p 2p bond

F F F F

bond length 1.42 ÅBDE 159 kJ/mol

bond length 0.74 ÅBDE 435 kJ/mol

Bonding and Antibonding MOs

+s s

s *antibondings bonding

+

p p

p *antibonding

p bonding

+

p p

p *antibondingp bonding

combining atomic orbitals molecular orbitals

71

• The Structure of Methane and Ethane: sp3 Hybridization• The structure of methane with its four identical

tetrahedral bonds cannot be adequately explained using the electronic configuration of carbon

• Hybridization of the valence orbitals (2s and 2p) provides four new identical orbitals which can be used for the bonding in methane• Orbital hybridization is a mathematical

combination of the 2s and 2p wave functions to obtain wave functions for the new orbitals

Hybrid Orbitals and Molecular Shape

sp3 hybridizationCH4

The ground state electron configuration of C is

1s2 2s2 2p2 or1s 2s 2px 2py 2pz

valence level

This electron configuration explains neither the bonding capacity of C nor the shape of CH4 .

Hybrid Orbitals

Step One

ground state of C1s 2s 2px 2py 2pz

Electron Promotion 2s

1s 2s 2px 2py 2pz

excited state

2p

+energy

Step Two

This set of valenceorbitals does notexplain the molecularshape of methane.

1s 2s 2px 2py 2pz 1s sp3 sp3 sp3 sp3

Orbital Hybridization

hybrid orbitals

Overviewelectron promotion

+ energy

excited state1s 2s 2px 2py 2pz

1s

2s

2px 2py 2pz

hybrid orbitals

orbital hybridization

1s sp3 sp3 sp3 sp3

sp3 sp3 sp3 sp3

1s

ground state for C

1s

2s

2px 2py 2pz

ener

gy

1s 2s 2px 2py 2pz

The Three-Dimensional Symmetry of sp3 Hybrid Orbitals

x

z

y

2s orbital

+

2px orbital

mixing of the 2s, 2px,2py and 2pz orbitals

2py orbital

2pz orbital yields four sp3 hybridorbitals directedtowards the cornersof a tetrahedron

76

• When one 2s orbital and three 2p orbitals are hybridized four new and identical sp3 orbitals are obtained• When four orbitals are hybridized, four orbitals must

result• Each new orbital has one part s character and 3

parts p character• The four identical orbitals are oriented in a

tetrahedral arrangements• The antibonding orbitals are not derived in the

following diagram• The four sp3 orbitals are then combined with the 1s

orbitals of four hydrogens to give the molecular orbitals of methane• Each new molecular orbital can accommodate 2

electrons

77

78

• An sp3 orbital looks like a p orbital with one lobe greatly extended• Often the small lobe is not drawn

• The extended sp3 lobe can then overlap well with the hydrogen 1s to form a strong bond

• The bond formed is called a sigma () bond because it is circularly symmetrical in cross section when view along the bond axis

79

• A variety of representations of methane show its tetrahedral nature and electron distribution• a. calculated electron density surface b. ball-and-

stick model c. a typical 3-dimensional drawing

80

• Ethane (C2H6)• The carbon-carbon bond is made from overlap of

two sp3 orbitals to form a bond • The molecule is approximately tetrahedral around

each carbon

81

• The representations of ethane show the tetrahedral arrangement around each carbon• a. calculated electron density surface b. ball-and-

stick model c. typical 3-dimensional drawing

• Generally there is relatively free rotation about bonds • Very little energy (13-26 kcal/mol) is required to

rotate around the carbon-carbon bond of ethane

82

• The Structure of Ethene (Ethylene) : sp2 Hybridization• Ethene (C2H2) contains a carbon-carbon double bond and is

in the class of organic compounds called alkenes• Another example of the alkenes is propene

• The geometry around each carbon is called trigonal planar• All atoms directly connected to each carbon are in a

plane• The bonds point towards the corners of a regular

triangle• The bond angle are approximately 120o

83

• There are three bonds around each carbon of ethene and these are formed by using sp2 hybridized orbitals

• The three sp2 hybridized orbitals come from mixing one s and two p orbitals • One p orbital is left unhybridized

• The sp2 orbitals are arranged in a trigonal planar arrangement• The p orbital is perpendicular (orthoganol) to the plane

The Hybrid Orbital ModelThe structural and electronic properties of ethene are consistent with the hybrid orbital model using carbons that are sp2 hybridized.

A set of valence level hybrid orbitals is obtained by mathematically combining the 2s and two 2p atomic orbitals of carbon. This process can be broken down into two steps, electron promotion and hybridization or mixing.

electronpromotion

+ energy

excited state of C

1s

2s

2px 2py 2pz2pz

sp2 sp2 sp2

hybridization

1s

valence-level orbitals

This process is overall energetically favorable (despite electron promotion) because it allows more complete use of the valence electrons in forming bonds.

1s

2s

2px 2py 2pz

ener

gy

ground state of C

2pz

sp2 sp2 sp2

1s

Three equivalent sp2 orbitalsare in the X-Y plane. The idealized inter-orbital angle is 120o.

Spatial Arrangement of the Hybrid Orbitals

sp2 hybridized carbon

valence level

sp2sp2

sp2

pz

bonding orbitals

C

The Carbon-Carbon Double Bond

The carbon-carbon double bond results from valence level orbital interaction between two sp2 hybridized carbons as shown below. In this picture, the two atomic centers are brought together along an axis that allows overlap of sp2 hybrid orbitals.

sp2 sp2

pz pz

CC

The double bond is made up of a bond from overlapping sp2 orbitals, and a bond from overlapping pz orbitals.

C C

87

• Overlap of sp2 orbitals in ethylene results in formation of a framework• One sp2 orbital on each carbon overlaps to form a carbon-carbon bond; the remaining sp2 orbitals form bonds to hydrogen

• The leftover p orbitals on each carbon overlap to form a bonding bond between the two carbons

• A bond results from overlap of p orbitals above and below the plane of the bond

88

• The bonding orbital is lower in energy than the antibonding orbital • In the ground state two spin paired electrons are in the bonding

orbital• The antibonding *orbital can be occupied if an electron

becomes promoted from a lower level ( e.g. by absorption of light)

89

• The bonding orbital results from overlap of p orbital lobes of the same sign• The antibonding * orbital results from overlap of p orbital lobes of opposite sign

• The antibonding orbital has one node connecting the two nuclei and another node between the two carbons

90

• The orbital is lower in energy than the orbital• The ground state electronic configuration of

ethene is shown

Molecular Orbitals of Ethene

atomic orbitals

sp2

pz

1s

sp2

pz

sp2

CH H

C

H

H

C

H

H

atomic orbitals

sp2

pz

1s

CHH

pz

pz atomic orbitalscombine to formbonding and antibonding MOs

*

Complete Set of MO’s for Ethene

Molecular Orbitals of Ethene

atomic orbitals

sp2

pz

1s

sp2

pz

sp2

CH H

C

H

H

C

H

H

* atomic orbitals

sp2

pz

1s

CHH

pz

*c-c

c-c

sp2 atomic orbitalscombine to formbonding and antibonding C-C MOs

Molecular Orbitals of Ethene

atomic orbitals

sp2

pz

1s

sp2

pz

sp2

CH H

C

H

H

C

H

H

* atomic orbitals

sp2

pz

1s

CHH

pz

*c-c

c-c

combine to form (C-H) bondingand antibonding MOs

combine to form (C-H) bondingand antibonding MOs

*C-H

(4 filled MOs)

C-H

Molecular Orbitals of Ethene

atomic orbitals

sp2

pz

1s

sp2

pz

sp2

CH H

C

H

H

C

H

H

atomic orbitals

sp2

pz

1s

CHH

pz

C CH

H

H

H

*

*c-c

c-c

Approximate MOScheme for Ethene

*C-H

(4 filled MOs)

C-H

95

• Restricted Rotation and the Double Bond• There is a large energy barrier to rotation (about 264

kJ/mol) around the double bond• This corresponds to the strength of a bond • The rotational barrier of a carbon-carbon single bond

is 13-26 kJ/mol• This rotational barrier results because the p orbitals

must be well aligned for maximum overlap and formation of the bond • Rotation of the p orbitals 90o totally breaks the bond

Restricted Rotation Around the Double BondThe picture of the carbon-carbon double bond as separate and bonds is consistent with the observed large barrier (approx. 251 kJ/mol) to rotation around the C-C axis. While -bonds are cylindrically symmetrical around the axis of the bond (meaning that rotation around the bond axis does not cause loss of orbital overlap), -bonds are not.

A rotation of one carbon relative to the other uncouples (loss of orbital overlap) the p-orbitals. When the p-orbitals are 90o apart, there is no overlap and the electronic energy is the same as for an electron residing in an isolated p-orbital.

-bond

or

C C

C C

90o

rotation

C C 90o

view along theC-C axis

localizedp-orbitals

loss of orbital overlap

C C

The Energy Barrier to Rotation

localizedp-orbitals

90o

C C

90o

-bond

C C

An energy barrier of close to250 kJ/mol is estimated during rotation around the carbon-carbon double bond.

-el

ectr

on p

oten

tial e

nerg

y

kJ/m

ol

250

0

degree of rotation45 90 135 180

-bond

C C

The two compounds below with the same formula of C2H2Cl2 illustrate this isomerism.

cis-1,2-dichloroethene trans-1,2-dichloroethene

Cl

H

Cl

H

Cl

H

H

Cl

"cis" (Latin: "on this side") "trans" (Latin: "across")MP -80o C -50o CBP 60o C 48o C

dipolemoment

1.90 D 0 D

These isomers are sometimes called geometric isomers.

The barrier of close to 251 kJ/mol means that rotation around the carbon-carbon double bond does not occur under ordinary conditions. This restricted rotation leads to a type of isomerism: the existence of different compounds with the same formula.

Cis-Trans Isomerism in Alkenes

99

• Cis-trans isomers• Cis-trans isomers are the result of restricted rotation

about double bonds• These isomers have the same connectivity of atoms

and differ only in the arrangement of atoms in space • This puts them in the broader class of

stereoisomers• The molecules below do not superpose on each other• One molecule is designated cis (groups on same side)

and the other is trans (groups on opposite side)

100

• Cis-trans isomerism is not possible if one carbon of the double bond has two identical groups

Quiz Chapter 1 Section 13

Identify the covalent bonds in ethene by type ( or ) and indicate the atomic orbitals from the atoms that form the covalent bonds.

ethene

C C

H H

H H

CC

combining atomic orbitalsbond type

CH

combining atomic orbitalsbond type

CC

combining atomic orbitalsbond type

pp

sp2s

sp2sp2

102

• The Structure of Ethyne (Acetylene): sp Hybridization

• Ethyne (acetylene) is a member of a group of compounds called alkynes which all have carbon-carbon triple bonds• Propyne is another typical alkyne

• The arrangement of atoms around each carbon is linear with bond angles 180o

103

• The carbon in ethyne is sp hybridized• One s and one p orbital are mixed to form

two sp orbitals• Two p orbitals are left unhybridized

104

• The two sp orbitals are oriented 180o relative to each other around the carbon nucleus• The two p orbitals are perpendicular to

the axis that passes through the center of the sp orbitals

105

• In ethyne the sp orbitals on the two carbons overlap to form a bond• The remaining sp orbitals overlap with hydrogen

1s orbitals• The p orbitals on each carbon overlap to form two bonds

• The triple bond consists of one and two bonds

106

• Depictions of ethyne show that the electron density around the carbon-carbon bond has circular symmetry• Even if rotation around the carbon-carbon

bond occurred, a different compound would not result

107

• Bond Lengths of Ethyne, Ethene and Ethane• The carbon-carbon bond length is shorter as

more bonds hold the carbons together• With more electron density between the

carbons, there is more “glue” to hold the nuclei of the carbons together

108

• The carbon-hydrogen bond lengths also get shorter with more s character of the bond • 2s orbitals are held more closely to the nucleus than 2p

orbitals• A hybridized orbital with more percent s character is held more

closely to the nucleus than an orbital with less s character• The sp orbital of ethyne has 50% s character and its C-H bond is

shorter• The sp3 orbital of ethane has only 25% s character and its C-H

bond is longer

Orbital Hybridization, Bond Lengths and Bond Strengths

The greater the degree of s-character in a hybrid orbital that overlaps with another atomic orbital to form a covalent bond, the shorter the covalent bond and the stronger the bond.

hydrocarbon hybridization bond lengthsC-C C-H

Ho (C-H)(kJ/mol)

H

HH

HH

H

HH

HH

H H

410

452

523

sp3 1.54 Å 1.10 Å(sp3 - 1s)

sp2 1.34 Å 1.09 Å(sp2- 1s)

sp 1.20 Å 1.06 Å(sp- 1s)

Orbital Hybridization Influences on C-C Bond Lengths and Bond Strengths

orbitals C-C Bond Length Ho (C-C)(kJ/mol)

C CH3

H3C CH3

CH2=CH CH3

HC C CH3

Shorter bonds are generally stronger bonds.

sp3 sp3 1.54 Å 368

sp sp3 1.46 Å 490

sp2 sp3 1.50 Å 385

Quiz Chapter 1 Section 14

The strongest C-H bond among those labeled in the structure below is

C C C C C

The longest C-H bond among those labeled in the structure above is

HH

H H HH

A B CD

Section 15--A Summary of Important Concepts That Come from Quantum Mechanics

1. An atomic orbital (AO) corresponds to a region of space about the nucleus of a single atom where there is a high probability of finding an electron. Atomic orbitals called s orbitals are spherical; those called p orbitals are like two almost-tangent spheres. Orbitals can hold a maximum of two electrons when their spins are paired. Orbitals are described by a wave function, , and each orbital has a characteristic energy. The phase signs associated with an orbital may be (+) or (-).

2. When atomic orbitals overlap, they combine to form molecular orbitals (MOs). Molecular orbitals correspond to regions of space encompassing two (or more) nuclei where electrons are to be found. Like atomic orbitals, molecular orbitals can hold up to two electrons if their spins are paired.

3. When atomic orbitals with the same phase interact, they combine to form a bonding molecular orbital:

The electron probability density of a bonding molecular orbital is large in the region of space between the two nuclei where the negative electrons hold the positive nuclei together

4. An antibonding molecular orbital forms when orbitals of opposite phase sign overlap:

An antibonding orbital has higher energy than a bonding orbital. The electron probability density of the region between the nuclei is small and it contains a node--a region where = O. Thus, having electrons in an antibonding orbital does not help hold the nuclei together. The internuclear repulsions tend to make them fly apart.

5. The energy of electrons in a bonding molecular orbital is less than the energy of the electrons in their separate atomic orbitals. The energy of electrons in an antibonding orbital is greaterthan that of electrons in their separate atomic orbitals.

6. The number of molecular orbitals always equals the number of atomic orbitals from which they are formed. Combining two atomic orbitals will always yield two molecular orbitals--one bonding and one antibonding.

7. Hybrid atomic orbitals are obtained by mixing (hybridizing) the wave functions for orbitals of different types (i.e., s and p orbitals) but from the same atom.

8. Hybridizing three p orbitals with one s orbital yields four sp3 orbitals. Atoms that are sp3

hybridized direct the axes of their four sp3 orbitals toward the corners of a tetrahedron. The carbon of methane is sp3 hybridized and tetrahedral.

9. Hybridizing two p orbitals with one s orbital yields three sp2 orbitals. Atoms that are sp2

hybridized point the axes of their three sp2 orbitals toward the corners of an equilateral triangle. The carbon atoms of ethane are sp2 hybridized and trigonal planar.

10. Hybridizing one p orbital with one s orbital yields two sp orbitals. Atoms that are sp hybridized orient the axes of their two sp orbitals in opposite directions (at an angle of 180o). The carbon atoms of ethyne are sp hybridized and ethyne is a linear molecule.

11. A sigma () bond (a type of single bond) is one in which the electron density has circularsymmetry when viewed along the bond axis. In general, the skeletons of organic moleculesare constructed of atoms linked by sigma bonds.

12. A pi () bond, part of a double and triple carbon-carbon bonds, is one in which the electrondensities of two adjacent parallel p orbitals overlap sideways to form a bonding pi molecularorbital

Valence Shell Electron Pair Repulsion TheoryVSEPR theory provides a simple way to predict molecular geometries around a central atom. These predictions are consistent with hybrid molecular orbital theory..

Key Features of VSEPR Theory

Molecules or ions may be analyzed where a central atom is covalently bonded to two or more atoms or groups.

(1)

(2) All pairs of valence electrons around the central atom are counted: bonding and nonbonding.

(3) Because of electron-electron repulsion, pairs of electrons tend to stay as far apart as possible. Repulsion due to nonbonding pairs of electrons is greater than repulsion due to bonding pairs.

(4) The preferred geometry has all pairs of valence electrons as far apart as possible to minimize repulsion among electron pairs.

:::

:

Examples

Methane CH

HH

H

There are four pairs of bonding electrons in the valence level around the central carbon. Maximum separation of the four pairs is achieved with a tetrahedral geometry where each electron pair points to the corner of a tetrahedron.

109.5o an idealized tetrahedralgeometry

CH

HHH

• The number of molecular orbitals formed equals the number of the atomic orbitals used

• Hybridized orbitals are obtained by mixing the wave functions of different types of orbitals• Four sp3 orbitals are obtained from mixing one s and three p orbitals

• The geometry of the four orbitals is tetrahedral• This is the hybridization used in the carbon of methane

• Three sp2 orbitals are obtained from mixing one s and two p orbitals• The geometry of the three orbitals is trigonal planar• The left over p orbital is used to make a bond• This is the hybridization used in the carbons of ethene

• Two sp orbitals are obtained from mixing one s and one p orbital• The geometry of the two orbitals is linear• The two leftover p orbitals are used to make two bonds• This is the hybridization used in the carbons of ethyne

• Sigma () bonds have circular symmetry when viewed along the bond axis

• Pi () bonds result from sideways overlap of two p orbitals

119

• Molecular Geometry: The Valence Shell Electron Pair Repulsion (VSEPR) Model

• This is a simple theory to predict the geometry of molecules• All sets of valence electrons are considered including:

• Bonding pairs involved in single or multiple bonds• Non-bonding pairs which are unshared

• Electron pairs repel each other and tend to be as far apart as possible from each other• Non-bonding electron pairs tend to repel other

electrons more than bonding pairs do (i.e. they are “larger”)• The geometry of the molecule is determined by the

number of sets of electrons by using geometrical principles

120

• Methane• The valence shell of methane contains four

pairs or sets of electrons• To be as far apart from each other as

possible they adopt a tetrahedral arrangement (bond angle 109.5o)• The molecule methane is therefore

tetrahedral

121

• Ammonia• When the bonding and nonbonding electrons are

considered there are 4 sets of electrons• The molecule is essentially tetrahedral but the actual

shape of the bonded atoms is considered to be trigonal planar

• The bond angles are about 107o and not 109.5o because the non-bonding electrons in effect are larger and compress the nitrogen-hydrogen bond

122

• Water• There are four sets of electrons including 2 bonding pairs

and 2 non-bonding pairs• Again the geometry is essentially tetrahedral but the

actual shape of the atoms is considered to be an angular arrangement

• The bond angle is about 105o because the two “larger” nonbonding pairs compress the electrons in the oxygen-hydrogen bonds

123

• Boron Trifluoride• Three sets of bonding electrons are farthest apart

in a trigonal planar arrangement (bond angle 120o)• The three fluorides lie at the corners of an

equilateral triangle

• Beryllium Hydride• Two sets of bonding electrons are farthest

apart in a linear arrangement (bond angles 180o)

124

• Carbon Dioxide• There are only two sets of electrons around the central carbon

and so the molecule is linear (bond angle 180o) • Electrons in multiple bonds are considered as one set of

electrons in total

• A summary of the results also includes the geometry of other simple molecules

Quiz Chapter 1 Section 16

Use VSEPR theory to predict the geometry around the carbon atom in each of the following chemical species.

::

formaldehyde

-

methyl cation methyl anionH2C=O H3C+ H3C:

1 set (4) of bonding electrons and two pairs of bonding electrons

trigonal planar

C OH

H three pairs of bonding electrons

trigonal planar

C HH

H three pairs of bonding electrons and one pair of nonbonding electrons tetrahedral(trigonal pyramidal)

CH

HH

126

• Representations of Structural Formulas• Dot formulas are more cumbersome to draw

than dash formulas and condensed formulas • Lone-pair electrons are often (but not

always) drawn in. They are drawn when they are crucial to the chemistry being discussed

127

• Dash formulas• Each dash represents a pair of electrons• This type of representation is meant to emphasize

connectivity and does not represent the 3-dimensional nature of the molecule• The dash formulas of propyl alcohol appear to

have 90o angles for carbons which actually have tetrahedral bond angles (109.5o)

• There is relatively free rotation around single bonds so the dash structures below are all equivalent

128

• Constitutional isomers• Constitutional isomers have the same

molecular formula but different connectivity• Propyl alcohol (above) is a constitutional isomer

of isopropyl alcohol (below)

129

• Condensed Structural Formulas• In these representations, some or all of the dash lines are omitted• In partially condensed structures all hydrogens attached to an atom are

simply written after it but some or all of the other bonds are explicitly shown• In fully condensed structure all bonds are omitted and atoms attached to

carbon are written immediately after it • For emphasis, branching groups are often written using vertical lines to

connect them to the main chain

130

• Bond-Line Formulas• A further simplification of drawing organic molecules is to

completely omit all carbons and hydrogens and only show heteroatoms (e.g. O, Cl, N) explicitly

• Each intersection or end of line in a zig-zag represents a carbon with the appropriate amount of hydrogens• Heteroatoms with attached hydrogens must be drawn in

explicitly

131

• Cyclic compounds are condensed using a drawing of the corresponding polygon

• Multiple bonds are indicated by using the appropriate number of lines connecting the atoms

132

• Three-Dimensional Formulas• Since virtually all organic molecules have a 3-dimensional

shape it is often important to be able to convey their shape• The conventions for this are:

• Bonds that lie in the plane of the paper are indicated by a simple line

• Bonds that come forward out of the plane of the paper are indicated by a solid wedge

• Bonds that go back out of the plane of the paper are indicated by a dashed wedge

• Generally to represent a tetrahedral atom:• Two of the bonds are drawn in the plane of the paper

about 109o apart• The other two bonds are drawn in the opposite direction

to the in- plane bonds but right next to each other

Three-Dimensional RepresentationsThree-dimensional representations of structures are often important. By convention, a solid wedge is a bond projected out of the plane of paper or screen towards the viewer. A dashed wedge is a bond projected out of the plane away from the viewer. A solid line is a bond in the plane.

in planetowards viewer

away from viewer

Examples

HC

HBrH

CH3Br CH3OHOH

CH

HH

CH3CH2ClH

CCl

H3CH

134

135

• Trigonal planar arrangements of atoms can be drawn in 3-dimensions in the plane of the paper• Bond angles should be approximately

120o

• These can also be drawn side-on with the central bond in the plane of the paper, one bond forward and one bond back

• Linear arrangements of atoms are always best drawn in the plane of the paper

Quiz Chapter 1 Section 17

Are the following pairs of structural formulas the same or different compounds?

(CH3)2CHCH2CH3 CH3CH2CHCH3CH3

CH3CH2CHClCHCH3CH2CH3

CH3CH2CHClCHCH2CH3CH3

CH3CHCH2CHCH2CH3CH3 Cl

(CH3)2CHCHClCH2CH2CH3

same

same

different

137Chapter 1