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1Chemical Bonding

1.1 INTRODUCTION

Atoms combine to form molecules. The combining power of atoms to form molecules is calledvalency (Latin word valentia; meaning strength). Valency of an atom indicates the numberof atoms of hydrogen which combine with one atom of an element. This definition of valencyhas, however, failed in case of carbon, as the valency in the compounds C2H2, C2H4, C2H6and CH4 varies from 1 to 4.

With the advancement of knowledge about atomic structure, it was realized that electronsin atoms were primarily involved in chemical combinations. According to the ‘Lewis octetrule’, atoms of all elements have a tendency to acquire an electronic configuration similar tothat of inert gases because it represents the most stable electronic configuration. All atomshaving unstable or incomplete outer shell have a tendency to gain or lose electrons so as toacquire an electronic configuration of the nearest inert gas in the Periodic Table. It is thistendency of atoms to complete and hence stabilize their outermost orbit of electrons which ismainly responsible for chemical combination between the atoms.

Thus, according to ‘electronic theory of valency’ ‘a chemical bond is formed as a resultof electronic interactions. It may, however be noted that a molecule is formed only whenelectrons of the constituent atoms interact in such a way that the potential energy islowered. Greater the lowering of potential energy, greater is the strength of the bond.

Subsequently, the ‘wave mechanical theory’ was developed which gave logical under-standing of bonding between atoms. On the basis of wave mechanical theory, it is alsopossible to make fruitful predictions regarding the geometrical structure of molecules.

1.2 TYPE OF BONDS

According to the electronic theory of valency the interaction of extranuclear electrons leads tothe formation of following type of bonds:

(i) Electrovalent or ionic bond(ii) Covalent bond

(iii) Coordinate bond.There are mainly three ways by which the atoms may obtain a stable electronic configu-

ration, namely, by gaining, losing or sharing of electrons. We divide all the known elementson electronegativity scale into:(a) electropositive elements, whose atoms give up one or more electrons readily(b) electronegative elements, whose atoms take up electrons(c) elements whose atoms neither lose nor gain electrons.

1

2 Fundamentals of Engineering Chemistry

Thus, the following three types of bonds are possible by the different types of combinationsof the three types of elements:

(i) Electropositive elements + Electronegative elements Æ Ionic bond(ii) Electronegative elements + Electronegative elements Æ Covalent bond

(iii) Electropositive elements + Electropositive elements Æ Coordinate bond.

1.2.1 Electrovalent or Ionic Bond

The ionic bond is formed due to the “electrostatic attraction between stable ions formed bythe complete transfer of electrons from one atom to another”, and the combining atomsacquire inert gas configuration. The atom which loses electrons acquires a positive charge,whereas the one which gains electrons becomes negatively charged. These charged atoms arecalled ions and held together by electrostatic attraction forces. Such a mode of combination ofatoms is called electrovalency and the bond formed between the atom is called electrovalentor Ionic bond. The compound thus formed is called an electrovalent or ionic compound.

Atoms having a tendency to lose electrons are called electropositive whereas the atomswhich gain electrons are called electronegative. The number of electrons gained or lost by anatom in order to acquire an inert gas configuration gives numerical value of the electrovalencyof the atom.

Let us consider the formation of sodium chloride (NaCl) as an example. The electronicarrangement of Na and Cl atoms are:

Na (11) 2, 8, 1 (1s2, 2s2, 2p6, 3s1)Cl (17) 2, 8, 7, (1s2, 2s2, 2p6, 3s2, 3p5)

The electron from the outermost orbit of Na is completely transferred to the outermostorbit of Cl atom. As a result of this transfer, both atoms acquire inert gas structure. The Nabecomes Na+ (2, 8) and Cl become Cl– (2, 8, 8).

They attain inert gas structure of neon and argon respectively. The two +ve and –ve ionsare held together by electrostatic force of attraction acting between them. The formation ofNaCl is depicted below:

Na¥ + .Cl:....

Æ [Na]+ Cl:

..

..×.

(2, 8, 1) (2, 8, 7) (2, 8) (2, 8, 8)

Na Cl

+ –

In the formation of BaCl2, two electrons from outermost shell of Ba are completelytransferred to the outermost orbit of two chlorine atoms. By losing two electrons Ba becomesbivalent Ba2+ ion having two positive charges. It combines with two chlorine ions formed fromchlorine atoms by accepting one electron each.

:Cl.....

.Ba.× × Cl:..

..Æ [Ba]2+

: :

: :

Cl

Cl

.

..

...

xx

�

�

��

�

�

��

− 2

Other examples of ionic compounds are CaS, KCl, MgCl2, K2O etc.

Chemical Bonding 3

Electrovalent compounds exhibit following properties:(i) Electrovalent compounds are generally hard solids.

(ii) They have high melting and boiling point.(iii) Electrovalent compounds are generally sparingly soluble in organic solvents.(iv) Electrovalent compounds in solid state are poor conductors of electricity. But when

dissolved in solvents of relatively high dielectric constant, they exhibit a strong electricalconductivity. They also conduct electricity in the molten state.

1.2.2 Covalent Bond

Formation of molecules by the sharing of electrons between combining atoms is calledcovalency and the bond formed is called colvalent bond or covalent linkage. Compoundscontaining this type of linkage are called covalent compounds. In covalent bond formationthe inert gas configuration of the two concerned atoms is achieved by sharing equal numberof electrons.

The sharing of electrons to form chemical bond between two atoms is described by showingpairs of electrons between the bonded atoms. If one pair of electrons is shared, the bondformed is called single bond, whereas sharing of two or three pairs of electrons leads to theformation of double or triple bonds respectively. Due to sharing of electrons, both the bondingatoms acquire inert gas configuration.

Let us consider the formation of hydrogen molecule from two hydrogen atoms. Each hydro-gen atom has only one electron and thus its configuration is unstable but when both thehydrogen atoms share their electrons to form a pair of electrons equally shared between thetwo atoms i.e., the pair of electrons becomes a common property of the two hydrogen atoms;the resulting molecule acquires He configuration.

The covalent bond is represented by a dash (–).

H2 H. + xH Æ H x.H or H—H

[1s1] [1s1] [1s2]

Similarly, the formation of CCl4 and CH4 takes place as below:

:Cl:

:Cl. .Cl:

:Cl:

C

..

.. ..

.xxx

x.

.. ..

..

Cl

Cl

Cl—C—Cl

:Cl:

:Cl Cl:

:Cl:

C

..

.. ...x.x

.x

.x.. ..

..

or

H

H· ·H

H

C.x

xxx.

H

H

H—C—H

H

H H

H

C

.x.x

.x

.x

or

Some other examples of the formation of covalent compounds is shown below:(i) Single bonds:

H2 H· + ·H → H—H

Cl2 : .. .Cl.. . :

. .Cl.. → Cl—Cl


(ii) Double bonds:

O2 O. .

:.. + :O. ... O O

CO2 O OC.. .... ..

: :x xx x O OC

(iii) Triple bonds:

N2 :N� + �N: N N

C H2 2 H C C H

(acetylene)

· ·x xxxx

xxx

H—C C—H

In covalent compounds the numerical value of covalency of any element in the molecule isthe number of electron pairs shared between the atoms. Thus the valency of hydrogen in H2is one, oxygen in O2 is two, nitrogen in N2 is three and carbon in CH4 is four.

The covalent bonds are of two types:(A) Polar covalent bonds,(B) Non-polar covalent bonds.

(A) Polar Covalent BondsWhen a bond is formed between unlike atoms, the bonding electrons will not be equallyshared. The resulting bond is a polar covalent bond. e.g., formation of HCl.

H x . Cl: H—Cl�+ �–..

..

The shared electrons will be shifted more towards the atom having higher electronegativityand this will result in the accumulation of a –ve charge on it. The other atom will carry anequivalent +ve charge. In the above example of HCl, the chlorine atom acquires small amountof –ve charge because of its higher electronegativity and hydrogen has an equivalent +vecharge. The d+ and d – represents respectively the small +ve and –ve charge.

(B) Non-polar Covalent BondsWhen a bond is formed between atoms of the same element, the bonding electrons areequally shared on account of equal electronegativity of the atoms. The resulting bond is anon-polar covalent bond. In case of such a bond, the centre of +ve charge coincides with thecentre of –ve charge in the molecule.

For example, bonds involved in the formation of H2, Cl2, O2, N2 etc. are non-polar bonds.

H . . H H—H

xC Cl:xx

xx ....xx

. Cl—Cl

Covalent compounds possess following general characteristics:(i) Colvalent compounds possess definite geometrical shapes. They exhibit isomerism because

covalent bonds are rigid and possess directional characteristics.

Chemical Bonding 5

(ii) Covalent compounds are mostly liquids and gases. The solid compounds are generallyvolatile.

(iii) They are highly soluble in organic solvents but slightly soluble in water. Some compoundslike HCl and NH3 readily dissolve in water because they react with water.

HCl + H2Oæ Ææ [H3O]+ + Cl–

NH3 + H2Oæ Ææ [NH4]+ + OH–

(iv) The melting and boiling points of covalent compounds are relatively low because theforces involved in covalent compounds are less strong than those involved in electrovalentor ionic compounds.

(v) These compounds do not contain ions. Therefore, when dissolved, they do not conductelectricity. They even do not conduct electricity in the molten state.

Comparison of Electrovalent and Covalent CompoundsThe essential difference between electrovalent and covalent linkages is that in the former

case complete transference of electrons between the atoms takes place whereas in the lattercase there is no transfer of electrons between the bonding atoms but instead, there is sharingof electrons. Since no transfer of electrons is involved, colvalent compounds are non-ionic innature.

Sl. Electrovalent or Covalent CompoundsNo. Ionic Compounds

1. This type of bond is frequently encountered This type of bond is frequently found inin inorganic compounds. organic compounds.

2. Electrovalent compounds are soluble in Covalent compounds are soluble in organicwater but insoluble in organic solvents solvents and insoluble in water.

3. They possess high M.P. & B.P. They have low M.P. and B.P.4. Electrovalent compounds are not They are inflammable.

inflammable.5. They do not possess any characteristic They usually possess a characteristic smell.

smell.6. In electrovalent compounds reactions are In covalent compounds reactions are slow.

rapid.

1.2.3 Coordinate Bond

When, an atom having a complete octet donates a pair of free valence electrons to anotheratom which is short of two electrons, the resulting bond is known as coordinate bond. Thusboth the atoms acquire inert gas configurations.

The atom which donates a pair of electrons is called ‘donor’ and the other atom whichaccepts the electrons is called ‘acceptor’. The coordinate bond is similar to covalent bondexcept that both the shared electrons are donated by one atom. The formation of covalent andcoordinate bond is illustrated below:

A. + .B ææÆ A : B or A—B (Normal covalency)

A : + B A : B or A B (Coordinate valency)��


When one atom furnishes both electrons for the formation of a covalent bond as describedabove, the process is called ‘coordination’.

Since one atom donates an electron pair and the other accepts, the molecule acquirespolarity. These bonds, therefore, are also known as ‘semi polar bonds’ or ‘dative bond’.The extent of polarity is larger than that of covalent bonds although less than electrovalentbonds. Coordinate bond is represented by the symbol (Æ).

Formation of some coordinate compounds is illustrated below:

(i) Ammonium ion [NH4+ ]

H H

H

H HN

H

N

.

.

.

xxxxx

x

H H+

or �

+

(ii) Phosphate ion [PO 43− ]

P P+ 3e–

��x x

x

x x xx x x

x x

xx

–3

O

O

OO P

:

:

::

:

:

::

::

::

x

x

x

xxxx

x

–3

or

O

O

OO P�

��

–3

(iii) Sulphate ion [SO42–]

S S+ 2e–

��x

x

x

x

x x xx x x

x

x

x

x

–2

O

O

OO S

:

:

::

:

:

::

::

::

x

x

x

xxxx

x

or

O

O

OO S�

��

–2

(iv) Compounds of NH3 + BCl3

H Cl

Cl

ClH

H

N B

x

xx

x

x

.

.

.

:

:

:

:

:

:

::

::

:

: or

H Cl

H Cl

H—N B—Cl�

Chemical Bonding 7

Following are the main characteristics of coordination compounds:(i) Coordinate compounds, like covalent compounds, exhibit space isomerism. This is due to

directional characteristics possessed by coordinate linkage.(ii) The B.P. and M.P. of these compounds have intermediate value between electrovalent

and covalent compounds.(iii) They are only slightly soluble in water and most of them are soluble in organic solvents.

(A) Exceptions to the Octet RuleThere are certain stable compounds where the octet rule is not obeyed, that is, their valenceshells contain more or less than 8 electrons. The compounds containing less than 8 electronsin the valence shells are called electron deficient compounds such as B2F6, Al2Cl6 etc. Onthe other hand, the compounds containing more than 8 electrons in the valence shells may becalled electron surplus compounds e.g., PCl5, SF6, OsF8 etc.

In an electron deficient compound such as B2F6, the available electrons are insufficientfor sharing between the two boron atoms and the six fluorine atoms. Each boron atom hasthree electrons so that the two boron atoms have six electrons which are just sufficient forbinding the three fluorine atoms. It has been suggested that boron atoms in B2F6 completetheir octet by accepting a pair of electrons from fluorine atoms. The existence of Al2Cl6 canalso be explained on the same basis. The structure of B2F6 and Al2Cl6 are given below:

F F or F—B—F B B

F

F

F F

F FFF

B. ..

x x

x

: :

:

: :

: :

::B F2 6

Cl

Cl

Cl or Cl—Al—Cl Al Al

Cl Cl Cl

Cl Cl ClCl

Al..

.x

x

x:

:

:

: :

:

: :

:

Al Cl2 6

It has been found that AlCl3 and BF3 exist as dimers, Al2O6 and B2F6 respectively.Since a bond involves one pair of electrons, the phosphorous atom in PCl5 would be

surrounded by 10 electrons, the sulphur in SF6 by 12 electrons and the Osmium in OsF8 by16 electrons. The octet rule can be preserved in these compounds if it is assumed that someatoms are joined by single electron bond or singlet linkage to the central atom. A singletlinkage is formed when an atom in a molecule having complete octet, donates one electron toanother atom which it needs to complete its own octet.

The singlet linkage may be assumed as a coordinate linkage formed by donation of oneelectron as shown below:

A A BA BB+ ��: :: : :.

: : ::

: : ::

..

.


Structure of some compounds involving singlet linkages are shown below:

OsSP

FFCl

FFCl FFCl

F F

FFClFF

FFCl

PCl5 SF6 O Fs 8

(two singlet linkage) (four singlet linkage) (eight singlet linkage)

(B) Odd Electron BondsIt has been observed that almost all the compounds of non-transition elements contained aneven number of bonding electrons. Very few exceptions like NO, NO2 etc. possess odd numberof bonding electrons. Such type of compounds are called Odd Molecules. The odd moleculesare classified into following two categories.(i) One Electron Bond Molecule

In such molecules, only one electron forms the bond, e.g., H2+ , Li2

+ , Na2+ , K2

+

[+H.H] [H.H+]In general, odd bonds are represented as resonance hybride of two or more structures.

(ii) Three Electron Bond MoleculesThree electron bond is formed when an odd electron of an atom becomes associated with a

loan pair of electrons on another atoms

[A .: B]resonance hybrid structure [A .: B] [A:.B]

The three electron bond may also be represented by three dots i.e., [A . . . B]e.g., He2

+

[He . . . He]+

resonating structure of He2+

[He :. He+] [He+ .: He]

Such molecules which have three electron bonds in addition to an ordinary electron pairbond is represented as follows :

[A � B]These molecules exhibit strong tendency to dimerise.

(C) ResonanceCarbon dioxide molecule can be represented by the following three electronic structures:

–O C—O+ O C O +O—C O–

(i) (ii) (iii)

There is resonance between these structures. The contribution of structures (i) and (iii)involving triple bond is confirmed by the fact that the carbon to oxygen bond length in CO2 is

Chemical Bonding 9

slightly smaller than the normal carbon-oxygen double bond. The real structure of carbondioxide is something intermediate between these structures, which, infact, cannot be repre-sented by the conventional diagrams and is called a ‘resonance hybrid’.

Benzene molecules can be represented as follows:

��

Kekule structure Dewar structure

It has been observed that carbon to carbon single bond length is 1.54 Å, the carbon tocarbon double bond length is 1.33 Å. In case of benzene, carbon to carbon distance is 1.39 Åwhich is intermediate between that of a single and a double bond. This shows that actualbonds in benzene are neither single or double but intermediate in character.

The resonance structure should flufil the following requirements:(i) Resonance structure should be similar in terms of energy.

(ii) In resonance structures, the constituent atoms should be in the same position.(iii) These structures should have the same number of electrons pairs.(iv) These structures should differ only in the location of electrons around the constituent

atoms.

1.3 THEORIES OF COVALENT BOND FORMATION

Two theories have been put forward to explain the formation of the bond, viz.,(i) Electronic theory of valency, and

(ii) Wave Mechanical theory of covalency.

1.3.1 Electronic Theory of Valency

G.N. Lewis explained valency in terms of interaction between extranuclear electrons of thecombining atoms. It was suggested that during the formation of molecule the combiningatoms tend to attain a stable electronic configurations similar to that of inert gases. The inertgases have s2p6 configuration is their outermost shell (except He, 1s2). According to theelectronic theory of valency, when atoms combine to form molecules, the electrons in theoutermost shells of the atoms tend to acquire inert gas structure (1s2 or s2p6) which hasmaximum stability and minimum energy. The atoms after bond formation contain eightelectrons is their outermost shells.

The interaction of extranuclear electrons leads to the formation of the following types ofbonds:

(a) Electrovalent or ionic bond(b) Covalent bond(c) Coordinate bond.The above three has already been discussed earlier in details

1.3.2 Wave Mechanical Theory of Covalency

Electronic theory of covalency cannot account for some important characteristics of moleculessuch as spatial distribution of bonds, i.e., geometry of molecules, the lengths of bonds involved


and their strength etc. Wave mechanics provides better understanding of the characteristicsof molecules containing covalent bonds. Following two approaches have been evolved:

(i) Molecular orbital (MO) theory(ii) Valence bond (VB) theory

1.3.2.1 Molecular Orbital (MO) TheoryAccording to MO theory a covalent bond is formed when two half filled orbitals of two atomscome nearer and then overlap each other to form a new bigger orbital known as ‘MolecularOrbital’. The molecular orbital surrounds the atomic nuclei of both the atoms and each ofthe electrons, which are now paired (one electron from one atomic orbitals) in the molecularorbital, is electrostastically attracted by both the nuclei. It is important to note that energy ofthe molecular orbital is less than the sum of energies of the two atomic orbitals and conse-quently the resulting molecule is more stable than the two separate atoms. Like atomicorbitals, the molecular orbitals also obey Paulies exclusion principle and thus one molecularorbital can accommodate only two electrons with antiparallel spins.

We consider below the case of hydrogen molecule on the basis of above theory. We imaginthat in the hydrogen molecule there are two nuclei A and B corresponding to two hydrogenatoms. Let yA (1s) be the wave function of hydrogen atom A and yB (1s) be the wave functionof the electron of atom B. The molecular orbital wave function is expressed as a combinationof two atomic wave function as,

yMo = yA(1s) ± yB(1s)

The expression is applicable to diatomic molecule and this type of approach for obtainingMO of a molecule known as Linear Combination of Atomic Orbitals (LCAO).

Furthermore, it must be noted that when two atomic orbitals overlap each other, twomolecular orbitals are produced, namely;

(i) Bonding orbitals(ii) Anti-bonding orbitals.

These two new molecular orbitals spread over both the atom and either may contain twoelectrons.

The bonding molecular orbital have lesser energy than the energies of the separate atomicorbitals whereas the antibonding molecular orbital have higher energy than the energies ofthe two separate atomic orbitals.

Let us consider the 1s orbitals of hydrogen atom degenerated but when they combine toform molecule, they split into two new energy states, one having high energy and the otherhaving lower energy than the original 1s states. This is illustrated in figure 1.1.

Ene

rgy

�A(1s) �B(1s)

Antibonding

�A

�B

Bonding

��

Chemical Bonding 11

The wave function for these molecular orbitals are given by the following equations:ys = yA(1s) + yB(1s)

yA = yA(1s) – yB(1s)

where ys corresponds to the lower energy state and yA to the higher energy state.In the bonding orbital, the electron density is concentrated between the two nuclei whereas

in the antibonding molecular orbital, the electron density moves away from the region betweentwo nuclei.

If overlap of the two atomic orbitals has taken place along their major axes, the resultingmolecular orbitals is known as sigma (s ) orbital and the bond fromed as s bond.

(A) sssss (Sigma) and sssss* (Sigma Star) Molecular OrbitalsIn order to understand the meaning of s and s* orbitals, let us consider the M.O. formed

by the combination of orbitals of the two hydrogen atoms as shown in figure 1.2.

Antibonding * 1smolecular orbital

�

Bonding 1s molecular orbital�

��

The dots ( ) refer to the position of nuclei. The electron density is concentrated betweenthe two nuclei in bonding s orbital.

In the ‘antibonding orbital’ the electron density move away from the region between twonuclei. Antibonding orbitals are marked with asterisks (*). In the case of H2 molecule, theantibonding orbital is represented as s* 1s. The subscripts 1s in s 1s and s* 1s denote theatomic orbits from which the molecular orbitals are formed. Furthermore the s 1s and s* 1sorbitals are symmetric about the bond axis or internuclear axis. It is evident that s bondingM.O. has no nodal plane containing the molecular axis.

On the other hand, if overlapping of two atomic orbitals has taken place sideways i.e., intheir parallel axes, the resulting molecular orbitals are known as p (Pi orbitals) and thenewly formed bonds as p bonds.

(B) ppppp (Pi) and ppppp * (Pi Star) Molecular OrbitalsThe formation of molecular orbitals by combination of p-orbitals is shown in figure 1.3.In case I, px orbitals of atom 1 combine with px orbital of atom 2 to give two M.Os, spx and

s*px (antibonding). From the figure it becomes clear that both are symmetric around the linejoining the two nuclei (bond axis). In case II, the two p-orbitals overlap sidewise and producetwo M.Os, p pz and p*pz. The bonding Pi orbital (p pz) possesses a nodal plane containing themolecular axis. The antibonding orbital (p *pz) has four top like lobes extending outwardsfrom the two nuclei. In the case III, the formation of p*py and p *py takes place in the samemanner as that of p*pz and p*pz respectively. The only difference is that the M.Os in theformer case lie in a plane at right angles to the plane containing the p*pz and p *pz orbitals.


zy

x – –+ +

+

+

–

– –

z

zy

y

x

+ +

– –

+

+

+

–

–

–

x

+

+ +

+–

–

– –

Case I

Case II

Case III

atom 1

atom 1

atom 1

atom 2

atom 2

atom 2

�*px

*pz

*py

py

pz

�px

��

(C) Sigma (sssss) and Pi (ppppp) BondsThe bonds formed from end-on-end overlap of orbitals are called s bonds. Now since two

orbitals overlap along their axes, maximum overlapping is possible and hence the bondformed (s) is strong. A s bond may be formed by the overlapping of s-s, s-p, p-p, sp3-sp3,sp2-sp2, sp-sp, sp3-s or p, sp2-s or p and sp-s or p-orbitals of two or more atoms.

s-s overlap s-p overlap p-p overlap

�� σ��

On the other hand, the bonds formed from sideways (lateral) overlapping of orbitalsare known as Pi (p) bonds. Now here since the lateral overlapping is only partial, the bondsthus formed are weak bonds. A p bond is formed by the overlap of two orbitals.

OR

�� π��

Chemical Bonding 13

Molecular Orbital Energy Levels for Diatomic MoleculesThe wave function describing a molecular orbital (ψAB) for a heteronuclear diatomic molecule

can be obtained from linear combination of the atomic orbitals ψA and ψB

ψAB = N [CA ψA + CB ψB]

Here CA ≠ CB because the electron distribution in the internuclear region is not symmetrical.

�B�A

�AB

�ABAO’s AO’s

MO’s

��

I. Nitric Oxide (NO) Molecule (simple Heteronuclear Diatomic Molecule)

The N and O atom contain 7 and 8 electron respectively. Total 15 of e– need to be accom-modated in the molecular orbitals of NO molecule.

The molecular orbital electronic configuration of NO molecule is

�2 �2 �2 �2 �22

2

�

0

Increasing Energy

1s 1s 2s 2s 2px2py

2py 2py

2pz

Bond order = No. of in bonding orbital No. of in antibonding orbital

2e e− −−

= 10 5

2−

= 2.5

Because the NO molecule contains one unpaired electron in π* 2py orbital so the NOmolecule is paramagnetic.


*2py *

2py 2pz

�2s

�*1s

�1s

2p2p

2s 2s

1s 1s

N ONO

�*2px

�2px

�*2s

2pz

En

erg

yE

nerg

y

II. HF Molecule

�*spx

(Non-bonding)

(2 )py (2 )pz

( )�spx

2px 2py 2pz

1sEn

erg

y

HF

(MO)

H

(AO)

F

(AO)

Chemical Bonding 15

1s2

2s2 �2

spx

2p2

y

2p2z

�*spx

Increasing Energy

BO = 12

(Nb – Na) = 12

(2 – 0) = 1

Since all the molecular orbitals (whether non-bonding or bonding molecular orbitals) arecompletely filled, so HF molecule is diamagnetic.

III. N2

N2 molecule contains 14 electrons.

�1 , *1 , 2 , *2 ,s s s s2 2 2 2

� � �2py

2

2p z

2 �2px

2

*2py *2pz

�*2px

�2px

2py 2pz

2pz 2py 2px 2px 2py 2pz

�*2s

�2s

2s2

2s2

N N2 N

Molecule

En

erg

y

��

Bond order = 12

[Nb – Na]

= 12

[8 – 2] = 3

Unpaired electron is zero, hence dimagnetic in nature.


IV. O2

Total number of electrons = 16These are arranged in MOs:

� �1 , *1 , 2 , *2 , 2s s s s p2 2 2 2 2

x� � �2py

2

2pz

2,

, 2py

1*

2p z*1

*2py *2pz

�*2px

�2px

2py 2pz

2px 2py 2pz 2px 2py 2pz

�*2s2

�2s2

2s 2s

O O2 O

E E

En

erg

y

En

erg

y

��

Bond order = 12

[Nb – Na]

= 12

[8 – 4] = 2

Unpaired electron, = 2, hence paramagnetic in nature.V. O–

2 (Superoxide Ion)Total number of electrons = 17One extra electron than the O2 molecule

σ1s2, σ*1s2, σ2s2, σ*2s2, σ2px2

ππ

ππ

2 2

2

2

1222

pp

pp

y

z

y

z

��

��

**

Chemical Bonding 17

BO = 12

[Nb – Na]

BO = 12

[8 – 5] = 1.5

Unpaired electrons 1.5 hence paramagnetic in nature.VI. O2

– – (Peroxide Ion)Total number of electron = 18On extra electron than the O2

– molecule.

σ1s2, σ* 1s2, σ2s2, σ* 2s2, σ2px2

π

π

π

π

2

2

2

2

2

2

2

2

p

p

p

py

z

y

z

��

��

*

*

BO = 12

[8 – 6] = 1

Unpaired electrons 1, hence diamagnetic in nature.VII. CO

Total number of electron = 14 electron

σ1s2, σ*1s2, σ2s2, σ*2s2, ππ2

2

2

2

p

py

z

��

σ2px

2

*2py *2pz

�*2px

�2px

2py 2pz

2px 2py 2pz 2py 2pz 2px

�*2s2

�2s2

C CO O

En

erg

y

��


BO = 12

[Nb – Na]

= 12

[8 – 2] = 3

Unpaired electrons 3, hence dimagnetic in nature.

Bond OrderIt is defined as one half of the difference between the number of electrons in bonding molecularorbitals and the number of electrons in anti bonding molecular orbitals.

BO = No. of bonding electrons – No. of anti bonding electrons2

or BO = Nb – Na2

Bond order is a measure of the stability of a molecule. Higher the bond order, greater thestability of the molecule. Zero bond order means that formation of the molecule will not take place.

Bond orders of some diatomic molecules are as given below:

(i) H2 ≡ σ 1s2 BO = 2 − 0

2 = 1

(ii) He2 ≡ σ 1s2, σ* 1s2 BO = 2 2

0−

= 0

(iii) Li2 ≡ σ 1s2, σ* 1s2, σ 2s2 BO = 4 2

2−

= 1

(iv) Be2 ≡ σ 1s2, σ* 1s2, σ 2s2, σ* 2s2 BO = 4 4

2−

= 0

(v) B2 ≡ σ 1s2, σ* 1s2, σ 2s2, σ* 2s2, π 2py1, π 2pz

1 BO = 6 4

2−

= 1

Because of the presence of two unpaired electrons, it is paramagnetic in nature.(vi) N2 ≡ σ 1s2, σ* 1s2, σ 2s2, σ* 2s2, σ 2px

2, π 2py2, π 2pz

2

BO = 10 4

2−

= 62

= 3

(vii) O2 = σ 1s2, σ* 1s2, σ 2s2, σ* 2s2, σ 2px2, π 2py

2, π 2pz2, π* 2py

1, π* 2pz1

BO = 10 6

2–

= 42

= 2

Paramagnetic in nature due to presence of unpaired electrons

(viii) O 2+ ≡ σ 1s2, σ* 1s2, σ 2s2, σ* 2s2, σ 2px

2, π 2py2, π 2pz

2, π* 2py1

BO = 10 5

2–

= 52

= 2.5

(ix) O2– BO = 8 5

2– = 3

2 = 1.5

(x) O2–2 BO = 8 6

2– = 2

2 = 1

Since O2+ has the highest bond order, meaning shortest bond length and hence the maximum

bond strength.

(xi) F2 = BO = 8 62– = 2

2 = 1

Chemical Bonding 19

(xii) Ne2 ; BO = 10 10

2–

= 02

= 0

(xiii) NO ;KK, σ 2s2, σ* 2s2, σ 2px

2, π 2py2, π 2pz

2, π* 2py1, π* 2pz

0

BO = 10 5

2–

= 52

= 2.5

(xiv) NO+ ; BO = 8 2

2–

= 62

= 3.0

(xv) NO2+ ; BO = 7 22– = 5

2 = 2.5

(xvi) NO– ; BO = 8 42– = 4

2 = 2.0

Bond LengthIt is defined as the straight line distance between nuclei of two atoms that are bondedtogether in a covalent molecule. It is measured in angstrom unit (Å) (1Å = 10–8 cm = 10–10 m).

• Bond length between two bonded atoms is smaller than expected if one of the atoms ismore electronegative. Larger the difference in electronegativity, shorter the bond length.

• Bond length depends on the state of hybridisation e.g., s character of sp, sp2 and sp3

hybrid orbital is 50%, 33.3% and 25%. Larger the s character, shorter the bond length.e.g., CH4 sp3 hybridisation; 1.54 Å

C2H4 sp2 hybridisation; 1.34 Å C2H2 sp hybridisation; 1.20 Å

• As the bond order increases, the bond length decreases.• Resonance also affect the bond length (decreases).

Bond Energy or Bond StrengthIt may be defined as the amount of energy that is required to break the bond between twoatoms. Bond energy is directly proportional to bond strength. It is also known as bonddissociation energy and is measured in kJ/mol.

• Larger the difference in electronegativity of bonded atoms greater the bond energy.• Smaller size of atoms (shorter bonds), greater bond energy.• Greater number of covalent bond, greater bond energy.• Lone pair of electrons decreases bond energy.• Greater the bond angle, greater the bond energy.

Bond AngleIt may be defined as the internal angle between the orbitals containing electron pairs in thevalency shell of central atom in a molecule. Bond angle depends upon the state of hybridisationat central atom in a compound. e.g.,

sp3 109.28°sp2 120°sp 180°

• Greater the bond angle, greater is the stability of the molecules.• Lone pairs of electrons at central atom decreases the bond angle.


1.4 METALLIC BOND

Metallic bond results from a delocalized covalent bonding by the overlap of valence-orbitalsbetween nearest neighbour atoms. Thus, metallic crystal lattice consists of positive ionscalled kernels, permeated by a cloud of valency electrons called electron gases, as illustratedin figure 1.10.

Ion cores

Sea of valenceelectrons

+ + + +

+ + + +

+ + + +

+ + + +

– – –

– – –

– – –

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The binding force is attraction between kernels of atoms (atom minus valency electrons)and the electron cloud. In other words, all valency electrons belong to the crystal as a whole.These electrons are free to migrate throughout the crystal lattice, thereby giving rise to highelectrical conductivity to metals. The high reflectance of metal arises, due to the ease withwhich the free electrons get accelerated by high frequency radiations and then, radiateimmediately, virtually all the energy of the incident radiation absorbed.

Metals are characterised by properties such as good thermal and electrical conductivity, abright appearance called metallic lustre, high malleability, ductility and tensile strength.

There are three major theories applied for bonding in metals, viz.;(i) Free electron theory, (ii) VB theory, and

(iii) MO theory.

1.4.1 Free Electron Theory

According to this theory each atom in a metal crystal loses all its valency electrons due to lowionization energy of the metal atoms. These electrons form an electron pool or gas. Now ametal is regarded as a group of +ve metal ions are believed to be held together in a regulargeometric pattern by this electron pool or gas. The force that binds a metal ion to the mobile,electrons within its sphere of influence is known as metallic bond.

+–

–

–

–

–––––

– – –

–

–

+

+

+–

–

–

–

+

+

+–

–

+

+

+–

–

–

–+

Positive metal cores

Mobile electrons

1.4.2 Valence Bond (VB) Theory

Valence bond theory explains the nature of a chemical bond in a molecule in terms of atomicvalencies. VB theory summarizes the rule that the central atom in a molecule tends to form

Chemical Bonding 21

electron pair bonds in accordance with geometric constraints as defined by the octet rule.According to this theory, outermost orbitals of the atoms overlap during covalent bondformation. Two atoms can form a bond only when both have unpaired electrons with oppositespins.

The overlapping of atomic orbitals can differ. There are two types of overlapping orbitalsnamely; sigma (σ) and pi (π). Sigma bonds formed when orbitals of two shared electronsoverlap head-to-head, and pi bonds formed when two orbitals overlap when they are parallel.e.g.,

A bond between two s-orbital electrons is a σ bond, because two spheres are alwayscoaxial. In terms of bond order, single bond have one σ bond, double bonds consist one σ andone π bond and triple bonds consist one σ and two π bonds. The strength of bond depend uponthe amount of overlap. Greater the overlap stronger the bond.

Following three types of overlapping occurs:(i) s-s overlapping e.g., H2 molecule

(ii) s-p overlapping e.g., HF molecule(iii) p-p overlapping e.g., Cl2 molecules-s overlapping: In the formation of hydrogen molecule, the spherical 1-s orbital of each

of hydrogen atoms overlaps with one another forming a single covalent bond.

: HH H2 molecule or H—H

s-p overlapping: In the formation of HF molecule the spherical 1-s orbital of hydrogenatom overlaps with 2pz orbital of fluorine.

Electronic configuration of fluorine is:

9F = 1s2, 2s2, 2px2, 2py

2, 2pz1

:Hx

zy

x HF molecule or H—F

p-p overlapping: Chlorine molecule would be formed by the overlapping of the 3pz orbitalsof two chlorine atoms. Electronic configuration of chlorine is:

17Cl = 1s2, 2s2, 2p6, 3s2, 3px2, 3py

2, 3pz1

:: Cl2 molecule or Cl—Cl


Some other examples of overlapping in different molecules are as illustrated:H2O (water) Molecule:

O = 1s2, 2s2, 2px2, 2py

1, 2pz1

z

x

y

H

HBond angle

Theoretically 90°

Actually 104° 3�

Ammonia (NH3) Molecule:N = 1s2, 2s2, 2px

1, 2py1, 2pz

1

xH

H

H

:

:

:

Bond angle for HNH in NHTheoretically 90°Actually 107° 20'

3

z y

An important aspect of the VB theory is the condition of maximum overlap which leads tothe formation of the strongest possible bonds. This theory is used to explain the covalentbond formation in many molecules. As we see the case of H2 and F2 molecules, the bondstrength and bond length differ between H2 and F2 molecules.

1.4.3. Molecular Orbital (MO) Theory

According to this theory, metallic bond results from the delocalisation of the free electronsorbital over all the atoms of a metal structure.

With the help of Molecular orbital theory of metals, materials can be classified into follow-ing three categories, depending on the energy gap between the valence and conduction bands:(a) Conductors, (b) Insulators, and(c) Semiconductors.

Chemical Bonding 23

The above three energy bands are diagrammatically represented in figure 1.11.

Bon

den

ergy

Conductionband (CB)

Valencebondband (VB)

( )i ( )ii

OR

Empty

Filled

VB Large energy gap

CBCB CB

VBVB VB

Small gap Impurity band

( ) Intrinsici ( ) Extrinsicii

(A) Conductors (B) Insulators (C) Semiconductors

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In conductors (metallic elements) either the valence bands and conduction bands overlapor the valence band is only partly full. As the filled and unfilled molecular orbitals are notseparated by significant gap, hence perturbation can occur readily.

In insulators (non-metallic elements), there is a large band gap between the filledvalence bands and empty conduction band. Therefore electrons cannot be promoted from theVB to CB where they could move freely.

Semiconductors are of two types, intrinsic and extrinsic semiconductors. Intrinsicsemiconductors have small energy gap between the filled VB and empty CB sufficient topromote an electron from VB to CB. The hole left in the VB and the promoted electrons in theCB both contribute towards conductivity. It is obvious that number of electrons promoted toCB increases with rise in temperature, thus conductivity of semiconductors increases withtemperature. The conductance of semiconductors can be improved by doping. Doping meanstreatment of Si and Ge with impurity atoms of group III and V giving respectively p-type andn-type semiconductors. Basically the band from the impurity lies in between the VB and CB,so that electrons may be easily excited from VB to impurity band and hence conductanceincreases. Details are given under heading 1.3.2.1 (page 10).

1.5 HYDROGEN BONDING

As we know that hydrogen has one electron in its outermost orbit. By losing an electron itforms H+ while by gaining one electron from outside it forms H–. When hydrogen lies betweentwo strong electronegative atoms (N, O, F etc.) or elements, the hydrogen atom form a bondor bridge between them. With one electronegative atom it forms a normal covalent bondwhile with other electronegative atom it forms a weak bond. This weak bond is known ashydrogen bond and the phenomenon of bonding is known as hydrogen bonding. The hydrogenbond is denoted by dotted (......) line.As hydrogen bond is very weak, it possesses a bond energy in the range of 2–10 kcal/mol.Hydrogen bonding occurs in compounds like alcohols, water, aldehydes, ketones, ethers,ammonia, amines, carboxylic acids, hydrogen fluoride etc. e.g.,


H—F H—F H—F H—F

�� %��

O

O

O

H

O

H

HHH

HH

H

��%�� #%&�$��

Greater the difference in electronegativity stronger the hydrogen bonding. The increasingorder of hydrogen bonding in some atoms is:

S < Cl < N < O < F e.g., H F 41.8 kJ/molHH

O 29.3 kJ/molN 12.6 kJ/mol

H—O

R

H—O

R

H—O

R

�� %�� #'(�%$��

H N

H

H

H N

H

H

H N

H

H

�� %�� #)%*$��

R—C

O H O

O H O

C—R

Dimer of carboxylic acid

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1.5.1 Types of Hydrogen Bonding

There are two types of hydrogen bonding; namely:(i) Intermolecular and

(ii) Intramolecular hydrogen bonding.

Chemical Bonding 25

Intermolecular Hydrogen Bonding : Intermolecular hydrogen bonding occurs when bond-ing takes place between two or more molecules of the same or different types. e.g.,

HF, H2O, ROH, RCOOH, etc.,Various molecules of the same compound.

H2O—ROH, H2O—NH3

O H

R

O H

H

O H

R

O H

H

Alcohol Water

Various molecules of different compound.Intermolecular hydrogen bonding is responsible for the increase in BP of the compound

and also its solubility in water. For a substance to be soluble in water, it should be able tomake hydrogen bond with water, e.g., ethanol and methanol are miscible with water in allproportions while ethers, higher alcohols and hydrocarbons are not soluble. Intermolecularhydrogen bonding lower the strength of an acid.

Intramolecular Hydrogen Bonding: Intramolecular hydrogen bonding occurs whenbonding takes place between two atoms of the same molecule. e.g.,

H

O O

O

O OO

O

N N

H

C

o-Nitrophenol Salicylic acido-Nitro benzoic acid

H

HO O

O

C

Intramolecular hydrogen bonding decreases the BP of the compounds as well as its solubil-ity in water. Intramolecular hydrogen bonding increases the strength of an acid.

��

1. Discuss the salient features of molecular orbital theory of bonding. How does it differfrom valence bond theory.

2. Explain valence shell electron pair repulsion theory on the basis of bond angle of methane,ammonia and water.

3. Calculate the bond order in B2, N2, O2, F2 and NO.4. What do you understand by covalent bond. Give three characteristics of a covalent

bond?5. What is the effect of temperature and impurities on conductivity of semiconductor?6. State the factors which favour covalency.


7. What is hybridisation? Calculate % S orbital character of a hybrid orbital if bond anglebetween hybrid orbital is 105°.

8. State differences between s (Sigma) and p (Pi) bonds.9. Calculate number of s (Sigma) and p (Pi) bonds in C2H2, C2H4, CO3

- - , NH3, PCl5.10. Predict shape, bond angle dipole moment and hybridisation of the following compounds

on the basis of VSEPR theory:

SO4- - , NH4

+ , BF4- , XeO4, NH3

11. Explain paramagnetic nature of O2 and its less stability in comparison to that of N2.12. Write order for the filling of electrons in various molecular orbitals.13. What is meant by ‘Bond order’? Give a formula to calculate it. Calculate bond order for

NO.14. Explain formation of bonding and antibonding molecular orbitals on the basis of wave

function.15. State rules for LCAO method for formation of molecular orbits.16. Which of the following is paramagnetic:

O2- , O2

- - , N2, C6H6, CO3- -

17. Explain order of acidity in BF3 < BCl3 < BBr3.18. Arrange the following in the decreasing order of acidity and C—H bond length: CH4,

C2H6, C2H4, C2H2.

chemical bonding - newagepublishers.comthe sharing of electrons to form chemical bond between two...

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