Samacheer Class 11 Chemistry - Chemical Bonding

c) All five sp 3 d hybrid orbitals are not equivalent out of these five sp 3 d hybrid orbitals, three are at an angle of 120° remaining two are perpendicular to the plane containing the other three

i) Bond order:
The number of bonds formed between the two bonded atoms in a molecule is called the bond order.
ii) Hybridisation:
Hybridisation is the process of mixing of atomic orbitals of the same atom with comparable energy to form an equal number of new equivalent orbitals with the same energy.
iii) σ – bond:
When two atomic orbitals overlap linearly along the axis, the resultant bond is called a sigma (σ) bond.

When two atomic orbitals overlap sideways, the resultant covalent bond is called a pi (π) bond. When we consider x-axis as the molecular axis, the p y – p y and p z – p z overlaps will result in the formation of a π – bond.

According to VSEPR theory, as H 2 O has two lone pairs so it repels the bond pairs much more and makes the bond angle shorter of 104.5 degrees, and as NH 3 has one lone pair that repels the three bond pairs but not much effectively and strongly as two lone pairs of water repel one bond pair.
So the bond angle between the Hydrogen atom of ammonia is 107.5 greater than that of water. Similarly, methane molecules have no lone pair and bond pair repels each other with an equal bond angle between two adjacent hydrogen atoms becomes 109°.28′.

Consider boron trifluoride molecule. The valence shell electronic configuration of the boron atom is [He]2s 2 2p 1.
In the ground, state boron has only one unpaired electron in the valence shell. In order to form three covalent bonds with fluorine atoms, three unpaired electrons are required. To achieve this, one of the paired electrons in the 2s orbital is promoted to the 2p y orbital in the excited state. In boron, the s orbital and two p orbitals (p x and p y ) in the valence shell hybridises, to generate three equivalent sp 2 orbitals as shown in the Figure. These three orbitals lie in the same xy plane and the angle between any two orbitals is equal to 120°.
Overlap with 2p z orbitals of fluorine:
The three sp 2 hybridised orbitals of boron now overlap with the 2p z orbitals of fluorine (3 atoms). This overlap takes place along the axis as shown below.

Electronic configuration of O atom:
1s 2 2s 2 2p 4
Electronic configuration of O 2 molecule:
σ 1s 2, σ 1s *2, σ 2s 2, σ 2s *2, σ 2px 2, π 2py 2 π 2pz 2 π 2py *1 π 2pz *1
Bond order = \(\frac{N_{b}-N_{a}}{2}\)
= \(\frac{10-6}{2}\)
= 2
The molecule has two unpaired electrons hence it is paramagnetic.

Bonding in some hetero nuclear di-atomic molecules:
Molecular orbital diagram of Carbon monoxide molecule (CO)
Electronic configuration of C atom: 1s 2 2s 2 2p 2
Electronic configuration of O atom: 1s 2 2s 2 2p 4
Electronic configuration of CO molecule:
σ 1s 2, σ 1s *2, σ 2s 2, σ 2s *2, π 2py 2, π 2pz 2 σ 2px 2
Bond order = \(\frac{N_{b}-N_{a}}{2}\)
= \(\frac{10-4}{2}\)
= 3
The molecule has no unpaired electrons hence it is diamagnetic.

The wave functions for the molecular orbitals can be obtained by solving the Schrodinger wave equation for the molecule. Since solving the Schrodinger equation is too complex, approximation methods are used to obtain the wave function for molecular orbitals. The most common method is the linear combination of atomic orbitals (LCAO).
We know that the atomic orbitals are represented by the wave function ψ. Let us consider two atomic orbitals represented by the wave function ψ A and ψ B with comparable energy, combines to form two molecular orbitals. One is bonding molecular orbital(ψ bonding ) and the other is antibonding molecular orbital (ψ antibonding ) The wave functions for these two molecular orbitals can be obtained by the linear combination of the atomic orbitals ψ A and ψ B as below,
ψ bonding = ψ A + ψ B;
ψ antibonding = ψ A – ψ B
The formation of bonding molecular orbital can be considered as the result of constructive interference of the atomic orbitals and the formation of anti-bonding molecular orbital can be the result of the destructive interference of the atomic orbitals. The formation of the two molecular orbitals from two is orbitals is shown below.
Constructive interaction:
The two 1s orbitals are in phase and have the same sign,
Destructive interaction:
The two orbitals are out phase

Molecular orbital diagram of nitrogen molecule (N 2 )
Electronic configuration of N atom 1s 2 2s 2 2p 3
Electronic configuration of N 2 molecule:
σ 1s 2, σ 1s *2, σ 2s 2, σ 2s *2, π 2py 2, π 2pz 2 σ 2px 2
Bondorder = \(\frac{N_{b}-N_{a}}{2}\)
= \(\frac{10-4}{2}\) = 3
Molecule has no unpaired electrons hence it is diamagnetic.

The polarity of a covalent bond can be measured in terms of dipole moment which is defined as
μ = q × 2d
Where μ is the dipole moment, q is the charge and 2d is the distance between the two charges. The dipole moment is a vector and the direction of the dipole moment vector points from the negative charge to positive charge.
representation of dipole
The unit of dipole moment is coloumb meter (C m). It is usually expressed in Debye unit (d). The conversion factor is 1 Debye = 3.336 × 10 -30 C m.

The linear form of carbon dioxide has zero dipole moment, even though it has two polar bonds. In CO 2, the dipole moments of two polar bonds (CO) are equal in magnitude but have opposite direction. Hence, the net dipole moment of the CO 2 is,
μ = μ 1 + μ 2 = μ 1 + (-μ 1 ) = 0

Bond formation of BeCl 2:
Be = 4;
Electronic configuration of Be atom is = 1s 2 2s 2
Bond formation of MgCl 2:
Mg (Z = 12), 1s 2 2s 2 2p 6 3s 2 it loses two of its valence electron and became Mg 2+ with inert gas configuration Neon.
The chlorine accepts one electron in its valence shell and because Cl – ion with Ar electron configuration.
Mg + Cl 2 → Mg 2+ + 2 Cl – → MgCl 2
Magnesium cation and two chlorides are attracted by strong electrostatic force to form MgCl 2 crystals.
Mg = 12,
Electronic configuration: 1s 2 2s 2 2p 6 3s 2
Mg +2:
Electronic configuration: 1s 2 2s 2 2p 6 3s 0
Cl = 17, 1s 2 2s 2 2p 6 3s 2 3p 5
Cl –:
Electronic configuration: 1s 2 2s 2 2p 6 3s 2 3p 6

1. Sigma bonds (σ) are stronger than Pi bonds (π). Because, sigma bonds are formed from bonding orbitals directly between the nuclei of the bonding atoms, resulting in greater overlap and a strong sigma bond (axial overlapping).
2. π bonds result from the overlap of atomic orbitals that are in contact through two areas of overlap (lateral overlapping). Pi bonds are more diffused bonds than sigma bonds.

The bond enthalpy is defined as the minimum amount of energy required to break one mole of a particular bond in molecules in their gaseous state. The unit of bond enthalpy is kJ mol -1.

The molecular orbital electronic configuration of the hydrogen molecule is (σ 1s 2 ). The molecular orbital energy level diagram of the H 2 molecule is given in
Here, N 2 = 2, N a = 0
Bond order = \(\frac{N_{b}-N_{a}}{2}=\frac{2-0}{2}\) = 1
He 2: σ 1s 2 σ 1s *2
The molecular orbital energy level diagram of He 2 (hypothetical) is given in
Here, N b = 2 and N a = 2
Bond order = \(\frac{N_{b}-N_{a}}{2}=\frac{2-2}{2}\) = 0
As the bond order for He 2 comes out to form between two hydrogen atoms. But as the bond order of helium is zero, there is no bond between helium atoms and hence it is monoatomic.
Result:
As the bond order of the H 2 molecule is one, it is diatomic and a single bond is formed between two hydrogen atoms. But as the bond order of helium is zero, there is no bond between helium atoms and hence it is monoatomic.

Polar covalent bond is a chemical bond in which the electrons required to form a bond is unequally shared between two atoms. The atom which is more electronegative attracts more electrons from the bonded pair than the other atom. As a result there is a slight separation of charges in a molecule in which more electronegative atom (comparatively) carries a slight negative charge and less electronegative atom carries a positive charge. The bonds formed between two atoms have a permanent electric dipole.
In water (H 2 O) molecule, covalent bond exists between Hydrogen and Oxygen. Being more electronegative Oxygen carries negative charge and Hydrogen carries positive charge. In a water molecule Oxygen carries a negative charge (anionic in nature) and hydrogen’s carries positive charge (cationic in nature) which forms a polar covalent bond. The size of an oxygen atom is comparatively higher than a hydrogen atom, hence it polarizes the molecule towards itself i.e., it attracts shared pair of bonding electrons towards itself and makes the bond to be more polarized. Hydrogen which is comparatively a small-sized cation makes the bond to be polarized better.

i) 1s and 2p y: No sigma bond
ii) 2p x and 2p y: sigma bond
iii) 2p x and 2p z: No sigma bond
iv) 1s and 2p z: No sigma bond

It is evident from the experimental results that all carbon-oxygen bonds in carbonate ions are equivalent. The actual structure of the molecules is said to be resonance hybrid, an average of these three resonance forms. It is important to note that carbonate ion does not change from one structure to another and vice versa. is not possible to picturise the resonance hybrid by drawing a single Lewis structure. However, the following structure gives a qualitative idea about the correct structure.
(b) Resonance structure of CO 3 2-:
Resonance Hybrid structure of CO 3 2-:
It is found that the energy of the resonance hybrid (structure 4) is lower than that of all possible canonical structures (Structure 1, 2 & 3). The difference in energy between structure 1 or 2 or 3, (most stable canonical structure) and structure 4 (resonance hybrid) is called resonance energy.

Bonding in ethylene:
The bonding in ethylene can be explained using the hybridization concept. The molecular formula of ethylene is C 2 H 4. The valency of carbon is 4. The electronic configuration of valence shell of carbon in ground state is [He] 2s 2 2p x 1 2p y 1 2p z 0. To satisfy the valency of carbon promote an electron from 2s orbital to 2p z orbital in the excited state.
In ethylene both the carbon atoms undergo sp 2 hybridization involving 2s, 2p x, and 2p y, orbitals, resulting in three equivalent sp 2 hybridised orbitals lying in the XY plane at an angle of 120° to each other. The unhybridized 2p z orbital lies perpendicular to the XY plane.
Formation of sigma bond:
One of the sp 2 hybridised orbitals of each carbon lying on the molecular axis (x-axis) linearly overlaps with each other resulting in the formation of a C-C sigma bond. The other two sp 2 hybridised orbitals of both carbons linearly overlap with the four is orbitals of four hydrogen atoms leading to the formation of two C-H sigma bonds on each carbon.
Formation of sigma bond:
The unhybridized 2p z orbital of both carbon atoms can overlap only sideways as they are not in the molecular axis. This lateral overlap results in the formation of a pi bond between the two carbon atoms as shown in the figure.
Bonding in acetylene:
Similar to ethylene, the bonding in acetylene can also be explained using hybridization concept. The molecular formula of acetylene is C 2 H 2. The electronic configuration of valence shell of carbon in ground state is [He] 2s 2 2p x 1 2p y 1 2p z 0. To satisfy the valency of carbon promote an electron from 2s orbital to 2pz orbital in the excited state.
In acetylene molecule, both the carbon atoms are in sp hybridized state. The 2s and 2p x orbitals, resulting in two equivalent sp hybridized orbitals lying in a straight line along the molecular axis (x-axis). The unhybridized 2p y and 2p z orbitals lie perpendicular to the molecular axis.
Formation of sigma bond:
One of the two sp hybridized orbitals of each carbon linearly overlaps with each other resulting in the formation a C – C sigma bond. The other sp hybridized orbitals of both carbons linearly overlap with the two 1s orbitals of two hydrogen atoms leading to the formation of one C – H sigma bond on each carbon.
Formation of pi bond:
The unhybridized 2p y and 2p z orbitals of each carbon overlap sideways. This lateral overlap results in the formation of two pi bonds (p y – p y and p z – p z ) between the two carbon atoms as shown in the figure.

Lewis’s concept of the structure of molecules deals with the relative position of atoms in the molecules and sharing of electron pairs between them. However, we cannot predict the shape of the molecule using Lewis concept. Lewis theory in combination with VSEPR theory will be useful in predicting the shape of molecules.
IF 7:
Iodine has 7 valence electrons in the valence shell. In an excited state it has 6 valency electrons by 1st and 2nd excited state & under sp 3 d 2, hybridization and combines with 7 Fluorine to get pentagonal bipyramidal shape. There are no lone pairs.
I = ns 2 np 5 nd 0
SF 6:
Sulphar attain six valence electron in 1st and 2nd excited states undergoes sp 3 d 2 hybridization and combines with six ‘F’ atoms, as there no lone pair electrons it geometry in octahedral.
S = 16 = ns 2 np 4 nd 0

(i) N 2
N 2 = 14
σ 1s 2 σ 1s *2 σ 2s 2 σ 2s *2 π 2py 2 π 2pz 2 π 2px 2
Bond order = \(\frac{6}{2}\) = 3
(ii) N 2 +
σ 1s 2 σ 1s *2 σ 2s 2 σ 2s *2 π 2py 2 π 2pz 2 π 2px 1
Bond order = \(\frac{5}{2}\) = 2.5
(iii) N 2 –
σ 1s 2 σ 1s *2 σ 2s 2 σ 2s *2 π 2py 2 π 2pz 2 π 2px *1
Bond order = \(\frac{5}{2}\) = 2.5
The highest bond order is N 2

Like the partial ionic character in covalent compounds, ionic compounds show partial covalent character. For example, the ionic compound, lithium chloride shows covalent character and is soluble in organic solvents such as ethanol.
The partial covalent character in ionic compounds can be explained on the basis of a phenomenon called polarisation. We know that in an ionic compound, there is an electrostatic attractive force between the cation and anion. The positively charged cation attracts the valence electrons of anion while repelling the nucleus.
This causes a distortion in the electron cloud of the anion and its electron density shift towards the cation, which results in some sharing of the valence electrons between these ions. Thus, a partial covalent character is developed between them. This phenomenon is called polarisation.
The ability of a cation to polarise an anion is called its polarising ability and the tendency of an anion to get polarised is called its polarisability.

1. The ability of a cation to polarise an anion is called its polarising ability and the tendency of an anion to get polarised is called its polarisibility. The extent of polarisation in an ionic compound is given by the Fajans rule.
2. To show greater covalent character, both the cation and anion should have high charge on them. Higher the positive charge on the Cation greater will be the attraction on the electron cloud of the anion.
Similarly higher the magnitude of negative charge on anion, greater is its polansability. For example, Na + < Mg 2+ < Al 3+, the covalent character also follows the order – NaCI < MgCl 2 < AICI 3
3. The smaller cation and larger anion show greater covalent character due to the greater extent of polarisation. e.g., LiCl is more covalent than NaCI.
4. Cation having ns 2 np 6 nd 10 configuration shows greater polarising power than the cations with ns 2 np 6 configuration. e.g., CuCI is more covalent than NaCl.