Chemistry: Class 11 — Chapter 4: Chemical Bonding and Molecular Structure

Lewis pictured the atom as a positively charged 'Kernel' (nucleus + inner electrons) surrounded by an outer shell that can accommodate up to eight electrons at its corners.

• Valence Electrons: Only outer shell electrons participate in chemical bonding.
• Lewis Symbols: Notations where valence electrons are represented as dots around the chemical symbol.
• Octet Rule: Atoms combine either by transfer of valence electrons or by sharing of valence electrons to achieve a stable octet in their valence shells.

Langmuir (1919) refined Lewis's postulations by introducing the term Covalent Bond, which is formed by the sharing of electron pairs between atoms.

• Single Covalent Bond: Sharing of one electron pair (e.g., $Cl_2$, $H_2O$).
• Double Bond: Sharing of two electron pairs (e.g., $CO_2$, $C_2H_4$).
• Triple Bond: Sharing of three electron pairs (e.g., $N_2$, $C_2H_2$).

The formal charge of an atom in a polyatomic molecule or ion is the difference between the valence electrons of that atom in an isolated state and the number of electrons assigned to it in the Lewis structure:

$$\text{F.C.} = [\text{Total valence } e^- \text{ in free atom}] - [\text{Total non-bonding (lone pair) } e^-] - \frac{1}{2}[\text{Total bonding (shared) } e^-]$$

• Incomplete Octet of Central Atom: Compounds like $LiCl$, $BeH_2$, and $BCl_3$ have fewer than eight electrons around the central atom.
• Odd-Electron Molecules: Molecules like nitric oxide ($NO$) and nitrogen dioxide ($NO_2$) do not satisfy the octet rule for all atoms.
• Expanded Octet: Elements in and beyond the third period use $3d$ orbitals to accommodate more than eight valence electrons (e.g., $PF_5$, $SF_6$, $H_2SO_4$).
• Other drawbacks: It does not account for the shape of molecules or their relative stabilities.

• Bond Length: The equilibrium distance between the nuclei of two bonded atoms in a molecule.
• Bond Angle: The angle between orbitals containing bonding electron pairs around the central atom.
• Bond Enthalpy: The amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state (expressed in $\text{kJ mol}^{-1}$).
• Bond Order: In the Lewis description, it is given by the number of bonds between two atoms in a molecule. Isoelectronic molecules/ions have identical bond orders.

When a single Lewis structure cannot describe a molecule accurately, a number of structures with similar energy, positions of nuclei, bonding, and non-bonding pairs are taken as canonical structures. The actual molecule is a Resonance Hybrid of these structures (e.g., $O_3$, $CO_3^{2-}$).

In heteronuclear molecules, the shared electron pair is displaced towards the more electronegative atom, resulting in a polar covalent bond. The polarity is measured by the Dipole Moment ($\mu$):

$$\mu = \text{Charge } (Q) \times \text{distance of separation } (r)$$

Unit: Debye (D), where $1 \text{ D} = 3.33564 \times 10^{-30} \text{ C m}$.

• Fajans' Rules: Explain the partial covalent character of ionic bonds. Covalent character is favored by small cation size, large anion size, and high charge on the ions.

• The shape of a molecule depends upon the number of valence shell electron pairs (bonded or non-bonded) around the central atom.
• Pairs of electrons repel one another and tend to occupy positions in space that minimize repulsion.
• The repulsive interaction of electron pairs decreases in the order: lp-lp > lp-bp > bp-bp.

• Linear: $AB_2$ type (e.g., $BeCl_2$, $HgCl_2$) with $180^\circ$ bond angle.
• Trigonal Planar: $AB_3$ type (e.g., $BF_3$) with $120^\circ$ bond angle.
• Tetrahedral: $AB_4$ type (e.g., $CH_4$, $NH_4^+$) with $109.5^\circ$ bond angle.
• Trigonal Bipyramidal: $AB_5$ type (e.g., $PCl_5$) with $120^\circ$ and $90^\circ$ bond angles.
• Octahedral: $AB_6$ type (e.g., $SF_6$) with $90^\circ$ bond angles.

Covalent bonds are formed by the overlap of atomic orbitals of valence shells having electrons with opposite spins. Greater overlap leads to a stronger bond.

• Sigma ($\sigma$) Bond: Formed by end-to-end (head-on) overlap of bonding orbitals along the internuclear axis (s-s, s-p, or p-p overlap).
• Pi ($\pi$) Bond: Formed by lateral (sidewise) overlap of atomic orbitals perpendicular to the internuclear axis.

The process of intermixing atomic orbitals of slightly different energies to redistribute their energies, resulting in the formation of a new set of equivalent Hybrid Orbitals.

• $sp$ Hybridisation: Mixing of one $s$ and one $p$ orbital to form two linear hybrid orbitals (e.g., $BeCl_2$, $C_2H_2$).
• $sp^2$ Hybridisation: Mixing of one $s$ and two $p$ orbitals to form three trigonal planar hybrid orbitals (e.g., $BCl_3$, $C_2H_4$).
• $sp^3$ Hybridisation: Mixing of one $s$ and three $p$ orbitals to form four tetrahedral hybrid orbitals (e.g., $CH_4$, $NH_3$, $H_2O$).
• $sp^3d$ Hybridisation: Involves $d$ orbitals to form trigonal bipyramidal geometry (e.g., $PCl_5$).
• $sp^3d^2$ Hybridisation: Involves $d$ orbitals to form octahedral geometry (e.g., $SF_6$).

Atomic orbitals combine mathematically by addition or subtraction of their wave functions:

• Bonding Molecular Orbital: Formed by addition ($\sigma = \psi_A + \psi_B$), possessing lower energy and higher stability.
• Antibonding Molecular Orbital: Formed by subtraction ($\sigma^* = \psi_A - \psi_B$), possessing higher energy and lower stability.

$$\text{Bond Order} = \frac{1}{2}(N_b - N_a)$$

Where $N_b$ is the number of electrons in bonding orbitals and $N_a$ is the number of electrons in antibonding orbitals.

• If all molecular orbitals are doubly occupied, the molecule is Diamagnetic.
• If one or more molecular orbitals contain unpaired electrons, the molecule is Paramagnetic (e.g., $O_2$).