Chemical Bonding Formula: Molecular Structure

Chemical bonding involves atoms combining to form molecules through the attraction between positively charged protons and negatively charged electrons. There are three primary types: covalent, ionic, and metallic bonds. 

Covalent Bond

They are formed when atoms share electrons for stability.

Octet Rule

The Octet Rule is a chemical rule predicting atoms’ stability when their outermost shell is full, typically with eight electrons. It predicts bonding, with atoms with seven valence electrons likely to gain one electron and lose one. However, some atoms, like hydrogen and helium, can accommodate more than eight electrons, indicating their unique stability.

Formal Charge

A formal charge is the charge an atom would have if all of the atoms in the molecule had the same electronegativity. It does not necessarily represent the actual charge on that atom; this is an important distinction.

FC= V-N-B2

Where V = valence electrons in an tom

            N = number of lone pair (non bonding) electrons

            B = number of bonding electrons

Also Check – surface chemistry Formula

Ionic Bond Or Electrovalent Bond

 Ionic bonds involve electron transfers between atoms, forming positively and negatively charged ions.

M → M+ + e– (cation)

X + e– → X– (anion)

M+ + X– → MX (salt)

Lattice Energy

Lattice enthalpy (or lattice energy) is a measure of the energy released when ions are combined to make a compound. It is a measure of the strength of the forces between the ions in an ionic solid – the stronger the forces, the higher the lattice enthalpy.

∆U=∆H-p∆Vm

where ∆U= lattice enthalpy          

∆H= molar lattice enthalpy              

∆Vm= change of the volume per mole                

 p= outside pressure 

Also Check – Avogadro Law Formula

The lattice enthalpy of an ionic solid cannot be measured directly but can be calculated using Hess’s law and the Born-Haber cycle, or can be calculated from the charges on the ions and the distances between them (in a theoretical model of the structure) using the Born-Landé equation. 

Download PDF Chemical Bonding Formula

Hess’s Law

According to Hess’s law, the overall enthalpy change of a reaction is independent of the path taken and solely depends on the initial and final states. It’s a statement regarding energy conservation, and it applies since enthalpy is a state function. Hess’s law is very useful for determining the enthalpy change of difficult-to-measure processes.

If you have several reactions:

Reaction 1: A→ B; ∆H1

Reaction 2: B→ C; ∆H2

And, according to Hess’s law, you’re interested in the enthalpy shift from A to C:

ΔH (A → C) = ΔH₁ + ΔH₂

The Born-Haber Cycle is a Hess’s law application that is used to examine and compute the lattice energy of an ionic solid. The energy required to break up an ionic solid and convert its constituent atoms into gaseous ions is known as lattice energy.

Born-Haber Cycle

• It consists of multiple steps:
• The solid metal is sublimated.
• Metal atoms in gaseous form are ionized.
• If necessary, dissociation of the nonmetal from its diatomic state happens.
• If necessary, ionization of nonmetal atoms takes place.
• The formation of an ionic solid from gaseous ions occurs.
• Each step corresponds to an energy change, either endothermic or exothermic, and the aggregate of these energy changes, according to Hess’s law, yields the solid’s lattice energy.

The Born-Haber cycle for the formation of an ionic solid, MX, could be represented as:

M(s) → M(g) ;ΔHsub

½  X2(g) → X(g) ;ΔHdiss

M(g) → M+(g) + e- ;ΔHI

X(g) + e- → X-(g) ;ΔHEA

M+(g) + X-(g) → MX(s); ΔHf

According to Hess’s law, the sum of the enthalpy changes for these steps equals the lattice energy:

ΔHlattice = ΔHsub + ΔHdiss + ΔHI – ΔHEA – ΔHf

The Born-Lande Equation  

This equation can be derived from two forms:

1. First is potential energy

U=–NAM|Z+||Z–|e24πϵor

Where NA is Avogadro’s number

M is Madelung constant(varies with structure)

E is charge of an electron

Z+ is charge of cation

Z– is charge of an anion

o is the permittivity of free space

1. Second is repulsive interaction

                                                                   U=NABrn

  Where B is the repulsion coefficient 

N is born exponent(5-12 is the range used to know how much a solid can compress)

Combination of i & ii  is 

U(0K)=NAM|Z+||Z–|e24πϵoro(1-1n)

ro is the closest distance

Bond Parameters

Bond Length (or Bond Distance):

It is the average distance between the nuclei of two bonded atoms in a molecule. 

Factors Affecting Bond Length: Type of Bond: Single bonds are longer than double bonds, which are longer than triple bonds. This is because as more electron pairs are shared, the atoms are pulled closer together. 

Size of the Atoms: Larger atoms tend to have longer bond lengths than smaller atoms. 

Bond length α 1bond strength1stability

 Bond Order:

It represents the number of chemical bonds between a pair of atoms. It gives an indication of the bond’s strength and stability.

Bond order =Number of bonding electrons-Number of antibonding electrons2

B.O = NA–NB2

Relation with Bond order and Strength: Higher bond order usually corresponds to shorter bond lengths and stronger bonds. 

Bond order α bond strength α stability

Bond Angle:

It is the angle formed between three atoms across at least two bonds. For instance, the H-O-H bond angle in water is about 104.5°. 

Factors Affecting Bond Angle: 

Electronic Repulsion: The shape and bond angle in a molecule try to minimize the repulsion between electron pairs (both bonding and non-bonding or lone pairs). Lone pair-lone pair repulsion is greater than lone pair-bonding pair repulsion, which is greater than bonding pair-bonding pair repulsion. 

Bond angle α Bond order α bond strength 

Molecular Geometry: The bond angle is often determined by the shape or geometry of the molecule, which can be predicted using the VSEPR (Valence Shell Electron Pair Repulsion) theory.

Dipole Moment

A molecule is said to be polar if there is an uneven distribution of electron density, leading to a partial positive end and a partial negative end. This gives rise to a dipole moment in the molecule. 

Representation:

 It is represented by the symbol μ. Dipole moment is directed from the positive end to the negative end. 

Formula: The dipole moment is given by μ=q × d 

where μ = dipole moment 

q = magnitude of the partial charge 

d = distance between the charges 

Units: The SI unit of dipole moment is Coulomb-meter (C.m), but it is commonly expressed in Debye (D). 

1 Debye = 3.336 × 1 0 − 30 C.m.