Bond Parameters: Bond length, Bond Angle, Bond Enthalpy and Formulas

There are the following characteristics of chemical bonds are considered bond parameters. You can check the bond parameters discussed below.

• Bond length
• Bond Angle
• Bond order
• Bond Enthalpy
• Bond Polarity

When two atoms bind together to form a molecule, there is a certain distance between the nuclei of the two atoms. In general, this distance between nuclei in an equilibrium condition is considered as Bond Length. In covalent bonds, the bond length is nearly equal to the sum of the atomic radii of the two participating atoms. As explained in the below given NCERT figure, for two atoms A and B, the atomic radii are $r_a$ and $r_{\mathrm{b,}}$ respectively. The bond length will be equal to the sum of $r_a$ and $r_b$ .

Bond length = $r_a$+ $r_b$

Bond Length (NCERT image)

Important Points related to Bond Length

• It depends on three main key factors: the size of atoms, the bond order, and the bond type.
• The bond length decreases from single to triple bonds. Bond length is maximum for a single bond and then decreases as the number of bonds (Bond order) increases.
• The shorter the bond length, the stronger it will be.
• It is measured in picometres (pm) or angstroms (Å). {1 Å = 100 pm}
• It is measured using X-ray diffraction or spectroscopic methods.

When atoms combine to form a molecule, they form a certain geometrical shape. The angle between two adjacent bonds, which is important to hold that shape, is known as bond angle.

As per the NCERT definition," the angle between the orbitals containing bonding electron pairs around the central atom in a molecule/complex ion."

Bond angle in Ammonia

Key Points related to Bond Angle

• It helps in predicting the shape of the molecule.

• The bond angle of any molecule depends on its hybridization of the central atom, the electronegativity of surrounding atoms, and the number of lone pairs of electrons.

• Hybridization determines the bond angle due to the specific spatial arrangement of orbitals. 
  • In sp hybridization, the bond angle is  180°.
  • In sp² hybridization, the bond angle is 120°.
  • In sp³ hybridization, the ideal bond angle is 109.5°.
• Lone pairs generally have more electrostatic repulsion, which reduces bond angles, such as in the case of NH₃; even after sp³ hybridization, the bond angle is 107°.
• The electronegative atoms pull bonding electrons closer, so the higher the electronegativity, the smaller the bond angles will be.

All chemical bond needs some amount of energy to break free. Bond enthalpy defines the amount of energy required to do so. The bond enthalpy of any chemical bond will be equal to breaking one mole of the bond in the gaseous state. 

As per the NCERT definition," The amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state is called bond enthalpy." 

Key Points related to Bond Enthalpy

• The stronger the bond is, it will require more energy to break in a gaseous state, which means a higher bond enthalpy.
• It is measured in kJ mol⁻¹.

• A formula to estimate enthalpy changes in reactions:

  $$\mathrm{\Delta }H=\sum \text{Bond enthalpies of reactants}-\sum \text{Bond enthalpies of products}$$
• In polyatomic molecules, the term mean bond enthalpy is used instead of bond enthalpy. It is obtained by dividing the total bond dissociation enthalpy by the number of bonds broken.

As per the Lewis theory of formation of covalent bonds, the number of bonds formed between the two atoms in a molecule is called the Bond Order.  For Example, the bond order of diatomic nitrogen N≡N is three where whereas the bond order of diatomic Oxygen O=O is two. 

Key Points related to Bond Order

• As we increase in bond order, the bond enthalpy increases, and the bond length decreases.
• Formula for bond order in Molecular Orbital Theory:

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

• • $N_b$: Number of electrons in bonding orbitals

  • $N_a$: Number of electrons in anti-bonding orbitals

In general reality, no compound has either a completely covalent or an ionic bond.  When the shared electron pair between the two atoms gets displaced more towards the higher electronegative atom, the resultant covalent bond is a polar covalent bond. Basically, the difference in electronegativity of the two atoms sharing the pair of electrons gives rise Polarity of bonds. 

Key Points related to Bond Polarity

• A higher electronegative atom pulls shared electrons, so it develops a partial negative charge.

• The Less electronegative atom develops a partial positive charge.

• Examples:

• • H–Cl: polar (Cl more electronegative)

  • H–H or Cl–Cl: non-polar (same atoms)

Dipole moment of a bond is calculated as the product of charge (q) and distance (r) between the charges: it is denoted as $$\mu .$$

$$\mu =q\times r$$

Key Points of Dipole Moment

• Units: Debye (D)
  $1\ \text{D} = 3.336 \times 10^{-30}\ \text{C·m}$

• It is a Vector quantity.

• Symmetrical molecules are non-polar because their dipole moments cancel out. 

• Asymmetrical molecules are polar because there is a dipole moment.
• Examples:

• • HCl → 1.08 D (polar)

  • CO₂ → 0 D (linear, non-polar despite polar bonds)

  • NH₃ → 1.47 D