Bond Length and Bond Angle — Revision Notes

⚡ 30-Second Revision

Bond Length: — Average internuclear distance. Shorter = stronger.

- Factors: Atomic size ($\uparrow$ size, $\uparrow$ length), Bond order ($\uparrow$ order, $\downarrow$ length), Hybridization ($\uparrow$ s-char, $\downarrow$ length).

Bond Angle: — Angle between bonding orbitals around central atom. Determines molecular shape.

- Theory: VSEPR (Valence Shell Electron Pair Repulsion). - Repulsion Order: LP-LP > LP-BP > BP-BP. - Factors: Hybridization (sets ideal angle), Lone pairs (compress angles), Electronegativity of central/surrounding atoms, Steric hindrance. - Ideal Angles: $sp (180^\circ)$, $sp^2 (120^\circ)$, $sp^3 (109.5^\circ)$. - Examples: CH$_4$ ($109.5^\circ$), NH$_3$ ($107^\circ$), H$_2$O ($104.5^\circ$).

2-Minute Revision

Bond length is the distance between two bonded nuclei, and it's a key indicator of bond strength – shorter bonds are generally stronger. Remember that bond length decreases as bond order increases (triple < double < single) and also decreases with increasing s-character in hybridization ($sp < sp^2 < sp^3$).

Larger atomic size leads to longer bonds. Bond angle, on the other hand, defines a molecule's 3D shape and is primarily governed by VSEPR theory. This theory states that electron pairs (both bonding and lone pairs) around a central atom repel each other and arrange to minimize this repulsion.

Lone pairs exert greater repulsion than bonding pairs (LP-LP > LP-BP > BP-BP), causing bond angles to compress from their ideal values. For instance, while $sp^3$ hybridization ideally gives $109.5^\circ$, the presence of one lone pair (like in NH$_3$) reduces it to $107^circ$, and two lone pairs (like in H$_2$O) further reduce it to $104.

5^circ$. Electronegativity of surrounding atoms can also subtly influence angles.

5-Minute Revision

A comprehensive understanding of bond length and bond angle is vital for NEET. Bond length is the average distance between two bonded nuclei. It's inversely related to bond strength. Key factors influencing it are:

1
Atomic Size: — Larger atoms form longer bonds (e.g., C-I > C-Br > C-Cl > C-F).
2
Bond Order: — Higher bond order means more shared electrons, stronger attraction, and shorter bonds (e.g., C\equiv C < C=C < C-C).
3
Hybridization: — Greater s-character in hybrid orbitals leads to shorter bonds (e.g., C-H in $sp$ carbon < C-H in $sp^2$ carbon < C-H in $sp^3$ carbon).
4
Resonance: — In resonant structures, bond lengths are averaged (e.g., C-O bonds in CO$_3^{2-}$ are all equal and intermediate between single and double).

Bond angle is the angle between adjacent bonds around a central atom, determining molecular geometry. VSEPR theory is the guiding principle: electron pairs repel each other. The order of repulsion is LP-LP > LP-BP > BP-BP.

1
Hybridization: — Sets the ideal electron geometry and angles ($sp \rightarrow 180^\circ$ linear; $sp^2 \rightarrow 120^\circ$ trigonal planar; $sp^3 \rightarrow 109.5^\circ$ tetrahedral).
2
Lone Pairs: — Lone pairs occupy more space and exert stronger repulsion, compressing bond angles. For example, CH$_4$ ($109.5^\circ$), NH$_3$ ($107^circ$), H$_2$O ($104.5^circ$).
3
Electronegativity of Surrounding Atoms: — More electronegative surrounding atoms pull bonding electrons away from the central atom, reducing BP-BP repulsion and slightly decreasing the bond angle (e.g., H$_2$O ($104.5^\circ$) vs OF$_2$ ($103.1^circ$)).
4
Steric Hindrance: — Bulky groups can increase bond angles to minimize repulsion.

Worked Example: Compare the N-O bond lengths in NO$_2^+$, NO$_2$, and NO$_2^-$.

NO$_2^+$: — Linear, N is $sp$ hybridized. Two N=O double bonds. Bond order = 2. Shortest.
NO$_2$: — Bent, N is $sp^2$ hybridized, 1 lone electron. Resonance between N=O and N-O. Average bond order $\approx 1.5$. Intermediate.
NO$_2^-$: — Bent, N is $sp^2$ hybridized, 1 lone pair. Resonance between N=O and N-O. Average bond order $\approx 1.5$. However, the lone pair on N in NO$_2^-$ (compared to a single electron in NO$_2$) causes greater repulsion, slightly increasing the N-O bond length compared to NO$_2$ due to reduced double bond character contribution. Also, the negative charge is delocalized, contributing to a longer bond than a pure double bond.

Order of increasing bond length: NO$_2^+$ < NO$_2$ < NO$_2^-$.

Prelims Revision Notes

For NEET, quick recall of bond length and bond angle principles is key.

Bond Length (BL):

Definition: — Average distance between nuclei of bonded atoms.
Units: — pm or Å.
Relationship to Bond Strength: — Shorter BL $\implies$ Stronger bond.
Factors:

* Atomic Size: BL $\propto$ Atomic size. (e.g., C-F < C-Cl < C-Br < C-I) * Bond Order (BO): BL $\propto \frac{1}{\text{BO}}$. (e.g., C\equiv C < C=C < C-C) * Hybridization (s-character): BL $\propto \frac{1}{\text{s-character}}$. (e.g., C-H in $sp$ < C-H in $sp^2$ < C-H in $sp^3$) * Resonance: Bond lengths are averaged (e.g., C-O in CO$_3^{2-}$ are equal and intermediate).

Bond Angle (BA):

Definition: — Angle between bonding orbitals around central atom.
Theory: — VSEPR (Valence Shell Electron Pair Repulsion).
Repulsion Order: — LP-LP > LP-BP > BP-BP.
Factors:

* Hybridization: Determines ideal electron geometry and BA. * $sp$: Linear, $180^\circ$ (e.g., BeCl$_2$, CO$_2$, HCN) * $sp^2$: Trigonal planar, $120^\circ$ (e.g., BF$_3$, SO$_3$) * $sp^3$: Tetrahedral, $109.

5^\circ$(e.g., CH$_4$) *$sp^3d$: Trigonal bipyramidal *$sp^3d^2$: Octahedral * **Lone Pairs (LP):** Presence of LPs compresses BAs from ideal values. * CH$_4$(0 LP):$109.5^\circ$* NH$_3$(1 LP):$107^circ$(trigonal pyramidal) * H$_2$O (2 LP):$104.

5^circ$(bent) * **Electronegativity of Central Atom:** More electronegative central atom pulls bond pairs closer, increasing BP-BP repulsion, slightly increasing BA (e.g., H$_2$O > H$_2$S). * Electronegativity of Surrounding Atoms: More electronegative surrounding atoms pull bond pairs away, reducing BP-BP repulsion, slightly decreasing BA (e.

g., PF$_3$ ($97.8^circ$) < PCl$_3$ ($100.3^circ$)). * Steric Hindrance: Bulky groups can increase BAs.

Key Strategy: For any molecule, first draw Lewis structure, then determine central atom hybridization, count bond pairs and lone pairs, and apply VSEPR rules. For bond length, identify bond order and s-character.

Vyyuha Quick Recall

To remember the VSEPR repulsion order: Lone Pairs are Larger Pushers, then Lone Pairs Bond Pairs, then Bond Pairs Bond Pairs. (LP-LP > LP-BP > BP-BP).