Understanding Bond Length Comparisons

Bond length is the average distance between the nuclei of two bonded atoms. It is influenced by bond order (higher order = shorter bond), atomic size, and electron distribution (resonance, back-bonding). Let's analyze each case step by step.

Step 1: Analyze Statement (i) - N₂H₂ < N₂H₄ (N–N bond length)

N₂H₂ (diazene) has a N=N double bond (bond order = 2). N₂H₄ (hydrazine) has a N–N single bond (bond order = 1). Since bond length is inversely proportional to bond order, the double bond in N₂H₂ is shorter than the single bond in N₂H₄. Therefore, the statement N₂H₂ < N₂H₄ is correct.

Step 2: Analyze Statement (ii) - NO > NO⁺ (N–O bond length)

Nitric oxide (NO) has a bond order of 2.5. Its molecular orbital configuration is: ${\sigma }_1^2{\sigma }_2^{\mathrm{\ast 2}}{\sigma }_3^2{\pi }_1^4{\pi }_2^{\mathrm{\ast 1}}$. The nitrosyl ion (NO⁺) loses an antibonding electron, resulting in a configuration of ${\sigma }_1^2{\sigma }_2^{\mathrm{\ast 2}}{\sigma }_3^2{\pi }_1^4$, giving it a bond order of 3. A higher bond order means a shorter bond. Therefore, the bond in NO⁺ is shorter than in NO, making the statement NO > NO⁺ correct.

Step 3: Analyze Statement (iii) - C₂H₄ > K[PtCl₃(C₂H₄)] (C–C bond length)

In free ethene (C₂H₄), the C=C bond is a double bond. In Zeise's salt, K[PtCl₃(C₂H₄)], ethene acts as a π-acid ligand. The metal atom (Pt²⁺) donates electron density back into the π* antibonding orbital of ethene. This back-donation weakens the C=C bond, reducing its bond order and increasing its length. Therefore, the C–C bond is longer in the complex than in free ethene. The statement C₂H₄ > K[PtCl₃(C₂H₄)] is correct.

Step 4: Analyze Statement (iv) - POF₃ > POCl₃ (P–O bond length)

This involves comparing the P–O bond in two oxyhalides. The key concept is π-bonding or back-bonding. Oxygen can donate a lone pair to the vacant d-orbital of phosphorus, forming a dπ-pπ bond. This shortens and strengthens the P–O bond. The extent of this back-bonding is greater when the halogens attached to phosphorus are less electronegative. Chlorine (Cl) is less electronegative than Fluorine (F). Therefore, back-bonding is more significant in POCl₃ than in POF₃. This results in a shorter P–O bond in POCl₃. The statement claims POF₃ has a longer bond, so POF₃ > POCl₃ is correct.

Final Answer

All four statements (i), (ii), (iii), and (iv) are correct. However, looking at the provided options, the one that includes all correct statements is: (i), (ii) & (iv). Note that option (i), (ii) & (iv) is correct, and statement (iii) is also correct but is not included in this particular option. Based on the options given, (i), (ii) & (iv) is the best choice as it contains only correct statements.

Related Topics & Formulae

Key Concepts

• Bond Order: A measure of the number of chemical bonds between a pair of atoms. It is directly related to bond strength and inversely related to bond length. $$\text{Bond Length}\propto \frac{1}{\text{Bond Order}}$$
• Molecular Orbital Theory (MOT): Used to determine bond order in molecules like NO, O₂, etc. $$\text{Bond Order}=\frac{(\text{Number of bonding electrons}-\text{Number of antibonding electrons})}{2}$$
• Back-bonding (π-backdonation): A concept where an atom with lone pairs donates them to an atom with vacant orbitals (e.g., d-orbitals in P, Pt, etc.), affecting bond lengths and strengths. This is crucial in organometallic chemistry (e.g., metal-alkene complexes) and main group chemistry (e.g., P–O bonds).
• Electronegativity: The tendency of an atom to attract a shared pair of electrons. It influences bond polarity and, consequently, the extent of ionic character and π-bonding.

Important Theory

Bond length is a fundamental property that helps predict molecular geometry and reactivity. Factors decreasing bond length include:
- Increase in bond order (single < double < triple).
- Increase in s-character of the bond (sp³ > sp² > sp).
- Presence of π-backdonation (shortens the bond involved).
- Higher electronegativity difference can sometimes lead to shorter bonds due to increased ionic character.