Concept:Bond length correlates with bond order; double bonds (\( \text{C=O} \)) are substantially shorter than single bonds (\( \text{C-O} \), \( \text{C-N} \)). Resonance can lengthen a double bond by giving it partial single-bond character.
Solution:- Methyl amine (\( \text{C-N} \)) and Ethanol (\( \text{C-O} \)) possess only single bonds, which are long.
- Formamide (\( \text{H-CO-NH}_2 \)) contains a \( \text{C=O} \) bond, but the nitrogen's lone pair donates heavily into the carbonyl via resonance, significantly lengthening the \( \text{C=O} \) bond.
- Formic acid (\( \text{H-COOH} \)) also has a \( \text{C=O} \) bond, but oxygen is much less willing to donate its lone pair via resonance than nitrogen. Therefore, the \( \text{C=O} \) retains more pure double-bond character, making it the shortest bond among the choices.
Why other options are incorrect:Single bonds are inherently longer than double bonds. Nitrogen resonance in amides lengthens the carbonyl bond more than oxygen resonance in acids.
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