To arrange the given carbanions in the order of stability, we need to understand the factors that influence the stability of carbanions:
- Resonance Stabilization: Carbanions are more stable if the negative charge can be delocalized through resonance.
- Inductive Effect: Electron-withdrawing groups increase stability by dispersing the negative charge, whereas electron-donating groups decrease stability.
- Substituent Effects: Specific groups attached to the phenyl ring can either stabilize or destabilize the carbanion based on their electronic nature.
Let's analyze each carbanion:
- IV. $p$-$\mathrm{CHO{-}C_6H_4{-}CH_2^-}$: The $p$-CHO group is an electron-withdrawing group through resonance and inductive effects. It stabilizes the carbanion by delocalizing the negative charge.
- I. $p$-$\mathrm{Br{-}C_6H_4{-}CH_2^-}$: Bromine is slightly electron-withdrawing due to its inductive effect, providing moderate stability to the carbanion.
- II. $\mathrm{C_6H_5{-}CH_2^-}$: The benzyl carbanion is stabilized by resonance with the benzene ring but lacks additional substituents that further stabilize or destabilize it.
- V. $p$-$\mathrm{CH_3{-}C_6H_4{-}CH_2^-}$: The $p$-CH3 group is electron-donating, destabilizing the carbanion slightly due to a positive inductive effect (+I effect).
- III. $p$-$\mathrm{CH_3O{-}C_6H_4{-}CH_2^-}$: The $p$-OCH3 group is strongly electron-donating through resonance (+R effect), which significantly destabilizes the carbanion.
Based on this analysis, the stability order of the carbanions is:
\(IV > I > II > V > III\)
Therefore, the correct answer is:
IV $>$ I $>$ II $>$ V $>$ III