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(C) The stability of carbanions is determined by factors such as resonance,hybridization,and inductive effects.$IV$. $(C_6H_5)_2CH^{-}$: This carbanio

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$IV > II > I > III$

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(C) The stability of carbanions is determined by factors such as resonance,hybridization,and inductive effects.$IV$. $(C_6H_5)_2CH^{-}$: This carbanion is highly stable due to extensive resonance with two phenyl rings and the delocalization of the negative charge.$II$. $CH_2=CH-CH_2^{-}$: This is an allylic carbanion,which is stabilized by resonance (conjugation of the negative charge with the double bond).$I$. $HC \equiv C^{-}$: This is an $sp$-hybridized carbanion. The higher $s$-character $(50\%)$ makes the carbon more electronegative,thus stabilizing the negative charge.$III$. $H_2C=CH^{-}$: This is an $sp^2$-hybridized carbanion. It has less $s$-character $(33.3\%)$ compared to the $sp$-hybridized carbanion,making it less stable than $I$.Comparing these,the order of stability is $IV > II > I > III$.

The correct order of the relative stability of the following carbanions is:
$I$. $HC \equiv C^{-}$
$II$. $CH_2=CH-CH_2^{-}$
$III$. $H_2C=CH^{-}$
$IV$. $(C_6H_5)_2CH^{-}$

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The correct order of the relative stability of the following carbanions is:$I$. $HC \equiv C^{-}$$II$. $CH_2=CH-CH_2^{-}$$III$. $H_2C=CH^{-}$$IV$. $(C_6H_5)_2CH^{-}$