The decreasing order of acidic nature of the following compounds is
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Acidity of terminal alkynes is due to the relatively high electronegativity of $sp$-hybridized carbon.
Electron-withdrawing groups (EWGs) attached to the system stabilize the conjugate base (acetylide anion) and increase acidity. Examples: -NO$_2$, -CN, -COOH, halogens (-I effect).
Electron-donating groups (EDGs) destabilize the conjugate base and decrease acidity. Examples: -NH$_2$, -OH, -OR, alkyl groups (+I effect).
Resonance effects (-R for EWG, +R for EDG) are often stronger than inductive effects (-I, +I) when groups are conjugated with the system.
-NO$_2$ is strongly electron-withdrawing (-I, -R).
-NH$_2$ is electron-donating overall due to strong +R effect, despite -I effect of N.
The acidic nature of these compounds is due to the hydrogen atom attached to the $sp$-hybridized carbon of the terminal alkyne group (-C$\equiv$CH).
The $sp$-hybridized carbon is more electronegative than $sp^2$ or $sp^3$ carbons, making the C-H bond more polar and the hydrogen more acidic.
Acidity is determined by the stability of the conjugate base (acetylide anion, -C$\equiv$C$^-$) formed after deprotonation. Factors that stabilize the anion increase the acidity.
All three compounds have the phenylacetylene moiety. The difference lies in the substituent on the phenyl ring at the para position.
\begin{itemize}
\item Compound I: Phenylacetylene (C$_6$H$_5$-C$\equiv$CH)
This is the reference compound. The phenyl group itself has a mild electron-withdrawing inductive effect (-I) and can also participate in resonance.
\item Compound II: 4-Nitrophenylacetylene (O$_2$N-C$_6$H$_4$-C$\equiv$CH)
The nitro group (-NO$_2$) is a strong electron-withdrawing group. It exerts both a strong -I (inductive) effect and a strong -R (resonance or mesomeric) effect. These electron-withdrawing effects stabilize the acetylide anion formed after deprotonation, thereby increasing the acidity of the acetylenic hydrogen.
\item Compound III: 4-Aminophenylacetylene (H$_2$N-C$_6$H$_4$-C$\equiv$CH)
The amino group (-NH$_2$) is an electron-donating group. It exerts a -I effect (N is more electronegative than C) but a much stronger +R (resonance) effect due to the lone pair on nitrogen donating electron density into the ring. These electron-donating effects destabilize the acetylide anion, thereby decreasing the acidity of the acetylenic hydrogen.
\end{itemize}
Comparing the effects:
\begin{itemize}
\item -NO$_2$ group (in II): Strong electron-withdrawing. Increases acidity significantly.
\item No substituent (H in I, effectively): Reference.
\item -NH$_2$ group (in III): Strong electron-donating (via +R effect). Decreases acidity significantly.
\end{itemize}
Therefore, the order of acidity will be:
Compound with strong electron-withdrawing group (II)>Compound with no strong group (I)>Compound with strong electron-donating group (III).
So, II>I>III.
This matches option (c).
\[ \boxed{\text{II>I>III}} \]
